Method for simulating furnace atmosphere and method for heat treatment of metal materials

Abstract

To provide a simulation method of a furnace atmosphere that can simulate with high precision the change of a furnace atmosphere in a heat-treatment furnace as the heat treatment progresses in a heat treatment process of a metal material in which decarburization and carburization may occur, and a heat treatment method of a metal material that can utilize results of such simulation.SOLUTION: Provided is a simulation method of the change in a composition of a furnace atmosphere over time when a metal material is heat-treated in the furnace atmosphere comprising at least one of CO and CO2 in a heat-treating furnace. Simulation is performed by using a mathematical model that incorporates the change in the composition of the furnace atmosphere due to both the gas flow in and out of the heat-treating furnace, the gas phase reaction in the furnace atmosphere, and the chemical reaction of at least one of the gas-solid phase reaction on a surface of the metal material.SELECTED DRAWING: Figure 8

Description

[Technical Field]

[0001] The present invention relates to a method for simulating the atmosphere inside a furnace and a method for heat-treating a metallic material, and more specifically, to a method for simulating the composition of the atmosphere inside a furnace for heat-treating a metallic material, and to a method for controlling the atmosphere inside the furnace and heat-treating a metallic material using the simulation results obtained by the same method. [Background technology]

[0002] When metal materials, including steel, are heat-treated for tempering, decarburization, carburization, and oxidation often occur. Since the progression of these phenomena depends on the composition of the atmosphere inside the heat treatment furnace, the furnace atmosphere is controlled to prevent these phenomena or to adjust their progression to a desired degree, thereby controlling the composition and properties of the steel. To control decarburization and carburization, an endothermic modified gas (RX gas) containing CO, H2, and N2 is often used to adjust the furnace atmosphere.

[0003] When controlling the furnace atmosphere using gases containing CO and CO2, such as RX gas, the carbon potential factor (PF) is often used as an indicator for atmosphere control. PF is an indicator of carbon potential, where the CO concentration and CO2 concentration in the furnace are expressed as volume percent as [CO] and [CO2], respectively, and PF = [CO]. 2It is calculated as / [CO2]. The higher the PF value, the more carburizing progresses, and the lower the PF value, the more decarburization progresses. Therefore, a target value for PF is set according to the desired carbon concentration of the metal material, and feedback control such as PID control is performed while monitoring the CO concentration and CO2 concentration in the furnace atmosphere in order to bring the actual PF value of the furnace atmosphere closer to the target value, thereby controlling the inflow and outflow of gases into the furnace, such as the inflow of RX gas into the furnace, the inflow of N2 gas for safety (to ensure furnace pressure so that air does not enter the furnace and cause an explosion), the inflow of N2 gas and / or air to reduce PF, and the exhaust of the furnace atmosphere. Such a form of controlling the furnace atmosphere using the PF value as an indicator is disclosed, for example, in Patent Document 1. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 2-153017 [Overview of the project] [Problems that the invention aims to solve]

[0005] Inside a heat treatment furnace used to heat-treat metal materials, multiple chemical reactions occur that affect the concentration of components in the furnace atmosphere, including CO and CO2. Because these reactions correlate as the heat treatment progresses, the furnace atmosphere can undergo complex or rapid changes. Therefore, if the furnace atmosphere is controlled by monitoring the CO and CO2 concentrations and calculating the PF value, and then using feedback control, it may not be possible to quickly track the actual changes in the furnace atmosphere. This makes it difficult to appropriately control the carbon concentration of the metal material. In particular, when the contribution of gas-solid reactions, such as the reduction of oxides (scale) on the surface of the metal material, becomes significant, atmosphere control based on the PF value of the furnace atmosphere becomes less able to adequately track the actual changes in the furnace atmosphere. As a foundation for high-precision control of the furnace atmosphere, the development of a method that can accurately simulate how the composition of the furnace atmosphere changes during the heat treatment is desirable.

[0006] The problem that the present invention aims to solve is to provide a furnace atmosphere simulation method that can accurately simulate changes in the furnace atmosphere of a heat treatment furnace as the heat treatment progresses during a heat treatment process of a metal material in which decarburization and carburization may occur, and a heat treatment method for a metal material that can utilize the results of such a simulation. [Means for solving the problem]

[0007] [1] In order to solve the above problems, the simulation method for furnace atmosphere according to the present invention is a method for simulating the time change in the composition of a furnace atmosphere when heat treatment of a metal material is performed in a furnace atmosphere containing at least one of CO and CO2 in a heat treatment furnace, and the simulation is performed using a mathematical model that incorporates the change in the composition of the furnace atmosphere due to both the inflow and outflow of gas to and from the heat treatment furnace, a gas-phase reaction in the furnace atmosphere, and at least one of a gas-phase-solid reaction on the surface of the metal material.

[0008] [2] In the embodiment of [1] above, the inflow and outflow of gas to and from the heat treatment furnace may include the inflow of a gas that increases the carbon potential factor of the furnace atmosphere, the inflow of a gas that decreases the carbon potential factor, and the exhaust of the entire furnace atmosphere gas. [3] In the embodiment of [1] or [2] above, it is preferable to simulate the time change of the concentration of at least CO or CO2 as the time change of the composition of the furnace atmosphere. [4] In any one embodiment of [1] to [3] above, an error function may be incorporated into at least one of the gas inflow rate into the heat treatment furnace and the reaction rate of the chemical reaction. [5] In the embodiment described in [4] above, it is also preferable to incorporate an error function only into the reaction rate of the chemical reaction.

[0009] [6] In any one of the aspects [1] to [5] above, the reaction rate of the chemical reaction may be expressed by the modified Arrhenius equation represented by the following formula (A). [Number] In formula (A), k f (T) is the reaction rate constant at temperature T, k' f is the frequency factor, T is the temperature in the heat treatment furnace, b is a constant, E f is the activation energy, and R is the gas constant.

[0010] [7] In any one of the aspects [1] to [6] above, the metal material is Fe or an Fe-based alloy, and as the chemical reaction, each equilibrium reaction of the following formulas (1) to (7) or formulas (1) to (9) is considered, and the increase or decrease due to each equilibrium reaction is incorporated into the time change of the concentration of each gas component constituting the furnace atmosphere, and the simulation may be performed. [Chemistry] [[ID=2,4]][8] In the aspect [7] above, an error function may be incorporated into the reaction rate of the chemical reactions of formulas (6) and (7). [9] In the aspect [8] above, the incorporation of the error function is to add error coefficients Δ CO , Δ CO2 , Δ H2 , Δ H2O to the rates of change in the concentrations of CO, CO2, H2, and H2O in the heat treatment furnace, respectively, and Δ CO =-Δ CO2 , Δ H2 =-Δ H2O is set, and as Δ CO2 and Δ H2O , a function in which a positive value decreases with the passage of time and converges to zero may be used.

[0011]

[10] In any one embodiment of [1] to [9] above, the value of an unknown parameter included in the mathematical model may be determined by comparing the time evolution of the concentration of at least one of CO and CO2 between the results of the simulation and the measurement results in an actual heat treatment furnace.

[11] In the embodiment described in

[10] above, the mathematical model includes several unknown parameters, and the values ​​of these unknown parameters are determined in order from those that have the greatest impact on the results of the simulation.

[0012]

[12] The heat treatment method for a metallic material according to the present invention controls the inflow and outflow of gas to and from the heat treatment furnace when performing heat treatment on a metallic material in an actual heat treatment furnace, based on the simulation results obtained by the furnace atmosphere simulation method of any one of the embodiments of [1] to

[11] described above. [Effects of the Invention]

[0013] [1] In the simulation method for the furnace atmosphere according to the above invention, the change in the composition of the furnace atmosphere is simulated using a mathematical model that incorporates not only the inflow and outflow of gas to and from the heat treatment furnace, but also at least one of the chemical reactions: gas-phase reactions in the furnace atmosphere and gas-phase-solid reactions on the surface of the metal material being heat-treated. In the mathematical model, the composition of the furnace atmosphere is calculated at minute time intervals using differential equations based on the reaction rates of each chemical reaction, so that the change in the furnace atmosphere due to chemical reactions occurring in the furnace can be reproduced with high accuracy. Preferably, a mathematical model that incorporates both the gas-phase reactions in the furnace atmosphere and the gas-phase-solid reactions on the surface of the metal material being heat-treated is used.

[0014] [2] Here, if the inflow and outflow of gas to and from the heat treatment furnace includes the inflow of gases that increase the carbon potential factor of the furnace atmosphere, the inflow of gases that decrease the carbon potential factor, and the exhaust of the entire furnace atmosphere gas, then by incorporating the inflow of gases that increase or decrease the carbon potential factor, and the exhaust of the furnace atmosphere gas that is a factor that decreases the carbon potential factor, into the simulation, the changes in the concentrations of CO and CO2, which are components that determine the carbon potential factor in the furnace atmosphere, can be simulated with high accuracy. The carbon potential factor is an index that is closely related to the progress of decarburization / carburization of metallic materials and is important in controlling the carbon content of metallic materials.

[0015] [3] Furthermore, when simulating the time evolution of the composition of the furnace atmosphere, specifically the time evolution of the concentration of at least CO or CO2, CO and CO2 are gaseous components that contribute to the decarburization / carburization of metal materials. By simulating their concentrations with high accuracy and obtaining insights into their concentration changes, it is possible to use this information to accurately control the carbon content of metal materials. Preferably, the time evolution of the concentrations of both CO and CO2 is simulated.

[0016] [4] When an error function is incorporated into at least one of the gas inflow rate into the heat treatment furnace and the reaction rate of the chemical reaction, the error in the gas inflow rate that occurs in the actual heat treatment furnace, and the contribution of chemical reactions other than those explicitly included in the mathematical model, can be incorporated into the simulation. In particular, with respect to the latter contribution, even chemical reactions with small contributions can be easily incorporated into the simulation by incorporating them into the simulation in the form of a mathematical error function, without having to explicitly treat each chemical reaction in the form of a chemical reaction, thereby improving the accuracy of the simulation.

[0017] [5] In this case, if the error function is incorporated only into the reaction rate of the chemical reaction, the contribution of the error function in the simulation can be suppressed by considering the error function of the gas inflow rate. In actual heat treatment of metal materials, chemical reactions other than those explicitly incorporated into the mathematical model often occur in the heat treatment furnace, but the error in the gas inflow rate into the heat treatment furnace can be sufficiently suppressed by control.

[0018] [6] When expressing the reaction rate of a chemical reaction using the modified Arrhenius equation represented by equation (A) above, considering the temperature dependence of the reaction rate frequency factor allows for accurate incorporation of the change in the reaction rate of each chemical reaction into the simulation, thereby improving the accuracy of the simulation.

[0019] [7] When the metallic material is Fe or an Fe-based alloy, and the simulation is performed by considering the equilibrium reactions of equations (1) to (7) or equations (1) to (9) as chemical reactions, and incorporating the increase or decrease due to the above equilibrium reactions into the time change of the concentration of each gas component constituting the furnace atmosphere, it is possible to simulate with high accuracy the concentration changes of CO and CO2 in the furnace atmosphere, which contribute to decarburization and carburizing, which greatly affect the material properties when heat-treating Fe or an Fe-based alloy. In particular, by incorporating the chemical reaction of equation (6), which is a gas-phase-solid-phase reaction involving CO and CO2, a high level of accuracy in the simulation can be obtained. Furthermore, even if only the chemical reactions of equations (1) to (7) are considered, high accuracy can be obtained in the simulation, but by also considering the chemical reactions of equations (8) and (9), the accuracy of the simulation can be further improved.

[0020] [8] In this case, by incorporating error functions into the reaction rates of the chemical reactions in equations (6) and (7), the reduction reactions of Fe oxides other than FeO, such as Fe2O3 and Fe3O4, and oxides of metal elements other than Fe, such as Cr, can be collectively incorporated into the reduction reaction of FeO as error functions. In this way, the accuracy of the simulation can be easily improved by incorporating the reduction reactions of various metal oxides in the form of error functions.

[0021] [9] In addition, the error function was incorporated by assigning error coefficients Δ to the rates of change in the concentrations of CO, CO2, H2, and H2O in the heat treatment furnace. CO , Δ CO2 , Δ H2 , Δ H2O This is done by adding Δ CO =-Δ CO2 , Δ H2 =-Δ H2O Let Δ CO2 and Δ H2O If we use a function in which the positive value decreases over time and converges to zero, the consumption of CO and H2 by the reduction reaction of oxides of metal elements other than Fe, and the production of the corresponding CO2 and H2O, can be easily handled by an error coefficient. In this case, Δ CO2 and Δ H2O By adopting a function of the form described above, the behavior of metal oxide reduction reactions, which are active in the initial stages of heat treatment and become less frequent over time, can be accurately reproduced. Furthermore, defining the function form in this way prevents the contribution of the error function from becoming excessively large in the simulation.

[0022]

[10] When determining the values ​​of unknown parameters included in a mathematical model by comparing the time evolution of the concentration of at least one of CO and CO2 between the simulation results and the measurement results from an actual heat treatment furnace, the values ​​of the various parameters included in the mathematical model can be determined by comparing them with the measured results, and the mathematical model can be constructed.

[0023]

[11] If the mathematical model includes multiple unknown parameters, and the values ​​of these unknown parameters are determined in order of their impact on the simulation results, then the convergence to the solution can be accelerated in the parameter determination process.

[0024]

[12] In the heat treatment method for a metal material according to the above invention, the inflow and outflow of gas to and from the actual heat treatment furnace is controlled based on the simulation results obtained by the above simulation method. The above simulation method uses a mathematical model that incorporates not only the inflow and outflow of gas to and from the heat treatment furnace but also chemical reactions occurring in the furnace, and can accurately simulate changes in the composition of the furnace atmosphere. By using the results of the simulation to control the atmosphere in the actual heat treatment furnace, it becomes easier to accurately realize the desired furnace atmosphere compared to when feedback control such as PID control is performed based on the measurement results of the actual furnace atmosphere composition. Even when the concentration of each component of the furnace atmosphere changes in a complex correlation due to the contribution of chemical reactions, or when the composition of the furnace atmosphere changes rapidly, it is possible to quickly follow these changes and control the furnace atmosphere to obtain a metal material having the desired component composition. [Brief explanation of the drawing]

[0025] [Figure 1] This is a schematic diagram illustrating the inflow and outflow of gas to and from a heat treatment furnace that is the subject of a simulation according to one embodiment of the present invention. [Figure 2] This is a schematic diagram showing the relationship between target values ​​and actual measured values ​​for (a) PF value and (b) furnace temperature during the heat treatment process in an actual heat treatment furnace. [Figure 3] This graph shows the time evolution of the error coefficient. The upper panel shows the functional form applied to ΔCO2 and ΔH2O, and the lower panel shows the functional form applied to ΔCO and ΔH2. [Figure 4] (a) to (d) show a comparison of experimental data, simulation results considering only gas inflow and outflow, and simulation results considering chemical reactions, regarding the change in CO concentration during the heat treatment process of materials A to D. [Figure 5] (a) and (b) show a comparison of experimental data, simulation results considering only gas inflow and outflow, and simulation results considering chemical reactions, respectively, regarding the change in CO2 concentration during the heat treatment process of materials A and B. [Figure 6] This paper compares experimental data, simulation results using the Arrhenius equation, and simulation results using the modified Arrhenius equation regarding the changes in (a) CO concentration and (b) CO2 concentration during the heat treatment process of material B. [Figure 7] This paper compares experimental data, simulation results without error functions, and simulation results using error functions for gas inflow rate and chemical reaction rate during the heat treatment process of material B, specifically regarding the changes in (a) CO concentration and (b) CO2 concentration. [Figure 8] Figures (a) to (d) show a comparison of experimental data, simulation results considering only gas inflow and outflow, and simulation results considering chemical reactions, regarding the change in CO concentration during the heat treatment process of materials A to D. Here, the number of chemical reactions considered is greater than in Figure 4. Also, the experimental data used differs from that in Figure 4. [Figure 9] This figure shows the change in CO2 concentration corresponding to Figure 8. [Modes for carrying out the invention]

[0026] The following describes a simulation method for furnace atmosphere and a heat treatment method for metal materials according to one embodiment of the present invention, with reference to the drawings.

[0027] [Outline of simulation and heat treatment of metallic materials] One embodiment of the present invention provides a simulation method for the furnace atmosphere, which simulates the time change in the composition of the furnace atmosphere when heat-treating a metallic material in a heat treatment furnace. The type of metallic material is not particularly limited, but it is preferably Fe or an Fe-based alloy, and in the following description, a method for heat-treating a steel material that is an Fe-based alloy will be used as an example.

[0028] In a heat treatment furnace, the furnace atmosphere contains at least one, and often both, of CO and CO2, and steel materials can undergo carburization and decarburization during the heat treatment process. When the furnace atmosphere contains at least one of CO and CO2, a carbon potential factor (PF) can be defined. PF is an index value of carbon potential, and with [CO] representing the CO concentration (volume %) in the furnace and [CO2] representing the CO2 concentration (volume %), PF = [CO]. 2 It is calculated as / [CO2].

[0029] As schematically shown in Figure 1, the following gases flow into and out of the heat treatment furnace 1 containing the steel material 2, and the inflow and outflow of these gases are also considered in the simulation. First, an endothermic modification gas (RX gas) flows into the heat treatment furnace. RX gas is produced by an endothermic reaction between hydrocarbons (methane in this case) and oxygen in the air, and contains small amounts of CO2, H2O, and CH4 in addition to its main components CO, H2, and N2. RX gas contains a large amount of CO, which increases the PF value.

[0030] Furthermore, a supply of adjusting air is introduced into the heat treatment furnace to fine-tune the CO2 concentration in the furnace atmosphere. This adjusting air supplies CO2 to the furnace atmosphere, thereby lowering the PF value. Air is used as the adjusting air.

[0031] Furthermore, for safety reasons (to maintain furnace pressure and prevent atmospheric intrusion into the furnace leading to an explosion), N2 gas is introduced into the furnace. In addition, it is preferable that in a heat treatment furnace, a separate N2 gas for PF control is introduced, controlled independently of the N2 gas introduced to maintain furnace pressure. When PF control N2 gas is supplied into the furnace, the CO concentration and CO2 concentration in the furnace atmosphere decrease at the same rate, resulting in a decrease in the PF value. At the start and end of the heat treatment process, N2 gas is introduced alone using the introduction route for furnace pressure maintenance or PF control N2 gas to prevent the formation of a mixture of flammable gas (RX gas) and oxygen in the furnace.

[0032] In a heat treatment furnace, the furnace atmosphere gas is also exhausted as a whole. The exhaust of the furnace atmosphere gas is carried out in order to maintain a constant pressure inside the furnace.

[0033] Here, we will explain the conventional method of controlling the furnace atmosphere in actual heat treatment furnaces. In the heat treatment process, the furnace atmosphere is heated using a radiant tube burner. As shown in Figure 2(b), this heat treatment process includes a heating zone in which the furnace temperature is gradually increased, a soaking zone in which the furnace temperature is kept constant, and a cooling zone in which the furnace temperature is gradually decreased. As shown in Figure 2(a), in each zone, a target PF value is set according to the target temperature, and the inflow rates of various gases are adjusted so that the actual PF value approaches that target value. Here, the target PF value is set for each temperature according to the specific type of steel material and the specifications (composition and material properties) required for the steel material after heat treatment.

[0034] Regarding decarburization / carburizing, in order to reliably achieve an equilibrium state according to the furnace temperature, the inflow rate of each gas (mainly RX gas) into the heat treatment furnace is adjusted so that the PF value meets the target value at a certain furnace temperature, and the target temperature is changed only after the actual PF value reaches that target value. Therefore, if it takes a long time for the PF value to reach the target value, it becomes necessary to spend a long time in the heating region. For example, in the region enclosed by the dotted rectangle in Figure 2(a), it takes a long time to raise the actual PF value to the target value. The reason for this is as follows: In this region, the concentration of CO2 in the furnace atmosphere tends to rise rapidly with the inflow of RX gas, and this rapid rise causes the calculated PF value to temporarily decrease, and as a result of feedback control, RX gas is supplied at the maximum flow rate. At this time, the CO2 concentration rises at a rate that exceeds the amount of RX gas supplied, and the PF value drops sharply. As a result, despite the supply of RX gas at the maximum flow rate, the actual PF value decreases, making it difficult to reach the target value.

[0035] Here, the rapid increase in CO2 concentration accompanying the inflow of RX gas is due to the reduction of oxides (scale) on the steel surface by CO (see equation (6) below). CO2 is generated by the reduction of scale, but because the concentration of CO2 in the furnace atmosphere is low, the CO2 generated by the reduction of scale has a large impact on the concentration of CO2 in the furnace atmosphere, making a rapid increase in CO2 concentration likely. Thus, until the actual PF value reaches the target value, the furnace temperature cannot be increased, and as shown by the dotted rectangles in Figures 2(a) and (b), there is a long period in the heating zone where the temperature cannot be increased in order to wait for the PF value to rise. Consequently, the entire heat treatment process takes a long time.

[0036] Thus, when controlling the furnace atmosphere using only the PF value of the furnace atmosphere, which is a macroscopic parameter, as an indicator, it is difficult to control the furnace atmosphere in a swift manner in response to changes in the state inside the furnace. Therefore, in the simulation method according to this embodiment, as a basis for performing atmosphere control based on the state inside the furnace, changes in the furnace atmosphere are simulated based on microscopic phenomena occurring inside the furnace. For example, in the area enclosed by the rectangle in Figure 2(a), if we can gain knowledge about how the change in the furnace atmosphere due to scale reduction progresses, and adjust the inflow rate of RX gas based on that change so that a sudden generation of CO2 does not occur, it may be possible to increase the inflow rate of RX gas in a short time while avoiding a sudden generation of CO2.

[0037] As described above, in the simulation, chemical reactions occurring in the furnace are considered in order to correlate the microscopic phenomena occurring in the furnace with changes in the furnace atmosphere. Chemical reactions occurring in the furnace include at least one of gas-phase reactions in the furnace atmosphere and gas-phase-solid-phase reactions on the surface of the metal material, preferably both of these reactions. When the metal material is steel, the following nine chemical reactions are assumed to occur in the furnace, and these nine chemical reactions are also incorporated in this simulation. [ka]

[0038] Here, the reactions in equations (4) and (5) are gas-phase reactions, while equations (1), (2), (3), (6), (7), (8), and (9) are gas-phase-solid-phase reactions. Of the gas-phase-solid-phase reactions, equation (1) shows the oxidation reaction of Fe, which constitutes the steel, and the reactions in equations (2) and (3) are related to the decarburization / carburization of the steel. The reactions in equations (6) and (7) correspond to the reduction of scale by CO and H2, respectively. Equations (8) and (9) show oxidation-reduction reactions in which carbon on the surface of the steel and / or the furnace wall contributes. Equations (1) to (9) are all equilibrium reactions, and the simulation is performed by incorporating the increase or decrease due to each equilibrium reaction into the time change in the concentration of each gas component constituting the furnace atmosphere.

[0039] In this simulation, a mathematical model is used to simulate changes in the composition of the furnace atmosphere due to both gas inflow and outflow and chemical reactions. Gas inflow and outflow include the RX gas inflow, regulating air inflow, N2 gas inflow for furnace pressure maintenance and PF control, and atmospheric gas exhaust, as explained above with reference to Figure 1. Chemical reactions include all of the chemical reactions in equations (1) to (9) above, or only the major ones as shown in equations (1) to (7). In the mathematical model, the concentration changes of the constituent components of the furnace atmosphere over a small time interval are calculated from differential equations based on the gas inflow and outflow rates and the reaction rates (forward and reverse reactions) of each chemical reaction. By repeating this process, the time evolution of the constituent component concentrations in the furnace atmosphere during the heat treatment process is simulated. Furthermore, the time evolution of these constituent component concentrations obtained from the simulation is compared with actual measured results from a real heat treatment furnace. Furthermore, even if their contribution is negligible, other chemical reactions besides those shown in equations (1) to (9) may also occur in the heat treatment furnace. In such cases, other chemical reactions may be considered as appropriate, in addition to the chemical reactions shown in equations (1) to (9), or in place of some of the chemical reactions shown in equations (1) to (9).

[0040] [Simulation Method] Next, the simulation method will be described in detail. As described above, the simulation method according to this embodiment deals with changes in the furnace atmosphere due to the contributions of both the inflow and outflow of gas into the heat treatment furnace and chemical reactions.

[0041] <1> Contribution of chemical reactions inside the reactor First, we will explain the contribution of chemical reactions to the gas inflow and outflow of the heat treatment furnace. As mentioned above, when heat treating steel materials, the chemical reactions (1) to (9) above are assumed to occur in the furnace. However, even considering only the chemical reactions (1) to (7), it is possible to reproduce the time change in the composition of the furnace atmosphere with a certain degree of accuracy through simulation. Therefore, below, we will explain using the form that considers the reactions (1) to (7) as an example. Here, the equilibrium reaction is expressed as the general equation (10) below. [ka]

[0042] At this time, the reaction rate v of the forward reaction f and the reaction rate v of the reverse reaction r These are given by equations (11) and (12) below, respectively.

number

[0043] The reaction rate constants k for the forward and reverse reactions. f ,k r The relationship is expressed by equation (13) below, where K(T) is the equilibrium constant at temperature T.

number

[0044] The equilibrium constant K(T) in equation (13) can be expressed as in equation (14) by van't Hoff's equation.

number

[0045] Furthermore, the reaction rate constant k of the forward reaction at temperature T. f (T) can be expressed using the modified Arrhenius equation as shown in equation (15).

number

[0046] The reaction rate constants k for the forward and reverse reactions at each temperature are obtained in this way. f ,k r From this, we can determine the time evolution of each component of the furnace atmosphere. In the chemical reaction of equation (i) (here i=1 to 7), the concentration of the substance with a coefficient of 1 in the original system (left side) at time t is given by q. i The rate of change of the concentration of that substance v i (t) is expressed as shown in equation (16) below. Note that q i This is equivalent to the sign [ ] in equations (11) and (12).

number

[0047] From equation (16), for a substance whose coefficient in the original system of equation (i) is 1, the change in concentration over a small time interval dt is expressed as shown in equation (17).

number

number

number

[0048] In the above, we assumed the heat treatment of steel materials involving decarburization / carburizing, and considered the chemical reactions in equations (1) to (7). However, even if the chemical reactions to be considered differ depending on the type of metal material, the composition of the furnace atmosphere, the heat treatment conditions, etc., the same simulation method can be applied by summing the concentration changes for all the chemical reactions to be considered, similar to equation (18).

[0049] For example, it is conceivable to incorporate the chemical reactions in equations (8) and (9) in addition to the chemical reactions in equations (1) to (7) and perform simulations. Since the chemical reactions in equations (8) and (9) are thought to include a significant contribution from chemical reactions occurring on the walls of the heat treatment furnace, depending on the configuration of the heat treatment furnace and the heat treatment conditions, a sufficiently high accuracy can be obtained in the simulation even without considering the chemical reactions in equations (8) and (9). However, by considering these chemical reactions as well, the accuracy of the simulation can be further improved. When considering the chemical reactions in equations (1) to (9), the above equations (18) and (19) become equations (18') and (19') below.

number

[0050] <2> Contribution of gas exchange Next, we will explain the contribution of gas inflow and outflow into the heat treatment furnace, which is incorporated into the simulation along with the chemical reaction.

[0051] As explained above with reference to Figure 1, the gas inflow and outflow into the heat treatment furnace include the inflow of RX gas, the inflow of regulating air, the inflow of N2 gas for furnace pressure maintenance and PF control, and the exhaust of the furnace atmosphere gas. Of these, in actual heat treatment furnaces, the RX gas is generated by the combustion of hydrocarbons such as city gas, so its component ratio may fluctuate, but in the simulation, the component composition will be fixed to that shown in Table 1 below. [Table 1]

[0052] Here, component X is in the RX gas x RX Assuming it contains % of the gas, the volumetric flow rate of RX gas is v RX (t) when (unit: m) 3 / s), the change in the concentration of component X in the reactor due to the inflow of RX gas, dq' RX (X) is given by the following equation (20) (unit: mol / m³) 3 ).

number

number

[0053] Air is used as the adjusting air, and it contains the components listed in Table 2 below. [Table 2]

[0054] Here, component X is supplied to the adjusting air by x air Assuming it contains %, the volumetric flow rate of the adjusting air is v air When that happens (unit: m) 3 / s), the change in the concentration of component X inside the furnace due to the inflow of regulating air, dq' air (X) is given by the following equation (22) (unit: mol / m³) 3 ).

number

[0055] Next, let's consider the exhaust of the furnace atmosphere gas. The exhaust of the furnace atmosphere gas is carried out to maintain a constant pressure inside the furnace. In other words, the same volume of atmosphere gas as the sum of the RX gas introduced into the furnace, the N2 gas used for furnace pressure maintenance and PF control, and the regulating air is exhausted. That is, the volumetric flow rate of the RX gas is v RX The volumetric flow rate of N2 gas used to maintain furnace pressure is v N2 The volumetric flow rate of N2 gas for PF control is v N2’ The volume flow rate of the regulating air is v air Therefore, exhaust speed v ex However, v ex =v N2 +v RX +vN2’ +v air (Unit: m) 3 ( / s). The concentration of component X in the furnace atmosphere at time t is [X] t In that case (unit: mol / m³) 3 ), the change in the concentration of component X due to exhaust over a small time interval dt, dq'. ex (X) is expressed by the following equation (23). Note that the volumetric flow rate of the N2 gas for PF control is v N2’ and the volumetric flow rate of the regulating air is v air Regarding this, if the flow rate is small and negligible, those terms can be expressed as v ex It may be removed from the list.

number

number

[0056] Based on the above, for the gaseous component X in the furnace excluding N2, the concentration change dq'(X) over a small time interval dt associated with the inflow and outflow of gas into and out of the furnace is expressed by equation (25) below, by summing the contributions of the inflow of RX gas, the inflow of regulating air, and the exhaust of the furnace atmosphere gas, which are represented by equations (20), (22), and (23), respectively.

number

number

[0057] In the above, the inflow of four types of gases—RX gas, regulating air, and N2 gas for furnace pressure maintenance and PF control—and the exhaust of the entire furnace atmosphere gas were considered as gas inflows and outflows into the heat treatment furnace. However, even if the phenomena related to gas inflows and outflows that should be considered differ depending on the heat treatment conditions, the same simulation method can be applied to all of these gas inflows and outflows by summing up the contributions of the component of interest to the change in furnace concentration, similar to equation (25).

[0058] <3> Consideration of two types of contributions In this embodiment, as described above, the simulation of the concentration change of constituent components in the furnace atmosphere is performed, taking into account the contribution of chemical reactions in the heat treatment furnace and the inflow and outflow of gas into the heat treatment furnace. Therefore, for each gas component in the furnace (let's call it component X), the sum of the concentration change dq(X) due to the contribution of chemical reactions expressed by equation (18) and the concentration change dq'(X) due to the inflow and outflow of gas expressed by equation (25) is calculated, and the total amount of concentration change dq in the small time interval dt from time t is obtained. tot (X) can be calculated using the following equation (27).

number

[0059] Thus, in the simulation method according to this embodiment, in addition to the inflow and outflow of gas into the heat treatment furnace, which is also considered in the calculation method disclosed in Patent Document 1, the contribution of chemical reactions within the heat treatment furnace is also considered, and the time change in the concentration of each gas component in the heat treatment furnace is simulated. As shown in later examples, by considering the chemical reactions in the furnace, the accuracy of the simulation is improved compared to the case where only the inflow and outflow of gas into the heat treatment furnace is considered, as in Patent Document 1, and it becomes possible to reproduce with high accuracy the changes in the composition of the atmosphere inside the actual heat treatment furnace. In particular, considering the gas-phase-solid-phase reaction on the surface of the metal material being heat-treated greatly contributes to improving the accuracy of the simulation.

[0060] <4> Introduction of the error function When introducing gas into an actual heat treatment furnace, errors in the inflow velocity can inevitably occur due to factors such as the pressure difference across the valve. To incorporate this error into the simulation, an error function is introduced. Specifically, the volumetric flow rate v of gas Y. Y (1+Δ Y Multiply by ). Here, gas Y refers to RX gas, furnace pressure maintaining N2 gas, PF control N2 gas, and adjustment air, respectively, Δ Y This is the error coefficient corresponding to each of the gases Y. Error coefficient Δ Y This can be expressed using the Gaussian error function erf as shown in equation (28), where a, b, c, and d are arbitrary constants.

number

[0061] In actual heat treatment furnaces, if uncontrollable fluctuations in the gas inflow rate occur, such fluctuations can be incorporated into the simulation by considering errors in the gas inflow rate. However, in most heat treatment furnaces and under most heat treatment conditions, fluctuations in the gas inflow rate do not occur to a degree that cannot be ignored, and in such cases, it is not necessary to consider errors in the gas inflow rate in the simulation. Rather, if errors in the gas inflow rate are considered in the simulation, when searching for parameter values ​​that can reproduce experimental results, the contribution of errors in the gas inflow rate may be excessively incorporated, forcing a reproduction of experimental results and potentially deviating from the actual conditions inside the furnace. In such cases, it is better not to consider errors in the gas inflow rate.

[0062] Furthermore, by similarly introducing error functions to the reaction rates of at least some chemical reactions in the simulation, the accuracy of the simulation can be improved, as shown in later examples. In this case, the contribution of chemical reactions with small contributions, which are not explicitly considered based on chemical equations, can be mathematically incorporated using the error function. For example, equations (6) and (7) represent the reduction of FeO, the main component of scale on the surface of steel, but the scale also contains, in smaller amounts than FeO, Fe oxides in different oxidation states such as Fe2O3 and Fe3O4, as well as oxides of metal elements other than Fe added to the steel, such as Cr, which are also reduced. The contribution of the reduction of these metal oxides other than FeO can be incorporated into equations (6) and (7) as an error function. In this way, by using an error function, the contribution of chemical reaction pathways with small contributions can be easily incorporated into the simulation without explicitly considering reaction rates based on chemical equations, thereby improving the accuracy of the simulation.

[0063] Specifically, the error coefficient should be added to the rate of concentration change of the constituent components in the furnace due to chemical reactions. In other words, the error coefficient should be added to the rate of concentration change due to the contribution of the chemical reaction, which is represented by equation (18). The error coefficient of component X is Δ XThen, the time change of the concentration of component X is as shown in Equation (29).

Equation

Equation

[0064] Among Equations (1) to (9), for the chemical reactions of Equations (6) and (7) corresponding to scale reduction, introducing an error function can obtain a high effect in improving simulation accuracy. In particular, in the chemical reaction of Equation (6), the effect of introducing an error function is significant. Therefore, error coefficients Δ CO , Δ CO2 , Δ H2 , Δ H2O are added to the concentration change rates of CO, CO2, H2, and H2O according to Equation (29). At this time, from the equilibrium relationships of Equations (6) and (7), Δ CO = -Δ CO2 , Δ H2 = -Δ H2O . As for each error coefficient Δ CO , Δ CO2 , Δ H2 , Δ H2O , those having the same form as Equation (28) may be used.

[0065] However, as the error coefficients Δ CO , Δ​​​​​If a function of the same form as equation (28) above is used to consider this, the high degree of freedom in the equation may lead to the incorporation of excessive error coefficients into the simulation that would not occur in the actual reduction of scale in the heat treatment process. As a result, the contribution of these error coefficients may cause the simulation to forcibly reproduce the experimental results, and the furnace state reproduced by the simulation may actually deviate from the actual furnace state. In such cases, it is preferable to limit the degree of freedom in the error coefficient equation and set an error coefficient that is in line with the actual conditions inside the furnace. Specifically, since scale reduction occurs actively in the initial stages of heat treatment and becomes less likely to occur over time, Δ CO2 and Δ H2O It is preferable to use a function in which the positive value decreases over time and converges to zero. In this case, Δ CO =-Δ CO2 , Δ H2 =-Δ H2O Considering the relationship, Δ CO and Δ H2 This function takes negative values, and the absolute value of these negative values ​​decreases over time, converging to zero.

[0066] As a concrete example of such a function, it is conceivable to set the error coefficient in the form of equation (31) below, instead of equation (28) above.

number

[0067] Figure 3 shows an example of the time evolution of the error coefficient expressed by the function of equation (31). The upper row shows the case when a > 0, and Δ CO2 and Δ H2O This corresponds to the case where a < 0, and Δ CO and Δ H2This corresponds to Δ. Here, the graph curve is scaled vertically by the value of a, and scaled horizontally and shifted by the values ​​of b and c. Therefore, the specific form of time change of the error coefficient is determined by the selection of the values ​​of the constants a, b, and c. Note that in Figure 3, Δ CO2 and Δ H2O Also, Δ CO and Δ H2 Each of these is represented by a single graph curve, but the specific shapes of these graphs can be different from each other.

[0068] <5> Running the simulation As described above, by incorporating an appropriate error function into the concentration change expressed by equation (27), the concentration change of each gas component in the heat treatment furnace over a small time interval dt can be obtained. By applying the differential equations that show the time evolution of these concentrations to the set heat treatment conditions and calculating the concentration of each gas component in the furnace at small time intervals, the time evolution of the composition of the furnace atmosphere can be simulated.

[0069] Among the parameters incorporated into the simulation, some have unknown values, for example, because it is difficult to experimentally evaluate them in isolation from other parameters. For example, in many of the reactions in equations (1) to (9) above, the frequency factor k' f , constant b, activation energy E f It is not easy to know this. Also, the initial values ​​of the surface area used for the solid substance instead of the concentration value in the reaction rate equations (11) and (12), and each error coefficient Δ ~ These are also unknown parameters (where ~ represents each gas explained for Y, i.e., the error function, as well as CO, CO2, H2, and H2O). These unknown parameters can be determined by comparing the time evolution of the concentration of each gas component with the measurement results from an actual heat treatment furnace and the simulation results. In other words, the simulation should be performed many times while changing the parameter values, and the parameter values ​​that best reproduce the experimental results should be adopted.

[0070] Here, when comparing the concentrations between the measurement results and the simulation results, it is preferable to use at least one, preferably both, of CO and CO2 as the component species. This is because CO and CO2 undergo large concentration changes during heat treatment and have a significant impact on the progress of decarburization / carburization. In this case, the evaluation function J(x), which serves as an indicator of the proximity between the simulation results and the measurement results, can be set as shown in equation (32) below.

number

[0071] A genetic algorithm can be suitably used in the process of searching for a solution for the parameter values ​​by performing numerous simulations while changing the set of parameter values. In this case, it is preferable to determine the values ​​in order from the parameters with high parameter sensitivity, that is, the parameters whose effect on the simulation results when the parameter value is changed is large. This can speed up convergence to the solution. Specifically, the constant b and the activation energy E f , frequency factor k' f The parameter sensitivity increases in the order of initial value of the surface area of ​​the solid material, followed by the error function. Identification should be performed in this order.

[0072] [Heat treatment methods for metallic materials] In the heat treatment method for a metal material according to an embodiment of the present invention, the inflow and outflow of gas to and from the actual heat treatment furnace is controlled based on the simulation results obtained by the simulation method described above, thereby performing heat treatment on the metal material. How the simulation is used for atmosphere control in the actual heat treatment furnace is not particularly limited. For example, it is conceivable to perform actual atmosphere control while predicting changes in the composition of the furnace atmosphere using simulation. This makes it possible to proceed with the heat treatment process while preventing the occurrence of factors that hinder efficient heat treatment, such as phenomena where the concentration of a specific component in the furnace atmosphere changes rapidly. Alternatively, when considering the conditions related to heat treatment in advance, such as the furnace temperature and the set value of the PF value, simulations can be performed under various conditions to search for appropriate conditions.

[0073] As described above, since the simulation can accurately simulate the composition of the furnace atmosphere, using the simulation results for atmosphere control in an actual heat treatment furnace makes it easier to accurately control the furnace atmosphere compared to using feedback control such as PID control. In particular, even if the concentrations of each component in the furnace atmosphere change in a complex correlation, or if the composition of the furnace atmosphere changes rapidly, these changes can be followed quickly. As a result, it is possible to manufacture heat-treated materials with desired component composition and properties through the control of the furnace atmosphere. [Examples]

[0074] The present invention will be described in more detail below using examples. However, the present invention is not limited to these examples.

[0075] [Test Method] This study investigated whether the composition of the furnace atmosphere obtained during the actual heat treatment process of steel materials in a heat treatment furnace could be reproduced through simulation. Here, experimental data was prepared by monitoring the changes in the furnace atmosphere composition for four different types of steel materials (A-D) with varying component compositions. These materials were heat-treated using RX gas, N2 gas for furnace pressure maintenance, and adjustment air, under conditions set according to the material properties. Then, simulations were performed under the corresponding conditions, and the time-dependent changes in CO and CO2 concentrations were compared between the experimental data and the simulation results.

[0076] For the simulation, experimental data was used directly as the values ​​for the furnace temperature and the flow rates of RX gas, N2 gas for furnace pressure maintenance, and regulating air. Of the parameters involved in the chemical reactions in equations (1) to (9), the standard free energy change ΔG 0 For values ​​known from databases, etc., those values ​​were used. The frequency factor k' of each chemical reaction. f , constant b, activation energy E f , the initial value of the surface area of ​​the solid material, and the error coefficient Δ ~ This parameter was unknown, and its value was determined by simulation. The simulation results shown in each figure represent the results obtained by adopting the set of parameters that best reproduced the experimental results. Furthermore, the specific simulation method used was the one described in the "Simulation Method" section above. The simulation was performed throughout the heat treatment process, encompassing the heating, soaking, and cooling zones. However, the initial stages of the heating zone and the final stages of the cooling zone, during which the heat treatment furnace was purged with nitrogen gas, were excluded from the simulation. Also, the pumping speed v in equation (23) was also considered. ex In this case, the contribution of the adjusting air is negligible and therefore can be ignored. ex =v N2 +v RX The error coefficient Δ was used. Y However, adjustment air was not considered.

[0077] [Test Results] <1> Effects of considering chemical reactions First, we investigated how considering chemical reactions within the furnace affects the simulation results. Here, we compared the simulation results under two conditions: one where only the inflow and outflow of gas to and from the heat treatment furnace is considered as a phenomenon contributing to the change in the composition of the furnace atmosphere (incorporating only dq'(X) in equation (27)); and another where the contribution of the chemical reactions in equations (1) to (7) is also considered (incorporating both dq(X) and dq'(X) in equation (27)). In both simulations, the modified Arrhenius equation was used to calculate the reaction rate constant, and an error function of the form of equation (28) was introduced into the gas inflow rate and the reaction rate of the chemical reactions. Note that the chemical reactions in equations (8) and (9) are not considered here.

[0078] Figures 4(a) to 4(d) show the time evolution of CO concentration during the heat treatment process for materials A to D, respectively. Figures 5(a) and 5(b) show the time evolution of CO2 concentration during the heat treatment process for materials A and B, respectively. Each figure displays experimental data, simulation results considering only gas inflow and outflow (gas only), and simulation results considering chemical reactions (gas + reaction).

[0079] Looking at each figure, for both CO and CO2, and for all materials A through D, the simulation that only considers the inflow and outflow of gases fails to adequately reproduce the concentration changes in the experimental data, resulting in a large deviation from the experimental data. On the other hand, the simulation that also considers chemical reactions reproduces the experimental data well throughout the entire period. The simulation results and experimental data also overlap well regarding the rapid rise in concentration at the beginning.

[0080] In particular, the difference in CO2 concentration in Figure 5 is significant between simulations that consider chemical reactions and those that do not. The experimental data shows a behavior in which the concentration rises sharply and then gradually decreases, and this behavior is well reproduced in the simulation that considers chemical reactions. However, in the simulation that only considers the inflow and outflow of gas, the CO2 concentration remains low throughout the entire period, which does not match the experimental data at all.

[0081] From these results, it is confirmed that by considering chemical reactions within the furnace, in addition to the inflow and outflow of gases, the time-dependent changes in the furnace atmosphere composition can be accurately reproduced in the simulation. In particular, for CO2, the concentration inside the furnace is low, and the contribution of reactions on the steel surface, such as the reduction reaction on the scale of equation (6), becomes relatively large. Therefore, by taking these chemical reactions into account, the accuracy of the simulation is greatly improved, and it is possible to reproduce the experimental results.

[0082] <2> Effects of applying the modified Arrhenius formula Next, we examined how considering the temperature dependence of the frequency factor by using the modified Arrhenius equation shown in equation (15) to calculate the reaction rate constant affects the simulation. Here, we compared the simulation results when using the modified Arrhenius equation with b≠0 in equation (15) and when using the standard Arrhenius equation with b=0. In both simulations, we considered both the inflow and outflow of gas and the chemical reactions inside the furnace, and introduced error functions into the gas inflow rate and the reaction rate of the chemical reactions.

[0083] Figures 6(a) and 6(b) show the time evolution of CO and CO2 concentrations during the heat treatment process for material B, respectively. Each figure displays experimental data, simulation results using the Arrhenius equation, and simulation results using the modified Arrhenius equation. The experimental data and simulation results using the modified Arrhenius equation are the same as those shown in Figures 4(b) and 5(b).

[0084] For both CO and CO2, the modified Arrhenius equation reproduces the experimental data better than the Arrhenius equation. In particular, for CO2, the Arrhenius equation fails to reproduce the behavior of the concentration decreasing after an initial rise, whereas the modified Arrhenius equation shows good overlap between the experimental data and the simulation results throughout the entire period. From these results, it is confirmed that by using the modified Arrhenius equation to calculate the reaction rate constant in the simulation and considering the temperature dependence of the frequency factor, the time change in the composition of the furnace atmosphere can be reproduced with high accuracy. As shown in Figure 2(b), the temperature changes over a wide range of over 200°C in the heat treatment process, and it is considered that the temperature dependence of the frequency factor makes a significant contribution to the reaction rate.

[0085] <3> Effects of introducing the error function Next, we examined how incorporating error functions into the gas inflow rate and the reaction rate of the chemical reaction affects the simulation. Here, we used the error coefficient Δ for the gas inflow rate described above. RX , Δ N2 , and the error coefficient Δ of the reaction rate CO , Δ CO2 , Δ H2 , Δ H2O We compared the simulation results with and without incorporating the error function into the differential equation. In both simulations, we considered both the inflow and outflow of gas and the chemical reactions inside the furnace, and used the modified Arrhenius equation to calculate the reaction rate constant.

[0086] Figures 7(a) and 7(b) show the time evolution of CO and CO2 concentrations during the heat treatment process for material B, respectively. Each figure displays experimental data, simulation results with and without the error function. The experimental data and simulation results with the error function are the same as those shown in Figures 4(b) and 5(b).

[0087] For both CO and CO2, the experimental data is reproduced better when the error function is introduced compared to when it is not. In particular, for CO2, the behavior of the concentration rising sharply and then gradually decreasing is not reproduced when the error function is not introduced, whereas this behavior is reproduced well when the error function is introduced. From these results, it is confirmed that the time change in the composition of the furnace atmosphere can be reproduced with high accuracy by introducing the error function to the gas inflow rate and the reaction rate of chemical reactions in the simulation. In particular, the error function for the reaction rate of chemical reactions incorporates the contribution of the reduction of oxides other than FeO, and even if the reduction of these oxides is small in proportion, it certainly contributes to the change in the furnace atmosphere, so it is highly significant to consider it in the simulation.

[0088] <4> Effects of the types of chemical reactions considered Next, we examined how increasing the number of chemical reactions considered affects the simulation. <1> ~ <3> In the previous simulation, only the chemical reactions in equations (1) to (7) were considered; however, here, all chemical reactions in equations (1) to (9) were considered in the simulation. For other aspects, the simulation method is as described above. <1> The same approach is used. However, the error coefficient is not incorporated into the gas inflow rate, but rather the error coefficient Δ is applied to the reaction rate. CO , Δ CO2 , Δ H2 , Δ H2O Only this was incorporated in a form with restricted degrees of freedom from the above equation (31).

[0089] Figures 8(a) to 8(d) show the time evolution of CO concentration during the heat treatment process for materials A to D, respectively. Figures 9(a) to 9(d) show the corresponding time evolution of CO2 concentration. Each figure displays experimental data, simulation results considering only gas inflow and outflow (gas only), and simulation results considering chemical reactions (gas + reaction). Except for material A, the experimental data is as described above. <1> This differs from the one used in the simulation.

[0090] As shown in Figures 8 and 9, for both CO and CO2, and for all materials A through D, the simulation, which considers chemical reactions in addition to gas inflow and outflow, reproduces the experimental data well over the entire period. Comparing the simulation results with those considering only the chemical reactions in equations (1) through (7) in Figures 4 and 5, the simulation reproduces the experimental data with equal or even greater accuracy. In particular, for materials C and D, the simulation reproduces the experimental data with higher accuracy than in Figure 4.

[0091] These results confirm that by considering not only the chemical reactions in equations (1) to (7), but also the chemical reactions in equations (8) and (9) in the simulation, experimental data can be reproduced with high accuracy. Furthermore, <1> In the simulation, an error coefficient was incorporated not only into the reaction rate but also into the gas inflow rate, whereas, <4> In this simulation, the error coefficient is only incorporated into the reaction rate, and moreover, a functional error coefficient with low degrees of freedom is used. In other words, the reproducibility of experimental data by adjusting the error coefficient is, <1> Rather than the simulation <4> Despite the simulation showing a lower value, the results obtained indicated that <4> The simulation reproduces the experimental data better. This indicates that the improvement in simulation accuracy due to considering the chemical reactions in equations (8) and (9) outweighs the effect of the reduced degrees of freedom in the error coefficient.

[0092] Although embodiments of the present invention have been described in detail above, the present invention is not limited to the above embodiments, and various modifications are possible without departing from the spirit of the invention. [Explanation of Symbols]

[0093] 1. Heat treatment furnace 2 Steel materials (metal materials)

Claims

1. In a heat treatment furnace, CO and CO ２ A method for performing a simulation to simulate the time change in the composition of a furnace atmosphere when performing heat treatment on a metallic material in a furnace atmosphere containing both of the following: The rate at which gas enters and leaves the heat treatment furnace, The reaction rates of the forward and reverse reactions of each of a plurality of chemical reactions, including both gas-phase reactions in the furnace atmosphere and gas-phase-solid-phase reactions on the surface of the metal material, Using a mathematical model that incorporates the changes in the composition of the furnace atmosphere due to both the inflow and outflow of the gas and the chemical reaction, including differential equations based on the above, A method for simulating a furnace atmosphere, comprising the step of repeatedly calculating the change in concentration of the constituent components of the furnace atmosphere over a small time interval from the differential equation, thereby performing the simulation to simulate the change in concentration of the constituent components over time for the furnace atmosphere during heat treatment.

2. The inflow and outflow of gas to and from the heat treatment furnace is as follows: The inflow of gas that increases the carbon potential factor of the furnace atmosphere, The inflow of gas that reduces the carbon potential factor, A method for simulating the atmosphere inside a furnace according to claim 1, comprising exhausting the entire furnace atmosphere gas.

3. As for the time change in the composition of the furnace atmosphere, at least CO or CO ２ A method for simulating the atmosphere inside a furnace according to claim 1, which simulates the time change in the concentration of a substance.

4. A method for simulating the atmosphere inside a furnace according to claim 1, comprising incorporating an error function into at least one of the gas inflow rate into the heat treatment furnace and the reaction rate of the chemical reaction.

5. The method for simulating the atmosphere inside a furnace according to claim 4, wherein an error function is incorporated only into the reaction rate of the aforementioned chemical reaction.

6. The method for simulating the atmosphere inside a furnace according to claim 1, wherein the reaction rate of the aforementioned chemical reaction is expressed by the modified Arrhenius equation shown in the following equation (A). [Math 1] In equation (A), k ｆ (T) is the reaction rate constant at temperature T, k' ｆ is the frequency factor, T is the temperature inside the heat treatment furnace, b is a constant, E ｆ is the activation energy, and R is the gas constant.

7. The metallic material is Fe or an Fe-based alloy, and the chemical reaction is considered to be one of the equilibrium reactions of the following formulas (1) to (7), or formulas (1) to (9). The simulation method for the atmosphere inside a furnace according to claim 1, wherein the simulation is performed by incorporating the increase or decrease due to the following equilibrium reactions into the time change of the concentration of each gas component constituting the atmosphere inside the furnace. 【Chemistry 1】

8. The method for simulating the atmosphere inside a furnace according to claim 7, wherein an error function is incorporated into the reaction rates of the chemical reactions in equations (6) and (7).

9. The incorporation of the error function is performed by adding error coefficients Δ ２ , H ２ , H ２ O to the rates of change in the concentrations of CO, CO ＣＯ , Δ ＣＯ２ , Δ Ｈ２ , Δ Ｈ２Ｏ respectively, D ＣＯ =-D ＣＯ２ 、D Ｈ２ =-D Ｈ２Ｏ とく、 Δ ＣＯ２ and Δ Ｈ２Ｏ The method for simulating the atmosphere inside a furnace according to claim 8, wherein a function is used in which a positive value decreases over time and converges to zero.

10. CO and CO ２ A method for simulating the atmosphere inside a furnace according to claim 1, wherein the value of an unknown parameter included in the mathematical model is determined by comparing the time change of at least one of the concentrations between the results of the simulation and the measurement results in an actual heat treatment furnace.

11. The method for simulating the atmosphere inside a furnace according to claim 10, wherein the mathematical model includes multiple unknown parameters, and the values ​​of these unknown parameters are determined in order from those that have the greatest influence on the results of the simulation.

12. When performing heat treatment on metal materials in an actual heat treatment furnace, A heat treatment method for a metal material, comprising controlling the inflow and outflow of gas to and from the heat treatment furnace based on simulation results obtained by the furnace atmosphere simulation method described in any one of claims 1 to 11.

Images