A numerical calculation method for defining electromagnetic stirring zone of continuous casting
By establishing a three-dimensional billet model and coupling multiphysics field calculations, the electromagnetic stirring region is dynamically adjusted, solving the problem of poor adaptability of traditional electromagnetic stirring and achieving efficient improvement of billet quality.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TAIYUAN UNIVERSITY OF SCIENCE AND TECHNOLOGY
- Filing Date
- 2026-05-11
- Publication Date
- 2026-06-05
AI Technical Summary
Existing continuous casting electromagnetic stirring technology cannot dynamically adjust the position, direction and range, and cannot adapt to different steel grades and working conditions, resulting in frequent defects in the quality of the cast billet.
Numerical calculation methods are employed to establish a three-dimensional billet model, coupled with flow, heat transfer, mass transfer, and solidification models, and embed Maxwell's equations to calculate the electromagnetic stirring region in real time, dynamically adjust the position and direction of the stirrer, and achieve multi-physics coupled calculation.
It improves the adaptability and control precision of electromagnetic stirring, reduces center segregation and shrinkage defects in the billet, and enhances the density and quality of the billet.
Smart Images
Figure CN122154361A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of metallurgical continuous casting technology, and in particular to a numerical calculation method for defining the electromagnetic stirring zone in continuous casting. Background Technology
[0002] Continuous casting is a crucial crystallization process in which steel transforms from a liquid to a solid state. Affected by factors such as casting speed, superheat, and secondary cooling water supply during production, the solidification endpoint of the billet continuously changes, which can easily lead to defects.
[0003] Electromagnetic stirring improves billet quality by utilizing the principle of electromagnetic induction: an alternating current passes through the stirrer coil to generate an alternating magnetic field. The molten metal in this magnetic field generates eddy currents due to electromagnetic induction. These eddy currents interact with the magnetic field to produce a Lorentz force, propelling the molten metal forward. Electromagnetic stirring in the crystallizer can refine grains and reduce surface defects; in the secondary cooling zone, it can improve temperature distribution and reduce segregation; and at the end of solidification, it can eliminate central shrinkage cavities and increase billet density.
[0004] However, current electromagnetic stirring in continuous casting faces technical bottlenecks: traditional fixed electromagnetic stirring is difficult to adapt to different steel grades, temperatures, casting speeds, and other working conditions; the position of the solidification front changes dynamically with the water volume; accurately judging the position of the solidification end is the key to the effective functioning of electromagnetic stirring, but during the stable casting process, the position of the solidification end is not fixed due to changes in working conditions, and existing technologies cannot accurately and dynamically control it. Summary of the Invention
[0005] This application provides a numerical calculation method for defining the electromagnetic stirring zone in continuous casting, aiming to solve three core problems in existing electromagnetic stirring technology for continuous casting: First, the position, direction, and range of action of traditional fixed electromagnetic stirring devices are fixed and cannot be dynamically adjusted according to working conditions such as steel grade and casting speed, resulting in poor adaptability to different billets; Second, during continuous casting, the position of the solidification front is continuously changing due to the influence of parameters such as the amount of secondary cooling water and the superheat of molten steel, and existing technologies cannot track its dynamic position in real time, resulting in a mismatch between the stirring effect and the solidification stage; Third, due to insufficient control precision, the incidence of defects such as central segregation and shrinkage cavities in the billet remains high, making it difficult to meet the quality requirements of high-end steel.
[0006] This application provides a numerical calculation method for defining the electromagnetic stirring zone in continuous casting, the method comprising: Step S1: Based on the continuous casting machine parameters and billet cross-sectional dimensions, establish a three-dimensional billet model and couple the flow, heat transfer, mass transfer and solidification models in the same solution domain. Use the finite element method to construct a transient solidification simulation system covering the entire continuous casting process. Step S2: The Maxwell equations are embedded into the transient solidification simulation system as source terms through a user-defined function to establish a quantitative mapping relationship between coil current, frequency and magnetic field strength, so that the alternating magnetic field distribution and the flow-heat transfer-solidification field are coupled in two directions to obtain the multi-physics field distribution results, including temperature field and solidification fractional field, simultaneously. Step S3: Based on the temperature field distribution results, establish a correlation model between solidification rate and molten steel temperature, casting speed and time, calculate the characteristic solidification rate of the billet at different spatial locations in real time, and determine the target stirring zone; Step S4: Using the spatial position of the target stirring area as input, and combining the real-time detected molten steel temperature and casting speed, the optimal position coordinates of the electromagnetic stirrer are dynamically calculated using a spatial vector algorithm. At the same time, the orientation angle of the electromagnetic stirring shaft is dynamically corrected based on the solidified shell thickness distribution of the target stirring area, and its electromagnetic action range is adjusted synchronously to achieve coordinated optimization and control of the electromagnetic stirring position, direction and action range.
[0007] Compared with the prior art, the beneficial effects of the technical solution of this application are at least as follows: 1. Strong dynamic control adaptability: The position, direction and range of electromagnetic stirring can be dynamically adjusted through user-defined functions, which can adapt to different steel grades, casting speeds and other working conditions, and overcome the limitations of traditional fixed stirring.
[0008] 2. Improve the precision of control by coupling multi-physics simulation, accurately calculate the dynamic position of solidification rate, and adjust the stirring position in combination with real-time parameters to cope with the dynamic changes of the solidification front with the amount of water, thereby improving the precision of control.
[0009] 3. Improve billet quality, effectively improve molten steel flow, reduce defects such as center segregation and shrinkage cavities, lower the defect incidence rate, and improve billet density and core quality. Attached Figure Description
[0010] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0011] Figure 1 This is a flowchart of a numerical calculation method for defining the electromagnetic stirring zone in continuous casting, as described in this application. Figure 2 This is a mesh diagram of the solid model in an embodiment of this application; Figure 3 This is a geometric schematic diagram illustrating the algorithm principle of an embodiment of this application; Figure 4 The figure shows the simulation results of the electromagnetic stirring force in an embodiment of this application. Detailed Implementation
[0012] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms “comprising” or “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.
[0013] For ease of understanding, the specific process of the embodiments of this application is described below. Figure 1 The diagram shows a flowchart of a numerical calculation method for defining the electromagnetic stirring zone in continuous casting, provided by the present invention. The flowchart specifically includes the following steps: Step S1: Establish a three-dimensional billet model based on the continuous casting machine parameters and billet cross-sectional dimensions, and couple the flow, heat transfer, mass transfer and solidification models in the same solution domain. Use the finite element method to construct a transient solidification simulation system covering the entire continuous casting process.
[0014] In one specific embodiment, the transient solidification simulation system includes a flow model, a heat transfer model, a mass transfer model, and a solidification model. A dynamic calculation model is established by inputting continuous casting process parameters, including casting speed, molten steel superheat, and secondary cooling water distribution parameters.
[0015] Specifically, to achieve accurate simulation of the solidification behavior in the continuous casting process, a numerical simulation system integrating multiple physics fields needs to be constructed. This method begins by establishing a three-dimensional geometric model of the billet based on the arc radius of the continuous casting machine and the cross-sectional dimensions of the billet. This model constitutes the spatial domain for subsequent physics field calculations. Within this spatial domain, the momentum conservation equation describing the flow of molten steel, the energy conservation equation describing heat transfer, the solute transport equation describing compositional changes, and the solidification kinetics model describing the liquid-solid phase transition are coupled and solved within the same solution framework. This coupling mechanism manifests as the simultaneous iterative calculation of the governing equations of each physics field. Changes in the flow field affect heat transfer efficiency, the evolution of the temperature field directly determines the solidification process, and the advancement of the solidification front, in turn, affects the flow field structure and solute distribution. The finite element method is used to spatially discretize and temporally advance the coupled equations, thus forming a transient simulation system covering the entire continuous casting process from the meniscus to the fully solidified zone. The establishment of this system overcomes the limitations of traditional one-dimensional or two-dimensional models in failing to accurately reflect the three-dimensional spatial effects and transient evolution of the continuous casting process, and provides a computational basis for accurately capturing the internal temperature gradient, flow morphology and solidification structure of the billet.
[0016] In the specific implementation process, taking the continuous casting of 160mm×160mm square billets of 82B high-carbon steel as an example, a three-dimensional calculation model is constructed based on the parameters of a continuous casting machine with a 9-meter arc radius. The simulation system drives multi-physics coupled calculation by inputting process data such as a casting speed of 2.0 m / min, a superheat of 7.5℃, a crystallizer water flow rate of 124 m³ / h, and specific secondary cooling water distribution parameters. These process parameters participate in the solution of the equation system as boundary conditions and source terms. Among them, the casting speed determines the residence time of molten steel in the model, the superheat affects the initial temperature field distribution, and the secondary cooling parameters control the heat flux density on the billet surface. The temperature value, velocity vector, and solid fraction distribution at any spatial location of the billet are obtained through transient solution.
[0017] The multiphysics data output by this simulation system forms a functionally mutually supportive relationship with the dynamic judgment mechanism based on solidification rate in subsequent steps. The solidification fractional field data directly serves as the input condition for determining the electromagnetic stirring zone, while the flow field and temperature field data provide verification basis for evaluating the stirring effect. This interaction between technical features jointly solves the technical problem of the mismatch between traditional electromagnetic stirring due to its fixed position and the dynamically changing solidification front, laying a theoretical foundation for the accurate definition of the stirring zone.
[0018] Step S2: By embedding Maxwell's equations into the transient solidification simulation system as source terms through user-defined functions, a quantitative mapping relationship between coil current, frequency and magnetic field strength is established, enabling bidirectional coupling calculation of alternating magnetic field distribution and flow-heat transfer-solidification field, and simultaneously obtaining multi-physics field distribution results including temperature field and solidification fractional field.
[0019] Specifically, a user-defined function is embedded in the transient solidification simulation system. This function constructs an electromagnetic calculation module based on Maxwell's equations. This module uses coil current and frequency as input parameters and solves for the spatial magnetic field strength distribution using the magnetic vector potential-scalar potential method, thereby establishing a quantitative mapping relationship between current, frequency, and magnetic field strength. In the continuous casting example of 82B steel billet, when the input current is 450A and the frequency is 5Hz, this function calculates the magnetic induction intensity value of each unit node within the billet area in real time.
[0020] The electromagnetic field calculation results are transformed into physical field interaction quantities: induced eddy currents are calculated based on the electromagnetic field distribution, and then the electromagnetic volume force is obtained through the Lorentz force formula. This force is added as a momentum source term to the flow control equation. Simultaneously, the energy generated by Joule heating is calculated and added as a heat source term to the energy conservation equation. This embedding method creates a two-way coupling mechanism between the electromagnetic field and the flow-heat transfer-solidification field: the electromagnetic force drives the molten steel flow, changing the temperature distribution; temperature changes affect the electromagnetic field calculation through feedback from the material conductivity parameter; and the solidification process adjusts the flow resistance and thermophysical properties through changes in solid fraction.
[0021] In the simulation of the continuous casting process, this coupled system simultaneously solves for the electromagnetic field, flow field, and temperature field at each time step. For a 160mm×160mm square billet, under a casting speed of 2.0m / min, the temperature field distribution and solid fraction field evolution along the length of the billet are obtained synchronously through bidirectional coupling calculations. The temperature field data directly reflects the heat transfer efficiency of the secondary cooling zone, and the solid fraction field accurately identifies the position of the solidification front. These multiphysics field distribution results provide a data foundation for the subsequent dynamic determination of the electromagnetic stirring zone.
[0022] In one specific embodiment, in step S2, the Maxwell equations are solved by using a user-defined function and the magnetic vector potential-scalar potential method. The calculated Lorentz force and Joule heat are used as source terms of the momentum equation and energy equation, respectively, and then substituted back into the flow-heat transfer-solidification coupled field for iterative calculation to obtain the multiphysics field distribution results.
[0023] Specifically, a user-defined function is used to achieve deep coupling between electromagnetic fields and multiphysics. This function employs the magnetic vector potential-scalar potential method to numerically solve Maxwell's equations, where coil current and frequency are used as input parameters, and the spatial magnetic field distribution is obtained through finite element discretization.
[0024] Based on the magnetic field distribution results, the algorithm further calculates the induced eddy current density, obtains the Lorentz force density through vector cross product, and adds this force as a momentum source term to the flow control equation. Simultaneously, it calculates the Joule heat production rate based on the current density and electric field strength, adding it as a heat source term to the energy conservation equation. This approach establishes a two-way coupling mechanism between the electromagnetic field and the flow-heat transfer-solidification field. In the simulation calculation of the square billet section, the electromagnetic force drives the molten steel flow, altering the temperature distribution. Temperature changes influence the electromagnetic field calculation through feedback from the material conductivity parameter, and the solidification process adjusts the flow resistance and thermophysical properties through changes in solid fraction.
[0025] The coupled system performs iterative calculations at each time step until the flow field, temperature field, and electromagnetic field converge. This bidirectional coupled calculation simultaneously obtains the temperature field distribution and solid fraction field evolution along the length of the billet. The temperature field data directly reflects the heat transfer efficiency of the secondary cooling zone, and the solid fraction field accurately identifies the solidification front position. These multiphysics field distribution results provide a data foundation for the subsequent dynamic determination of the electromagnetic stirring region.
[0026] This technique solves the technical problem of the disconnect between electromagnetic stirring and solidification process in traditional numerical methods by coupling the electromagnetic field with the thermal flux solid field algorithm. It achieves accurate simulation of the electromagnetic stirring effect in continuous casting and provides a theoretical basis for the dynamic optimization of electromagnetic stirring parameters.
[0027] Step S3: Based on the temperature field distribution results, establish a correlation model between solidification rate and molten steel temperature, casting speed and time, calculate the characteristic solidification rate of the billet at different spatial locations in real time, and determine the target stirring zone.
[0028] In one specific embodiment, the target stirring area is the end area corresponding to the preset solidification rate range, and this area is updated in real time with the amount of secondary cooling water and the superheat of molten steel, with an update frequency of ≥1 Hz.
[0029] Specifically, step S3 establishes a dynamic judgment mechanism for the solidification process of the billet by processing the temperature field data output by the transient solidification simulation system. This step takes the temperature value of the spatial discrete element as input and maps the element temperature to the corresponding solid fraction according to the thermophysical parameters of the steel grade. This solid fraction is defined as the solidification rate of the element. In the continuous casting direction, the thermal history experienced by each point of the billet is jointly determined by the initial superheat of the molten steel, the casting speed, and the heat transfer conditions of the secondary cooling zone. These process parameters indirectly determine the spatial distribution of the solidification rate by affecting the evolution of the temperature field.
[0030] During continuous casting, the temperature field distribution at each calculation step is read. Based on the solidus and liquidus temperature ranges of the steel grade, a linear interpolation method is used to convert the current temperature of the unit into a solids fraction value. By traversing all calculation units of the billet, a spatial distribution map of solidification rate from the crystallizer to the solidification end is constructed in real time. This distribution map accurately identifies the spatial locations of the liquid phase zone, pasty zone, and fully solidified zone in the core of the billet.
[0031] Based on the solidification rate distribution, the system automatically identifies the location of electromagnetic stirring according to preset target stirring zone criteria. Taking electromagnetic stirring at the end of solidification as an example, the target area is set as the spatial range corresponding to 70% to 90% of the solidification rate. The system determines the three-dimensional spatial coordinates of the target stirring area by extracting the set of units that meet this condition. By monitoring the water flow and molten steel superheat parameters in each section of the secondary cooling zone in real time, the system dynamically senses changes in the continuous casting process. When the secondary cooling water flow increases or the molten steel superheat decreases, the billet cooling rate accelerates, the solidification endpoint shifts forward, and the system immediately recalculates the solidification rate distribution and updates the spatial coordinates of the target area. This update process is continuously performed at a frequency of no less than once per second, ensuring that the location of electromagnetic stirring always matches the actual solidification endpoint area when the casting speed fluctuates or the cooling conditions change. This dynamic update mechanism solves the problem of solidification position drift caused by changes in continuous casting process parameters, ensuring that electromagnetic stirring functions effectively within the optimal process window.
[0032] The method based on real-time calculation of solidification rate using temperature field solves the technical problem that the fixed position setting of traditional electromagnetic stirring cannot adapt to the fluctuation of operating conditions in continuous casting process, and provides an accurate spatial positioning benchmark for the dynamic optimization of subsequent electromagnetic stirring parameters.
[0033] In one specific embodiment, the correlation model is the Scheil-Gulliver microsegregation model based on the steel grade thermal analysis curve, local cooling rate, and drawing speed correction, with a solidification rate calculation error ≤3%.
[0034] Specifically, the solidification rate was calculated using a modified Scheil-Gulliver microsegregation model. This model uses the liquidus and solidus temperatures measured by thermal analysis of the steel grade as basic parameters, and dynamically corrects the equilibrium solidification path by introducing local cooling rate and casting speed variables. Based on the real-time temperature and cooling history of the billet's spatial location, the model calculates the changes in solid composition caused by solute redistribution, thereby determining the actual solid fraction corresponding to the current temperature. By coupling the actual heat transfer conditions in the secondary cooling zone with casting speed variations, the model accurately reflects the influence of manganese, silicon, and other element segregation on the solidification temperature range. Verification by comparison with the measured solidified shell thickness showed that the solidification rate calculation error of this model throughout the continuous casting process was controlled within three percent, providing a reliable theoretical basis for the precise positioning of the target stirring zone.
[0035] Step S4: Using the spatial position of the target stirring area as input, and combining the real-time detected molten steel temperature and casting speed, the optimal position coordinates of the electromagnetic stirrer are dynamically calculated using a spatial vector algorithm. At the same time, the orientation angle of the electromagnetic stirring shaft is dynamically corrected based on the solidified shell thickness distribution of the target stirring area, and its electromagnetic action range is adjusted synchronously to achieve coordinated optimization and control of the electromagnetic stirring position, direction and action range.
[0036] Specifically, step S4, based on the spatial coordinate data of the target stirring area and combined with the real-time collected steel temperature and casting speed parameters, dynamically optimizes the electromagnetic stirring parameters using a spatial vector algorithm. This algorithm uses the three-dimensional point cloud data of the target area as the processing object and calculates the geometric center coordinates of the area as the basic positioning reference for the electromagnetic stirrer. For example, in the 82B steel billet continuous casting embodiment, after the system identifies the target area corresponding to a solidification rate of 76%, it calculates the optimal stirring center coordinates (7123.4 mm, 0, 3632.0 mm) using spatial vector calculation, combining the real-time casting speed of 2.0 m / min and the steel temperature data.
[0037] Based on solidified shell thickness distribution data, the surface features of the solidification front are extracted using three-dimensional morphological methods, and the direction of the normal vector at each point on the surface is calculated. The spatial angle between the direction vector of the electromagnetic stirring shaft and the normal vector of the solidification front is calculated, and the spatial orientation of the stirring shaft is dynamically adjusted with the goal of minimizing the angle. Simultaneously, the electromagnetic field of action is dynamically adjusted according to the solidified shell thickness. For example, in the continuous casting process of a 160 mm square billet, the coil current is increased accordingly as the solidified shell thickness increases to maintain an effective electromagnetic penetration depth. This coordinated adjustment mechanism of position, direction, and field of action ensures that the electromagnetic stirring force always acts on the mushy region and propels the molten steel flow in the optimal direction.
[0038] This technology, through the deep integration of spatial vector algorithms and process parameters, solves the technical problem that traditional electromagnetic stirring devices, due to their fixed settings, cannot adapt to the dynamic changes in the continuous casting process. It achieves real-time matching between electromagnetic stirring parameters and the solidification process, providing an effective guarantee for improving the internal quality of the cast billet.
[0039] In one specific embodiment, the electromagnetic stirrer is any one or more combinations of crystallizer electromagnetic stirring (M-EMS), secondary cooling zone electromagnetic stirring (S-EMS), and solidification end electromagnetic stirring (F-EMS), and is adapted to the functional requirements of different stirring types through a dynamic control algorithm.
[0040] Specifically, the electromagnetic stirrer can be configured as an independent or combined form of crystallizer electromagnetic stirring, secondary cooling zone electromagnetic stirring, or solidification end electromagnetic stirring. The dynamic control algorithm automatically invokes the corresponding control strategy by identifying the currently active stirrer type. When the system detects crystallizer electromagnetic stirring activation, the algorithm optimizes the magnetic field parameters to improve initial solidification uniformity; for secondary cooling zone electromagnetic stirring, the algorithm adjusts the core adjustment intensity to improve the transformation of columnar crystals to equiaxed crystals; when solidification end electromagnetic stirring is running, the algorithm dynamically positions the stirring point to eliminate central shrinkage cavities. This algorithm analyzes the process requirements of each stirring type, transforming a uniform solidification rate signal into type-specific control commands, enabling adaptive management of multiple electromagnetic stirring modes by a single control architecture.
[0041] In one specific embodiment, step S4, dynamically calculating the optimal position coordinates of the electromagnetic stirrer using a spatial vector algorithm, includes: Three-dimensional morphology was used to extract the point cloud of the solidification front; The normal vector field is obtained by fitting the local surface of the point cloud at the solidification front. The objective function is to minimize the angle θ between the normal vector and the stirring axis. Combined with the coil ampere-turns constraint, the optimal axial direction vector is solved. The convergence criterion for the iteration is θ≤5°.
[0042] Specifically, the spatial vector algorithm dynamically calculates the optimal position coordinates of the electromagnetic stirrer through the following process: First, based on the solidification fraction field data, a three-dimensional morphological method is used to identify the set of spatial points corresponding to the critical value of the solidification fraction, and a three-dimensional point cloud model of the solidification front is constructed. Local surface fitting is then performed on this point cloud, and the normal vectors of each fitted micro-element are calculated using the spatial coordinates of adjacent points, forming a normal vector field covering the solidification front.
[0043] The algorithm uses the spatial angle θ between the electromagnetic stirring axis direction vector and the solidification front normal vector as the optimization objective, establishing an objective function to minimize this angle. During the solution process, technical constraints such as the coil ampere-turns are considered, and the optimal stirring axis direction vector satisfying these constraints is found through iterative calculation. When the spatial angle θ obtained from the iterative calculation reaches a convergence criterion of less than or equal to 5 degrees, the current stirring axis direction is determined as the optimal solution. Simultaneously, the spatial coordinates of the stirrer are determined based on the geometric characteristics of the solidification front.
[0044] This algorithm combines point cloud processing with vector calculation to transform the geometric features of the solidification front into spatial positioning parameters of the electromagnetic stirrer, ensuring that the electromagnetic force acts on the mushy region at the optimal angle, effectively improving the flow of molten steel.
[0045] In one specific embodiment, step S4, the dynamic correction of the electromagnetic stirring shaft includes: obtaining the solidification front profile through three-dimensional scanning and extracting its normal vector, calculating the angle between the stirring shaft direction vector and the normal vector based on the spatial vector, and adjusting the stirring direction according to the minimum angle criterion to match it with the solidification front.
[0046] Specifically, the dynamic correction of the electromagnetic stirring shaft is achieved through a geometric matching algorithm. This process begins with a three-dimensional scan of the solidification front profile. By acquiring the spatial coordinate point set of the solid fraction isosurface, a digital model of the solidification front is constructed. Based on this three-dimensional point cloud data, the algorithm calculates the normal vector direction of the local surface, forming a normal vector field characterizing the spatial orientation of the solidification front.
[0047] The system performs spatial vector calculations between the current direction vector of the electromagnetic stirring shaft and the normal vector of the solidification front to determine the spatial angle between them. Based on the minimum angle criterion, the algorithm generates a direction adjustment command for the stirring shaft, using rotation to bring the stirring shaft direction closer to the normal vector of the solidification front. This dynamic correction mechanism ensures that the direction of the Lorentz force generated by electromagnetic stirring maintains an optimal orthogonal relationship with the solidification front, enabling the electromagnetic force to act efficiently on the mushy region and drive the molten steel flow along the tangential direction of the solidification front.
[0048] This technology solves the problem of low stirring efficiency caused by mismatched direction in fixed electromagnetic stirring by matching the stirring direction with the geometric characteristics of the solidification front in real time, and significantly improves the control effect of electromagnetic stirring on the solidification process of the billet.
[0049] In one specific embodiment, in step S4, the effective range of the electromagnetic stirring shaft is adaptively adjusted according to the change in the thickness of the solidified shell. Specifically, this is achieved by changing the coil current intensity. The current adjustment amount ΔI is linearly related to the thickness of the solidified shell δ. The calculation formula is: ΔI=k·(δ-δ0), where k is the steel grade sensitivity coefficient and δ0 is the reference shell thickness.
[0050] Specifically, the adaptive adjustment of the electromagnetic stirring range is achieved through linear control of the coil current. Real-time data on the solidified shell thickness distribution of the cast billet is acquired and compared with a preset reference shell thickness. The required current adjustment is calculated based on the linear relationship between the current adjustment and the solidified shell thickness. The steel grade sensitivity coefficient reflects the differences in electromagnetic properties among different steel grades, and the reference shell thickness corresponds to the thickness at which the electromagnetic stirring effect is optimal.
[0051] When the thickness of the solidified shell increases, the coil current intensity is increased proportionally to enhance the magnetic field penetration capability; when the thickness of the solidified shell decreases, the current intensity is reduced accordingly to avoid energy waste and excessive stirring.
[0052] This control mechanism based on the linear relationship between thickness and current allows the electromagnetic stirring range to be automatically adjusted as the solidification process progresses, ensuring that the electromagnetic force effectively acts on the pasty region and maintains a stable stirring intensity, thereby solving the problem of electromagnetic stirring efficiency fluctuations caused by changes in the thickness of the solidified shell.
[0053] In one specific embodiment, a real-time judgment mechanism is used to adapt to the dynamic changes in the solidification front with the amount of secondary cooling water and the superheat of molten steel, thereby achieving dynamic optimization of the electromagnetic stirring position.
[0054] Specifically, the real-time judgment mechanism achieves dynamic adaptation by continuously monitoring the secondary cooling water flow rate and the superheat parameters of the molten steel. When the secondary cooling water flow rate increases, an increase in the cooling rate is detected, and the recalculation process for the solidification front position is immediately initiated. When the superheat of the molten steel increases, the prediction of the solidification initiation point is adjusted according to the temperature compensation model. This mechanism scans for changes in process parameters at a frequency of no less than 1 Hz, and each parameter fluctuation triggers an update of the solidification rate field and a recalibration of the target stirring zone.
[0055] Based on the updated solidification front position, the optimal coordinates of the electromagnetic stirrer are recalculated using a spatial vector algorithm, and the direction and range of the stirring shaft are adjusted simultaneously. This closed-loop control method ensures that the electromagnetic stirring position always maintains spatial consistency with the actual solidification end region, effectively solving the problem of stirring position inaccuracy caused by fluctuations in continuous casting conditions, and realizing full-process adaptive optimization of electromagnetic stirring parameters.
[0056] Taking 82B high carbon steel, an arc-shaped square billet continuous casting machine with a radius of 9 meters, and a square billet cross-section of 160mm×160mm as an example, the technical solution of the present invention will be analyzed and explained.
[0057] The process parameters are: pulling speed 2.0 m / min, superheat 7.5℃, and crystallizer water flow rate 124 m³ / h.
[0058] The electromagnetic stirring parameters are: initial current 450A, frequency 5Hz, and the target stirring area is the end position with a solidification rate of 70% to 80%.
[0059] Execution process: (1) Initialization stage: Using coordinates (0, 0, 9000) as the center of the arc-shaped continuous casting machine, a transient heat transfer solidification model with a radius of 9 meters and a cross-sectional size of 160mm × 160mm is established. The model is imported into ICEM for structured mesh generation, and the mesh model is imported into Fluent software for flow field analysis calculation. Figure 2 As shown.
[0060] (2) Let A (a1, 0, b1) be a point on the billet, and P (x, y, z) be any point in space. Draw a tangent line to the billet model through point A in the XOZ plane, as follows: Figure 3As shown, the equation of the tangent is , Let point B(h, 0, z) be a point on the tangent line, then let... , Draw a perpendicular line from point P to the tangent line, with point N (x2, 0, z2) as the foot of the perpendicular. Find vectors , , , From vector with vector Vertical , Point N lies on line AB. According to the collinearity of vectors, we have... , Solving .
[0061] Substituting K into the equation, we obtain the coordinates of the foot of the perpendicular N: ; ; The length from point A to point N is ; , θ is The angle with the Y-axis.
[0062] , , Distance from point P to the tangent line .
[0063] (3) The code structure and calculation logic of the function are used to calculate the torque source terms about the x-axis, y-axis and z-axis respectively. By obtaining coordinates, calculating intermediate quantities, judging conditions and applying specific formulas, the corresponding torque source term values are calculated and assigned to the corresponding storage locations.
[0064] By defining multiple user-defined functions, the electromagnetic force related to electromagnetic stirring in the continuous casting process is calculated. Through mathematical formulas and conditional judgments, combined with pre-set parameters, the calculation and assignment of these physical quantities are realized to simulate the effect of electromagnetic stirring in the continuous casting process.
[0065] (4) Position calculation: The coordinates of the actual position required for electromagnetic stirring are calculated based on relevant parameters such as molten steel temperature, casting speed and solidification rate. In this example, the unstirred position is selected for the experiment. Stirring position calculation: Based on the position corresponding to 76% solidification rate of 8.06m, the optimal stirring center coordinates are calculated to be (7123.4mm, 0, 3632.0mm).
[0066] (5) Effect Verification: Initialize the parameters, and then manually run the UDF after initialization. After the UDF runs, the result of applying electromagnetic stirring force to the billet position can be viewed in the result cloud diagram. For example Figure 4 As shown.
[0067] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.
Claims
1. A numerical calculation method for defining the electromagnetic stirring zone in continuous casting, characterized in that, The method includes: Step S1: Based on the continuous casting machine parameters and billet cross-sectional dimensions, establish a three-dimensional billet model and couple the flow, heat transfer, mass transfer and solidification models in the same solution domain. Use the finite element method to construct a transient solidification simulation system covering the entire continuous casting process. Step S2: The Maxwell equations are embedded into the transient solidification simulation system as source terms through a user-defined function to establish a quantitative mapping relationship between coil current, frequency and magnetic field strength, so that the alternating magnetic field distribution and the flow-heat transfer-solidification field are coupled in two directions to obtain the multi-physics field distribution results, including temperature field and solidification fractional field, simultaneously. Step S3: Based on the temperature field distribution results, establish a correlation model between solidification rate and molten steel temperature, casting speed and time, calculate the characteristic solidification rate of the billet at different spatial locations in real time, and determine the target stirring zone; Step S4: Using the spatial position of the target stirring area as input, and combining the real-time detected molten steel temperature and casting speed, the optimal position coordinates of the electromagnetic stirrer are dynamically calculated using a spatial vector algorithm. At the same time, the orientation angle of the electromagnetic stirring shaft is dynamically corrected based on the solidified shell thickness distribution of the target stirring area, and its electromagnetic action range is adjusted synchronously to achieve coordinated optimization and control of the electromagnetic stirring position, direction and action range.
2. The method according to claim 1, characterized in that, The transient solidification simulation system includes a flow model, a heat transfer model, a mass transfer model, and a solidification model. A dynamic calculation model is established by inputting continuous casting process parameters, including casting speed, molten steel superheat, and secondary cooling water distribution parameters.
3. The method according to claim 1, characterized in that, In step S2, the Maxwell equations are solved by using a user-defined function and the magnetic vector potential-scalar potential method. The calculated Lorentz force and Joule heat are used as source terms of the momentum equation and energy equation, respectively, and then substituted back into the flow-heat transfer-solidification coupled field for iterative calculation to obtain the multiphysics field distribution results.
4. The method according to claim 1, characterized in that, The correlation model is the Scheil-Gulliver microsegregation model based on the steel grade thermal analysis curve, local cooling rate, and drawing speed correction, with a solidification rate calculation error of ≤3%.
5. The method according to claim 1, characterized in that, The target stirring area is the end area corresponding to the preset solidification rate range, and this area is updated in real time with the amount of secondary cooling water and the superheat of molten steel, with an update frequency of ≥1 Hz.
6. The method according to claim 1, characterized in that, The electromagnetic stirrer can be any one or more combinations of crystallizer electromagnetic stirring, secondary cooling zone electromagnetic stirring, and solidification end electromagnetic stirring, and can be adapted to the needs of different stirring types through dynamic control algorithms.
7. The method according to claim 1, characterized in that, In step S4, the dynamic calculation of the optimal position coordinates of the electromagnetic stirrer using a space vector algorithm includes: Three-dimensional morphology was used to extract the point cloud of the solidification front; The normal vector field is obtained by fitting the local surface of the point cloud at the solidification front. The objective function is to minimize the angle θ between the normal vector and the stirring axis. Combined with the coil ampere-turns constraint, the optimal axial direction vector is solved. The convergence criterion for iteration is θ≤5°.
8. The method according to claim 1, characterized in that, In step S4, the dynamic correction of the electromagnetic stirring shaft includes: obtaining the solidification front contour through three-dimensional scanning and extracting its normal vector, calculating the angle between the stirring shaft direction vector and the normal vector based on the spatial vector, and adjusting the stirring direction according to the minimum angle criterion to match it with the solidification front.
9. The method according to claim 1, characterized in that, In step S4, the range of action of the electromagnetic stirring shaft is adaptively adjusted according to the change of the solidified shell thickness. Specifically, this is achieved by changing the coil current intensity. The current adjustment amount ΔI is linearly related to the solidified shell thickness δ. The calculation formula is: ΔI=k·(δ-δ0), where k is the steel grade sensitivity coefficient and δ0 is the reference shell thickness.
10. The method according to claim 1, characterized in that, By adapting to the dynamic changes in the solidification front with the amount of secondary cooling water and the superheat of molten steel through a real-time judgment mechanism, the position of the electromagnetic stirring is dynamically optimized.