Method for calculating carbon concentration field in spring steel square billet heating process

Abstract

The application discloses a kind of spring steel square billet heating process carbon concentration field calculation method, belong to the technical field of high line steel rolling.The calculation method is S1, according to two-dimensional non-steady-state heat conduction equation, the calculation model of the temperature field of spring steel square billet heating process is established;S2, the calculation model of the temperature field of spring steel square billet heating process in S1 and carbon concentration field parameter are coupled, the carbon diffusion coefficient and convective mass transfer coefficient of spring steel square billet are obtained;S3, according to two-dimensional non-steady-state diffusion equation, the carbon diffusion coefficient and convective mass transfer coefficient of spring steel square billet in S2 are combined, the calculation model of the carbon concentration field of spring steel square billet heating process is established, and the carbon concentration field data of spring steel square billet heating process is calculated according to the aforementioned calculation model.The application realizes the forecast of the carbon concentration field of spring steel square billet and the thickness of surface layer and corner decarburization by using two-dimensional carbon concentration field prediction model in heating process, can adjust process parameters to control decarburization layer thickness, improve spring steel surface layer quality.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of high-speed wire rod rolling and relates to a method for calculating a carbon concentration field in a spring steel bloom during a heating process. BACKGROUND

[0002] At present, springs are widely used in the fields of automobiles, railways, engineering machinery, electronics and electrical appliances as key basic structural parts of the equipment manufacturing industry. With the increasingly harsh working conditions of spring steel, the requirements for the surface layer quality of spring steel are becoming more and more stringent.

[0003] The control of the thickness of the surface decarburized layer of spring steel during the heating process is one of the key technologies for surface quality control. Therefore, how to accurately and effectively realize real-time monitoring of the change of the carbon concentration field of the surface layer of the spring steel billet is the top priority for controlling the surface quality of spring steel. Based on this, it is increasingly important to explore, research and regulate the accurate evolution law of the thickness of the surface decarburized layer of spring steel under different heating conditions.

[0004] In the prior art, some technologies mainly aim at the measurement method of the decarburized layer thickness and the selection of the decarburization process parameters. These technologies obviously cannot monitor the change of the carbon concentration field of the surface layer of the spring steel billet in real time. Some technologies mainly aim at the calculation and prediction of the decarburized layer thickness. Some technologies can monitor the change of the decarburized layer thickness in real time, but the specific evolution law of the decarburized layer and the numerical change of the carbon concentration field are difficult to accurately control.

[0005] Chinese patent CN112378328A discloses a method for measuring the thickness of a decarburized layer in an iron-based material. An electromagnetic induction eddy current detection device is used. The conductivity and magnetic permeability of the upper surface of the sample change due to the change in the depth of the decarburized layer, causing the induced alternating current to change, and the output electromagnetic signal to change correspondingly. The relationship between the thickness of the decarburized layer and the electromagnetic signal is found out according to the standard sample, and the thickness of the decarburized layer is determined according to the strength and grade of the electromagnetic signal. This method obviously cannot be used for real-time measurement of the thickness of the decarburized layer in the iron-based material during the hot working process, and does not focus on the specific evolution law of the decarburized layer and the numerical change of the carbon concentration field.

[0006] Chinese patent CN109385516A discloses a method for determining the decarburization process parameters of a rolling heating furnace. Various detection data and furnace conditions during the combustion process of the rolling heating furnace are used as input signals, and the thickness data of the decarburized layer after the heating of the billet is used as an output signal. Through the neuron network training and optimization process, various complex nonlinear projection relationships in the decarburization process data such as the measurement data and the furnace condition data can be represented by a neuron network model. This method requires a large number of detection values, otherwise the neuron network training and optimization process is difficult to effectively implement, and the accurate evolution law of the thickness of the surface decarburized layer of spring steel under different heating conditions is not studied.

[0007] Chinese patent CN110648421A discloses a method for calculating the thickness of the decarburized layer on the surface of a decarburized spring steel. Real-time data of the furnace atmosphere, heating temperature and heating time in the actual process of hot continuous rolling are combined as input parameters to realize real-time online prediction of the change of the thickness of the decarburized layer. The advantage is that the operation is simple and the prediction is accurate, but the disadvantage is that the real-time carbon concentration field of the bloom heating process and the change law of the carbon concentration field with the heating process cannot be calculated and studied.

[0008] Chinese patent CN113868832A discloses a method for predicting the thickness of the decarburized layer formed by continuous heating and holding of high-carbon chromium bearing steel. The heating process and the thickness of the decarburized layer of bearing steel GCr15 in the atmosphere furnace are used as experimental data to construct a multiple linear regression equation between heating temperature, holding time, heating speed and oxygen concentration and the thickness of the decarburized layer of bearing steel, which is used to predict the thickness of the decarburized layer on the surface of bearing steel. The advantage is that the influence of different heating processes on the billet is considered; the disadvantage is that experimental data collection is required in the prediction method, the experimental data collection of the four factors involved is difficult and has low accuracy, the process is relatively troublesome, and it is difficult to predict the real-time carbon concentration field of the spring steel bloom heating process and study the change law of the carbon concentration field with the heating process.

[0009] Chinese patent CN105302952A discloses a finite element method for predicting the decarburization of spring steel bloom. According to the actual measurement data of the thermocouple, a bloom temperature field calculation model is established by using finite element software, a carbon diffusion model is established inside the bloom, and the actual detection results are corrected to the model calculation results, so that the model can accurately predict the decarburization of the spring steel bloom under actual working conditions. The advantage is that the accuracy of the calculation model can be well guaranteed by comparing the model simulation calculation with the actual detection results; the disadvantage is that the decarburized layer is calculated in one dimension only, and the thickness of the decarburized layer at the corner of the bloom cannot be predicted; and the time and number of repeated correction of the simulation temperature field results by the thermocouple test results are more, the thermocouple arrangement loss is more, and the cost is higher.

[0010] In summary, the existing technology does not involve and consider the coordinated calculation of the carbon concentration field of the spring steel bloom heating process and the thickness of the surface and corner decarburization, the calculation and prediction method is complex, the numerical accuracy obtained is poor, the actual values need to be corrected and modified, the establishment time of the calculation model and the required process parameter values are more, and the real-time carbon concentration field of the bloom heating process and the change law of the carbon concentration field with the heating process cannot be obtained conveniently, efficiently and accurately by the calculation method, which is not conducive to the actual production and application of the enterprise site. SUMMARY

[0011] The technical problem solved by the present application is how to overcome the problems in the prior art that the prediction and calculation of the surface decarburized layer thickness of the spring steel bloom only involves the prediction and calculation of the surface decarburized layer thickness, the carbon concentration field of the spring steel bloom and the collaborative calculation of the surface layer and the corner decarburized thickness are not considered, the calculation result cannot be obtained in real time and quickly, the calculation result has poor precision and needs to be corrected through repeated detection results, the real-time carbon concentration field of the bloom heating process and the variation law of the carbon concentration field with the heating process are not accurate even if they are obtained, and the like.

[0012] To solve the above technical problems, the present application provides the following technical solutions.

[0013] A calculation method of a carbon concentration field in a spring steel bloom heating process, the calculation method is performed according to the following steps:

[0014] S1, a calculation model of a temperature field of the spring steel bloom in the heating process is established according to a two-dimensional non-steady-state heat conduction equation;

[0015] S2, the calculation model of the temperature field of the spring steel bloom in the heating process in step S1 is coupled with carbon concentration field parameters to obtain a carbon diffusion coefficient and a convective mass transfer coefficient of the spring steel bloom;

[0016] S3, a calculation model of the carbon concentration field of the spring steel bloom in the heating process is established according to a two-dimensional non-steady-state diffusion equation combined with the carbon diffusion coefficient and the convective mass transfer coefficient of the spring steel bloom in step S2, and the carbon concentration field data of the spring steel bloom in the heating process can be calculated according to the foregoing calculation model.

[0017] Preferably, the two-dimensional non-steady-state heat conduction equation in step S1 is: The two-dimensional non-steady-state diffusion equation in step S3 is:

[0018] Preferably, step S1 specifically includes the following steps:

[0019] S11, corresponding thermal physical property parameter values are obtained according to the steel grade of the spring steel bloom;

[0020] S12, spatial discretization of a two-dimensional temperature field is performed according to the geometric size of the spring steel bloom;

[0021] S13, time discretization is performed according to the heating time of the spring steel bloom;

[0022] S14, boundary conditions are set according to the heating conditions of the spring steel bloom;

[0023] S15, an initial temperature is assigned to the spring steel bloom;

[0024] S16, a temperature field coefficient matrix of the spring steel bloom is obtained in combination with the thermal physical property parameter values in step S11;

[0025] S17: Combining the temperature field coefficient matrix in the step S16, using the ADI iteration method to calculate the two-dimensional temperature field data of the spring steel square billet.

[0026] Preferably, the step S2 specifically comprises the following steps:

[0027] S21: According to the two-dimensional temperature field data calculated in the step S17, obtaining the temperature calculation value of each control body at each time step;

[0028] S22: Spatially discretizing the two-dimensional carbon concentration field according to the geometric size of the spring steel square billet;

[0029] S23: According to the grid divided by the spatial discretization of the two-dimensional temperature field in the step S12 and the spatial discretization of the two-dimensional carbon concentration field in the step S22, performing two-dimensional interpolation calculation on the temperature calculation value of each control body at each time step obtained in the step S21 to obtain;

[0030] S24: According to the temperature field obtained in the step S23, the iron-carbon phase diagram and the carbon concentration field of the previous time step, calculating the carbon diffusion coefficient and the convective mass transfer coefficient of the spring steel square billet.

[0031] Preferably, the temperature field coupled with the carbon concentration field in the step S23 needs to be two-dimensionally interpolated to shorten the calculation time.

[0032] Preferably, the calculation formula of the carbon diffusion coefficient D(T, c) in the step S24 is as follows:

[0033]

[0034] Wherein, D0 is the frequency factor; Q is the diffusion activation energy; b is a constant reflecting the relationship between carbon concentration and diffusion coefficient, taking 0.8; c0 is the carbon content of the spring steel; c is the carbon concentration calculated at the previous time step; R is the gas constant; T is the temperature.

[0035] Preferably, the diffusion coefficient of the steel billet in the heating process when the temperature is in the ferrite + pearlite mixed zone and the single-phase ferrite zone is calculated according to the single-phase ferrite.

[0036] The calculation method of the diffusion coefficient D of the steel billet in the heating process when the temperature is in the ferrite + austenite two-phase mixed zone is as follows:

[0037] D = (D α ) p · (D γ ) 1-p

[0038] where D α is the diffusion coefficient of the α phase, D γ is the diffusion coefficient of the γ phase, p is the percentage of the α phase, 1 - p is the percentage of the γ phase, and p is calculated according to the phase diagram using the lever rule;

[0039] In the heating process in step S24, the diffusion coefficient in the single - phase austenite region of the steel billet is calculated according to single - phase austenite.

[0040] Preferably, the calculation formula for the convective mass transfer coefficient β in step S24 is as follows:

[0041]

[0042] where f is the influencing factor, representing the influence of factors such as the oxide layer structure on the rate of interfacial carbon mass transfer, which is determined by decarburization experiments; β0 is a constant; and E is the reaction activation energy.

[0043] Preferably, step S3 specifically includes the following steps: <​​​​​​​​​​​​​​​​​​In the above scheme, the present application combines the temperature field and the carbon concentration field, uses the finite volume method to calculate the temperature field in the heating process of the square billet, transmits the temperature field data of the current time step to the two-dimensional carbon concentration field model to obtain the carbon concentration of different positions in the two-dimensional section of the square billet. In combination with the heating temperature and the heating time in the heating process, the carbon concentration field in the heating process is obtained, and the change of the decarburization layer thickness can be predicted.

[0051] The present application realizes the prediction of the carbon concentration field of the spring steel square billet and the decarburization thickness of the surface layer and the corner portion by using the two-dimensional carbon concentration field prediction model in the heating process, so that the process parameters are adjusted to control the decarburization layer thickness, and the quality problem of the surface layer of the spring steel is improved.

[0052] The grid calculation and the precision of the two-dimensional carbon concentration field model are optimized, the calculation amount is reduced, and the model calculation time is greatly shortened. The calculation result can be obtained in real time and quickly, and at the same time, the calculation result does not need to be repeatedly corrected by the detection result. The operation is simple, the cost is low, and it is beneficial to industrial production application.

[0053] In summary, the present application combines the temperature field and the carbon concentration field, establishes the carbon concentration field calculation model of the spring steel square billet in the heating process, considers the temperature change of the steel billet, reduces the complexity and the calculation amount of modeling, can predict the thickness of the surface decarburization layer through the carbon concentration field, and has important significance for the actual production of the enterprise site. BRIEF DESCRIPTION OF DRAWINGS

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creating laborious work.

[0055] Figure 1 The iron-carbon phase diagram for judging the carbon diffusion coefficient calculation scheme in the calculation method of the carbon concentration field of the spring steel square billet in the heating process of the present application embodiment 1;

[0056] Figure 2 The two-dimensional grid schematic diagram for the simulation calculation of the carbon concentration field of the square billet in the calculation method of the carbon concentration field of the spring steel square billet in the heating process of the present application embodiment 1;

[0057] Figure 3 The carbon concentration field calculation cloud diagram of the 55SiCr spring steel square billet in the heating process in the calculation method of the carbon concentration field of the spring steel square billet in the heating process of the present application embodiment 1;

[0058] Figure 4Iron-carbon phase diagram for judging carbon diffusion coefficient calculation scheme in the calculation method of carbon concentration field of the spring steel square billet heating process of embodiment 2 of the present application;

[0059] Figure 5 Two-dimensional grid schematic diagram for square billet carbon concentration field simulation calculation in the calculation method of carbon concentration field of the spring steel square billet heating process of embodiment 2 of the present application;

[0060] Figure 6 Cloud chart for 60Si2Mn spring steel square billet carbon concentration field calculation in the calculation method of carbon concentration field of the spring steel square billet heating process of embodiment 2 of the present application;

[0061] Figure 7 Iron-carbon phase diagram for judging carbon diffusion coefficient calculation scheme in the calculation method of carbon concentration field of the spring steel square billet heating process of embodiment 3 of the present application;

[0062] Figure 8 Two-dimensional grid schematic diagram for square billet carbon concentration field simulation calculation in the calculation method of carbon concentration field of the spring steel square billet heating process of embodiment 3 of the present application;

[0063] Figure 9 Cloud chart for 65Mn spring steel square billet carbon concentration field calculation in the calculation method of carbon concentration field of the spring steel square billet heating process of embodiment 3 of the present application. DETAILED DESCRIPTION

[0064] The technical solutions in the embodiments of the present application and the technical problems solved by the embodiments will be described below in conjunction with the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all embodiments.

[0065] Embodiment 1

[0066] The present application adopts 55SiCr spring steel, 150*150mm square billet.

[0067] A calculation method of carbon concentration field of spring steel square billet heating process, specifically comprising the following steps:

[0068] S1: establishing a spring steel square billet heating process temperature field calculation model according to a two-dimensional non-steady-state heat conduction equation:

[0069] The two-dimensional non-steady-state heat conduction equation is:

[0070] S11: obtaining corresponding thermal physical property parameter values of 55SiCr spring steel, the density ρ is 7850kg / m 3 , the thermal conductivity λ is 36J / (m·s·℃), and the specific heat capacity C is 600J / (kg·℃);

[0071] S12: Discretize the two-dimensional temperature field in space according to the geometric dimensions of the spring steel bloom, divide the temperature field into 150x150 grids, and the grid side length dx=1 mm, dy=1 mm;

[0072] S13: Discretize the heating time according to the heating time of the spring steel bloom, the heating time is 60 min, and the single time step dt=30 s;

[0073] S14: Set the boundary conditions according to the heating conditions, the environmental temperature is 1000℃, and the convective heat transfer coefficient is 250 J / (m 2 ·s·℃);

[0074] S15: Assign the initial temperature to the spring steel bloom, and the initial temperature field is 30℃;

[0075] S16: Obtain the temperature field coefficient matrix combined with the parameter values in S11;

[0076] S17: Calculate the two-dimensional temperature field data of the spring steel bloom by using the ADI iteration method;

[0077] S2: Perform temperature field and carbon concentration field parameter coupling:

[0078] S21: Obtain the temperature calculation value of each control body at each time step according to the temperature field calculated in S17;

[0079] S22: Discretize the two-dimensional carbon concentration field in space according to the geometric dimensions of the spring steel bloom, divide the carbon concentration field into 3000x3000 grids, and the grid side length dx=0.05 mm, dy=0.05 mm;

[0080] S23: Perform two-dimensional interpolation calculation on the temperature field obtained in S21 according to the grids divided in S12 and S22;

[0081] S24: Calculate the carbon diffusion coefficient D(T,c) and the convective mass transfer coefficient β of the spring steel bloom according to the temperature field obtained in S23, the iron-carbon phase diagram, and the carbon concentration field at the previous time step;

[0082] According to the above-mentioned method, the temperature field and the carbon concentration field of the spring steel bloom are calculated, and the carbon concentration field of the spring steel bloom is obtained. Figure 1The shown part of iron-carbon phase diagram, when T≤T1, the average carbon concentration of each control body is in region ①, which is ferrite + pearlite mixed region, and the diffusion coefficient is calculated according to single-phase ferrite; when T1≤T≤T2, the average carbon concentration of each control body is in region ②, which is single-phase ferrite region, and the diffusion coefficient is calculated according to single-phase ferrite; when T1≤T≤T2, the average carbon concentration of each control body is in region ③, which is ferrite + austenite two-phase mixed region, and the calculation method is as follows; when T1≤T≤T2, the average carbon concentration of each control body is in region ④, which is single-phase austenite region, and the diffusion coefficient is calculated according to single-phase austenite; when T≥T2, the average carbon concentration of each control body is in region ④, which is single-phase austenite region, and the diffusion coefficient is calculated according to single-phase austenite.

[0083] Carbon diffusion coefficient D(T, c) formula:

[0084]

[0085] Wherein, R=8.314; b=0.8; c0=0.55; ferrite α: D0=0.2×10 -5 m 2 ·s -1 , Q=84×10 3 J·mol -1 ; Austenite γ: D0=2.0×10 -5 m 2 ·s -1 , Q=140×10 3 J·mol -1 ;

[0086] The diffusion coefficient D of the two-phase region is calculated as follows:

[0087] D=(D α ) p ·(D γ ) 1-p

[0088] Wherein D α is the diffusion coefficient of α phase, D γ is the diffusion coefficient of γ phase, p is the percentage of α phase, and 1-p is the percentage of γ phase, p is calculated according to the lever rule using the phase diagram;

[0089] Formula of convective mass transfer coefficient:

[0090]

[0091] Wherein, f=1; β0=3.47×10 -6 m / s; E=34000 J / mol;

[0092] S3: a two-dimensional unsteady diffusion equation is established to calculate the carbon concentration field of the spring steel square billet during the heating process:

[0093] The two-dimensional unsteady diffusion equation is:

[0094] S31: the initial carbon concentration of the spring steel square billet is set, and the initial carbon concentration field is 0.55;

[0095] S32: the boundary condition is set according to the heating atmosphere, and the interface equilibrium carbon concentration is 0;

[0096] S33: the carbon concentration field coefficient matrix is obtained in combination with the parameter values in S24;

[0097] S34: the optimized ADI iteration method is used to calculate the two-dimensional carbon concentration field data of the spring steel square billet, wherein only 600 boundary grids are calculated, the center 1800*1800 grids are not involved in the calculation, and the two-dimensional grid diagram of the simulation calculation of the carbon concentration field of the 55SiCr spring steel square billet is as shown in Figure 2 The cloud chart of the carbon concentration field of the 55SiCr spring steel square billet during the heating process is as shown in Figure 3

[0098] Example 2

[0099] The present application adopts 60Si2Mn spring steel, and the square billet is 200*200mm.

[0100] A kind of calculation method of carbon concentration field of spring steel square billet during heating process, specifically includes the following steps:

[0101] S1: a two-dimensional unsteady heat conduction equation is established to calculate the temperature field of the spring steel square billet during the heating process:

[0102] The two-dimensional unsteady heat conduction equation is:

[0103] S11: the corresponding thermal physical property parameter values of 60Si2Mn spring steel are obtained, the density ρ is 7740kg / m 3 , the thermal conductivity λ is 44J / (m·s·℃), and the specific heat capacity C is 460J / (kg·℃);

[0104] S12: the two-dimensional temperature field is discretized according to the geometric size of the spring steel square billet, the temperature field is divided into 200*200 grids, the grid side length dx=1mm, dy=1mm;

[0105] S13: the time is discretized according to the heating time of the spring steel square billet, the heating time is 60min, and the single time step dt=30s;

[0106] ​S14: Set boundary conditions according to heating conditions; ambient temperature is 1000℃, and convective heat transfer coefficient is 250 J / (m²). 2 (·s·℃);

[0107] S15: Apply an initial temperature to the spring steel billet; the initial temperature field is 30℃.

[0108] S16: Combine the parameter values ​​in S11 to obtain the temperature field coefficient matrix;

[0109] S17: Calculate the two-dimensional temperature field data of spring steel billet using the ADI iterative method;

[0110] S2: Couple the temperature field and carbon concentration field parameters:

[0111] S21: Based on the temperature field calculated in S17, obtain the calculated temperature values ​​of each control volume at each time step;

[0112] S22: Based on the geometric dimensions of the spring steel billet, the two-dimensional carbon concentration field is spatially discretized, and the carbon concentration field is divided into 4000×4000 grids with grid side lengths dx=0.05mm and dy=0.05mm;

[0113] S23: Perform two-dimensional interpolation calculations on the temperature field obtained in S21 based on the grids divided in S12 and S22;

[0114] S24: Based on the temperature field, iron-carbon phase diagram and carbon concentration field obtained in S23, calculate the carbon diffusion coefficient D(T,c) and convective mass transfer coefficient β of the spring steel billet.

[0115] According to such Figure 4 The partial iron-carbon phase diagram shown illustrates the following: When T≤T1, the average carbon concentration of each control phase is in region ①, a ferrite + pearlite mixed region, and the diffusion coefficient is calculated as a single-phase ferrite; when T1≤T≤T2, the average carbon concentration of each control phase is in region ②, a single-phase ferrite region, and the diffusion coefficient is calculated as a single-phase ferrite; when T1≤T≤T2, the average carbon concentration of each control phase is in region ③, a ferrite + austenite two-phase mixed region, calculated as follows; when T1≤T≤T2, the average carbon concentration of each control phase is in region ④, a single-phase austenite region, and the diffusion coefficient is calculated as a single-phase austenite; when T≥T2, the average carbon concentration of each control phase is in region ④, a single-phase austenite region, and the diffusion coefficient is calculated as a single-phase austenite.

[0116] The formula for the carbon diffusion coefficient D(T,c) is as follows:

[0117]

[0118] Where R = 8.314; b = 0.8; c0 = 0.60; ferrite α: D0 = 0.2 × 10⁻⁶-5 m 2 ·s -1 , Q = 84 x 10 3 J·mol -1 -1 -5 m 2 ·s -1 , Q = 140 x 10 3 J·mol -1 -1

[0119] The diffusion coefficient D of the two-phase region is calculated as follows:

[0120] D = (D α ) p · (D γ ) 1-p

[0121] where D α is the diffusion coefficient of the α phase, D γ is the diffusion coefficient of the γ phase, p is the percentage of the α phase, and 1-p is the percentage of the γ phase. p is calculated using the lever rule according to the phase diagram;

[0122] The formula for the convective mass transfer coefficient is:

[0123]

[0124] where f = 1; β0= 3.47 x 10 -6 m / s; E = 34000 J / mol;

[0125] S3: A calculation model for the carbon concentration field of a spring steel square billet during heating is established based on two-dimensional unsteady diffusion:

[0126] The two-dimensional unsteady diffusion equation is:

[0127] S31: The initial carbon concentration of the spring steel square billet is assigned, and the initial carbon concentration field is 0.60;

[0128] S32: The boundary conditions are set according to the heating atmosphere, and the interface equilibrium carbon concentration is 0;

[0129] S33: The carbon concentration field coefficient matrix is obtained in combination with the parameter values in S24;

[0130] S34: The optimized ADI iteration method is used to calculate the two-dimensional carbon concentration field data of the spring steel square billet, where only the 600 boundary grids are calculated, and the center 2800 x 2800 grids are not involved in the calculation. The two-dimensional grid diagram for the simulation calculation of the carbon concentration field of the 60Si2Mn spring steel square billet is shown in Figure 5 ; and the cloud chart for the calculation of the carbon concentration field of the 60Si2Mn spring steel square billet during heating is as shown inFigure 6 As shown.

[0131] Embodiment 3

[0132] The present application adopts 65Mn spring steel, 140*140mm square billet.

[0133] A method for calculating carbon concentration field in spring steel square billet heating process, specifically comprising the following steps:

[0134] S1: according to two-dimensional unsteady heat conduction equation, establish spring steel square billet heating process temperature field calculation model:

[0135] Two-dimensional unsteady heat conduction equation is:

[0136] S11: according to 65Mn spring steel, get the corresponding thermal physical property parameter value, density ρ is 7820kg / m 3 , thermal conductivity λ is 48J / (m·s·℃), specific heat capacity C is 450J / (kg·℃);

[0137] S12: according to the geometric size of spring steel square billet, the space of two-dimensional temperature field is dispersed, the temperature field is divided into 140*140 grids, the grid side length dx=1mm, dy=1mm;

[0138] S13: according to the heating time of spring steel square billet, time is dispersed, the heating time is 60min, the single time step dt=30s;

[0139] S14: according to the heating condition, set the boundary condition, the environmental temperature is 1100℃, the convective heat transfer coefficient is 275J / (m 2 ·s·℃);

[0140] S15: assign initial temperature to spring steel square billet, the initial temperature field is 30℃;

[0141] S16: get temperature field coefficient matrix combined with parameter value in S11;

[0142] S17: use ADI iteration method to calculate two-dimensional temperature field data of spring steel square billet;

[0143] S2: coupling of temperature field and carbon concentration field parameters:

[0144] S21: according to the temperature field calculated in S17, get the temperature calculation value of each control body at each time step;

[0145] S22: according to the geometric size of spring steel square billet, the space of two-dimensional carbon concentration field is dispersed, the carbon concentration field is divided into 2800*2800 grids, the grid side length dx=0.05mm, dy=0.05mm;

[0146] S23: Perform two-dimensional interpolation calculations on the temperature field obtained in S21 based on the grids divided in S12 and S22;

[0147] S24: Based on the temperature field, iron-carbon phase diagram and carbon concentration field obtained in S23, calculate the carbon diffusion coefficient D(T,c) and convective mass transfer coefficient β of the spring steel billet.

[0148] According to such Figure 7 The partial iron-carbon phase diagram shown illustrates the following: When T≤T1, the average carbon concentration of each control phase is in region ①, a ferrite + pearlite mixed region, and the diffusion coefficient is calculated as a single-phase ferrite; when T1≤T≤T2, the average carbon concentration of each control phase is in region ②, a single-phase ferrite region, and the diffusion coefficient is calculated as a single-phase ferrite; when T1≤T≤T2, the average carbon concentration of each control phase is in region ③, a ferrite + austenite two-phase mixed region, calculated as follows; when T1≤T≤T2, the average carbon concentration of each control phase is in region ④, a single-phase austenite region, and the diffusion coefficient is calculated as a single-phase austenite; when T≥T2, the average carbon concentration of each control phase is in region ④, a single-phase austenite region, and the diffusion coefficient is calculated as a single-phase austenite.

[0149] The formula for the carbon diffusion coefficient D(T,c) is as follows:

[0150]

[0151] Where R = 8.314; b = 0.8; c0 = 0.65; ferrite α: D0 = 0.2 × 10⁻⁶ -5 m 2 ·s -1 Q = 84 × 10 3 J·mol -1 Austenite γ: D0 = 2.0 × 10⁻⁶ -5 m 2 ·s -1 Q = 140 × 10 3 J·mol -1 ;

[0152] The diffusion coefficient D in the two-phase region is calculated using the following formula:

[0153] D=(D α ) p ·(D γ ) 1-p

[0154] Where D α D is the diffusion coefficient of the α phase. γ denoted as γ, p is the percentage of α phase, 1-p is the percentage of γ phase, and p is calculated using the phase diagram and lever theorem.

[0155] The convective mass transfer coefficient formula is:

[0156]

[0157] Wherein, f = 1; β0= 3.47 x 10 -6 m / s; E = 34000 J / mol;

[0158] S3: a two-dimensional unsteady diffusion model for calculating the carbon concentration field of the spring steel square billet during the heating process is established;

[0159] The two-dimensional unsteady diffusion equation is:

[0160] S31: the initial carbon concentration of the spring steel square billet is set, and the initial carbon concentration field is 0.65;

[0161] S32: the boundary conditions are set according to the heating atmosphere, and the interface equilibrium carbon concentration is 0;

[0162] S33: the carbon concentration field coefficient matrix is obtained in combination with the parameter values in S24;

[0163] S34: the optimized ADI iteration method is used to calculate the two-dimensional carbon concentration field data of the spring steel square billet, wherein only 600 boundary grids are calculated, and the center 1600 x 1600 grids do not participate in the calculation, and the two-dimensional grid diagram of the carbon concentration field simulation calculation of the 65Mn spring steel square billet is as shown in Figure 8 ; and the carbon concentration field calculation cloud chart of the 65Mn spring steel square billet during the heating process is as shown in Figure 9 .

[0164] In the above scheme, the temperature field and the carbon concentration field are combined, the temperature field during the square billet heating process is obtained by using the finite volume method, the temperature field data of the current time step is transmitted to the two-dimensional carbon concentration field model, and the carbon concentration of different positions of the square billet two-dimensional section is obtained. In combination with the heating temperature and the heating time during the heating process, the carbon concentration field during the heating process is obtained, and the change of the decarburization layer thickness can be predicted.

[0165] The present application realizes the prediction of the carbon concentration field of the spring steel square billet and the decarburization thickness of the surface layer and the corner part by using the two-dimensional carbon concentration field prediction model during the heating process, so as to adjust the process parameters to control the decarburization layer thickness and improve the surface layer quality problem of the spring steel.

[0166] The grid calculation and precision of the two-dimensional carbon concentration field model are optimized, the calculation amount is reduced, the model calculation time is greatly shortened, the synergistic calculation of the carbon concentration field of the spring steel square billet and the decarburization thickness of the surface layer and the corner part is considered, the calculation result can be obtained in real time and quickly, and at the same time, the calculation result does not need to be repeatedly corrected by the detection result, the operation is simple, the cost is low, and it is beneficial to industrial production application.

[0167] In summary, the application establishes a heating process spring steel billet carbon concentration field calculation model by combining the temperature field with the carbon concentration field, considers the change of the billet temperature, reduces the complexity and calculation amount of modeling, and can predict the thickness of the surface decarburized layer through the carbon concentration field, which has important significance for the actual production of the enterprise site.

[0168] The above describes the preferred embodiments of the present application. It should be noted that, for those skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, which should also be considered within the scope of protection of the present application.

Claims

1. A method of calculating a carbon concentration field in a spring steel bloom heating process, characterized by, The calculation method is performed according to the following steps: S1, a calculation model of a temperature field of the spring steel bloom in a heating process is established according to a two-dimensional non-steady heat conduction equation; The step S1 specifically comprises the following steps: S11, obtaining corresponding thermal physical property parameter values according to the steel grade of the spring steel bloom; S12, spatially discretizing a two-dimensional temperature field according to the geometric size of the spring steel bloom; S13, time discretizing according to the heating time of the spring steel bloom; S14, setting boundary conditions according to the heating conditions of the spring steel bloom; S15, assigning an initial temperature to the spring steel bloom; S16, obtaining a temperature field coefficient matrix of the spring steel bloom in combination with the thermal physical property parameter values of the step S11; S17, calculating two-dimensional temperature field data of the spring steel bloom by using an ADI iteration method in combination with the temperature field coefficient matrix in the step S16; S2, coupling the calculation model of the temperature field of the spring steel bloom in the heating process in the step S1 and carbon concentration field parameters to obtain a carbon diffusion coefficient and a convective mass transfer coefficient of the spring steel bloom; The step S2 specifically comprises the following steps: S21, obtaining temperature calculation values of each control body at each time step according to the two-dimensional temperature field data calculated in the step S17; S22, spatially discretizing a two-dimensional carbon concentration field according to the geometric size of the spring steel bloom; S23, performing two-dimensional interpolation calculation on the temperature calculation values of each control body at each time step obtained in the step S21 according to the grid divided by the spatial discretization of the two-dimensional temperature field of the step S12 and the spatial discretization of the two-dimensional carbon concentration field of the step S22; S24, calculating the carbon diffusion coefficient and the convective mass transfer coefficient of the spring steel bloom according to the temperature field obtained in the step S23, an iron-carbon phase diagram and the carbon concentration field of the previous time step; The calculation formula of the carbon diffusion coefficient D(T, c) in the step S24 is as follows: Wherein, D0 is a frequency factor; Q is a diffusion activation energy; b is a constant reflecting the relationship between carbon concentration and diffusion coefficient, and is 0.8; c0 is the carbon content of the spring steel; c is the carbon concentration calculated at the previous time step; R is a gas constant; T is the temperature; The calculation formula of the convective mass transfer coefficient β in the step S24 is as follows: Wherein, f is an influence factor, indicating the influence of the structure factor of the oxidation layer on the speed of carbon mass transfer at the interface, and is determined by a decarburization experiment; β0 is a constant; E is a reaction activation energy; S3, a calculation model of a carbon concentration field of the spring steel bloom in a heating process is established according to a two-dimensional non-steady diffusion equation in combination with the carbon diffusion coefficient and the convective mass transfer coefficient of the spring steel bloom in the step S2, and the aforementioned calculation model can be used to calculate carbon concentration field data of the spring steel bloom in the heating process.

2. The method for calculating the carbon concentration field during the heating process of spring steel billets according to claim 1, characterized in that, The two-dimensional unsteady heat conduction equation in the step S1 is: The two-dimensional unsteady diffusion equation in the step S3 is:

3. The method of claim 1, wherein the carbon concentration field is calculated by the following equation: ###0001### where C is the carbon concentration, t is the time, D is the diffusion coefficient, and C0 is the initial carbon concentration. The temperature field coupled with the carbon concentration field in the step S23 needs to be calculated by two-dimensional interpolation, the temperature field coarse grid in S12 and the carbon concentration field fine grid in S22 are calculated by two-dimensional interpolation to obtain the temperature value corresponding to the carbon concentration field grid, thereby shortening the calculation time.

4. The method of claim 1, wherein the carbon concentration field is calculated by the following equation: ###0001### where C is the carbon concentration, t is the time, D is the diffusion coefficient, and C0 is the initial carbon concentration. In the step S24, the diffusion coefficient in the heating process of the bloom is calculated according to the single-phase ferrite when the temperature of the bloom is in the ferrite+pearlite mixed zone and the single-phase ferrite zone. The diffusion coefficient D of the steel billet temperature in the step S24 in the heating process is in the ferrite + austenite two-phase mixed zone and is calculated as follows: D = (D α ) p • (D γ ) 1-p where D α is the diffusion coefficient of the α phase, D γ is the diffusion coefficient of the γ phase, p is the percentage of the α phase, 1-p is the percentage of the γ phase, and p is calculated using a lever rule from a phase diagram. The diffusion coefficient of the steel billet temperature in the step S24 in the heating process is in the single-phase austenite zone and is calculated according to the single-phase austenite.

5. The method according to any one of claims 3 to 4, c h a r a c t e r i z e d in that The step S3 specifically comprises the following steps: S31: assigning an initial carbon concentration to the spring steel billet; S32: setting a boundary condition according to the heating atmosphere of the spring steel billet; S33: combining the carbon diffusion coefficient and the convective mass transfer coefficient of the spring steel billet in the step S24 to obtain a carbon concentration field coefficient matrix; S34: combining the carbon concentration field coefficient matrix in the step S33 and using an optimized ADI iteration method to calculate the two-dimensional carbon concentration field data of the billet.

6. The method of claim 5, wherein the carbon concentration field is calculated by the following equation: ###0001### where C is the carbon concentration, t is the time, D is the diffusion coefficient, and C0 is the initial carbon concentration. In the step S34, the ADI algorithm only calculates the boundary designated grid; the billet is two-dimensionally meshed, there are n control bodies in the x direction and m control bodies in the y direction, and there are n x m control bodies in the whole region; assuming that N layers of boundary grids are calculated, the values of the x direction from the N+1 to n-N layers are set to the carbon content of the spring steel, and the values of the y direction from the N+1 to m-N layers are set to the carbon content of the spring steel, that is, the central region grid does not participate in the calculation, and only the "back" type boundary grid region is calculated.

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