An ac variable frequency self-baking electrode baking state prediction method for ferroalloy ac electric arc furnaces

Abstract

The present application relates to the technical field of self-baking electrode, in particular to a kind of AC frequency conversion self-baking electrode baking state prediction method for ferroalloy submerged arc furnace, including obtaining the input parameter of self-baking electrode, and the electromagnetic field and heat transfer process involved in self-baking electrode are simplified as two-dimensional axisymmetric state;Electromagnetic field mathematical model is constructed, and the expression of the magnetic field intensity and current density of self-baking electrode is obtained;Temperature field mathematical model of submerged arc furnace self-baking electrode and expression of electrode pressure release time are constructed;The electromagnetic field and temperature field mathematical model are discretized using finite volume method, and based on input parameter and electromagnetic thermal boundary condition, implicit solving method with good convergence and stability and large grid size is used to solve the magnetic field intensity, current density, temperature distribution and electrode pressure release time of self-baking electrode.The present application can accurately and quickly predict electrode pressure release time, and effectively reduce the baking control cost of submerged arc furnace self-baking electrode.

Description

Technical Field

[0001] This invention relates to the field of self-baking electrode technology, and more specifically to a method for predicting the baking state of an AC variable frequency self-baking electrode used in a ferroalloy submerged arc furnace. Background Technology

[0002] In the operation system of submerged arc furnaces, self-baking electrodes are core components that directly affect smelting energy consumption, efficiency, and safety. However, due to the interaction of multiple factors such as the electric field, temperature field, and material characteristics within the furnace, their roasting state is difficult to accurately assess. The lack of reliable assessment methods makes it impossible to scientifically control electrode pressing and releasing time on-site, leading to frequent accidents such as soft and hard electrode breakage. This reduces production efficiency and increases equipment maintenance costs and safety risks.

[0003] Currently, many numerical simulations rely on commercial software. Commercial software, through highly optimized numerical solution methods and efficient computational algorithms, can handle complex simulation tasks. However, the computation time for these complex models is typically long, and the licensing fees for commercial software are high, usually charged annually, with costs increasing with usage time. Therefore, writing custom numerical calculation code using programming languages ​​can not only effectively reduce computation time but also significantly save economic costs. Thus, how to effectively achieve rapid online prediction of the roasting state of self-baking electrodes in submerged arc furnaces under different operating conditions to guide the rational pressing and releasing of electrodes is a problem that urgently needs to be solved by those skilled in the art.

[0004] Application CN 116304492A discloses a method for calculating the temperature distribution during the roasting process of a self-baking electrode in a DC submerged arc furnace. The technical solution utilizes the coupling principle of the electromagnetic field and temperature field during the roasting process of the self-baking electrode to establish the electrothermal conversion relationship between various components of the self-baking electrode and the electrode paste, solve the energy equation and Maxwell's equations, and calculate the temperature distribution of the self-baking electrode during roasting. However, this technical solution has the following problems and drawbacks: First, the application assumes that the electrode moves at a uniform speed and has no roasting completion time, but in reality, the electrode is pressed and released approximately once per hour, making it impossible to accurately simulate and calculate the electrode roasting completion time; second, the method for calculating the temperature distribution in this application relies solely on commercial software and cannot be easily implemented through custom programming. Summary of the Invention

[0005] Technical problems to be solved

[0006] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a method for predicting the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces. This method solves the technical problem of frequent electrode soft breakage and hard breakage caused by the lack of a low-cost, short-time, and high-precision technical solution for predicting the baking state of self-baking electrodes in submerged arc furnaces under different operating conditions in actual production.

[0007] Technical solution

[0008] To achieve the above objectives, the main technical solutions adopted by the present invention are as follows:

[0009] This invention provides a method for predicting the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces, comprising:

[0010] Step 1: Obtain the input parameters of the self-baking electrode and simplify the electromagnetic field and heat transfer process involved in the self-baking electrode into a two-dimensional axisymmetric state;

[0011] Step 2: Based on the electromagnetic field changes during the self-baking electrode calcination process, and using Maxwell's equations, an electromagnetic field mathematical model with magnetic field strength as the basic variable is constructed. This model is then applied to a two-dimensional axisymmetric cylindrical coordinate system, yielding the magnetic field univariance equation:

[0012] ;

[0013] In the formula, , For frequency; σ is the magnetic permeability; σ is the electrical conductivity; H θ θ represents the magnetic field strength component in the θ direction;

[0014] Based on the equation of magnetic field singularity, H θ Divided into real part H θR and the imaginary part H θI， The expression for the magnetic field strength H is:

[0015] ;

[0016] In the formula, H θR H θI They are H θ The magnetic field strength of the real and imaginary parts;

[0017] Based on the constructed electromagnetic field mathematical model, the expression for the current density J is obtained as follows:

[0018] ;

[0019] In the formula, E is the electric field strength;

[0020] Step 3: Based on the law of conservation of energy, construct a mathematical model of the temperature field of the self-baking electrode in a submerged arc furnace with temperature as the basic variable, and construct the electrode pressing and releasing time. The expression:

[0021] ;

[0022] In the formula, τ is the electrode pressing and releasing time; t1 is the electrode pressing and releasing end time; t2 is the electrode calcination completion time;

[0023] Step 4: Use the finite volume method to determine the magnetic field strength. Discretize the expression and the mathematical model of the temperature field to obtain a set of nonlinear equations;

[0024] Step 5: Based on the input parameters and preset electromagnetic thermal boundary conditions, solve for the current density using the finite volume method. The expression for the current density of the self-baking electrode is obtained. ;

[0025] Step 6: Adjust the current density Substituting the equations into the nonlinear equation set and solving them, the real-time temperature distribution of the self-baking electrode is obtained. The temperature field of the self-baking electrode is updated by pressure discharge and the electrode pressure discharge time is calculated. The prediction of the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces was completed.

[0026] Furthermore, in the method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace of the present invention, the input parameters of the self-baking electrode in step 1 include: electrode current. Electrode diameter Electrode height copper tile location and height .

[0027] Furthermore, in the method for predicting the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces of the present invention, step 2 specifically comprises:

[0028] Based on the electromagnetic field changes during the calcination of self-baking electrodes, and using Maxwell's equations, an electromagnetic field mathematical model is constructed as follows:

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] In the formula, Permeability; It represents the magnetic flux density; The magnetic field strength; Current density;

[0035] Furthermore, in the method for predicting the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces of the present invention, step 3 specifically comprises:

[0036] Based on the law of conservation of energy, a mathematical model of the temperature field of the self-baking electrode in a submerged arc furnace is constructed as follows:

[0037] ;

[0038] In the formula, Density; Specific heat; Thermal conductivity; The electrode temperature; , , and These are the axial directions of the self-baking electrode. and self-baking electrode radial The real and imaginary current densities;

[0039] Furthermore, in the method for predicting the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces of the present invention, step 4 specifically comprises:

[0040] Step 4.1: Use the finite volume method to determine the magnetic field strength. Discretizing the expression yields:

[0041] ;

[0042] ;

[0043] In the formula, These are the matrix coefficients; For source terms; , , , , Let P, E, W, N, and S be the real parts of the magnetic field strength at nodes P, E, W, N, and S of the confined volume element, respectively. , , , , These are the imaginary parts of the magnetic field strength at nodes P, E, W, N, and S of the confined volume element, respectively. , , , These are the distances from node P of the confined volume element to nodes E, W, N, and S of the confined volume element, respectively. , , , , Let P, E, W, N, and S be the radii of the nodes P, E, W, N, and S of the finite volume element, respectively. and These are the radial and axial dimensions of the finite volume element, respectively; the superscript asterisk indicates that the parameter was obtained from the previous iteration.

[0044] Step 4.2: Discretize the mathematical model of the temperature field using the finite volume method, and obtain:

[0045] ;

[0046] In the formula, Let E be the temperature component along the finite volume control surface E in the nth iteration step; Let W be the temperature component along the direction of the finite volume control surface in the nth iteration. Let N be the temperature component along the N-direction of the finite volume control surface in the nth iteration. Let S be the temperature component along the S direction of the finite volume control surface in the nth iteration step; The temperature is the temperature at the (n+1)th iteration step.

[0047] Furthermore, in the method for predicting the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces of the present invention, the preset electromagnetic thermal boundary conditions in step 5 include:

[0048] The boundary condition expression for the magnetic field strength at the top of the electrode is:

[0049] ;

[0050] In the formula, The radius of the electrode;

[0051] The boundary condition expression for the magnetic field strength on the electrode sidewall above the lower edge of the copper tile is:

[0052] ;

[0053] The boundary condition expression for the magnetic field strength on the electrode sidewall below the lower edge of the copper tile is:

[0054] ;

[0055] The boundary condition expression for the magnetic field strength at the bottom of the electrode is:

[0056] ;

[0057] The expression for the symmetric boundary condition at the electrode axis of symmetry is:

[0058] ;

[0059] The expression for the ambient temperature boundary condition at the top of the electrode is:

[0060] ;

[0061] The expression for the heat flow boundary condition of the electrode sidewall is:

[0062] ;

[0063] In the formula, The convective heat transfer coefficient; The air temperature at the electrode sidewall;

[0064] The expression for the heat flow boundary condition at the bottom of the electrode is:

[0065] .

[0066] Furthermore, in the method for predicting the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces of the present invention, step 5 specifically comprises:

[0067] Step 5.1: Determine the current density using the finite volume method. The component formulas in the directions n, s, e, and w of the finite volume control surface are:

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] The current density is obtained from the component formula. radial of self-baking electrode and self-baking electrode axial direction The directional components are:

[0073] ;

[0074] ;

[0075] Current density and Divided into real part and imaginary part , , and .

[0076] Furthermore, in the method for predicting the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces of the present invention, step 6 specifically comprises:

[0077] Step 6.1: Divide the current density into real and imaginary parts. , , and By substituting the linear equations and solving the nonlinear equations using the Gauss-Seidel iterative method, the real-time temperature distribution of the self-baking electrode can be obtained. ;

[0078] Step 6.2: Update the temperature field of the self-baking electrode according to the following formula, and calculate the electrode discharge time. :

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] In the formula, The electrode temperature distribution after pressure discharge; Electrode height; This refers to the pressure release distance; For ambient temperature, This represents the temperature distribution before compression.

[0085] Furthermore, in the method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace of the present invention, the self-baking electrode is an AC electrode.

[0086] Furthermore, in the method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace of the present invention, the self-baking electrode current... The fluctuation range is 50000A~110000A, and the current frequency is... The range is 0~50Hz.

[0087] Beneficial effects

[0088] The present invention provides a method for predicting the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces, which has the following beneficial effects:

[0089] This invention discretizes the electromagnetic field and temperature field mathematical models of the self-baking electrode in a submerged arc furnace using the finite volume method, solves the discrete equations, obtains the real-time temperature distribution and electrode pressing and releasing time of the self-baking electrode, and calculates the time to complete the click-and-burn process by simulating each pressing and releasing of the electrode. This enables rapid prediction of the baking state of the AC variable frequency self-baking electrode used in ferroalloy submerged arc furnaces. The method of this invention has strong versatility.

[0090] This invention offers high computational efficiency and low cost. Because it discloses the discrete equations for the electromagnetic and temperature fields, those skilled in the art can solve these equations using programming languages ​​such as C or Python. This allows designers to quickly and efficiently evaluate and calculate the calcination state of self-baking electrodes in submerged arc furnaces, achieving highly efficient evaluation of the calcination state and reducing the evaluation cycle to minutes. This method has significant guiding significance and engineering application value for the design, optimization, and performance evaluation of self-baking electrodes in submerged arc furnaces. Attached Figure Description

[0091] Figure 1 A schematic diagram of a rapid online prediction method for the baking state of self-baking electrodes in a submerged arc furnace;

[0092] Figure 2 A schematic diagram of the structure of a self-baking electrode in a submerged arc furnace;

[0093] Figure 3 This is a schematic diagram of a typical control volume in the discrete domain;

[0094] Figure 4 The results show the predicted baking state of the self-baking electrode in a submerged arc furnace.

[0095] Explanation of reference numerals in the attached figures:

[0096] 1: Electrode above the upper edge of the copper tile during the melting stage; 2: Electrode inside the copper tile during the baking stage; 3: Electrode below the lower edge of the copper tile after baking is complete; 4: Copper tile. Detailed Implementation

[0097] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0098] To better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present invention can be understood more clearly and thoroughly, and that the scope of the present invention can be fully conveyed to those skilled in the art.

[0099] This invention provides a method for predicting the baking state of AC variable frequency self-baking electrodes used in ferroalloy submerged arc furnaces, such as... Figure 1 As shown, the specific steps are as follows:

[0100] Step 1: Obtain the input parameters of the self-baking electrode and simplify the electromagnetic field and heat transfer process involved in the self-baking electrode into a two-dimensional axisymmetric state.

[0101] In this invention, the input parameters of the self-baking electrode include the electrode current. Electrode diameter Electrode height copper tile location and height .

[0102] In this invention, the input parameters are set based on the actual operating data and dimensions of the self-baking electrode. Figure 2 The diagram shows the structure of a self-baking electrode in a submerged arc furnace, and the key input parameters are explained. The self-baking electrode in this invention comprises electrode 1, which is in the melting stage above the upper edge of the copper tile; electrode 2, which is in the baking stage inside the copper tile; electrode 3, which is in the baking stage below the lower edge of the copper tile; and copper tile 4. The electrode current, electrode size, and copper tile height affect the distribution of the electrode electromagnetic field and thermal field in subsequent steps.

[0103] Step 2: Based on the electromagnetic field changes during the self-baking electrode calcination process, construct an electromagnetic field mathematical model with magnetic field strength as the basic variable, based on Maxwell's equations, and obtain the magnetic field strength of the self-baking electrode. and current density The expression.

[0104] In industrial applications, the frequency of alternating current is typically 100 Hz. =50Hz. At this frequency, the time scale of electromagnetic field change is much smaller than that of temperature field change. Therefore, the eddy current model can be used to calculate the electromagnetic field in the frequency domain. Ignoring the chemical reaction and phase transition process of the electrode paste, the heat source generated by the Joule effect is determined by the average value of one period. According to Maxwell's equations, the eddy current model can be obtained, as shown in (1)-(5):

[0105] (1)

[0106] (2)

[0107] (3)

[0108] (4)

[0109] (5);

[0110] In the formula, , For frequency; Permeability; Electrical conductivity; It represents the magnetic flux density; Electric field strength; The magnetic field strength; Let be the current density; since the frequency is very low, the electric displacement time derivative term is ignored.

[0111] A single equation for the magnetic field can be derived from Maxwell's equations (1)-(5):

[0112] (6);

[0113] Because the self-baking electrode is cylindrical and axially symmetric, the current density exist No component in direction, magnetic field Only the tangential component exists, i.e.:

[0114] (7)

[0115] (8);

[0116] Applying the constructed electromagnetic field mathematical model to a two-dimensional axisymmetric cylindrical coordinate system, equation (8) simplifies the single equation (6) of the magnetic field to:

[0117] (9);

[0118] Will Divided into real part and the virtual part The magnetic field strength is obtained. The expression is:

[0119] (10).

[0120] Step 3: Based on the law of conservation of energy, construct a mathematical model of the temperature field of the self-baking electrode in a submerged arc furnace with temperature as the basic variable, and construct the electrode pressing and releasing time. The expression;

[0121] The expression for heat transfer in the temperature field is:

[0122] (11);

[0123] In the formula, Density; Specific heat; For speed; Thermal conductivity, As a heat source (Joule heating), electrode temperature Depends on the point and time .

[0124] The self-baking electrode is pressed and released vertically to compensate for bottom wear caused by high temperature and chemical reaction. In actual operation, the electrode is pressed and released approximately every hour, with each release being about 30 mm, and each release taking less than one minute. Therefore, when calculating the temperature field between two releases, the electrode can be approximated as being in a stationary state, i.e., the velocity... =0. Assuming the heat source is the time average of one period of the Joule effect, then the Joule heat... for:

[0125] (12);

[0126] Divide the current density into real parts and the virtual part Calculations are performed using the electromagnetic field expression (1) and equation (6), yielding:

[0127] (13);

[0128] Therefore, the temperature field expression (11) can be simplified to:

[0129] (14);

[0130] In the formula, , , and These are the axial directions of the self-baking electrode. and self-baking electrode radial The real and imaginary current densities.

[0131] Constructing electrode discharge time The expression is:

[0132] (15);

[0133] In the formula, This refers to the electrode discharge time; This refers to the electrode discharge end time; The time for electrode calcination to complete.

[0134] Step 4: Use the finite volume method to determine the magnetic field strength. Discretize the expression and the mathematical model of the temperature field to obtain a system of linear equations.

[0135] Due to nonlinear factors, iterative solutions to the partial differential equations are necessary. The finite volume method is used to obtain the magnetic field intensity and temperature distribution throughout the computational domain. The core of this method is to divide the physical computational domain into non-overlapping control volumes, within which the physical quantities are conserved. For example... Figure 3 As shown, the geometric center of each control volume is the integration point of the discrete domain.

[0136] Equation (10) is discretized using a second-order central difference scheme, and the nonlinear terms are integrated into the source terms. The nonlinear equations for the real and imaginary parts of the magnetic field strength are obtained as follows:

[0137] (16)

[0138] (17)

[0139] In the formula, These are the matrix coefficients; For source terms; , , , , Let P, E, W, N, and S be the real parts of the magnetic field strength at nodes P, E, W, N, and S of the confined volume element, respectively. , , , , These are the imaginary parts of the magnetic field strength at nodes P, E, W, N, and S of the confined volume element, respectively. , , , These are the distances from node P of the confined volume element to nodes E, W, N, and S of the confined volume element, respectively. , , , , Let P, E, W, N, and S be the radii of the nodes P, E, W, N, and S of the finite volume element, respectively. and These are the radial and axial dimensions of the finite volume element, respectively; the superscript asterisk indicates that the parameter was obtained from the previous iteration.

[0140] Discretizing the mathematical model of the temperature field yields the following nonlinear equation for temperature:

[0141] (18)

[0142] In the formula, Let E be the temperature component along the finite volume control surface E in the nth iteration step; Let W be the temperature component along the direction of the finite volume control surface in the nth iteration. Let N be the temperature component along the N-direction of the finite volume control surface in the nth iteration. Let S be the temperature component along the S direction of the finite volume control surface in the nth iteration step; The temperature is the temperature at the (n+1)th iteration step.

[0143] Step 5: Based on the input parameters and preset electromagnetic thermal boundary conditions, solve for the current density using the finite volume method. The expression for the current density of the self-baking electrode is obtained. .

[0144] The preset electromagnetic thermal boundary conditions in the method for predicting the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces of the present invention include:

[0145] First, establish the electromagnetic boundary conditions. The expression for the boundary condition of the magnetic field strength at the top of the electrode is as follows:

[0146] ; (19)

[0147] In the formula, Where is the electrode radius.

[0148] The boundary condition expression for the magnetic field strength on the electrode sidewall above the lower edge of the copper tile is:

[0149] ; (20)

[0150] The boundary condition expression for the magnetic field strength on the electrode sidewall below the lower edge of the copper tile is:

[0151] ; (twenty one)

[0152] The boundary condition expression for the magnetic field strength at the bottom of the electrode is:

[0153] ; (twenty two)

[0154] The expression for the symmetric boundary condition at the electrode axis of symmetry is:

[0155] ; (twenty three)

[0156] Secondly, thermal boundary conditions are established. The expression for the room-temperature boundary condition at the top of the electrode is as follows:

[0157] ; (twenty four)

[0158] The expression for the heat flow boundary condition of the electrode sidewall is:

[0159] ; (25)

[0160] In the formula, The convective heat transfer coefficient; The air temperature at the electrode sidewall;

[0161] The expression for the heat flow boundary condition at the bottom of the electrode is:

[0162] (26).

[0163] Solving the nonlinear equations (16) and (17) using the Gauss-Seidel iterative method yields:

[0164] The formulas for the components of the current density J in the n, s, e, and w directions of the finite volume control surface are as follows:

[0165] (27)

[0166] (28)

[0167] (29)

[0168] (30).

[0169] The current density is obtained from the component formula. radial of self-baking electrode and self-baking electrode axial direction The directional components are:

[0170] (31)

[0171] (32)

[0172] Current density and Divided into real part and imaginary part , , and .

[0173] Step 6: Adjust the current density Substituting the equations into the nonlinear equation set and solving them, the real-time temperature distribution of the self-baking electrode is obtained. The temperature field of the self-baking electrode is updated by pressure discharge and the electrode pressure discharge time is calculated. The prediction of the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces was completed.

[0174] Will , , and Substituting this into the nonlinear equation (18), we obtain the temperature distribution.

[0175] As the baking process progresses, the electrode temperature gradually rises. When the electrode temperature at the lower edge of the copper tile reaches 800℃, it indicates that the electrode paste inside the copper tile has been baked and solidified, at which point the electrode pressing and releasing operation needs to be performed. This process requires updating the electrode temperature field to calculate the baking completion time. The specific operation is as follows: after pressing and releasing, the top height of the electrode is... The electrode paste area is updated to ambient temperature, which is equivalent to adding a height of [missing information] to the top of the electrode cylinder. The room temperature electrode paste; at the same time, the temperature field before pressing, except for the bottom height, is... Outside the designated area, the entire section is shifted downwards. This operation corresponds to the downward shift of the already baked electrode segment, as shown in the following expression:

[0176] (33)

[0177] (34);

[0178] In the formula, The electrode temperature distribution after pressure discharge; Electrode height; This refers to the pressure release distance; For ambient temperature, This represents the temperature distribution before compression.

[0179] The firing completion time is calculated by measuring the temperature at the lower edge of the copper tile, thereby predicting the electrode release time. :

[0180] (35)

[0181] (36)

[0182] (37);

[0183] In practice, the self-baking electrode is an AC electrode, and the self-baking electrode current... The fluctuation range is 50000A~110000A, and the current frequency is... The range is 0~50Hz.

[0184] By substituting the roasting operation parameters of the self-baking electrode of the submerged arc furnace into the formula of the above method, and adjusting the parameters and boundary conditions, the roasting state of the self-baking electrode of the submerged arc furnace can be predicted.

[0185] like Figure 4 As shown, this is an implementation example based on the method proposed in this invention, where the predicted value of the self-baking electrode roasting temperature in the submerged arc furnace is in high agreement with the actual value.

[0186] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0187] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, then this invention should also include these modifications and variations.

[0188] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make modifications, alterations, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for predicting the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces, characterized in that, include: Step 1: Obtain the input parameters of the self-baking electrode and simplify the electromagnetic field and heat transfer process involved in the self-baking electrode into a two-dimensional axisymmetric state; Step 2: Based on the electromagnetic field changes during the self-baking electrode calcination process, and using Maxwell's equations, an electromagnetic field mathematical model with magnetic field strength as the basic variable is constructed. This model is then applied to a two-dimensional axisymmetric cylindrical coordinate system, yielding the magnetic field univariance equation: ； In the formula, , For frequency; σ is the magnetic permeability; σ is the electrical conductivity; H θ θ represents the magnetic field strength component in the θ direction; Based on the equation of magnetic field singularity, H θ Divided into real part H θR and the imaginary part H θI， The expression for the magnetic field strength H is: ； In the formula, H θR H θI They are H θ The magnetic field strength of the real and imaginary parts; Based on the constructed electromagnetic field mathematical model, the expression for the current density J is obtained as follows: ； In the formula, E is the electric field strength; Step 3: Based on the law of conservation of energy, construct a mathematical model of the temperature field of the self-baking electrode in a submerged arc furnace with temperature as the basic variable, and construct the electrode pressing and releasing time. The expression: ； In the formula, τ is the electrode pressing and releasing time; t1 is the electrode pressing and releasing end time; t2 is the electrode calcination completion time; Step 4: Use the finite volume method to determine the magnetic field strength. Discretize the expression and the mathematical model of the temperature field to obtain a set of nonlinear equations; Step 5: Based on the input parameters and preset electromagnetic thermal boundary conditions, solve for the current density using the finite volume method. The expression for the current density of the self-baking electrode is obtained. ; Step 6: Adjust the current density Substituting the equations into the nonlinear equation set and solving them, the real-time temperature distribution of the self-baking electrode is obtained. The temperature field of the self-baking electrode is updated by pressure discharge and the electrode pressure discharge time is calculated. The prediction of the baking state of AC variable frequency self-baking electrodes for ferroalloy submerged arc furnaces was completed.

2. The method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace according to claim 1, characterized in that, The self-baking electrode input parameters in step 1 include: electrode current. Electrode diameter Electrode height copper tile location and height .

3. The method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace according to claim 1, characterized in that, Step 2 specifically involves: Based on the electromagnetic field changes during the calcination of self-baking electrodes, and using Maxwell's equations, an electromagnetic field mathematical model is constructed as follows: ； ； ； ； ； In the formula, Permeability; It represents the magnetic flux density; The magnetic field strength; denoted as current density.

4. The method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace according to claim 1, characterized in that, Step 3 specifically involves: Based on the law of conservation of energy, a mathematical model of the temperature field of the self-baking electrode in a submerged arc furnace is constructed as follows: ； In the formula, Density; Specific heat; Thermal conductivity; For electrode temperature, , , and These are the axial directions of the self-baking electrode. and self-baking electrode radial The real and imaginary current densities.

5. The method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace according to claim 1, characterized in that, Step 4 specifically involves: Step 4.1: Use the finite volume method to determine the magnetic field strength. Discretizing the expression yields: ； ； In the formula, These are the matrix coefficients; For source terms; , , , , Let P, E, W, N, and S be the real parts of the magnetic field strength at nodes P, E, W, N, and S of the finite volume element, respectively. , , , , Let P, E, W, N, and S be the imaginary parts of the magnetic field strength at nodes P, E, W, N, and S of the finite volume element, respectively. , , , , respectively, are the distances from node P of the finite volume element to nodes E, W, N, and S of the finite volume element; , , , , Let P, E, W, N, and S be the radii of the nodes P, E, W, N, and S of the finite volume element, respectively. and These are the radial and axial dimensions of the finite volume element, respectively; the superscript asterisk indicates that the parameter was obtained from the previous iteration. Step 4.2: Discretize the mathematical model of the temperature field using the finite volume method, and obtain: ； In the formula, Let E be the temperature component along the finite volume control surface E in the nth iteration step; Let W be the temperature component along the direction of the finite volume control surface in the nth iteration. Let N be the temperature component along the N-direction of the finite volume control surface in the nth iteration. Let S be the temperature component along the S direction of the finite volume control surface in the nth iteration step; The temperature is the temperature at the (n+1)th iteration step.

6. The method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace according to claim 1, characterized in that, The preset electromagnetic thermal boundary conditions in step 5 include: The boundary condition expression for the magnetic field strength at the top of the electrode is: ； In the formula, The radius of the electrode; The boundary condition expression for the magnetic field strength on the electrode sidewall above the lower edge of the copper tile is: ； The boundary condition expression for the magnetic field strength on the electrode sidewall below the lower edge of the copper tile is: ； The boundary condition expression for the magnetic field strength at the bottom of the electrode is: ； The expression for the symmetric boundary condition at the electrode axis of symmetry is: ； The expression for the ambient temperature boundary condition at the top of the electrode is: ； The expression for the heat flow boundary condition of the electrode sidewall is: ； In the formula, The convective heat transfer coefficient; The air temperature at the electrode sidewall; The expression for the heat flow boundary condition at the bottom of the electrode is: 。 7. The method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace according to claim 1, characterized in that, Step 5 specifically involves: Step 5.1: Determine the current density using the finite volume method. The component formulas in the directions n, s, e, and w of the finite volume control surface are: ； ； ； ； The current density is obtained from the component formula. radial of self-baking electrode and self-baking electrode axial direction The directional components are: ； ； Current density and Divided into real part and imaginary part , , and .

8. The method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace according to claim 1, characterized in that, Step 6 specifically involves: Step 6.1: Divide the current density into real and imaginary parts. , , and By substituting the linear equations and solving the nonlinear equations using the Gauss-Seidel iterative method, the real-time temperature distribution of the self-baking electrode can be obtained. ; Step 6.2: Update the temperature field of the self-baking electrode according to the following formula, and calculate the electrode discharge time. : ； ； ； ； ； In the formula, The electrode temperature distribution after pressure discharge; Electrode height; This refers to the pressure release distance; For ambient temperature, This represents the temperature distribution before compression.

9. The method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace according to claim 1, characterized in that, The self-baking electrode is an AC electrode.

10. The method for predicting the baking state of an AC variable frequency self-baking electrode for a ferroalloy submerged arc furnace according to claim 1, characterized in that, The self-baking electrode current The fluctuation range is 50000A~110000A, and the current frequency is... The range is 0~50Hz.

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