A method for predicting cross-section temperature of rolled product during plate and strip rolling process

Abstract

The present invention provides a method for predicting the cross-sectional temperature of a rolled piece during a plate and strip rolling process, and relates to the technical field of automatic control of steel rolling. The method first determines the modeling parameters of a finite element model of a rolled piece during edge induction heating and the value ranges of various influencing factors affecting the cross-sectional temperature of the rolled piece, and then establishes and solves the model, and extracts cross-sectional temperature parameter data of the rolled piece according to the numerical simulation results; arranges numerical simulation experiments, repeatedly establishes and solves finite element models of multiple groups of rolled pieces during edge induction heating, analyzes the influence of the various influencing factors on the cross-sectional temperature parameters of the rolled piece, extracts multiple groups of cross-sectional temperature parameter data of the rolled piece to perform cross-sectional temperature parameter function fitting; substitutes the values ​​of each group of influencing factors arranged in the numerical simulation experiment into the cross-sectional temperature parameter function of the rolled piece to determine the cross-sectional partition position of the rolled piece, extracts the cross-sectional temperature data of the rolled piece to perform cross-sectional temperature function fitting of the rolled piece, and accurately predicts the cross-sectional temperature distribution of the rolled piece after edge induction heating.

Description

Technical Field

[0001] The invention belongs to the technical field of steel rolling automatic control, and in particular relates to a method for predicting the cross-section temperature of a rolled piece in a plate and strip rolling process. Background Art

[0002] Good temperature distribution of the rolled product section can effectively reduce product quality anomalies such as edge cracking, edge warping, and uneven performance, reduce uneven wear of the rolls, and increase the service life of the rolls. During the transportation process, the temperature drop of the edge of the rolled product is faster than that of the middle part, and the temperature difference between the edge and the middle is large. For this reason, domestic and foreign studies have found that using induction heating technology to compensate for the temperature drop of the edge of the rolled product can better achieve the consistency of the temperature of the edge and the middle of the rolled product, and improve the temperature uniformity of the rolled product section. At present, induction heating technology has been widely used in the process of controlling the temperature uniformity of the cross-section of hot-rolled products. Compared with traditional heating methods, induction heating has the advantages of fast heating speed, high heating efficiency, and high degree of automation control.

[0003] The equipment that realizes induction heating technology to compensate for the temperature drop at the edge of the rolled piece is called an edge induction heater (hereinafter referred to as EH). The cross-sectional temperature distribution of the rolled piece after edge induction heating is related to the product specifications and process parameters. The temperature measuring device is installed on site at the exit of the rough rolling unit and the exit of the EH. The single-point temperature measuring device installed on site can obtain the temperature at the center position of the width of the rolled piece surface, and the cross-sectional temperature measuring device can only obtain the surface temperature at the key position of the width of the rolled piece. In fact, the temperature distribution in the thickness direction of the rolled piece is not uniform, so it is not accurate to use the surface temperature to describe the cross-sectional temperature distribution of the rolled piece; at the same time, the iron oxide scale generated during the rolling process will also affect the measurement accuracy of the rolled piece temperature, making it difficult to accurately measure the cross-sectional temperature distribution of the rolled piece, which seriously affects the product quality of the subsequent rolling process.

[0004] At present, researchers at home and abroad have studied the temperature variation law of the rolled piece during the edge induction heating process by establishing a finite element model of the rolled piece for edge induction heating, solved the coupling problem of the eddy current field and the temperature field in the model, obtained the temperature distribution of the rolled piece through transient thermal analysis, and analyzed the influence of the current frequency, excitation current and head shape of the edge induction heater on the temperature of the rolled piece. However, the models in these studies are based on many assumptions, the model accuracy is not high, and the influence of factors such as the thickness of the rolled piece and the rolling speed on the temperature of the rolled piece is not considered. At the same time, there is no in-depth and systematic study on the temperature distribution of the rolled piece section, and no description of the modeling of the temperature of the rolled piece section is given, which makes it difficult to guide the actual production process on site and has low practicality. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a method for predicting the cross-sectional temperature of a rolled piece in a plate and strip rolling process, aiming to obtain the influence rules of various influencing factors including product specifications and process parameters on the cross-sectional temperature parameters of the rolled piece through finite element numerical simulation, and then perform nonlinear fitting on the cross-sectional temperature function of the rolled piece, so as to obtain the corresponding relationship between the cross-sectional temperature distribution of the rolled piece and the product specifications and process parameters, and realize the modeling description of the cross-sectional temperature distribution of the rolled piece.

[0006] The technical solution of the present invention is:

[0007] A method for predicting the cross-section temperature of a rolled piece during a strip rolling process, the method comprising the following steps:

[0008] Step 1: Determine relevant parameters: According to the actual production process, determine the modeling parameters of the finite element model of the edge induction heating process of the rolled piece and the value range of each influencing factor affecting the cross-section temperature of the rolled piece;

[0009] Step 2: Establishment of finite element model of edge induction heating process of rolled piece: Based on the relevant parameters determined in step 1, a 1 / 2 geometric model of edge induction heating process of rolled piece is created by finite element analysis software, and material physical property parameters are assigned to the geometric model, boundary conditions are set, and meshing is performed;

[0010] Step 3: Solve the finite element model of the edge induction heating process of the rolled piece: set coupling nodes under multi-physics field coupling, and solve the transient temperature field by sequential coupling;

[0011] Step 4: Extraction of temperature parameter data of the rolled product section: Extract the strong influence range of induction heating based on the temperature field calculation results. a Data, weak influence range of induction heating b Data of and data of edge temperature T0 of rolled piece;

[0012] The temperature rise caused by induction heating can rapidly increase the temperature of the rolled piece within a certain distance along the width direction. This distance is defined as the strong influence range of induction heating. a ; After that, the temperature rise caused by induction heating gradually decreases within a certain distance in the width direction of the rolled piece until the temperature of a certain point within this distance is close to the temperature of the middle part of the rolled piece. This distance is defined as the weak influence range of induction heating l b The edge temperature T0 of the rolled piece after induction heating is used to evaluate the induction heating effect. Since the temperature in the thickness direction of the rolled piece is unevenly distributed, the edge temperature T0 of the rolled piece is replaced by the average temperature in the thickness direction.

[0013] Step 5: Numerical simulation experiment: Use the orthogonal test method to arrange the influencing factors, substitute the specific values ​​of each group of influencing factors into steps 2 to 4, and implement the finite element modeling, solution, and numerical simulation experiment of extracting the cross-section temperature parameters of the rolled piece during the edge induction heating process;

[0014] Step 6: Study on the regularity of the temperature parameters of the section of the rolled piece and function fitting: According to the temperature parameter data of the section of the rolled piece obtained in step 5, analyze the influence of various factors on the temperature parameter of the section of the rolled piece. a , l b , T0, and thus the temperature parameter l of the rolled section a , l b , T0 function is fitted;

[0015] Step 7: Partitioning of the cross section of the rolled piece and fitting of the cross section temperature function of the rolled piece: Substitute the values ​​of the influencing factors arranged by the orthogonal test method in step 5 into the cross section temperature parameter l obtained in step 6. a and l b The function l is calculated from a and l b , according to l a , l b The section of the workpiece is divided into two parts according to the width B of the workpiece, and the range of each area of ​​the section of the workpiece is determined. Points are taken at fixed intervals along the width direction within each area. The temperature of each point is expressed as the average temperature in the thickness direction of the point. The section temperature data of the workpiece is extracted, and the section temperature function of the workpiece is nonlinearly fitted using all the section temperature data of the workpiece to obtain the section temperature function T(x).

[0016] Further, according to the method for predicting the cross-sectional temperature of a rolled piece during the strip rolling process, the modeling parameters include the initial length of the rolled piece, the width of the rolled piece, the initial cross-sectional temperature of the rolled piece before entering the edge induction heater EH, the relative position of the rolled piece and the EH, the air gap between the upper and lower magnetic heads of the EH, the number of turns of the EH coil, and the diameter of the EH coil;

[0017] The influencing factors include product specification parameters and process parameters; wherein the product specification parameters include the initial thickness H of the rolled piece; and the process parameters include the current frequency f of the edge induction heater EH, the excitation current I of EH and the running speed v of the rolled piece.

[0018] Further, according to the method for predicting the cross-section temperature of the rolled piece in the plate and strip rolling process, the step 2 of assigning material physical properties to the geometric model refers to assigning material physical property parameters to the yoke and coil of the edge induction heater EH in the geometric model, and the rolled piece, and the material physical property parameters include relative magnetic permeability, resistivity, thermal conductivity and specific heat capacity.

[0019] Further, according to the method for predicting the cross-sectional temperature of the rolled piece during the plate and strip rolling process, the boundary conditions set in step 2 include: assigning a value to the initial cross-sectional temperature of the rolled piece at the entrance of the EH; giving a running speed of the rolled piece according to the value range of the running speed v of the rolled piece and setting the rolled piece to move at a uniform speed along the rolling direction; setting the ambient temperature; setting the surface of the rolled piece for convection and radiation heat exchange and setting the heat transfer coefficient and surface emissivity; setting the width boundary of the rolled piece to a symmetric boundary; setting the initial value condition of the magnetic field to 0, and applying the excitation current given according to the value range of the excitation current I of the EH to the cross-section of the EH coil as an excitation condition for the eddy current field.

[0020] Furthermore, according to the method for predicting the cross-section temperature of the rolled piece in the plate and strip rolling process, the coupling nodes set under multi-physical field coupling described in step 3 include electromagnetic thermal nodes and temperature coupling nodes, the electromagnetic thermal nodes implement the application of induced current as a load to the temperature field, and the temperature coupling nodes implement the updating of the material physical performance parameters of the rolled piece according to temperature changes.

[0021] Furthermore, according to the method for predicting the cross-section temperature of a rolled piece during the strip rolling process, it is characterized in that the orthogonal test method used in step 5 to arrange the influencing factors specifically adopts 4 factors and 5 levels, and L25(5 4 )Orthogonal test table to arrange influencing factors.

[0022] Furthermore, according to the method for predicting the cross-section temperature of a rolled piece during a strip rolling process, it is characterized in that the cross-section temperature parameter l a , l b The function expressions of T0 are fitted with cubic polynomial functions, and their expressions are as follows:

[0023] y=A+a1f+b1f 2 +c1f 3 +a2I+b2I 2 +c2I 3 +a3H+b3H 2 +c3H 3 +a4v+b4v 2 +c4v 3

[0024] Replace y with the output variable l in sequence a , l b , T0 and find the corresponding unknown coefficients A, a 1～4 、b 1～4 、c 1～4 , the cross-section temperature parameters l of the rolled piece can be obtained in turn a , l b , function expression of T0.

[0025] Furthermore, according to the method for predicting the cross-section temperature of a rolled piece during the strip rolling process, the cross-section of the rolled piece is divided into the following three regions with the edge of the rolled piece at the entrance of the edge induction heater EH as the origin and the width direction as the x-axis:

[0026] Zone I: 0 <x<l a ;

[0027] Zone II: l a ≤x <l a +l b ;

[0028] Zone III: l a +l b ≤x≤B / 2.

[0029] Furthermore, according to the method for predicting the cross-section temperature of a rolled piece during the strip rolling process, it is characterized in that a cubic polynomial function is used to fit the temperature function of each region of the cross-section of the rolled piece to obtain the unknown coefficients A and a of each region. 1～5 、b 1～5 、c 1～5 , we can get the cross-section temperature function of the rolled piece:

[0030] T(x)=A+a1f+b1f 2 +c1f 3 +a2I+b2I 2 +c2I 3 +a3H+b3H 2 +c3H 3 +a4v+b4v 2 +c4v 3 +a5x+b5x 2 +c5x 3 .

[0031] Compared with the prior art, the beneficial effects of the above technical solution are as follows:

[0032] 1. The present invention comprehensively considers the initial cross-sectional temperature distribution of the rolled piece at the entrance of the EH, the change of the physical property parameters of the rolled piece material with temperature, and the relative movement of the rolled piece and the EH, and restores the actual situation on site to the greatest extent, and establishes a three-dimensional solid simulation model of the edge induction heating process of the rolled piece during hot rolling.

[0033] 2. The present invention establishes a functional expression between the cross-sectional temperature parameters of the rolled piece and the influencing factors (including product specifications and process parameters). The specific values ​​of any three influencing factors can be given to analyze the influence of another single influencing factor on the cross-sectional temperature parameters of the rolled piece.

[0034] 3. The present invention divides the cross section of the rolled piece into zones, determines the range of each area of ​​the rolled piece according to the temperature parameter function of the cross section of the rolled piece, proposes to use the average temperature in the thickness direction to represent the temperature of each position point in the width direction when extracting the temperature data of the cross section of the rolled piece, further performs nonlinear fitting on the temperature function of the cross section of the rolled piece, accurately predicts the temperature distribution of the cross section of the rolled piece after edge induction heating, and solves the problem of difficulty in measuring the cross section temperature of the rolled piece in the actual production process. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the specific methods in the embodiments of the present invention, the relevant drawings involved in the embodiments will be briefly described below. The following drawings are only preferred embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative changes.

[0036] Figure 1 This is a flow chart of the method for predicting the cross-section temperature of a rolled piece during the plate and strip rolling process of this embodiment;

[0037] Figure 2 A geometric model diagram of the edge induction heating process of the rolled piece in this embodiment;

[0038] Figure 3 This is the cross-sectional area and temperature cloud diagram of the rolled piece in this embodiment;

[0039] Figure 4 This is an example diagram comparing the simulated data of the rolled piece surface temperature in this embodiment with the data of the rolled piece surface temperature actually measured on site;

[0040] Figure 5 This is an example diagram comparing the simulated curve of the cross-section temperature of the rolled piece and the function curve of the cross-section temperature of the rolled piece in this embodiment. DETAILED DESCRIPTION

[0041] In order to facilitate the understanding of the present application, the present application will be described more fully below with reference to the relevant drawings. The preferred embodiments of the present application are given in the drawings. However, the present application can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present application more thoroughly and comprehensively understood.

[0042] The core idea of ​​the present invention is: first determine the modeling parameters of the finite element model of the edge induction heating process of the rolled piece and the value range of each influencing factor affecting the cross-sectional temperature of the rolled piece, including product specifications and process parameters, and then establish and solve the model, and extract the cross-sectional temperature parameter data of the rolled piece according to the numerical simulation results; arrange numerical simulation experiments, repeatedly establish and solve multiple groups of finite element models of the edge induction heating process of the rolled piece, analyze the influence of the various influencing factors on the cross-sectional temperature parameters of the rolled piece, extract multiple groups of cross-sectional temperature parameter data of the rolled piece to fit the cross-sectional temperature parameter function of the rolled piece; substitute the numerical value of each group of influencing factors arranged in the numerical simulation experiment into the cross-sectional temperature parameter function of the rolled piece to determine the cross-sectional partition position of the rolled piece, extract the cross-sectional temperature data of the rolled piece to fit the cross-sectional temperature function of the rolled piece; finally, take the model under a specific influencing factor numerical value as an example to verify the accuracy of the cross-sectional temperature function of the rolled piece.

[0043] Figure 1 Flow chart of the method for predicting the cross-section temperature of a rolled piece during the strip rolling process according to this embodiment. Figure 1 As shown, the method for predicting the cross-section temperature of a rolled piece during a strip rolling process comprises the following steps:

[0044] Step 1: Determine relevant parameters: According to the actual production process, determine the modeling parameters of the finite element model of the edge induction heating process of the rolled piece and the value range of each influencing factor affecting the cross-section temperature of the rolled piece.

[0045] The modeling parameters include the initial length of the rolled piece, the width of the rolled piece, the initial cross-section temperature of the rolled piece before entering the EH, the relative position of the rolled piece and the EH, the air gap between the upper and lower magnetic heads of the EH, the number of turns of the EH coil, and the diameter of the EH coil. The influencing factors include product specification parameters and process parameters, wherein the product specification parameters include the initial thickness H of the rolled piece; the process parameters include the current frequency f of the EH, the excitation current I of the EH, and the running speed v of the rolled piece.

[0046] In this embodiment, the modeling parameters specifically include: the initial length of the rolled piece is 1500mm; the width of the rolled piece is 1140mm; the initial cross-sectional temperature of the rolled piece before entering the EH is given by the temperature meter on the production line, where the edge temperature of the rolled piece is 982℃ and the middle temperature is 1064℃; the relative position of the rolled piece and the EH (expressed by the overlap Lap), Lap is 50mm; the air gap between the upper and lower magnetic heads of the EH is 200mm, the number of coil turns is 20 turns, and the coil diameter is 60mm. The value ranges of the influencing factors include: the range of the initial thickness H of the rolled piece is 30mm to 50mm; the range of the current frequency f of the EH is 100Hz to 900Hz, the range of the excitation current I of the EH is 1500A to 2500A; the range of the running speed v of the rolled piece is 0.6m / s to 1.4m / s.

[0047] Step 2: Establishment of finite element model of edge induction heating process of rolled piece: Based on the relevant parameters determined in step 1, create a 1 / 2 geometric model of edge induction heating process of rolled piece through finite element software, assign material physical property parameters to the geometric model, set boundary conditions, and perform meshing.

[0048] In this embodiment, first, according to the relevant parameters determined in step 1, a 1 / 2 geometric model of the edge induction heating process of the rolled piece is created by COMSOL software. Figure 2 As shown in the figure, combined with the characteristic that EH is symmetrically distributed on both sides of the rolled piece in the actual production process, a 1 / 2 model is used to reduce the calculation time. The model consists of EH including a yoke and a coil and the rolled piece.

[0049] Then, the material physical property parameters are assigned to the EH yoke, the EH coil and the rolled product as shown in Table 1 and Table 2. The material physical property parameters mainly include relative magnetic permeability, resistivity, thermal conductivity and specific heat capacity, among which the material physical property parameters of the rolled product change with temperature.

[0050] Table 1 Physical properties of yoke and coil materials

[0051]

[0052] Table 2 Variation of material physical properties of rolled products with temperature

[0053]

[0054] Then, boundary conditions are applied to the established model: the initial section temperature of the workpiece at the EH entrance is assigned a value, which is given by the temperature meter on the production line described in step 1, that is, 982°C is assigned to the edge of the workpiece and 1064°C is assigned to the middle of the workpiece; the workpiece running speed is given according to the range of 0.6m / s to 1.4m / s and the workpiece is set to move at a uniform speed along the rolling direction; the ambient temperature is set to 25°C; the workpiece surface is set to conduct convection and radiation heat exchange, and the heat transfer coefficient is set to 5W / (m 2 *K), the surface emissivity is 0.7; the width boundary of the rolled piece is set as a symmetric boundary; the initial value condition of the model magnetic field is set to 0, and the excitation current given by the excitation current I of EH in the range of 1500A to 2500A is applied to the cross section of the EH coil as the excitation condition of the eddy current field.

[0055] Finally, the geometric model is meshed: this embodiment uses COMSOL software to mesh the rolled piece: to ensure calculation accuracy, a free triangle mesh is used on the cross section of the rolled piece entrance, and then the cross section mesh is swept and divided into 4 layers of mesh within the skin depth; EH uses a free tetrahedral mesh.

[0056] Step 3: Solve the finite element model of the edge induction heating process of the rolled piece: set the coupling node under multi-physics field coupling, select the solver type, and use the sequential coupling method to solve the transient temperature field.

[0057] In this embodiment, coupling nodes are set under multi-physics field coupling, including electromagnetic heat nodes and temperature coupling nodes. The electromagnetic heat nodes implement the application of induced current as load to the temperature field, and the temperature coupling nodes implement the updating of the physical performance parameters of the rolled material according to the temperature change for the next step of electromagnetic field calculation. This multi-physics field coupling node setting method can achieve bidirectional coupling between the electromagnetic field and the temperature field. When selecting the solver type, this embodiment first selects the coil geometry analysis solver to calculate the induced current in the electromagnetic field, and then uses the frequency-transient solver to set the current frequency and solve the transient temperature field.

[0058] Step 4: Extraction of temperature parameter data of the rolled product section: Extract the strong influence range of induction heating based on the temperature field calculation results. a Data, weak influence range of induction heating b and data of the edge temperature T0 of the rolled piece.

[0059] According to the temperature field calculation results obtained in step 3, it is found that the temperature rise caused by induction heating can rapidly increase the temperature of the rolled piece within a certain distance along the width direction. This distance is defined as the strong influence range of induction heating l a After that, the temperature rise caused by induction heating gradually decreases within a certain distance in the width direction of the rolled piece until the temperature of a certain point within this distance is close to the temperature of the middle part of the rolled piece. This distance is defined as the weak influence range of induction heating l b In addition, the edge temperature T0 of the rolled piece after induction heating can be used to evaluate the induction heating effect. Since the temperature distribution in the thickness direction of the rolled piece is uneven, it is proposed that the edge temperature be replaced by the average temperature in the thickness direction. So far, the cross-sectional temperature parameters of the rolled piece include the strong influence range of induction heating l a 、Weak influence range of induction heating b And the edge temperature T0 of the rolled piece.

[0060] Step 5: Numerical simulation experiment: Use the orthogonal test method to arrange the influencing factors, substitute the specific values ​​of each group of influencing factors into steps 2 to 4, and implement the finite element modeling, solution, and numerical simulation experiment of extracting the cross-section temperature parameters of the rolled piece during the edge induction heating process.

[0061] In order to fully analyze the influence of various influencing factors on the cross-section temperature of rolled pieces, the orthogonal test method was used to select the influencing factors, using 4 factors and 5 levels, and L25 (5 4) The orthogonal test table is shown in Table 3. According to the influencing factors in Table 3, steps 2, 3 and 4 are repeated to establish finite element models of 25 groups of rolled pieces undergoing edge induction heating. Each group of models is solved and the temperature parameter data of the rolled piece section are extracted.

[0062] Table 3 Influencing factors of orthogonal experimental arrangement

[0063]

[0064] Step 6: Study on the law of the temperature parameters of the cross-section of the rolled piece and function fitting: Based on the cross-section temperature parameter data of the rolled piece obtained in step 5, analyze the influence of various influencing factors on the cross-section temperature parameters of the rolled piece, and further fit the cross-section temperature parameter function of the rolled piece.

[0065] Taking the change of EH current frequency as an example, taking the model with EH excitation current of 2500A, initial thickness of rolled piece of 30mm, running speed of rolled piece of 1m / s, and current frequency of 100Hz, 300Hz, 500Hz, 700Hz, and 900Hz as an example, the influence of current frequency change on the cross-sectional temperature parameters of rolled piece is analyzed: With the increase of current frequency, the edge temperature T0 of rolled piece increases rapidly. Due to the enhancement of skin effect, the induction heating strongly affects the range l a And the weak influence range of induction heating b Shortened, the heat source (eddy current loss) moves closer to the edge of the rolled piece.

[0066] In order to obtain the variation trend of the cross-section temperature parameters of the rolled piece under different influencing factors, this embodiment establishes the cross-section temperature parameters of the rolled piece. a , l b , T0. With the current frequency f, excitation current I, initial thickness H of the rolled piece and running speed v of the rolled piece as four input variables, and the output variable being the cross-sectional temperature parameter of the rolled piece, all the cross-sectional temperature parameter data of the rolled piece extracted in step 5 are used to perform nonlinear fitting on the cross-sectional temperature parameter function of the rolled piece, and the undetermined constants of the function expression are obtained;

[0067] The rolled piece section temperature parameter l a , l b The function expressions of T0 are fitted with cubic polynomial functions, and their expressions are as follows:

[0068] y=A+a1f+b1f 2 +c1f 3 +a2I+b2I 2 +c2I 3 +a3H+b3H 2 +c3H 3 +a4v+b4v 2 +c4v 3

[0069] Replace y with the output variable l in sequence a , l b , T0 to obtain the cross-section temperature parameters l of the rolled piece a , l b , T0. The Levenberg-Marquardt optimization algorithm in the Origin software is used to fit and calculate the above-mentioned rolled section temperature parameter function, and the obtained function coefficients are shown in Table 4 (each coefficient retains 4 significant figures):

[0070] Table 4 Undetermined coefficients and goodness of fit of the temperature parameter function of the rolled section

[0071]

[0072] Step 7: Partitioning of the cross section of the rolled piece and fitting of the cross section temperature function of the rolled piece: Substitute the values ​​of the influencing factors in Table 3 into the cross section temperature parameter l obtained in step 6. a and l b The function l is calculated from a and l b , according to l a , l b The cross section of the rolled piece is divided into zones according to the width B of the rolled piece, and the range of each area of ​​the rolled piece cross section is determined. Points are taken at fixed intervals along the width direction within each area, and the temperature of each point is expressed as the average temperature in the thickness direction of the position where the point is located, so as to extract the cross section temperature data of the rolled piece, and the cross section temperature function of the rolled piece is nonlinearly fitted using all the cross section temperature data of the rolled piece, that is, the cross section temperature function T(x) of the rolled piece is obtained;

[0073] Taking the edge of the rolled piece at the entrance of the EH as the origin and the width direction as the x-axis, the rolled piece section is divided into three regions according to the empirical judgment results of the temperature distribution trend of the rolled piece section on site and the finite element numerical simulation results. Figure 3 As shown, B refers to the width of the rolled piece, and the range of each area is as follows (where the temperature at x = 0 mm is calculated by the edge temperature function T0 in step 6):

[0074] Zone I: 0 <x<l a ;

[0075] Zone II: l a ≤x <l a +l b ;

[0076] Zone III: l a +l b ≤x≤B / 2

[0077] Substitute the values ​​of each group of influencing factors in Table 3 into the cross-sectional temperature parameter l obtained in step 6.a , l b The strong influence range of induction heating l can be obtained from the function a And the weak influence range of induction heating b , thereby determining the section partition position of the rolled piece under each group of models. Further, in this embodiment, points are taken every 2 mm along the width direction in each area of ​​the rolled piece, and the temperature of each point is calculated (the temperature of each point is represented by the average temperature in the thickness direction) to obtain the temperature data of each area of ​​the rolled piece section.

[0078] Establish a temperature function of the cross section of the rolled piece, with the current frequency f, the excitation current I, the initial thickness H of the rolled piece, the running speed v of the rolled piece, and the widthwise position x (the edge of the rolled piece is set to x = 0 mm, and the widthwise position x refers to the distance from the edge of the rolled piece) as five input variables, and the output variable is the temperature T at the corresponding position (the temperature at this point is represented by the average temperature in the thickness direction). Use all the cross-section temperature data of the rolled piece to perform nonlinear fitting on the cross-section temperature function of the rolled piece, that is, obtain the cross-section temperature function T(x);

[0079] The cubic polynomial function is used to fit the temperature function of each area of ​​the rolled product section. The cubic polynomial function is as follows:

[0080] y=A+a1f+b1f 2 +c1f 3 +a2I+b2I 2 +c2I 3 +a3H+b3H 2 +c3H 3 +a4v+b4v 2 +c4v 3 +a5x+b5x 2 +c5x 3

[0081] Calculate the unknown coefficients A and a in each area 1～5 、b 1～5 、c 1～5 , we can get the cross-section temperature function T(x) of the rolled piece.

[0082] The calculated temperature function coefficients of each area of ​​the rolled product section are shown in Table 5 (each coefficient retains 4 significant figures):

[0083] Table 5 Undetermined coefficients and goodness of fit of temperature functions in various regions of the rolled section

[0084]

[0085] In summary, the cross-section temperature function T(x) of the rolled piece is obtained.

[0086] The idea of ​​verifying the accuracy of the cross-sectional temperature function of the rolled piece in this embodiment is as follows: since the average temperature in the thickness direction of the rolled piece cannot be measured on site, the cross-sectional temperature function of the rolled piece of the present invention cannot be directly verified. Therefore, the simulated surface temperature of the rolled piece is first compared with the surface temperature of the rolled piece measured on site to verify the accuracy of the model in the present invention. The curve obtained by plotting the average temperature in the thickness direction at each point in the width direction of the rolled piece calculated based on the simulation results is further compared with the cross-sectional temperature function curve of the rolled piece to verify the accuracy of the cross-sectional temperature function of the rolled piece.

[0087] Here, we take the model with EH current frequency f = 300 Hz, excitation current I = 2500 A, initial thickness of rolled piece H = 30 mm, and running speed v = 1 m / s as an example, and substitute the values ​​of f, I, H and v into the l obtained in step 6. a , l b and T0, we can calculate l a =24mm, l b =58mm, edge temperature T0=1031℃, determine the section partition position of the rolled piece under this model, and further substitute the values ​​of f, I, H and v into the section temperature function of the rolled piece obtained in step 7 to obtain the expression of the section temperature of the rolled piece under this model with respect to the widthwise position x:

[0088]

[0089] Substituting the value of x into T(x) will give the temperature value of any point on the width of the rolled piece, which means that the goal of predicting the cross-sectional temperature of the rolled piece has been achieved. To verify the accuracy of the cross-sectional temperature function of the rolled piece, the simulated surface temperature data of the rolled piece under the model is first compared with the field measured surface temperature data of the rolled piece. The results are as follows: Figure 4 As shown in the figure, the temperature deviation of the edge of the rolled piece is 1.0℃, and the temperature deviation of the middle is 3.9℃, which verifies the accuracy of the model. The temperature values ​​of each point in the width direction (average temperature in the thickness direction) calculated based on the simulation results are plotted to obtain a simulation curve. The simulation curve is compared with the temperature function curve of the rolled piece section. The results are shown in Figure 5 As shown, the simulation curve is consistent with the function curve, the maximum temperature deviation between the two is 4.2℃, and the minimum temperature deviation is 0℃, which further verifies the accuracy of the temperature function of the rolled section.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, it should be understood by those skilled in the art that the technical solutions described in the aforementioned embodiments can still be modified, or some or all of the technical features therein can be replaced by equivalents. Therefore, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A method for predicting the cross-section temperature of a rolled piece during a strip rolling process, characterized in that: The method comprises the following steps: Step 1: Determine relevant parameters: According to the actual production process, determine the modeling parameters of the finite element model of the edge induction heating process of the rolled piece and the value range of each influencing factor affecting the cross-section temperature of the rolled piece; Step 2: Establishment of finite element model of edge induction heating process of rolled piece: Based on the relevant parameters determined in step 1, a 1 / 2 geometric model of edge induction heating process of rolled piece is created by finite element analysis software, and material physical property parameters are assigned to the geometric model, boundary conditions are set, and meshing is performed; Step 3: Solve the finite element model of the edge induction heating process of the rolled piece: set coupling nodes under multi-physics field coupling, and solve the transient temperature field by sequential coupling; Step 4: Extraction of temperature parameter data of the rolled product section: Extract the strong influence range of induction heating based on the temperature field calculation results. a Data, weak influence range of induction heating b Data of and data of edge temperature T0 of rolled piece; The temperature rise caused by induction heating can rapidly increase the temperature of the rolled piece within a certain distance along the width direction. This distance is defined as the strong influence range of induction heating. a ; After that, the temperature rise caused by induction heating gradually decreases within a certain distance in the width direction of the rolled piece until the temperature of a certain point within this distance is close to the temperature of the middle part of the rolled piece. This distance is defined as the weak influence range of induction heating l b The edge temperature T0 of the rolled piece after induction heating is used to evaluate the induction heating effect. Since the temperature in the thickness direction of the rolled piece is unevenly distributed, the edge temperature T0 of the rolled piece is replaced by the average temperature in the thickness direction. Step 5: Numerical simulation experiment: Use the orthogonal test method to arrange the influencing factors, substitute the specific values ​​of each group of influencing factors into steps 2 to 4, and implement the finite element modeling, solution, and numerical simulation experiment of extracting the cross-section temperature parameters of the rolled piece during the edge induction heating process; Step 6: Study on the regularity of the temperature parameters of the section of the rolled piece and function fitting: According to the temperature parameter data of the section of the rolled piece obtained in step 5, analyze the influence of various factors on the temperature parameter of the section of the rolled piece. a , l b , T0, and thus the temperature parameter l of the rolled section a , l b , T0 function is fitted; Step 7: Partitioning of the cross section of the rolled piece and fitting of the cross section temperature function of the rolled piece: Substitute the values ​​of the influencing factors arranged by the orthogonal test method in step 5 into the cross section temperature parameter l obtained in step 6. a and l b The function l is calculated from a and l b , according to l a , l b The section of the workpiece is divided into two parts according to the width B of the workpiece, and the range of each area of ​​the section of the workpiece is determined. Points are taken at fixed intervals along the width direction within each area. The temperature of each point is expressed as the average temperature in the thickness direction of the point. The section temperature data of the workpiece is extracted, and the section temperature function of the workpiece is nonlinearly fitted using all the section temperature data of the workpiece to obtain the section temperature function T(x).

2. The method for predicting the cross-section temperature of a rolled piece during a strip rolling process according to claim 1, characterized in that: The modeling parameters include the initial length of the rolled piece, the width of the rolled piece, the initial cross-sectional temperature of the rolled piece before entering the edge induction heater EH, the relative position of the rolled piece and the EH, the air gap between the upper and lower magnetic heads of the EH, the number of turns of the EH coil, and the diameter of the EH coil; The influencing factors include product specification parameters and process parameters; wherein the product specification parameters include the initial thickness H of the rolled piece; and the process parameters include the current frequency f of the edge induction heater EH, the excitation current I of EH and the running speed v of the rolled piece.

3. The method for predicting the cross-section temperature of a rolled piece during a strip rolling process according to claim 2, characterized in that: Assigning material physical property parameters to the geometric model in step 2 refers to assigning material physical property parameters to the yoke and coil of the edge induction heater EH and the rolled product in the geometric model, and the material physical property parameters include relative magnetic permeability, resistivity, thermal conductivity and specific heat capacity.

4. The method for predicting the cross-section temperature of a rolled piece during a strip rolling process according to claim 2, characterized in that: The boundary conditions set in step 2 include: assigning a value to the initial cross-sectional temperature of the workpiece at the entrance of the EH; setting the workpiece running speed according to the value range of the workpiece running speed v and setting the workpiece to move at a uniform speed along the rolling direction; setting the ambient temperature; setting the surface of the workpiece for convection and radiation heat exchange and setting the heat transfer coefficient and surface emissivity; setting the workpiece width boundary to a symmetric boundary; setting the initial value condition of the magnetic field to 0, and applying the excitation current given according to the value range of the excitation current I of the EH to the cross section of the EH coil as an excitation condition for the eddy current field.

5. The method for predicting the cross-section temperature of a rolled piece during a strip rolling process according to claim 3, characterized in that: The coupling nodes set under multi-physical field coupling described in step 3 include electromagnetic thermal nodes and temperature coupling nodes. The electromagnetic thermal nodes implement the application of induced current as a load to the temperature field, and the temperature coupling nodes implement the updating of the material physical performance parameters of the rolled piece according to temperature changes to achieve bidirectional coupling between the electromagnetic field and the temperature field.

6. The method for predicting the cross-section temperature of a rolled piece during a strip rolling process according to claim 2, characterized in that: The orthogonal test method described in step 5 is to arrange the influencing factors by using 4 factors and 5 levels, and select L25 (5 4 )Orthogonal test table to arrange influencing factors.

7. The method for predicting the cross-section temperature of a rolled piece during a strip rolling process according to claim 2, characterized in that: The rolled piece section temperature parameter l a , l b The function expressions of T0 are fitted with cubic polynomial functions, and their expressions are as follows: <h2 style=";text-align:left;direction:ltr">y = A + a1f + b1f<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +c1f<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> +a2I+b2I<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +c2I<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> +a3H+b3H<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +c3H<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> +a4v+b4v<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +c4v<h2 style=";text-align:left;direction:ltr"> 3 Replace y with the output variable l in sequence a , l b , T0 and find the corresponding unknown coefficients A, a 1～4 、b 1～4 、c 1～4 , the cross-section temperature parameters l of the rolled piece can be obtained in turn a , l b , function expression of T0.

8. The method for predicting the cross-section temperature of a rolled piece during a strip rolling process according to claim 7, characterized in that: Taking the edge of the rolled piece where the rolled piece enters the entrance of the edge induction heater EH as the origin and the width direction as the x-axis, the cross section of the rolled piece is divided into the following three areas: Zone I: 0<x<l a ; Zone II: l a ≤x<l a +l b ; Zone III: l a +l b ≤x≤B / 2.

9. The method for predicting the cross-section temperature of a rolled piece during a strip rolling process according to claim 8, characterized in that: Use cubic polynomial function to fit the temperature function of each area of ​​the rolled product section, and calculate the unknown coefficients A and a of each area 1～5 、b 1～5 、c 1～5 , we can get the cross-section temperature function of the rolled piece: T(x)=A+a1f+b1f 2 +c1f 3 +a2I+b2I 2 +c2I 3 +a3H+b3H 2 +c3H 3 +a4v+b4v 2 +c4v 3 +a5x+b5x 2 +c5x 3 。

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