A Computer Simulation Method for Continuous Casting Process

Abstract

This invention discloses a computer simulation method for a continuous casting process. The initial conditions for the metal are set as the initial temperature of the metal when molten metal is injected into the mold, and the initial conditions for the mold are the temperature at the metal inlet. The three-dimensional model of the metal and the mold is evenly divided into several segments. After setting the corresponding temperature boundary conditions for each segment of the metal and the mold, it is not necessary to perform flow filling simulation analysis as in general casting processes. Instead, numerical simulation of cooling and solidification can be used to obtain the temperature distribution of the metal and the mold and the microstructure evolution process of the metal at any time.

Description

Technical Field

[0001] This invention relates to the technical field of continuous casting, and more particularly to a computer simulation method for a continuous casting process. Background Technology

[0002] Casting is a metal processing method in which solid metal is melted into a liquid state and poured into a mold cavity of a specific shape and size under pressure or gravity. After cooling and solidification, a part or blank is obtained. Casting has a wide range of applications in manufacturing. Computer simulation of the casting process uses numerical techniques to simulate the pouring, filling, and solidification process of castings in the mold cavity. It obtains the flow and filling of molten metal in the cavity, as well as the temperature changes of the casting and the mold. It predicts the solidification structure and mechanical properties of the casting, and obtains the quantitative relationship between the main process parameters and the solidification structure of the casting, thus providing a theoretical basis for optimizing the casting process and achieving optimal quality control. Conventional casting is an intermittent process. Its computer simulation process involves: 1. Establishing numerical models of the casting parts and molds; 2. Setting initial and boundary conditions for the molten metal and molds during casting; 3. Performing numerical simulation calculations of the molten metal flow and filling within the mold cavity, obtaining information on flow, filling, and temperature changes at different times; 4. Performing numerical simulation calculations of the casting and mold temperatures, as well as the solidification of the casting, obtaining information on temperature changes, solidification, and microstructure changes at different times; 5. Analyzing the process characteristics of casting based on the flow, filling, temperature changes, solidification process, and microstructure changes at different times.

[0003] Continuous metal casting involves pouring molten metal into a mold cavity from one end of a crystallizer, allowing it to solidify gradually, and then continuously pulling it out from the other end. This process can produce castings of arbitrary length or with a fixed cross-section, such as... Figure 2 As shown.

[0004] The continuous casting process differs significantly from conventional casting in terms of molten metal flow and solidification, and the relationship between the casting and the mold. In continuous casting, the molten metal exhibits minimal flow relative to the mold in the crystallizer, but it moves synchronously with the mold to the next location, gradually cooling and solidifying until it finally exits the mold. At any given moment, the spatial distribution of various parameters, such as temperature, in the corresponding regions of the crystallizer is almost identical for both the casting and the mold. Conventional computer simulation methods for casting cannot accurately simulate the continuous casting process to obtain the details of the casting's flow, filling, temperature changes, solidification process, and microstructure changes at different times.

[0005] Furthermore, in the process of computer simulation of continuous metal casting, if a small section of metal in the crystallizer is taken as the object for numerical simulation analysis, it is difficult to handle the thermal conductivity relationship and temperature boundary conditions between the part of the analysis object and the metal before and after it because the metal is constantly moving and the temperature conditions are changing from the inlet to the outlet. If the entire section of metal in the crystallizer is taken as the object for numerical analysis, it is difficult to apply temperature boundary conditions because the metal is constantly moving, with new metal flowing in at the inlet and metal being pulled out at the outlet, and the temperature conditions are different at different locations when the metal is moving. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a computer simulation method for a continuous casting process.

[0007] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0008] A computer simulation method for a continuous casting process includes:

[0009] Establish three-dimensional models of the metal and molds for analysis of the continuous casting process;

[0010] Input the thermal properties of the metal and the mold, and the material parameters for the solidification structure evolution;

[0011] Set the initial conditions for the metal and the mold;

[0012] The three-dimensional model of the metal and mold is divided into several segments evenly.

[0013] The computer simulation analysis time of the metal continuous casting process is divided into several identical segments accordingly;

[0014] Input the corresponding temperature boundary conditions for the metal and mold for each time period and each segment of the model region;

[0015] By combining the input thermal performance parameters of the metal and the mold with the material parameters of solidification evolution, numerical calculations are performed on the heat conduction process of the metal and the mold and the solidification process of the metal, so as to obtain the temperature distribution of the metal and the mold and the microstructure evolution process of the metal at any time.

[0016] Furthermore, the initial conditions for the metal are set as the initial temperature of the metal when molten metal is injected into the mold;

[0017] The initial conditions for the mold are set as the temperature at the metal inlet of the mold.

[0018] Furthermore, based on the required analytical accuracy, the established three-dimensional models of the metal and mold are evenly divided into several segments, and then the segmented models are meshed using surface mesh and volume mesh finite element methods.

[0019] Furthermore, based on the required analytical precision, the computer simulation analysis time for the metal continuous casting process is divided into several segments identical to those in the model.

[0020] Furthermore, suppose the established three-dimensional model of the metal and the mold is uniformly divided into M segments, and the time of computer simulation analysis is also divided into M segments. The i-th segment of the metal and mold is set with temperature boundary conditions from the first time period to the i-th time period. The first time period to the (i-1)-th time period is the same as the (i-1)-th segment. There are no restrictions on whether the boundary conditions of different time periods of each segment are the same. The (i+1)-M-th time period is set as adiabatic boundary conditions.

[0021] Furthermore, the thermal properties of metals include thermal conductivity, density, enthalpy, solid fraction, Newtonian viscosity, and Poisson's ratio.

[0022] Furthermore, the material parameters for the solidification evolution of metals include dendrite tip growth kinetics coefficients and nucleation parameters;

[0023] Dendrite tip growth kinetic coefficient a 2 and a 3 All of these are determined by the initial composition of the metal, the slope of the liquidus, the solute equilibrium partition coefficient, the solute self-diffusion coefficient, and the Gibbs-Thomson coefficient.

[0024] Furthermore, the required dendrite tip growth kinetic coefficient a 2 and a 3 The initial composition of the metal, the slope of the liquidus, the solute equilibrium partition coefficient, and the solute self-diffusion coefficient were all calculated using the Scheil diffusion model, and the Gibbs-Thomson coefficient was a constant set based on experimental experience.

[0025] Furthermore, the nucleation parameters include surface nucleation parameters and volume nucleation parameters, both of which include the mean undercooling of nucleation, standard deviation, and nucleation density;

[0026] The surface kernel parameters and the volume kernel parameters are related as follows:

[0027]

[0028] N v For the body shape kernel parameter, N S These are the kernel parameters for the surface shape.

[0029] Furthermore, when performing numerical calculations on the heat conduction process of metal and mold and the solidification process of metal, the temperature field of metal solidification in the model is first calculated, and then it is divided into fine and uniform nodes. Nucleation and growth calculations are performed using the cellular automata method.

[0030] The model is obtained by coupling the cellular automata method with the finite element method.

[0031] Compared with existing technologies, the principles and advantages of this technical solution are as follows:

[0032] The initial conditions for the metal in this technical solution are the initial temperature of the metal when the molten metal is injected into the mold, and the initial conditions for the mold are the temperature of the mold at the metal inlet. The three-dimensional model of the metal and the mold is evenly divided into several segments. After setting the corresponding temperature boundary conditions for each segment of the metal and the mold, it is not necessary to perform flow filling simulation analysis like in general casting processes. It is only necessary to directly perform numerical simulation of cooling and solidification to obtain the temperature distribution of the metal and the mold and the microstructure evolution process of the metal at any time. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the services required in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a flowchart illustrating the principle of a computer simulation method for a continuous casting process according to the present invention.

[0035] Figure 2 This is a schematic diagram of the continuous casting process for metals.

[0036] Figure 3 This is a schematic diagram of a three-dimensional model of continuously cast metal.

[0037] Figure 4 This is a graph showing the relationship between the thermal properties of pure copper and temperature.

[0038] Figure 5 This is a schematic diagram of the segmentation of continuously cast metal.

[0039] Figure 6 This is the temperature boundary condition curve for segment 50.

[0040] Figure 7 This is a schematic diagram of temperature field distribution and grain structure distribution (temperature field distribution is on the left, and grain structure distribution is on the right);

[0041] Figure 8 The diagram shows the temperature field distribution, solid-liquid field distribution, and grain structure field distribution of different metal sections at various time periods (temperature field distribution on the left, solid-liquid field distribution in the middle, and grain structure field distribution on the right). Detailed Implementation

[0042] The present invention will be further described below with reference to specific embodiments:

[0043] like Figure 1 As shown in this embodiment, a computer simulation method for a continuous casting process includes:

[0044] S1. Establish a three-dimensional model of the metal and mold for analysis of the continuous casting process;

[0045] according to Figure 2 A simplified diagram illustrating the continuous casting process of metal, and the construction of a 3D CAD model of the continuously cast metal, such as... Figure 3 The three-dimensional CAD model of the continuously cast metal is shown. Its specific parameters are shown in Table 1.

[0046] Table 1 Specific parameters of the 3D CAD model

[0047]

[0048] S2, Input the thermal performance parameters of the metal and mold, and the material parameters for the solidification structure evolution;

[0049] (1) Thermal performance parameters

[0050] Accurate thermal performance parameters are crucial for achieving high-quality simulations. A comprehensive thermodynamic database allows for the automatic calculation of curves for key parameters such as thermal conductivity, density, enthalpy, solid fraction, Newtonian viscosity, and Poisson's ratio based on user-input chemical composition. This data is automatically saved for later use during the simulation. Furthermore, if more accurate data becomes available, these automatically calculated results can be manually adjusted to ensure the accuracy of the simulation. The various thermal performance parameters of metallic copper obtained from the thermodynamic database are as follows: Figure 4 As shown.

[0051] (2) Material parameters of solidification evolution

[0052] The microstructure of metals is simulated, and the simulation parameters are mainly the dendrite tip growth kinetic coefficient and nucleation parameters.

[0053] (a) Dendrite tip growth kinetic coefficient

[0054] The dendrite tip growth kinetics coefficient influences the dendrite growth behavior at the solidification front, including growth rate and direction. This coefficient is jointly determined by the initial metal composition (C0), liquidus slope (m), solute equilibrium partition coefficient (k), solute self-diffusion coefficient (Dl), and the Gibbs-Thomson coefficient. The Gibbs-Thomson coefficient relates to the solid-liquid interface energy and grain size, and has a significant regulatory effect on the curvature and growth kinetics of the dendrite tip, thus determining the dendrite growth kinetics coefficient α during solidification simulation. 2 and a 3In simulations, these coefficients are typically determined using experimental data or theoretical models (such as the Kurz-Giovanola-Trivedi (KGT) model). The Gibbs-Thomson coefficients are difficult to obtain experimentally. Based on experimental experience, this parameter is set to 2 x 10⁻⁶. -7 .

[0055] The required dendrite growth kinetic coefficient α can be calculated using the Scheil diffusion model. 2 =2.805561×10 -8 and a 3 =4.717442×10 -6 And the initial composition of the metal (C0), the slope of the liquidus (m), the solute equilibrium partition coefficient (k), the solute self-diffusion coefficient (Dl), etc.

[0056] (b) Nucleation parameters

[0057] According to the cellular automata (CA) model, nucleation parameters are divided into surface nucleation parameters and volume nucleation parameters. Both of these parameters include the mean supercooling of nucleation, standard deviation, and nucleation density.

[0058] In actual solidification simulations, these parameters need to be precisely determined through experimental data or theoretical calculations so that the simulation results can accurately reflect the solidification behavior of the alloy under actual production conditions. There is a relationship between surface nucleation parameters and volume nucleation parameters:

[0059]

[0060] In the experimental design below, the surface nucleation density N is taken as... s,max =1.5x10 7 Then the body shape and nuclear density are taken as N. v,max =1.5x10 8 Take the average undercooling ΔT of the surface nucleation. s,max =1K, mean supercooling of the bulk core ΔT v,max =3, the standard deviation ΔT of the surface kernel and the volume kernel s,σ ΔT v,σ Both are 0.5K, used for simulation calculations.

[0061] Table 2 Microscopic Simulation Parameters

[0062]

[0063] S3, Set the initial conditions for the metal and the mold;

[0064] In this step,

[0065] The initial conditions for the metal were set at an initial temperature of 1120°C when the molten metal was poured into the mold. This temperature is higher than the melting point of pure copper (1083.4°C), ensuring that the copper is completely liquid while providing sufficient superheat to optimize the casting process. Superheating helps reduce the oxide and gas content in the molten metal, improves fluidity, which in turn facilitates filling the mold cavity and reduces turbulence and oxidation during the filling process, thereby improving the overall quality of the casting and reducing casting defects.

[0066] The initial conditions for the mold are set at a temperature of 300°C at the metal inlet. This temperature is below the melting point of copper. This temperature difference helps to create a suitable temperature gradient, ensuring that the molten metal cools rapidly upon entering the mold and begins the solidification process. It also avoids cold shuts caused by rapid cooling of the molten metal. This facilitates the rapid formation of a solidified shell, which helps to control the dimensions of the casting and reduce deformation. It also allows for the formation of a fine-grained structure on the casting surface, thereby improving the mechanical properties of the casting.

[0067] S4. Divide the established 3D model of the metal and mold into 100 segments. Then, perform finite element meshing (FEM) on the 100 segments using surface and volume meshes. Meshing is a crucial step in the preprocessing of finite element analysis, as the quality of the mesh directly determines the quality of the subsequent finite element calculations. To obtain more accurate results, the overall geometric model is meshed relatively densely. The mesh size is set to 4mm, the number of mesh nodes is 182,945, the number of surface meshes is 38,536, and the number of volume meshes is 144,409. The meshing results are shown below. Figure 5 As shown.

[0068] S5. Based on the required analytical accuracy, the computer simulation analysis time for the metal continuous casting process is divided into several segments identical to those in the model.

[0069] S6. Input the corresponding temperature boundary conditions for the metal and mold for each time period and each segment of the model area;

[0070] Since the established three-dimensional model of the metal and mold is uniformly divided into 100 segments, the computer simulation analysis time is also divided into 100 segments. The i-th segment of the metal and mold is set with temperature boundary conditions from the first time period to the i-th time period. The first time period to the (i-1)-th time period is the same as the (i-1)-th segment. There are no restrictions on whether the boundary conditions of different time periods in each segment are the same. The (i+1)-100th time period is set as adiabatic boundary conditions.

[0071] Heat transfer parameters need to be set between the metal and the mold, and between the mold and the water-cooled area. Referring to casting handbooks, the recommended value for the heat transfer coefficient h at the metal-to-metal interface is 1000–5000. Under natural convection or low-speed forced convection conditions during water cooling, the heat transfer coefficient may be 800–6000 W / (m²).2 ·K) Through production verification and numerical simulation, the heat transfer coefficient of copper is found to be 1000-3000. The heat transfer coefficient between the metal and the mold, and the heat transfer coefficient of the mold water cooling is selected as h = 1300.

[0072] The metal and mold were divided into 100 segments, and the total analysis time was also divided into 100 segments. The total duration of the temperature field simulation was 24.3 s, and the crystallization time was 25 s. Temperature boundary conditions were set for the first segment of the metal and mold, based on the first time period, while adiabatic boundary conditions were set for segments 2 to 100. Temperature boundary conditions were set for the i-th segment of the metal and mold, from segment 1 to the i-th time period, while adiabatic boundary conditions were set for segments i+1 to 100. Temperature boundary conditions were set for the 100th segment of the metal and mold, based on the first to 100th time periods.

[0073] For example, the temperature boundary conditions for the 50th region of the metal and mold, from the 1st time segment to the 50th time segment, are set with a boundary heat transfer of 1300 W / (m²). 2 ·K), adiabatic boundary conditions were set from time 51 to time 100. That is, heat exchange occurs from 0 to 12.15s in the 50th segment, and the state is adiabatic from 12.18 to 25s.

[0074] Similarly, set corresponding temperature boundary conditions for each segment. There are no restrictions on whether the boundary conditions for each segment are the same; they can be the same or different. The temperature boundary condition curve for segment 50 is shown below. Figure 6 As shown.

[0075] S6. Combining the input thermal performance parameters of the metal and mold with the material parameters of solidification evolution, numerical calculations are performed on the heat conduction process of the metal and mold and the solidification process of the metal to obtain the temperature distribution of the metal and mold and the microstructure evolution process of the metal at any time.

[0076] In this step, after all the parameters required for numerical simulation are prepared, the simulation calculation can be carried out. First, the temperature field of metal solidification in the model is calculated, and then it is divided into fine and uniform nodes. Nucleation and growth calculations are performed using the cellular automata method.

[0077] The CAFE method is used here to simulate the grain structure. The CAFE model is a model established by coupling the cellular automata method (CA) and the finite element method (FE). Its main function is to simulate the growth of copper grain structure and can clearly show the growth state of the grains, reflecting the process of high-temperature copper liquid solidifying into copper layers.

[0078] By opening the file obtained after numerical calculation, you can observe the changes in the temperature field, solidification field, and simulated growth of micrograins in the metal over time. Switching between different views allows you to observe specific changes.

[0079] The temperature field distribution and grain structure distribution calculated under steady state are as follows: Figure 7 As shown in the figure, as the horizontal continuous casting proceeds, the temperature of the copper billet gradually decreases from the head to the tail of the crystallizer under cooling, completing the solidification process of copper-clad steel. The figure also shows that during solidification, a certain thickness of copper microstructure has formed on the outer surface of the front section of the mold. As time progresses, under water cooling, the amount of copper microstructure in the rear section increases dramatically, and the entire rear section solidifies.

[0080] By slicing, one can observe schematic diagrams of temperature field distribution, solid-liquid field distribution, and grain structure field distribution in different metal sections at various time periods, such as... Figure 8 As shown.

[0081] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Therefore, any changes made in accordance with the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A computer simulation method for a continuous casting process, characterized in that, include: Establish three-dimensional models of the metal and molds for analysis of the continuous casting process; Input the thermal properties of the metal and the mold, and the material parameters for the solidification structure evolution; Set the initial conditions for the metal and the mold; The three-dimensional model of the metal and mold is divided into several segments evenly. The computer simulation analysis time of the metal continuous casting process is divided into several identical segments accordingly; Input the corresponding temperature boundary conditions for the metal and mold for each time period and each segment of the model region; By combining the input thermal performance parameters of the metal and the mold with the material parameters of solidification evolution, numerical calculations are performed on the heat conduction process of the metal and the mold and the solidification process of the metal, so as to obtain the temperature distribution of the metal and the mold and the microstructure evolution process of the metal at any time.

2. The computer simulation method for a continuous casting process according to claim 1, characterized in that, The initial conditions for the metal are set as the initial temperature of the metal when molten metal is injected into the mold; The initial conditions for the mold are set as the temperature at the metal inlet of the mold.

3. The computer simulation method for a continuous casting process according to claim 1, characterized in that, Based on the required analytical accuracy, the established three-dimensional models of the metal and mold are evenly divided into several segments, and then the segmented models are meshed using surface mesh and volume mesh finite element methods.

4. The computer simulation method for a continuous casting process according to claim 1, characterized in that, Based on the required analytical accuracy, the computer simulation analysis time for the metal continuous casting process is divided into several segments identical to those in the model.

5. The computer simulation method for a continuous casting process according to claim 1, characterized in that, Suppose that the established three-dimensional model of the metal and the mold is uniformly divided into M segments, and the time of computer simulation analysis is also divided into M segments. The i-th segment of the metal and mold is set with temperature boundary conditions from the first time period to the i-th time period. The first time period to the (i-1)-th time period is the same as the (i-1)-th segment. There are no restrictions on whether the boundary conditions of different time periods of each segment are the same. The (i+1)-M-th time period is set as adiabatic boundary conditions.

6. The computer simulation method for a continuous casting process according to claim 1, characterized in that, The thermal properties of metals include thermal conductivity, density, enthalpy, solid fraction, Newtonian viscosity, and Poisson's ratio.

7. The computer simulation method for a continuous casting process according to claim 1, characterized in that, Material parameters for the solidification evolution of metals include dendrite tip growth kinetics coefficients and nucleation parameters; Dendrite tip growth kinetic coefficient a 2 and a 3 All of these are determined by the initial composition of the metal, the slope of the liquidus, the solute equilibrium partition coefficient, the solute self-diffusion coefficient, and the Gibbs-Thomson coefficient.

8. The computer simulation method for a continuous casting process according to claim 6, characterized in that, Required dendrite tip growth kinetic coefficient a 2 and a 3 The initial composition of the metal, the slope of the liquidus, the solute equilibrium partition coefficient, and the solute self-diffusion coefficient were all calculated using the Scheil diffusion model, and the Gibbs-Thomson coefficient was a constant set based on experimental experience.

9. The computer simulation method for a continuous casting process according to claim 6, characterized in that, Nucleation parameters include surface nucleation parameters and volume nucleation parameters, both of which include mean undercooling, standard deviation, and nucleation density. The surface kernel parameters and the volume kernel parameters are related as follows: N v For the body shape kernel parameters, N S These are the surface kernel parameters.

10. The computer simulation method for a continuous casting process according to claim 1, characterized in that, When performing numerical calculations on the heat conduction process of metals and molds and the solidification process of metals, the temperature field of metal solidification in the model is first calculated, and then it is divided into fine and uniform nodes. Nucleation and growth calculations are performed using the cellular automata method. The model is obtained by coupling the cellular automata method with the finite element method.

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