Method for simulating an atmosphere in a furnace and method for heat treating a metallic material

Abstract

The present invention relates to a method of simulating an in-furnace atmosphere, comprising simulating a change over time of a composition of the in-furnace atmosphere comprising at least one of CO and CO2 when a heat treatment of a metallic material is performed in a heat treatment furnace under the in-furnace atmosphere, wherein the simulation is performed using a mathematical model comprising a change of the composition of the in-furnace atmosphere, and the change of the composition of the in-furnace atmosphere takes into account a flow rate of a gas flowing into the heat treatment furnace, a flow rate of a gas flowing out of the heat treatment furnace, and a reaction rate of at least one chemical reaction selected from the group consisting of a gas phase chemical reaction in the in-furnace atmosphere and a gas phase / solid phase chemical reaction on a surface of the metallic material.

Description

Technical Field

[0001] This invention relates to methods for simulating furnace atmosphere and methods for heat-treating metallic materials. More specifically, this invention relates to methods for simulating the composition of furnace atmosphere for heat-treating metallic materials, and to methods for controlling the furnace atmosphere using simulation results obtained by this method during the heat treatment of metallic materials. Background Technology

[0002] When metallic materials, including steel, are heat-treated for tempering, decarburization, carburization, and oxidation frequently occur. The progress of these phenomena depends on the composition of the atmosphere in the heat treatment furnace. Therefore, the furnace atmosphere is controlled to suppress or regulate the progress of these phenomena to a desired degree, thereby adjusting the composition and properties of the steel. In controlling decarburization and carburization, an endothermic modifying gas (RX gas) containing CO, H2, and N2 is typically used to regulate the furnace atmosphere.

[0003] When using gases containing CO or CO2, as well as RX gases, to control the furnace atmosphere, the carbon potential factor (PF) is typically used as an indicator of the atmosphere control. PF is an indicator of carbon potential, expressed as PF = [CO]. 2 The PF value is calculated using [CO], where [CO] and [CO2] represent the CO and CO2 concentrations in the furnace, respectively, expressed as volume percent. A higher PF value indicates more carburizing, while a lower PF value indicates more decarburization. Therefore, a target PF value is set based on the desired carbon concentration of the metal material, and feedback control, such as PID control, is implemented while monitoring the CO and CO2 concentrations in the furnace atmosphere to ensure the actual PF value of the furnace atmosphere is close to the target value. This involves controlling the gases flowing into and out of the furnace, such as RX gas flowing into the furnace, N2 gas flowing in for safety (to ensure furnace pressure and prevent air from entering the furnace and causing an explosion), N2 gas and / or air flowing in to reduce PF, and the gases discharged from the furnace atmosphere. For example, Patent Document 1 discloses a method for controlling the furnace atmosphere using the PF value as an indicator.

[0004] [Patent Document 1] JP-A-H2-153017 Summary of the Invention

[0005] Inside the heat treatment furnace where metallic materials are heat-treated, multiple chemical reactions occur, affecting the concentrations of the furnace atmosphere's components, including CO and CO2. Heat treatment is carried out with these reactions interconnected. Therefore, the furnace atmosphere undergoes complex or abrupt changes. However, when monitoring the CO and CO2 concentrations in the furnace atmosphere to calculate the power factor (PF) and controlling the atmosphere via feedback control, there may be situations where the furnace atmosphere control cannot quickly keep up with the actual changes in the atmosphere. This makes it difficult to properly control the carbon concentration of the metallic material. Especially when gas-phase / solid-phase reactions, such as the reduction of surface oxides (scale) on the metallic material, contribute significantly, atmosphere-based PF value control cannot adequately reflect the actual changes in the furnace atmosphere. As the basis for high-precision control of the furnace atmosphere, a technique that highly accurately simulates how the composition of the furnace atmosphere changes during the heat treatment process is desired.

[0006] The purpose of this invention is to provide a furnace atmosphere simulation method that can highly accurately simulate the changes in the furnace atmosphere during the heat treatment process of metal materials that can undergo decarburization and carburization, and to provide a metal material heat treatment method that can utilize the simulation results.

[0007] In order to solve the above problems, the present invention relates to the following configurations [1] to

[12] .

[0008] [1] A method for simulating furnace atmosphere, comprising simulating the change over time of the composition of a furnace atmosphere containing at least one of CO and CO2 when a metallic material is heat-treated in a heat treatment furnace under a furnace atmosphere.

[0009] The simulation uses a mathematical model that includes changes in the composition of the furnace atmosphere.

[0010] The compositional changes of the furnace atmosphere are considered to be due to the following factors:

[0011] The rate of gas flowing into the heat treatment furnace.

[0012] The flow rate of the gas exiting the heat treatment furnace, and

[0013] The reaction rate of at least one chemical reaction selected from the group consisting of gas-phase chemical reactions in the furnace atmosphere and gas-phase / solid-phase chemical reactions on the surface of the metal material.

[0014] [2] According to the method for simulating furnace atmosphere described in [1],

[0015] The gases flowing into and out of the heat treatment furnace include:

[0016] The inflow gas that increases the carbon potential factor of the furnace atmosphere.

[0017] The inflow gas that reduces the carbon potential factor of the furnace atmosphere, and

[0018] The gas that is completely discharged from the furnace atmosphere.

[0019] [3] According to the method for simulating furnace atmosphere described in [1] or [2],

[0020] The composition of the furnace atmosphere changes over time, including the change in the concentration of CO or CO2 over time.

[0021] [4] The method for simulating furnace atmosphere according to any one of [1] to [3],

[0022] At least one of the flow rate of the gas flowing into the heat treatment furnace and the reaction rate of the chemical reaction includes an error function.

[0023] [5] According to the method for simulating furnace atmosphere described in [4], the reaction rate of only chemical reaction includes an error function.

[0024] [6] The method for simulating furnace atmosphere according to any one of [1] to [5],

[0025] The reaction rate of the chemical reaction is represented by the modified Arrhenius equation shown in equation (A): [Mathematical Formula 1]

[0026]

[0027] Where k f (T) is the reaction rate constant at temperature T, k' f Here, T is the frequency factor, T is the temperature in the heat treatment furnace, b is a constant, and E is a frequency factor. f R is the activation energy, and R is the gas constant.

[0028] [7] The method for simulating furnace atmosphere according to any one of [1] to [6],

[0029] The metallic material is Fe or an Fe-based alloy, and the equilibrium reaction represented by formulas (1) to (7) or (1) to (9) is considered the chemical reaction, and

[0030] The simulation is performed by incorporating the increase or decrease of gaseous components due to the following equilibrium reaction into the change in the concentration of each gaseous component contained in the furnace atmosphere over time.

[0031] [Chemical Formula 1]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] [8] According to the method for simulating furnace atmosphere described in [7],

[0042] The reaction rates of the chemical reactions in equations (6) and (7) each include an error function.

[0043] [9] According to the method for simulating furnace atmosphere described in [8],

[0044] Among them, by using the error coefficient Δ CO Δ CO2 Δ H2 and Δ H2O The error function is thus included by adding the rates of change of concentrations of CO, CO2, H2, and H2O in the heat treatment furnace, respectively.

[0045] The error coefficients have the following relationship: Δ CO =-Δ CO2 and Δ H2 =-Δ H2O ,and

[0046] Where, Δ CO2 and Δ H2O Each is a function that makes the positive value decrease over time and converge to zero.

[0047]

[10] The method for simulating furnace atmosphere according to any one of [1] to [9] further includes determining the unknown parameters contained in the mathematical model by comparing the simulation results of the change of concentration of at least one of CO and CO2 over time with the actual test results in the actual heat treatment furnace.

[0048]

[11] The method for simulating furnace atmosphere according to

[10] includes a mathematical model comprising multiple unknown parameters, and the values ​​of these unknown parameters are determined in descending order of their influence on the simulation results.

[0049]

[12] A method for heat-treating a metallic material, comprising, when heat-treating the metallic material in an actual heat treatment furnace, controlling the flow rate of gas flowing into the heat treatment furnace and the flow rate of gas flowing out of the heat treatment furnace based on simulation results obtained by the method for simulating the furnace atmosphere according to any one of [1] to

[11] .

[0050] [1] In the method for simulating the furnace atmosphere according to the present invention, a mathematical model is used to simulate the compositional changes of the furnace atmosphere. The mathematical model includes the reaction rate of at least one chemical reaction selected from the group consisting of gas-phase chemical reactions in the furnace atmosphere and gas-phase / solid-phase chemical reactions on the surface of the metal material, as well as the flow rate of the gas flowing into the heat treatment furnace and the flow rate of the gas flowing out of the heat treatment furnace.

[0051] Based on this mathematical model, the composition of the furnace atmosphere during each minute time period is calculated using differential equations based on the reaction rates of each chemical reaction. This allows for a highly accurate reproduction of the changes in the furnace atmosphere caused by the chemical reactions occurring within the furnace. Preferably, a mathematical model is used that includes the reaction rates of both gas-phase chemical reactions within the furnace atmosphere and gas-phase / solid-phase chemical reactions on the surface of the metal material.

[0052] [2] In the case where the gases flowing into and out of the heat treatment furnace include inflow gases that increase the carbon potential factor of the furnace atmosphere, inflow gases that decrease the carbon potential factor, and gases discharged from the furnace atmosphere as a whole, the inflow of gases that increase or decrease the carbon potential factor of the furnace atmosphere and the discharge of furnace atmosphere gases that help decrease the carbon potential factor are incorporated into the simulation. Therefore, the concentration changes of CO and CO2, the carbon potential factor control components in the furnace atmosphere, can be simulated with high accuracy. The carbon potential factor is an indicator closely related to the decarburization / carburization process of metallic materials, and is therefore crucial for controlling the carbon content of metallic materials.

[0053] [3] By simulating the change in concentration of at least CO or CO2 over time as a change in the composition of the furnace atmosphere over time, the concentrations of gaseous components CO and CO2 that contribute to the decarburization / carburization of metal materials are simulated with high accuracy, thereby obtaining results on their concentration changes, and these results can be used to precisely control the carbon content of the metal materials. Preferably, the changes in the concentrations of both CO and CO2 over time are simulated.

[0054] [4] When at least one of the flow rate of the gas flowing into the heat treatment furnace and the reaction rate of the chemical reaction includes an error function, it is possible to incorporate the flow rate error of the gas flowing into the actual heat treatment furnace and the contribution of chemical reactions other than those explicitly included in the mathematical model into the simulation. In particular, with regard to this contribution, chemical reactions that are not specifically treated as chemical reactions can be incorporated into the simulation as a mathematical error function. Therefore, even when the contribution of chemical reactions is limited, this contribution can be easily incorporated into the simulation, thereby improving the accuracy of the simulation.

[0055] [5] In this case, where only the reaction rate of the chemical reaction includes an error function, it is possible to suppress the excessive increase in the contribution of the error function due to the consideration of the inflow gas flow rate in the simulation. In the actual heat treatment of metallic materials, although chemical reactions other than those explicitly included in the mathematical model frequently occur in the heat treatment furnace, the error in the flow rate of the gas flowing into the heat treatment furnace can be sufficiently reduced through control.

[0056] [6] When the chemical reaction rate is represented by the modified Arrhenius equation as shown in equation (A), the changes in the chemical reaction rate can be accurately incorporated into the simulation by taking into account the temperature dependence of the reaction rate frequency factor, thereby improving the accuracy of the simulation.

[0057] [7] When the metallic material is Fe or an Fe-based alloy and the equilibrium reaction represented by formulas (1) to (7) or (1) to (9) is considered as the chemical reaction, and the simulation is performed by incorporating the increase or decrease caused by the above equilibrium reaction into the change in the concentration of each gaseous component contained in the furnace atmosphere over time, the concentration changes of CO and CO2 in the furnace atmosphere that contribute to decarburization and carburization can be simulated with high accuracy during the heat treatment of Fe or Fe-based alloys, thus significantly affecting the material properties. In this case, in particular, the chemical reaction including formula (6) is very effective in improving the accuracy of the simulation, which is a gas-phase / solid-phase reaction involving CO and CO2. Although the simulation can achieve high accuracy by considering only the chemical reactions of formulas (1) to (7), the simulation accuracy can be further improved by considering the chemical reactions of formulas (8) and (9) in addition to these chemical reactions.

[0058] [8] In this case, where the reaction rates of the chemical reactions in equations (6) and (7) include error functions, the reduction reactions of Fe oxides other than FeO (e.g., Fe2O3 or Fe3O4) and the reduction reactions of oxides of metal elements other than Fe (e.g., Cr) can all be included as error functions in the reduction reaction of FeO. By incorporating the reduction reactions of various metal oxides in the form of error functions in this way, the accuracy of the simulation can be easily improved.

[0059] [9] By using the error coefficient Δ CO Δ CO2 Δ H2 and Δ H2O The error function is included by adding the concentration change rates of CO, CO2, H2, and H2O in the heat treatment furnace, respectively; the error coefficient has Δ. CO =-Δ CO2 and Δ H2 =-Δ H2O The relationship, and Δ CO2 and Δ H2O When each function is a function whose positive value decreases over time and converges to zero, the consumption of CO and H2 and the corresponding formation of CO2 and H2O caused by the reduction reaction of oxides of metal elements other than Fe can be easily handled using an error function. In this case, by employing a function such as Δ... CO2 and Δ H2O This form of function can satisfactorily reproduce the behavior of metal oxides during the initial stages of heat treatment, where the reduction reaction occurs actively and becomes less likely to occur over time. Furthermore, by pre-fixing this function form, it is possible to prevent the error function from contributing excessively in the simulation.

[0060]

[10] When the unknown parameters included in the mathematical model are determined by comparing the simulation results of the change in concentration of at least one of CO and CO2 over time with the actual test results in the actual heat treatment furnace, the values ​​of various parameters included in the mathematical model can be determined by comparing with the actual test results even when the parameters are unknown. This allows the mathematical model to be improved.

[0061]

[11] When the mathematical model includes multiple unknown parameters and the values ​​of these unknown parameters are determined in descending order of their influence on the simulation results, it is possible to accelerate the convergence of these values ​​to the solution when determining each parameter.

[0062]

[12] In the method for heat-treating metallic materials according to the present invention, the flow rate of the gas flowing into and out of the actual heat treatment furnace is controlled based on simulation results obtained by a simulation method. This simulation method can simulate the compositional changes of the furnace atmosphere with high precision using a mathematical model that includes the rate of chemical reactions occurring in the furnace, as well as the flow rates of the gas flowing into and out of the heat treatment furnace. Compared to feedback control such as PID control based on verification results of the actual furnace atmosphere composition, controlling the atmosphere in the actual heat treatment furnace using the simulation results makes it easier to accurately achieve the desired furnace atmosphere. Even when the compositional concentrations of the furnace atmosphere vary due to contributions from chemical reactions and are complexly interrelated, or when the composition of the furnace atmosphere changes drastically, the furnace atmosphere can be quickly controlled to follow these changes, thereby obtaining metallic materials with the desired composition. Attached Figure Description

[0063] Figure 1 A schematic diagram illustrating the gas flowing into and out of a heat treatment furnace as a simulated target according to one embodiment of the present invention.

[0064] Figure 2A This is a schematic diagram illustrating the relationship between the target and actual values ​​of PF values ​​during the heat treatment steps in an actual heat treatment furnace.

[0065] Figure 2B This is a schematic diagram illustrating the relationship between the target and actual furnace temperatures during the heat treatment steps in an actual heat treatment furnace.

[0066] Figure 3 To illustrate the change of the error coefficient over time, the upper part of the graph shows the functional forms applied to ΔCO2 and ΔH2O, and the lower part shows the functional forms applied to ΔCO and ΔH2.

[0067] Figure 4A The experiment data on the CO concentration change during the heat treatment of material A, the simulation results considering only gas inflow and outflow, and the simulation results also considering chemical reactions are shown in comparison.

[0068] Figure 4B The experiment data on the CO concentration change during the heat treatment of material B is shown, along with simulation results considering only gas inflow and outflow, and simulation results also considering chemical reactions.

[0069] Figure 4CThe experiment data on the CO concentration change during the heat treatment of material C is shown, along with simulation results considering only gas inflow and outflow, and simulation results also considering chemical reactions.

[0070] Figure 4D The experiment data on the CO concentration change during the heat treatment of material D is shown, along with simulation results considering only gas inflow and outflow, and simulation results also considering chemical reactions.

[0071] Figure 5A The experiment data on the CO2 concentration change during the heat treatment of material A are shown, along with simulation results considering only gas inflow and outflow, and simulation results also considering chemical reactions.

[0072] Figure 5B The experiment data on the CO2 concentration change during the heat treatment of material B is shown, along with simulation results considering only gas inflow and outflow, and simulation results also considering chemical reactions.

[0073] Figure 6A The experiment data on the CO concentration change during the heat treatment of material B, the simulation results using the Arrhenius equation, and the simulation results using the modified Arrhenius equation are shown.

[0074] Figure 6B The experiment data on the CO2 concentration change during the heat treatment of material B, the simulation results using the Arrhenius equation, and the simulation results using the modified Arrhenius equation are shown.

[0075] Figure 7A Experimental data on CO concentration changes during the heat treatment of material B, simulation results without using error functions, and comparisons between simulation results including error functions for the inflow gas flow rate, outflow gas flow rate, and chemical reaction rate are presented.

[0076] Figure 7B Experimental data on CO2 concentration changes during the heat treatment of material B, simulation results without using error functions, and comparisons between simulation results including error functions for the inflow gas flow rate, outflow gas flow rate, and chemical reaction rate are presented.

[0077] Figure 8A The diagram shows a comparison between experimental data on CO concentration changes during the heat treatment of material A, simulation results considering only gas inflow and outflow, and simulation results also considering chemical reactions. Here, the comparison is made between... Figure 4A More types of chemical reactions, and the experimental data used are consistent with... Figure 4AThe experimental data used are different.

[0078] Figure 8B The diagram shows a comparison between experimental data on CO concentration changes during the heat treatment of material B, simulation results considering only gas inflow and outflow, and simulation results also considering chemical reactions. Here, the comparison is made between... Figure 4B More types of chemical reactions, and the experimental data used are consistent with... Figure 4B The experimental data used are different.

[0079] Figure 8C The diagram shows a comparison between experimental data on CO concentration changes during the heat treatment of material C, simulation results considering only gas inflow and outflow, and simulation results also considering chemical reactions. Here, the comparison is made between... Figure 4C More types of chemical reactions, and the experimental data used are consistent with... Figure 4C The experimental data used in the two studies are different.

[0080] Figure 8D The diagram shows a comparison between experimental data on CO concentration changes during the heat treatment of material D, simulation results considering only gas inflow and outflow, and simulation results also considering chemical reactions. Here, the comparison is made between... Figure 4D More types of chemical reactions, and the experimental data used are consistent with... Figure 4D The experimental data used in the two studies are different.

[0081] Figure 9A To show the corresponding Figure 8A The graph shows the changes in CO2 concentration under the conditions shown.

[0082] Figure 9B To show the corresponding Figure 8B The graph shows the changes in CO2 concentration under the conditions shown.

[0083] Figure 9C To show the corresponding Figure 8C The graph shows the changes in CO2 concentration under the conditions shown.

[0084] Figure 9D To show the corresponding Figure 8D The graph shows the changes in CO2 concentration under the conditions shown. Detailed Implementation

[0085] Hereinafter, with reference to the accompanying drawings, a method for simulating furnace atmosphere according to an embodiment of the present invention and a method for heat-treating metallic materials according to an embodiment of the present invention will be described.

[0086] [Overview of Simulation and Heat Treatment of Metallic Materials]

[0087] According to one embodiment of the present invention, a method for simulating furnace atmosphere involves simulating the change in the composition of the furnace atmosphere over time during the heat treatment of metallic materials in a heat treatment furnace. While the type of metallic material is not limited, Fe or Fe-based alloys are preferred. In the following description, an embodiment for heat treatment of steel, which is an Fe-based alloy, will be used as an example.

[0088] In a heat treatment furnace, the furnace atmosphere contains at least one of CO and CO2, and in many cases both CO and CO2, and the steel can undergo carburizing and decarburizing during the heat treatment steps. When the furnace atmosphere contains at least one of CO and CO2, a carbon potential factor (PF) can be specified. PF is an indicator value of carbon potential, expressed as PF = [CO]. 2 / [CO2] is used for calculation, where [CO] and [CO2] are the CO concentration (volume %) and CO2 concentration (volume %) in the furnace, respectively.

[0089] like Figure 1 As shown in the schematic diagram, examples of gases flowing into and out of the heat treatment furnace 1 containing steel 2 include the following cases, and gas inflow and outflow are considered for simulation. First, endothermic modified gas (RX gas) flows into the heat treatment furnace. RX gas is a gas produced by the endothermic reaction of hydrocarbons (methane in this case) with oxygen in the atmosphere, and therefore contains CO, H2, and N2 as the main components, and also contains small amounts of CO2, H2O, and CH4. RX gas contains a large proportion of CO, thereby increasing the PF value.

[0090] In addition, conditioning air is introduced into the heat treatment furnace to finely regulate the CO2 concentration in the furnace atmosphere. The conditioning air serves to supply CO2 to the furnace atmosphere and reduce the PF value. Air is used as the conditioning air.

[0091] For safety reasons (to maintain furnace pressure to prevent air from entering the furnace and causing an explosion), N2 gas is introduced into the furnace. Preferably, the N2 gas for PF control is controlled separately from the N2 gas introduced to maintain furnace pressure, and the N2 gas for PF control can be introduced into the heat treatment furnace. Supplying N2 gas for PF control into the furnace reduces the CO and CO2 concentrations in the furnace atmosphere by the same proportion, thus resulting in a decrease in the PF value. Incidentally, at the beginning and end of the heat treatment step, to prevent the formation of a gaseous mixture of combustible gas (RX gas) and oxygen in the furnace, N2 gas is introduced into the furnace only through the N2 gas introduction line for maintaining furnace pressure or for PF control.

[0092] In addition, the atmosphere inside the furnace is exhausted from the entire heat treatment furnace. This venting of the atmosphere is done to maintain a constant furnace pressure.

[0093] Here, the furnace atmosphere control, which is typically performed in actual heat treatment furnaces, is explained according to convention. During the heat treatment process, radiant tube burners are used to heat the furnace atmosphere. For example... Figure 2B As shown, this heat treatment process includes a heating period where the furnace temperature gradually increases, a soaking period where the furnace temperature remains constant, and a cooling period where the furnace temperature gradually decreases. Figure 2A As shown, for each time period, a target PF value is set based on the target temperature. The flow rates of various gases are adjusted to make the actual PF value close to the target PF value. Based on the specific type of steel and the required composition (composition and material properties) of the heat-treated steel, a target PF value is set for each temperature.

[0094] Regarding decarburization / carburization, from the perspective of reliably achieving an equilibrium state consistent with the furnace temperature, the flow rate of the gas (mainly RX gas) flowing into the heat treatment furnace is adjusted to ensure that the power factor (PF) value meets the target value at a certain furnace temperature, and the target temperature is changed after the actual PF value reaches that target value. Therefore, if the PF value takes a long time to reach the target value, the heating period needs to be very long. For example, in Figure 2A In the region enclosed by the dashed rectangle, it takes a long time to increase the actual power factor (PF) value to the target PF value. The reason is as follows: In this region, the CO2 concentration in the furnace atmosphere tends to increase suddenly due to the inflow of RX gas. This sudden increase in CO2 concentration causes a temporary decrease in the calculated PF value, so the feedback control results in supplying RX gas at the maximum flow rate. At this time, the CO2 concentration increases at a higher rate than the RX gas supply flow rate, leading to a sudden decrease in the PF value. As a result, despite supplying RX gas at the maximum flow rate, the actual PF value decreases, making it less likely to reach the target value.

[0095] The sudden increase in CO2 concentration with the inflow of RX gas is due to the reduction of oxides (scale) on the surface of the steel by CO (see Equation (6) below). The reduction of scale produces CO2. Since the furnace atmosphere has a low CO2 concentration, the CO2 produced by the reduction of scale significantly affects the CO2 concentration in the furnace atmosphere and tends to cause a sudden increase in CO2 concentration. Therefore, the furnace temperature cannot be increased while the actual PF value has not reached the target value, and there is a long period during the heating period during which the furnace temperature cannot be increased while waiting for the PF value to rise. Figure 2A and Figure 2B The area enclosed by the dashed rectangle represents the time period corresponding to the time when the actual PF value did not reach the target value.

[0096] Therefore, when using the PF value, a macroscopic parameter of the furnace atmosphere, as the sole indicator for controlling the furnace atmosphere, it is difficult to control the atmosphere in a way that allows the control to rapidly adapt to changes in the furnace state. Therefore, in the simulation method according to an embodiment of the present invention, changes in the furnace atmosphere are simulated based on microscopic phenomena occurring within the furnace, thus serving as the basis for atmosphere control based on the furnace state. Figure 2A In the rectangular region, for example, if the results of how the furnace atmosphere will change when the scale is reduced are obtained in advance, and if the inflow RX gas flow rate can be adjusted based on this change to prevent sudden changes in CO2, then the inflow RX gas flow rate can be increased for a short time while avoiding sudden changes in CO2.

[0097] To correlate the microscopic phenomena occurring within the furnace with changes in the simulated furnace atmosphere, the chemical reactions occurring within the furnace are treated. These chemical reactions are at least one of gas-phase reactions in the furnace atmosphere and gas-phase / solid-phase reactions on the surface of the metal material, and preferably include both. In the case of steel, the following nine chemical reactions are presumed to occur within the furnace. These nine chemical reactions are included in the simulation.

[0098] [Chemical Formula 2]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] The reactions in equations (4) and (5) are gas-phase reactions, and the reactions in equations (1), (2), (3), (6), (7), (8), and (9) are gas-phase / solid-phase reactions. In the gas-phase / solid-phase reactions, equation (1) represents the oxidation reaction of Fe contained in the steel, and the reactions in equations (2) and (3) are reactions related to decarburization / carburization of the steel. The reactions in equations (6) and (7) are the reduction of oxide scale by CO and H2, respectively. Equations (8) and (9) represent oxidation / reduction reactions involving carbon on the steel surface and / or carbon in the furnace wall. All reactions in equations (1) to (9) are equilibrium reactions, and the simulation is performed by incorporating the increase or decrease of gaseous components caused by each equilibrium reaction into the change in the concentration of each gaseous component contained in the furnace atmosphere over time.

[0109] This simulation uses a mathematical model to simulate the changes in the composition of the furnace atmosphere, taking into account the gases flowing into and out of the furnace, as well as chemical reactions. The gas inflow and outflow processes include: the inflow of RX gas, the inflow of conditioning air, the inflow of N2 gas for maintaining furnace pressure and PF control, and the discharge of atmospheric gases, all of which have been referenced above. Figure 1 The explanation is provided. The chemical reactions include all the chemical reactions of equations (1) to (9), or only the major chemical reactions of equations (1) to (7), for example. Using this mathematical model, the concentration changes of the components of the furnace atmosphere over a short period of time are calculated using differential equations based on the flow rates of the inflow and outflow gases and the reaction rates of each chemical reaction (forward and reverse reactions). By repeating this calculation, the change in the concentration of the components of the furnace atmosphere over time during the heat treatment step is simulated. Furthermore, the concentration changes of the components over time obtained by simulation are compared with actual test results in an actual heat treatment furnace. Incidentally, chemical reactions other than those of equations (1) to (9) may also occur in the heat treatment furnace, although the contribution of these chemical reactions may be small. In this case, these other chemical reactions are appropriately taken into account in addition to the chemical reactions of equations (1) to (9), or by replacing a portion of the chemical reactions of equations (1) to (9).

[0110] [Simulation Method]

[0111] Next, the simulation method will be described in detail. As described above, in the simulation method according to an embodiment of the present invention, the contributions of the gas flowing into the heat treatment furnace, the gas flowing out of the heat treatment furnace, and the chemical reaction to the changes in the furnace atmosphere are taken into account.

[0112] <1> The contribution of in-furnace chemical reactions

[0113] Of the contributions of the gas flowing into the heat treatment furnace, the gas flowing out of the heat treatment furnace, and the chemical reactions, the contribution of the chemical reactions will be explained first. As mentioned above, when heat treating steel, it is assumed that chemical reactions (1) to (9) occur inside the furnace. By taking only chemical reactions (1) to (7) into account, the change in the composition of the furnace atmosphere over time can be reproduced with a certain degree of accuracy through simulation. Therefore, an implementation scheme that takes into account reactions (1) to (7) will be explained as an example. Here, the equilibrium reaction is represented by the following formula (10) as a general formula.

[0114] [Chemical Formula 3]

[0115]

[0116] In this reaction, the reaction rate v of the forward reaction is... f The reaction rate v of the reverse reaction r As shown in equations (11) and (12) respectively.

[0117] [Mathematical Expression 2]

[0118] v f =k f [A] a [B] b (11)

[0119] v r =k r [C] c [D] d (12)

[0120] Here, the values ​​in square brackets [] represent the concentrations of the substances. In the case of solid substances, the surface area occupied by the substance on the surface of the solid (steel) is used instead of the concentration.

[0121] The rate constant k of the forward reaction f The reaction rate constant k of the reverse reaction r The relationship between them is expressed by the following equation (13), where K(T) is the equilibrium constant at temperature T.

[0122] [Mathematical Expression 3]

[0123] k r =k f K(T) (13)

[0124] The equilibrium constant K(T) in equation (13) can be expressed by equation (14) using the van der Hoff equation.

[0125] [Mathematical Expression 4]

[0126]

[0127] Here, ΔG 0 Let R be the standard free energy change, R be the gas constant, and T be the furnace temperature.

[0128] Meanwhile, the rate constant k of the forward reaction at temperature T f (T) can be expressed by the modified Arrhenius equation (15).

[0129] [Mathematical Expression 5]

[0130]

[0131] Here, k' f E is the frequency factor. f Let be the activation energy of the forward reaction, and b be a constant without a clearly defined physical meaning. Incidentally, when b = 0 in this equation to neglect the temperature dependence of the frequency factor, it is the general Arrhenius equation. In simulations according to embodiments of the present invention, as shown in the examples below, higher accuracy can be obtained by using the modified Arrhenius equation with b ≠ 0 compared to the case using the general Arrhenius equation.

[0132] Furthermore, substituting equations (14) and (15) into equation (13), we obtain the reaction rate constant k of the reverse reaction at temperature (T). r (T) can also use the parameter ΔG 0 、k' f E f Let b represent it.

[0133] The reaction rate constant k of the forward reaction at each temperature obtained therefrom is thus obtained. f The reaction rate constant k of the reverse reaction r This allows us to determine the changes in each component of the furnace atmosphere over time. Regarding the chemical reaction in equation (i) (where i = 1 to 7), when the concentration of the substance with a coefficient of 1 in the reactants (left side) changes from q at time t... i When expressed, the rate of change of the substance's concentration, v i (t) is represented by the following equation (16), where q i It has the same meaning as the symbol [] in equations (11) and (12).

[0134] [Mathematical Expression 6]

[0135]

[0136] Here, v fi (t) and v ri (t) represents the forward and reverse reaction rates of the chemical reaction in equation (i) at time t, respectively, and is calculated using equations (11) to (15).

[0137] According to equation (16), the concentration change of the substance with a coefficient of 1 in the reactants of equation (i) during a short time period dt is represented by equation (17).

[0138] [Mathematical Expression 7]

[0139] dq i =v i (t)dt (17)

[0140] When a substance of interest is involved in multiple chemical reaction equations, the concentration change dq of that substance will be calculated based on the chemical reaction equations. i Multiply by a coefficient and add the products. The sum is the concentration change of the substance throughout the furnace atmosphere. That is, when substance X has a coefficient x in the reactants... i In the case of , the concentration change dq(X) of substance X in a short time period dt is represented by the following equation (18).

[0141] [Mathematical Expression 8]

[0142]

[0143] For example, the concentration change dq(CO) of CO over a short time interval dt is represented by equation (19). Only the rate of concentration change determined by equation (16) needs to be used instead of the corresponding v. i (t).

[0144] [Mathematical Expression 9]

[0145] dq(CO)=(2v2(t)-v4(t)-2v5(t)-v6(t))dt (19)

[0146] In the above explanation, it is assumed that heat treatment of steel accompanied by decarburization / carburization is to be carried out, and the chemical reactions of equations (1) to (7) are considered. However, even if different chemical reactions should be considered 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, and the concentration changes are summed according to equation (18) for all chemical reactions to be considered.

[0147] For example, there may be cases where chemical reactions in equations (8) and (9) are included in addition to those in equations (1) to (7) for simulation. It is believed that chemical reactions occurring on the walls of the heat treatment furnace contribute considerably to the chemical reactions in equations (8) and (9). Therefore, depending on the structure of the heat treatment furnace and the heat treatment conditions, sufficiently high accuracy can be obtained in the simulation even without considering the chemical reactions in equations (8) and (9). However, considering these chemical reactions in equations (8) and (9) in addition to those in equations (1) to (7) can further improve the accuracy of the simulation. In the case of considering the chemical reactions in equations (1) to (9), equations (18) and (19) are modified to the following equations (18') and (19'), respectively.

[0148] [Mathematical Expression 10]

[0149]

[0150] dq(CO)=(2v2(t)-v4(t)-2v5(t)-v6(t)-2v8(t)-v9(t)dt (19')

[0151] <2> The contribution of gas inflow and gas outflow

[0152] Next, the contributions of the gases flowing into and out of the heat treatment furnace, which are included in the simulation along with the chemical reaction, will be explained.

[0153] As mentioned above Figure 1 The following gases are considered as flowing into and out of the heat treatment furnace: the incoming RX gas, the incoming conditioning air, the incoming N2 gas for maintaining furnace pressure and PF control, and the outgoing furnace atmosphere gas. Regarding the RX gas, since the RX gas used in actual heat treatment furnaces is generated by burning hydrocarbons (e.g., city gas), the composition ratio may fluctuate. However, in the simulation, the composition is fixed as shown in Table 1 below.

[0154] [Table 1]

[0155] Element <![CDATA[CO2]]> CO <![CDATA[H2]]> <![CDATA[H2O]]> <![CDATA[CH4]]> <![CDATA[N2]]> Concentration (volume %) 0.3 22.9 30.3 0.6 0.01 margin

[0156] The content of component X in RX gas is x. RX % and the volumetric flow rate of the RX gas is determined by v RX (t)(Unit: m) 3 In the case of / s), the change in concentration dq' of component X in the furnace caused by the inflow of RX gas. RX (X) is shown in equation (20) (unit: mol / m 3 As shown in the figure.

[0157] [Mathematical Expression 11]

[0158]

[0159] Here, the RX gas is considered an ideal gas, and in equation (20), p is the furnace pressure, and V 炉 Let R be the furnace internal volume, R be the gas constant, and T be the furnace temperature.

[0160] For example, the change in CO gas concentration is represented by the following equation (21).

[0161] [Mathematical Expression 12]

[0162]

[0163] Use air containing the components shown in Table 2 below as conditioning air.

[0164] [Table 2]

[0165] Element <![CDATA[N2]]> <![CDATA[O2]]> <![CDATA[H2O]]> <![CDATA[CO2]]> other Concentration (volume %) 76.55 20.54 2 0.03 0.88

[0166] The content of component X in the air used for conditioning is X. 空气 % and the volumetric flow rate of the air used for regulation is determined by V 空气 (Unit: m) 3 In the case of / s), the change in concentration dq' of component X in the furnace caused by the inflow of regulating air. 空气 (X) is derived from the following formula (22) (unit: mol / m 3 )express.

[0167] [Mathematical Expression 13]

[0168]

[0169] Here, the air used for conditioning is considered an ideal gas.

[0170] Next, the removal of the furnace atmosphere will be explained. The furnace atmosphere is removed to maintain a constant furnace pressure. That is, the volume of the removed atmosphere is equal to the sum of the volumes of the RX gas flowing into the furnace, the N2 gas used to maintain furnace pressure and PF control, and the conditioning air. Specifically, the volumetric flow rate of the RX gas is expressed as v. RX The volumetric flow rate of N2 gas used to maintain furnace pressure is expressed as v. N2 The volumetric flow rate of N2 gas used for PF control is expressed as v. N2' And the volumetric flow rate of the regulating air is expressed as v. 空气 Under these conditions, the gas discharge flow rate v ex By v ex =v N2 +vRX +v N2' +v 空气 (Unit: m) 3 / s) represents the concentration of component X in the furnace atmosphere at time t, which is [X]. t (Unit: mol / m) 3 Under the condition that the concentration change dq' of component X caused by the gas discharge over a short period of time dt is... ex (X) is represented by equation (23). Incidentally, the volumetric flow rate v of N2 gas used in PF control... N2' and regulating the volumetric flow rate v of air 空气 In cases where the value is low and negligible, it can be derived from v. ex These items were excluded from the list.

[0171] [Mathematical Expression 14]

[0172]

[0173] For example, the change in CO gas concentration is represented by the following equation (24).

[0174] [Mathematical Expression 15]

[0175]

[0176] Therefore, the concentration change dq'(X) of gaseous component X other than N2 in the furnace during a short time period dt caused by the gas flowing into and out of the furnace is the sum of the contribution of the inflow of RX gas as expressed by equation (20), the contribution of the inflow of conditioning air as expressed by equation (22), and the contribution of the exhaust of furnace atmosphere gas as expressed by equation (23), and is expressed by the following equation (25).

[0177] [Mathematical Expression 16]

[0178]

[0179] For example, the change in CO concentration is represented by the following equation (26).

[0180] [Mathematical Expression 17]

[0181]

[0182] In the above explanation, the inflow of four gases—RX gas, regulating air, N2 gas for maintaining furnace pressure, and N2 gas for PF control—as well as the discharge of the atmosphere gas in the furnace are considered as factors to be taken into account as gases flowing into and out of the heat treatment furnace. However, even when different phenomena are to be considered in the heat treatment furnace in terms of gas inflow and gas outflow depending on the heat treatment conditions, the same simulation can be applied, and the contributions of the gas inflow and gas outflow to the concentration changes of the components of interest in the furnace can be summed according to Equation (25).

[0183] <3> Both types of contributions are considered

[0184] In the embodiments of the present invention, the contributions of chemical reactions occurring in the heat treatment furnace, the gas flowing into the heat treatment furnace, and the gas flowing out of the heat treatment furnace are considered in the manner described above, thereby simulating the concentration changes of the constituent components of the furnace atmosphere. Therefore, as shown in equation (27), for the gaseous components of the furnace atmosphere (referred to as component X), by determining the sum of the concentration change dq(X) caused by the contribution of the chemical reactions as expressed by equation (18) and the concentration changes dq'(X) caused by the gas inflow and gas outflow as expressed by equation (25), the total concentration change dq over a short time period dt from time t can be calculated. tot (X).

[0185] [Mathematical Expression 18]

[0186] dq tot (X)=dq(X)+dq'(X) (27)

[0187] Considering the reactions of formulas (1) to (7) or formulas (1) to (9), the five gases O2, H2, H2O, CO2 and CO can be used as component X.

[0188] As described above, in the simulation method according to an embodiment of the present invention, not only are the contributions of the gas flowing into and out of the heat treatment furnace considered in the calculation method disclosed in Patent Document 1, but also the contributions of the chemical reactions occurring within the heat treatment furnace are considered, thereby simulating the change in the concentration of gaseous components in the heat treatment furnace over time. As shown in the embodiments described later, compared to the method of Patent Document 1 which only considers the gas flowing into and out of the heat treatment furnace, the accuracy of the simulation is improved by taking into account the chemical reactions occurring within the furnace, thereby enabling a highly accurate reproduction of the compositional changes of the furnace atmosphere in an actual heat treatment furnace. In particular, the consideration of gas-phase / solid-phase reactions occurring on the surface of the metal material to be heat-treated greatly contributes to improving the accuracy of the simulation.

[0189] <4> Include the error function

[0190] When gas flows into an actual heat treatment furnace, flow rate errors are sometimes unavoidable due to factors such as the pressure difference before and after a valve. To incorporate this error into the simulation, an error function is included. Specifically, the volumetric flow rate v of gas Y is... Y Multiply by (1+Δ) Y The term "gas Y" refers to each of the following: RX gas, N2 gas for maintaining furnace pressure, N2 gas for PF control, and conditioning air, and Δ Y Let be the error coefficients for each gas Y. Using the Gaussian error function erf, the error coefficients Δ are expressed by equation (28). Y The symbols a, b, c, and d are arbitrary constants.

[0191] [Mathematical Expression 19]

[0192]

[0193] For the volumetric flow rate v of N2 gas used in PF control N2' And the volumetric flow rate v of the air used for regulation 空气 In cases where the flow rate is so low that the contribution of error to the volumetric flow rate can be ignored, the error coefficient may not be included.

[0194] In cases where the flow rate of gas flowing into an actual heat treatment furnace may experience uncontrollable fluctuations, these fluctuations can be incorporated into the simulation by accounting for the flow rate error. However, in many heat treatment furnaces and under various heat treatment conditions, the flow rate of the inflow gas does not fluctuate to a non-negligible degree; therefore, in such cases, the flow rate error does not need to be considered in the simulation. However, if the flow rate error is considered in the simulation, there is a possibility that the contribution of the flow rate error is over-included when seeking parameter values ​​that can reproduce the experimental results, thereby undesirably leading to a poor reproduction of the experimental results and causing the simulation results to differ significantly from the actual conditions inside the furnace. In such cases, it is preferable not to consider the flow rate error of the inflow gas.

[0195] Furthermore, regarding the reaction rates of at least some chemical reactions, as illustrated in the examples described below, error functions can be similarly included in the simulation, thereby improving the accuracy of the simulation. In this case, the contributions of chemical reactions whose rates are not specifically considered based on the chemical reaction formula can be mathematically included through the error function. For example, equations (6) and (7) show the reduction of FeO, the main component of the oxide scale present on the surface of steel, which contains Fe oxides in different oxidation states, such as Fe2O3 and Fe3O4, but in smaller amounts than FeO, and also contains oxides of metallic elements (e.g., Cr) that have been added to the steel in addition to Fe. These oxides also undergo reduction reactions. The contributions of the reduction of these metal oxides other than FeO can be included as error functions in equations (6) and (7). Thus, by using error functions, the contributions of less contributing chemical reaction pathways can be easily included in the simulation without needing to specifically consider the reaction rates based on the chemical reaction formula, thereby improving the accuracy of the simulation.

[0196] Specifically, it is only necessary to add the error coefficient to the rate of concentration change of the components in the furnace atmosphere caused by the chemical reaction. That is, add the error coefficient to the rate of concentration change caused by the chemical reaction as expressed by equation (18). The error coefficient of component X is given by Δ X In the case of X, the change in concentration of component X over time is represented by equation (29).

[0197] [Mathematical Expression 20]

[0198]

[0199] For example, as shown in equation (30) below, the error function of CO (whose concentration change is represented by equation (19)) is included.

[0200] [Mathematical Expression 21]

[0201]

[0202] Including the error functions of chemical formulas (6) and (7) in equations (1) to (9) involving the reduction of oxide scale is very effective in improving the accuracy of the simulation. The effect of including the error function is particularly significant for the chemical reaction in equation (6). Therefore, it is only necessary to include the error coefficient Δ according to equation (29). CO Δ CO2 Δ H2 and Δ H2O The error coefficients are added to the concentration change rates of CO, CO2, H2, and H2O, respectively. In this case, according to the equilibrium relationships of equations (6) and (7), the error coefficients have the following relationship: Δ CO =-ΔCO2 and Δ H2 =-Δ H2O An error coefficient of the same form as that in equation (28) can be used as the error coefficient Δ. CO Δ CO2 Δ H2 and Δ H2O .

[0203] However, when considering the error coefficient Δ CO Δ CO2 Δ H2 and Δ H2O When using a function of the same form as equation (28), due to the high degree of freedom of this equation, there is a possibility that the simulation may include excessive error coefficients that are impossible to include in the actual scale reduction reaction of the heat treatment step. As a result, sometimes the simulation barely reproduces the experimental results due to the contribution of the error coefficients, and therefore the reproduced furnace state is quite different from the actual furnace state. In this case, it is preferable to limit the degree of freedom of the error coefficient formula and set the error coefficient according to the actual furnace state. Specifically, since the scale reduction reaction occurs rapidly in the early stage of heat treatment and becomes less likely to occur over time, it is preferable to use Δ CO2 and Δ H2O These are functions that cause the positive value to decrease over time and converge to zero, respectively. In this case, given Δ... CO =-Δ CO2 and Δ H2 =-Δ H2O The relationship, Δ CO and Δ H2 Each is a function with a negative value, and the absolute value of the negative value decreases over time and converges to zero.

[0204] In a possible specific instance of such a function, the error coefficient is set in the form shown in equation (31) to replace equation (28).

[0205] [Mathematical Expression 22]

[0206]

[0207] Here, for Δ CO2 and Δ H2O , a > 0, and for Δ CO and Δ H2 , a < 0.

[0208] Figure 3 An example of the error coefficient changing over time, expressed as a function of equation (31), is shown. The upper part of the graph represents the case where a > 0, corresponding to Δ. CO2 and Δ H2OThe lower part of the graph represents the case where a < 0, corresponding to Δ. CO and Δ H2 These curves expand / contract along the vertical axis according to the value of 'a', and expand / contract and shift along the horizontal axis according to the values ​​of 'b' and 'c'. Therefore, the specific pattern of how the error coefficient changes over time is determined by choosing the values ​​of the constants 'a', 'b', and 'c'. Although Δ CO2 and Δ H2O Depend on Figure 3 A curve in the diagram represents this, while Δ CO and Δ H2 Depend on Figure 3 Another curve in the diagram illustrates this, but the specific shapes of these error coefficient curves may differ from one another.

[0209] <5> Implementation of simulation

[0210] As described above, by appropriately incorporating an error function into the concentration change expressed by equation (27), the concentration changes of each gaseous component in the heat treatment furnace over a short time period dt are obtained. The differential equations representing these concentration changes over time are applied to set heat treatment conditions to calculate the concentrations of each gaseous component in the furnace atmosphere over each short time period, thereby simulating the change in the composition of the furnace atmosphere over time.

[0211] The parameters to be included in the simulation include those whose values ​​are unknown because they are difficult to evaluate experimentally separately from other parameters. For example, in many of the responses in equations (1) to (9), the frequency factor k' cannot be readily determined. f constant b and activation energy E f Furthermore, in reaction rate equations (11) and (12), the initial value of the surface area of ​​the solid substance and the error coefficient Δ are used instead of concentration. ～ These are also unknown parameters (the symbol ~ represents Y, i.e., any gas mentioned in the description of the error function, as well as CO, CO2, H2, and H2O). Each of these unknown parameters can be determined by comparing the experimental results of the changes in the concentration of each gaseous component over time in an actual heat treatment furnace with their simulation results. That is, a method can be used in which multiple simulations are performed using various parameter values, and the parameter values ​​that can most satisfactorily reproduce the experimental results are adopted.

[0212] Here, it is preferable to use at least one of CO and CO2, and preferably both CO and CO2, as the component types for comparing the concentration test results and simulation results. This is because CO and CO2 not only exhibit large concentration changes during heat treatment, but also significantly affect the decarburization / carburization process. In this case, the evaluation function J(x) can be set as an indicator of the closeness between the simulation results and the test results, as shown in Equation (32).

[0213] [Mathematical Expression 23]

[0214]

[0215] Here, x is the design variable, N is the number of samples, and the test results and simulation results for CO and CO2 concentrations are indicated by "experiment" and "analysis" respectively. The smaller J(x) is, the more accurate the experimental results reproduced by simulation. Therefore, only a set of parameter values ​​that minimizes J(x) is needed.

[0216] For the step of performing multiple simulations while changing a set of parameter values ​​to find a solution, a genetic algorithm can be advantageously used. In this case, it is preferable to determine the parameters in descending order of sensitivity (i.e., in descending order of the impact of changing parameter values ​​on the simulation results). This can accelerate convergence to the solution. Specifically, the parameter sensitivity is determined according to the constant b, activation energy E... f Frequency factor k' f The initial values ​​of the surface area of ​​solid materials and the error function decrease in order, so they can be determined in this order.

[0217] Methods for heat-treating metallic materials

[0218] In the method for heat-treating metallic materials according to the present invention, the metallic material is heat-treated while controlling the gas flowing into and out of the actual heat treatment furnace based on simulation results obtained by the above-described simulation method. There are no particular limitations on how this simulation is applied to the atmosphere control of the actual heat treatment furnace. For example, heat treatment can be performed in such a manner that the actual atmosphere is controlled while the compositional changes of the furnace atmosphere are predicted through simulation. This prevents any factors that inhibit effective heat treatment, such as sudden changes in the concentration of specific components of the furnace atmosphere, from occurring during the heat treatment step. Another example is a method in which heat treatment conditions, such as furnace temperature and PF value setpoints, are studied in advance through simulations under various conditions to seek suitable conditions.

[0219] As demonstrated above, this simulation can accurately mimic the composition of the furnace atmosphere. Therefore, compared to feedback control methods such as PID control, applying the simulation results to the atmosphere control of an actual heat treatment furnace allows for easy and precise control of the furnace atmosphere. In particular, even when changes in the concentration of furnace atmosphere components are complexly interrelated, or when there are sudden changes in the composition of the furnace atmosphere, the control can quickly follow these changes. As a result, control of the furnace atmosphere enables the production of heat-treated materials with the desired composition and properties.

[0220] Example

[0221] The invention is described in more detail below with reference to embodiments. The invention is not limited to these embodiments.

[0222] [Testing Method]

[0223] This study examined whether the furnace atmosphere composition obtained during the actual heat treatment process of steel could be reproduced through simulation. Four types of steel (A to D) with different compositions were heat treated under conditions set according to material properties, using RX gas, N2 gas for maintaining furnace pressure, and conditioning air. Changes in the composition of the furnace atmosphere were monitored to prepare experimental data. Simulations were then performed under conditions specific to each material, and the experimental data showing the changes in CO and CO2 concentrations over time were compared with the simulation results.

[0224] During the simulation, the furnace temperature and the flow rates of RX gas, N2 gas for maintaining furnace pressure, and conditioning air were set to be the same as those in the experimental data. Among the parameters involved in the chemical reactions in equations (1) to (9), for parameters with known values ​​(e.g., from a database), such as the standard free energy change ΔG... 0 Using known values. Frequency factor k' for each chemical reaction. f constant b and activation energy E f The initial value and error coefficient Δ of the surface area of ​​solid materials ～ Since these are unknown parameters, their values ​​are determined through simulation. Figures 4A to 9D The simulation results presented are obtained using the parameter set that most satisfactorily reproduces the experimental results. Other specific methods used for the simulation are described above in the "Simulation Methods" section. Although the entire heat treatment process, including the heating period, soaking period, and cooling period, was simulated, the initial portion of the heating period and the final portion of the cooling period, when the heat treatment furnace was purged with nitrogen, were excluded from the simulation. Regarding the gas discharge flow rate v in equation (23)... ex Since the flow rate of the regulating air is very small, its contribution is ignored, and therefore v is used. ex =v N2 +v RX The error coefficient Δ of the air used for regulation was not taken into account. Y .

[0225] [Test Results]

[0226] <1> Effects that take chemical reactions into account

[0227] First, the influence of considering chemical reactions in the furnace on the simulation results was examined. Here, the simulation results obtained when only the gas flowing into and out of the heat treatment furnace is considered as contributing to the compositional changes of the furnace atmosphere (i.e., only dq'(X) is included in equation (27)) are compared with the simulation results obtained when the contributions of the chemical reactions in equations (1) to (7) are further considered (i.e., both dq(X) and dq'(X) are included in equation (27)). In each simulation, the reaction rate constant is calculated using the modified Arrhenius equation, and the error coefficients in the form of equation (28) are included in the flow rate of the inflow gas and the reaction rate of the chemical reaction. The chemical reactions in equations (8) and (9) are not considered here.

[0228] Figures 4A to 4D The changes in CO concentration over time for materials A through D during the heat treatment process are shown respectively. Figure 5A and Figure 5B The figures show the changes in CO2 concentration over time for materials A and B during the heat treatment process. Each figure shows all of the following: experimental data; simulation results considering only gas inflow and outflow (gas only); and simulation results also considering chemical reactions (gas + reaction).

[0229] As can be seen from the figure, for each CO and CO2 concentration, the simulation that only considers gas inflow and outflow cannot accurately reproduce the experimental data for materials A to D, resulting in significant discrepancies between the simulation results and experimental data. In contrast, the simulation that also considers the chemical reaction can satisfactorily reproduce the experimental data throughout the process. For the case of a sudden increase in concentration in the initial stage, the simulation results coincide well with the experimental data.

[0230] In particular, regarding Figure 5A and Figure 5B The CO2 concentrations shown differ considerably between simulations that consider and do not consider chemical reactions. Experimental data show a concentration that rises to a high value and then gradually decreases, a behavior satisfactorily reproduced in simulations that consider chemical reactions. However, in simulations that only consider gas inflow and outflow, the CO2 concentration remains low throughout the process; the simulation results are completely different from the experimental data.

[0231] These results demonstrate that by simulating not only the gases flowing into and out of the heat treatment furnace but also the chemical reactions within the furnace, the composition of the furnace atmosphere over time can be reproduced with satisfactory accuracy. Particularly for CO2, it is understood that simulation methods that also consider these chemical reactions achieve significantly improved simulation accuracy, thus enabling the reproduction of experimental results, due to the low CO2 concentration within the furnace and the relatively large contribution of reactions occurring on the steel surface (e.g., the oxide scale reduction reaction of formula (6)).

[0232] <2> Effects of applying the modified Arrhenius equation

[0233] Next, the effect of considering the temperature dependence of the frequency factor in calculating the reaction rate constant using the modified Arrhenius equation, expressed by equation (15), on the simulation results was determined. Here, the simulation results obtained by the modified Arrhenius equation, expressed by equation (15) where b≠0, are compared with those obtained by the ordinary Arrhenius equation using b=0. In each simulation, gas inflow and outflow, as well as chemical reactions within the furnace, were considered, and the inflow gas flow rate and the reaction rate of the chemical reaction included error functions.

[0234] Figure 6A and Figure 6B The changes in CO and CO2 concentrations over time are shown separately during the heat treatment of material B. Each figure illustrates the following: 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 compared with... Figure 4B and Figure 5B The same as shown.

[0235] For both CO and CO2, simulations using the modified Arrhenius equation satisfactorily reproduced the experimental data compared to simulations using the Arrhenius equation. Particularly for CO2, simulations using the Arrhenius equation completely failed to reproduce the concentration increase-and-decrease behavior, while simulations using the modified Arrhenius equation closely matched the experimental results throughout the process. These results confirm that by using the modified Arrhenius equation in the simulation and considering the temperature dependence of the frequency factor in calculating the reaction rate constant, the change in the composition of the furnace atmosphere over time can be accurately reproduced. Figure 2B As shown, since the temperature in the heat treatment step varies over a wide range of more than 200°C, it is believed that the temperature dependence of the frequency factor contributes significantly to the reaction rate.

[0236] <3> The effect of including the error function

[0237] Next, the effects of the inflow gas flow rate and the chemical reaction rate, including the error function, on the simulation were determined. Here, the error coefficient Δ regarding the inflow gas flow rate, as described above, was included in the differential equation. RX and Δ N2 And the error coefficient Δ regarding the reaction rate CO Δ CO2 Δ H2 and Δ H2O Furthermore, the simulation results, which included the error function, were compared with those that did not. In each simulation, gas inflow and outflow, as well as chemical reactions within the furnace, were considered, and the reaction rate constants were calculated using the modified Arrhenius equation.

[0238] Figure 7A and Figure 7B The changes in CO and CO2 concentrations over time are shown separately during the heat treatment of material B. Each figure illustrates the following: experimental data; simulation results including the error function; and simulation results excluding the error function. Experimental data and simulation results including the error function are compared with... Figure 4B and Figure 5B The same as shown.

[0239] For both CO and CO2, simulations including error functions satisfactorily reproduce experimental data compared to simulations excluding error functions. Particularly for CO2, simulations excluding error functions cannot reproduce the behavior of a sudden increase followed by a slow decrease in concentration, while simulations including error functions satisfactorily reproduce this behavior. These results demonstrate that by including error functions in the flow rate of the inflow gas and the reaction rate of the chemical reactions, the changes in the composition of the furnace atmosphere over time can be accurately reproduced. In particular, the error functions related to the reaction rates of the chemical reactions are designed to include the contribution of the reduction of oxides other than FeO. Even in low proportions, the reduction of these oxides inevitably contributes to the changes in the furnace atmosphere, making it highly meaningful to consider these error functions in the simulation.

[0240] <4> The types of chemical reactions to consider and their effects

[0241] Next, the impact of increasing the number of chemical reactions to be considered on the simulation results was determined. In the above... <1> to <3> In the simulation described in this section, the chemical reactions considered are limited to those of equations (1) to (7). Here, all chemical reactions of equations (1) to (9) are considered in the simulation. Regarding other aspects, by referring to the above... <1> The simulation is performed using the same method described above, except that the flow rate of the inflowing gas does not include an error coefficient, while the error coefficient Δ for the reaction rate is included. CO ΔCO2 Δ H2 and Δ H2O It is included in the form of finite degrees of freedom as shown in equation (31).

[0242] Figures 8A to 8D The changes in CO concentration over time for materials A through D during the heat treatment process are shown respectively. Figures 9A to 9D The corresponding CO2 concentration changes over time are shown. Each figure shows all of the following: experimental data; simulation results considering gas inflow and outflow (gas only); and simulation results also considering chemical reactions (gas + reaction). Except for Material A, the experimental data differ from those above. <1> The experimental data used in the simulation.

[0243] Figures 8A to 9D This indicates that, regarding CO and CO2 concentrations, for each material A to D, the simulations, which considered not only gas inflow and outflow but also chemical reactions, satisfactorily reproduced the experimental data throughout the entire process. Figures 4A to 5B The comparison between the simulation results considering the chemical reactions of equations (1) to (7) and those considering the chemical reactions of equations (1) to (9) shows that the simulation considering all chemical reactions can reproduce the experimental data with substantially the same or higher accuracy. In particular, for materials C and D, the simulation can reproduce the experimental data with significantly higher accuracy than... Figures 4A to 4D The simulation shown reproduces the experimental data with higher accuracy.

[0244] These results confirm that by considering not only the chemical reactions of equations (1) to (7) but also the chemical reactions of equations (8) and (9) during simulation, experimental data can be reproduced with high accuracy. Furthermore, although in <1> In the simulation, not only the reaction rate but also the inflow gas flow rate included error coefficients. <4> In the simulation, only the reaction rate included error coefficients, and the error coefficients used were in a functional form with low degrees of freedom. That is to say, <4> The simulation is less capable of reproducing experimental data by adjusting the error coefficients than <1> The simulation, however, showed that <4> The simulation is able to reproduce the experimental data more satisfactorily. This shows that improving the accuracy of the simulation by considering chemical reactions, including those in equations (8) and (9), is more effective than reducing the degrees of freedom of the error coefficient.

[0245] The embodiments of the present invention have been described in detail above, but the present invention is not limited to these embodiments, and various changes can be made to the present invention without departing from the spirit of the present invention.

[0246] This application is based on Japanese Patent Application No. 2021-200722 filed on December 10, 2021 and Japanese Patent Application No. 2022-081345 filed on May 18, 2022, the contents of which are incorporated herein by reference.

[0247] 1 heat treatment furnace

[0248] 2. Steel (metallic materials)

Claims

1. A method for simulating furnace atmosphere, comprising simulating the change over time in the composition of a furnace atmosphere containing CO and CO2 when heat-treating metallic materials in a heat treatment furnace under a furnace atmosphere. in, Simulations were performed using a mathematical model that included changes in the composition of the furnace atmosphere, and The compositional changes of the furnace atmosphere take into account the following factors: The flow rate of the gas flowing into the heat treatment furnace. The flow rate of the gas exiting the heat treatment furnace, and The reaction rates of the gas-phase chemical reactions in the furnace atmosphere and the gas-phase / solid-phase chemical reactions on the surface of the metal material. The reaction rate of the chemical reaction is expressed by the modified Arrhenius equation shown in equation (A): Where k f (T) is the reaction rate constant at temperature T, k' f Here, T is the frequency factor, T is the temperature in the heat treatment furnace, b is a constant, and E is a frequency factor. f Where R is the activation energy and R is the gas constant. At least one of the flow rate of the gas flowing into the heat treatment furnace and the reaction rate of the chemical reaction includes an error function, wherein the error function for the flow rate of the gas flowing into the heat treatment furnace takes into account the contribution of the flow rate error of the gas, and the error function for the reaction rate of the chemical reaction takes into account the contribution of the reduction of oxides other than FeO. The metallic material is Fe or an Fe-based alloy, and the equilibrium reaction represented by formulas (1) to (7) or (1) to (9) is considered the chemical reaction, and The simulation is performed by incorporating the increase or decrease of gaseous components due to the following equilibrium reaction into the change in the concentration of each gaseous component contained in the furnace atmosphere over time.

2. The method for simulating furnace atmosphere according to claim 1, in, The gas flowing into the heat treatment furnace and the gas flowing out of the heat treatment furnace include: The inflow gas that increases the carbon potential factor of the furnace atmosphere. The inflow gas that reduces the carbon potential factor of the furnace atmosphere, and The gas discharged from the furnace atmosphere as a whole.

3. The method for simulating furnace atmosphere according to claim 1, The change in the composition of the furnace atmosphere over time includes the change in the concentration of CO or CO2 over time.

4. The method for simulating furnace atmosphere according to claim 1, wherein only the reaction rate of the chemical reaction includes the error function.

5. The method for simulating furnace atmosphere according to claim 1, The reaction rates of the chemical reactions in equations (6) and (7) each include an error function.

6. The method for simulating furnace atmosphere according to claim 5, in, By using the error coefficient Δ CO Δ CO2 Δ H2 and Δ H2O The error function is included by adding the concentration change rates of CO, CO2, H2, and H2O in the heat treatment furnace, respectively. The error coefficients have the following relationship: Δ CO =-Δ CO2 and Δ H2 =-Δ H2O ,and Where, Δ CO2 and Δ H2O Each is a function that makes the positive value decrease over time and converge to zero.

7. The method for simulating furnace atmosphere according to claim 1 further includes determining the unknown parameters contained in the mathematical model by comparing the simulation results of the change in concentration of at least one of CO and CO2 over time with the actual test results in an actual heat treatment furnace.

8. The method for simulating furnace atmosphere according to claim 7, wherein the mathematical model includes a plurality of unknown parameters, and the values ​​of the unknown parameters are determined in descending order of their influence on the simulation results.

9. A method for heat-treating a metallic material, comprising, when heat-treating the metallic material in an actual heat treatment furnace, controlling the flow rate of gas flowing into the heat treatment furnace and the flow rate of gas flowing out of the heat treatment furnace based on simulation results obtained by the method for simulating furnace atmosphere according to any one of claims 1 to 8.

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