Quantitative evaluation method of non-uniformity distribution in continuous casting mold process

Abstract

This invention provides a quantitative evaluation method for the non-uniform distribution of continuous casting crystallizer processes, belonging to the field of continuous casting technology in iron and steel metallurgy. First, the data is preprocessed, and the constructed Lorentz curve exhibits common and two extreme forms due to its distribution characteristics, corresponding to normal, absolutely average, and absolutely non-uniform temperature distributions, respectively. Besides the common form, the two extreme forms are only theoretical possibilities. Second, the non-uniform distribution coefficient is calculated. Finally, the non-uniformity of crystallizer behavior is evaluated. The evaluation method is applicable to the evaluation of the non-uniformity of metallurgical behavior of continuously cast billets such as slabs, square billets, round billets, and irregularly shaped billets. The data processing in this invention is essentially a data normalization process, which effectively overcomes the influence of the data mean on the evaluation results; a unified evaluation "metric" allows for quantitative evaluation of the crystallizer process, with evaluation results all falling within the range [0,1], demonstrating good adaptability to complex and variable crystallizer processes.

Description

Technical Field

[0001] This invention belongs to the field of continuous casting technology in iron and steel metallurgy, and relates to an evaluation method for the non-uniform distribution of physical field in the metallurgical process of continuous casting crystallizer. Background Technology

[0002] The crystallizer is the heart of the continuous casting machine. During continuous casting, complex metallurgical processes and phenomena such as heat transfer, solidification, flow, and mass transfer occur within the crystallizer. The stable and uniform distribution of physical fields such as temperature, solute, and stress is crucial for optimizing and improving the quality of continuously cast billets. The uniform distribution of process variables such as heat flow / temperature in the crystallizer copper plate, the thickness of the initial billet shell, and the thickness of the protective slag film (liquid slag, solid slag, and air gap) are prerequisites for smooth continuous casting and obtaining high-quality billets. However, when the uniformity of these process parameters decreases, it not only increases the probability of defects such as billet cracks but also easily leads to crystallizer leakage, causing significant economic losses and safety hazards. Therefore, quantitatively evaluating the uniformity of the distribution of various physical fields within the crystallizer is of positive significance for stabilizing and improving the quality of continuously cast billets.

[0003] The physical field data such as temperature, heat flux, and billet shell thickness inside the crystallizer are generally obtained through online detection combined with mathematical physics models, discretizing the crystallizer / billet and then performing numerical calculations. Reasonably evaluating the non-uniformity of the physical field distribution within the crystallizer is fundamental to optimizing the continuous casting process and crystallizer process control. Currently, the variance, root mean square error, and coefficient of variation of each physical quantity are typically used to evaluate the non-uniformity of temperature, heat flux, and other data along the horizontal direction at different heights from the meniscus of the crystallizer. However, due to the following factors: 1) significant differences in magnitude between different physical quantities; 2) drastic changes in the same physical quantity over time with large fluctuations; and 3) strong correlations between physical fields, there are significant limitations to uniformly evaluating the non-uniformity of each physical field. Although there is an urgent need for non-uniformity evaluation in production, the lack of suitable evaluation methods prevents the evaluation results from being directly applicable to guiding continuous casting production.

[0004] To address the magnitude, distribution, and variation characteristics of physical field data within the crystallizer, the applicable non-uniformity evaluation method should possess the following characteristics: 1) Using different units to represent the same set of physical field data, or fluctuations within the physical field, will cause changes in the data mean. The evaluation method needs to overcome the impact of mean changes on the evaluation results. For this reason, using variance and standard deviation methods will lead to significant deviations in the evaluation results. 2) The prerequisite for non-uniform distribution data to guide production is to provide quantitative and unified non-uniformity evaluation results for different casting machines, steel grades, processes, etc. The "measurement standard" must be strictly unified. In this regard, when using the coefficient of variation method for evaluation, different results and ranges of variation will occur depending on the object or conditions, resulting in a lack of unified "measurement standard." For example, for billets produced under two different casting cycles, the coefficient of variation range of the surface temperature of the copper plate in the crystallizer is 1-2 and 1.5-2.3, respectively. It is difficult to compare and evaluate the non-uniformity of the two based on this result. Therefore, the "measurement standard" of the unified evaluation method needs to meet the requirement of being able to evaluate multiple physical fields from the same magnitude and range, facilitating the comparison of specific physical fields and multiple different physical fields under different processes and production conditions.

[0005] In summary, commonly used methods are limited in evaluating the non-uniformity distribution of the continuous casting crystallizer process. New evaluation methods must meet two requirements: 1) they must be able to evaluate physical fields with large mean variations, overcoming the influence of mean variations on the evaluation results; 2) the "metric standard" for the evaluation results must be unified for different evaluation objects. Therefore, this invention proposes a quantitative evaluation method for the non-uniformity distribution of the crystallizer process that meets the above two requirements. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a quantitative evaluation method for the non-uniform distribution in the continuous casting crystallizer process. The technical solution of this invention is as follows:

[0007] A quantitative evaluation method for the non-uniform distribution of the metallurgical process in a continuous casting mold is disclosed. This method involves installing sensors to record in real-time the copper plate / cooling water temperature, cooling water volume, friction force, and liquid level fluctuations during the metallurgical process. Other process parameters, including casting temperature, casting speed, liquidus-solid phase line of the molten steel, billet size, and other data, are also recorded. Key physical field data of the metallurgical process in the mold are obtained using methods already maturely applied both domestically and internationally. The method is illustrated by evaluating the non-uniform distribution of slag channel / liquid slag / solid slag thickness during the continuous casting mold process. The evaluation methods for the non-uniform distribution of other physical fields in the mold process are the same as those for the non-uniform distribution of slag channel / liquid slag / solid slag thickness. The quantitative evaluation method includes the following steps:

[0008] Step 1: Preprocessing of slag channel / liquid slag / solid slag thickness data

[0009] (1) Discretize the billet. At a certain height h below the meniscus, there are n discrete slag channels / liquid slag / solid slag data (refer to...). Figure 3 ), define it as x i The value of i ranges from 1, 2, 3…n;

[0010] (2) x i Sort data from smallest to largest, and re-sort data from smallest to largest as defined by y. i Then y1 <y2<y3<…<y i-1 <y i <y i+1 … <y n ,make (The proportion of each data point to the sum of all data points), then z1 <z2<z3<…<z i-1 <z i <z i+1 … <z n .

[0011] Step 2: Construct the Lorentz curves for the thickness distribution of slag channel / liquid slag / solid slag.

[0012] (1) Let s i = z1 + z2 + ... + z i (s i =s i-1 +z i (Define s0 = 0), and set the point (i, s) i Plot the graph on a Cartesian coordinate system, starting from point (0, 0), and connect each point (i, s) in ascending order of i. i These curves, known as the Lorentz curve, form an approximate curve. The Lorentz curve exhibits a common form and two extreme forms depending on the distribution characteristics of the thickness of the slag channel / liquid slag / solid slag. The extreme forms are the absolutely uniform distribution form and the absolutely non-uniform distribution form, which correspond to the normal, absolutely uniform, and absolutely non-uniform distributions of the thickness of the slag channel / liquid slag / solid slag, respectively. Apart from the common form, the two extreme forms only exist as theoretical possibilities.

[0013] (2) When the thickness of the slag channel / liquid slag / solid slag is x i Absolutely uniform distribution (i.e., x1 = x2 = ... = x) i =…=x n When the Lorentz curve is transformed into a straight line (hereinafter referred to as the straight line L, see reference), the curve becomes a straight line. Figure 1 (middle line AB);

[0014] (3) When the thickness of the slag channel / liquid slag / solid slag is x i The Lorenz curve represents the normal distribution. (Reference) Figure 1 medium curve )

[0015] (4) When the thickness of the slag channel / liquid slag / solid slag is x i Absolutely non-uniform distribution (i.e., except for x) i When all values ​​except the maximum value are 0, the Lorentz curve transforms into a polygonal line (hereinafter referred to as PolyL, see reference). Figure 1 (The broken line ACB).

[0016] Step 3: Calculate the non-uniform distribution coefficient

[0017] (1) Define a right triangle ΔABC formed by a straight line L and a broken line PolyL, where point A is (0,0), the origin of the rectangular coordinate system, point B is (n,1), and point C is (n,0); S ΔABC Let S be the area of ​​ΔABC. 阴影 Let line L and The area of ​​the closed figure formed by the non-uniform distribution is then calculated using the following formula:

[0018]

[0019] When the temperature is absolutely non-uniformly distributed, the Lorentz curve coincides with the broken line PolyL, then S 阴影 The maximum value is equal to S ΔABC When the temperature is absolutely uniformly distributed, the Lorentz curve coincides with the straight line L, then S 阴影 The minimum value is 0; that is, Non-uniformindex∈[0,1], where 0 represents an absolutely uniform distribution and 1 represents an absolutely non-uniform distribution.

[0020] Step 4: Evaluation of the non-uniformity of thickness distribution in the crystallizer slag channel / liquid slag / solid slag

[0021] After changing the initial height *h*, repeating steps one, two, and three yields the non-uniformity distribution coefficient after changing the crystallizer height. Repeating the change in height *h* provides the non-uniformity distribution coefficients for slag channel / liquid slag / solid slag thickness at all heights below the meniscus. Changes in the non-uniformity distribution coefficients indicate variations in the non-uniformity of slag channel / liquid slag / solid slag thickness along the casting direction, thus achieving the purpose of evaluating the non-uniform distribution of slag channel / liquid slag / solid slag thickness.

[0022] The above evaluation method is applicable to the evaluation of the non-uniformity of the metallurgical behavior of continuously cast billets such as slabs, square billets, round billets, and irregularly shaped billets.

[0023] The beneficial effects of this invention are: 1) The data processing in the evaluation process of this invention is essentially a data normalization process, which effectively overcomes the influence of the data mean on the evaluation results. 2) A unified evaluation "metric standard" can uniformly and quantitatively evaluate the physical fields of multiple different crystallizer processes, and the evaluation results are all between [0,1], where 0 represents an absolutely uniform distribution and 1 represents an absolutely non-uniform distribution. This has good adaptability to complex and variable crystallizer metallurgical processes. Attached Figure Description

[0024] Figure 1 It is the Lorenz curve and the non-uniform distribution coefficient.

[0025] Figure 2 This refers to the dimensions of a crystallizer and the location of thermocouples in a steel plant. Figure 2 (a) Front view of the crystallizer; Figure 2 (b) Left view of the crystallizer; Figure 2 (c) Top view of the crystallizer.

[0026] Figure 3 This is the result of gridding a cast billet. In the figure, h is the distance from the meniscus to the location where the thickness data of the slag channel / liquid slag / solid slag is selected.

[0027] Figure 4 This is a comparison of the evaluation results of the non-uniformity of the thickness of the slag channel / liquid slag / solid slag in the crystallizer of a certain steel plant; Figure 4 (a) Evaluation results using the standard deviation method; Figure 4 (b) Evaluation results of coefficient of variation; Figure 4 (c) Evaluation results of the present invention.

[0028] Figure 5 It represents the variation of heat flux nonuniformity at different drawing speeds in a certain steel plant. Detailed Implementation

[0029] The present invention will be further described below through specific embodiments and in conjunction with the accompanying drawings (the embodiments take the evaluation of the uniformity of slag channel / liquid slag / solid slag thickness as an example).

[0030] like Figure 2 The diagram shows the crystallizer dimensions and thermocouple arrangement during the production of 2299mm × 220mm billets at a steel plant. First, the physical field to be evaluated is calculated based on monitored temperature, cooling water, and other process parameters. Second, physical field data for the copper plate / billet in the crystallizer is extracted. Third, the data is preprocessed and a Lorentz curve is constructed. Finally, the non-uniformity distribution coefficient at arbitrary height of the crystallizer is calculated, and the non-uniformity distribution of the crystallizer behavior is evaluated.

[0031] Step 1: Real-time monitoring of the crystallizer metallurgical process

[0032] Sensors installed in the factory record in real time the temperature of the copper plate / cooling water, the volume of cooling water, friction and liquid level fluctuations, as well as other process parameters such as casting temperature, casting speed, liquidus lines of molten steel and billet size.

[0033] Step 2: Crystallizer Process Modeling and Data Extraction

[0034] (1) The main methods for modeling the crystallizer process include, but are not limited to, the finite element method, the finite difference method, and the meshless method; the modeling and solution methods for the main physical fields of mature crystallizer process simulation technologies at home and abroad are as follows:

[0035] Heat flow from billet to crystallizer: inverse calculation method based on measured temperature, heat flow solution method based on dual thermocouple temperature measurement, and heat flow solution method based on fiber optic temperature measurement.

[0036] Temperature field of billet / crystallizer: finite difference method, finite element method.

[0037] Thickness distribution of slag channel / liquid slag / solid slag / air gap: a method for solving the heat flow resistance in the slag channel based on the surface temperature of the billet and the hot surface temperature of the crystallizer.

[0038] Billet shell thickness: Solidus line solution method for billet temperature field.

[0039] (2) When solving the thickness distribution of slag channel / liquid slag / solid slag according to the model in step (1), the cross section at any height h below the meniscus is discretized into 100 grids each for the outer and inner wide arcs in the horizontal direction, and 10 grids each for the left and right narrow arcs. 224 grid data points will be obtained at the grid intersection. The array containing 224 data points is used as the evaluation object (refer to...). Figure 3 ).

[0040] (3) The height h below the crescent is arbitrary, so the evaluation object is several arrays containing 224 data.

[0041] Step 3: Data Preprocessing and Lorenz Curve Construction

[0042] (1) Data preprocessing: Calculate the proportion of each data point to the sum of all data points, sort the proportions in ascending order, and obtain a new array z containing 224 data points. i (i = 1, 2, ..., 224).

[0043] (2) Construction of the Lorentz curve: Let s i = z1 + z2 + ... + z i Plot the point (i, s) on a rectangular coordinate system. i Connect all points starting from the origin, and connect to the point (224, s). 224 The approximate curve obtained after this process is the Lorentz curve (e.g., ...). Figure 1 middle ).

[0044] Step 4: Calculate the non-uniform distribution coefficient of the thickness of slag channel / liquid slag / solid slag at a height h below the meniscus of the crystallizer.

[0045] (1) Figure 1 Calculate the area of ​​the shaded region. Divide the shaded region vertically into 224 parts at point i on the horizontal axis. Each part can be approximated as a trapezoid. The area of ​​the i-th trapezoid is:

[0046]

[0047] In the formula T i Let s be the area of ​​the i-th trapezoid. i This is the result of step (2) in the second step (defined as s0 = 0). The area of ​​the shaded region and ΔABC can be calculated:

[0048]

[0049]

[0050] (2) Solving for the non-uniform distribution coefficient.

[0051]

[0052] Step 5: Evaluation of Crystallizer Non-uniformity Behavior

[0053] (1) In the third step, the area of ​​the shaded part represents the non-uniformity of the data distribution, that is, the degree of disorder and non-uniformity of the data. When the area of ​​the shaded part reaches the maximum and minimum, the corresponding non-uniformity distribution coefficients are 1 and 0, respectively. The non-uniform index ∈ [0,1], and the distribution of a certain physical field in the crystallizer process becomes more and more non-uniform as the value increases within the interval.

[0054] (2) Due to the arbitrariness of height h, the non-uniformity distribution coefficient at different heights on the entire crystallizer can be obtained by repeating the above steps. The change of the coefficient represents the change of the non-uniformity distribution of the crystallizer. The non-uniformity distribution coefficient is strictly between [0,1].

[0055] Example:

[0056] Taking a slab with dimensions of 2299mm×220mm produced by a domestic steel mill as an example, some process parameters are shown in Table 1, and the cooling water volume and temperature difference of the casting machine are shown in Table 2.

[0057] Table 1 Partial Process Parameters

[0058] billet dimensions 2299mm×220mm(Sx×Sy) liquid level 797mm Casting temperature 1545.9℃ The solidification temperature of protective slag 1095℃ Speed 0.9 m / min

[0059] Table 2 Cooling water volume and temperature difference of crystallizer

[0060]

[0061] like Figure 2 As shown, the dimensions of the copper plate on the outer arc of the crystallizer are 3000mm × 44mm × 900mm (P x ×Z2×P y The inner arc wide-face copper plate has dimensions of 3000mm × 40mm × 900mm (P). x ×Z1×P y The dimensions of the narrow sides on both the left and right are 220mm × 40mm × 900mm (S) y ×Z1×P y A total of 120 thermocouples (x1 = 200 mm, x2 = 150 mm, x3 = 100 mm, y1 = 210 mm, y2 = 325 mm, y3 = 445 mm) were embedded in the crystallizer. The 2299 mm wide billet was covered by 15 rows of thermocouples on the outer and inner wide arc surfaces and one row of thermocouples on each of the left and right narrow surfaces. Therefore, the test data of 96 thermocouples were recorded. During stable casting, the measured temperatures of the 96 thermocouples at a casting speed of 0.9 m / min are shown in Table 3.

[0062] Table 3 Measured temperature of copper plate in crystallizer (°C)

[0063]

[0064] Based on the technological foundation and conditions of this equipment, a mathematical physics model can be established to calculate the heat transfer behavior and slag channel thickness distribution, among other physical fields, during the crystallization metallurgical process. Different display formats for the non-uniformity evaluation results can be generated as needed. Figure 4 This is a comparison of the evaluation results of different methods for the slag film thickness in the crystallizer of this casting machine. Figure 5 It refers to the variation in heat flow nonuniformity at different casting speeds of the casting machine.

[0065] according to Figure 4 The evaluation results of the variance / standard deviation method, due to the inconsistency of data mean and measurement standards, cannot reflect the variation of non-uniformity in liquid slag thickness; the coefficient of variation overcomes the influence of the data mean, but the evaluation results lack a unified measurement standard. The evaluation results of the proposed method are as follows: Figure 4 (c) The data normalization process overcomes the influence of the mean and strictly unifies the measurement standard.

[0066] The above embodiments are only examples of the implementation of the present invention using the thickness of the slag channel / liquid slag / solid slag as an example, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention.

Claims

1. A quantitative evaluation method for the non-uniform distribution of the metallurgical process in a continuous casting crystallizer, characterized in that, First, by installing sensors, the temperature of the copper plate / cooling water, the cooling water volume, the friction force and the liquid level fluctuation of the continuous casting crystallizer are recorded in real time during the metallurgical process. Other process parameters, including casting temperature, casting speed, liquid-solid phase line of molten steel and billet size and other data, are also recorded to obtain important physical field data of the crystallizer metallurgical process. The evaluation of the non-uniform distribution of slag channel / liquid slag / solid slag thickness during continuous casting crystallization is used as an example. The evaluation method for the non-uniform distribution of other physical fields in the crystallization process is the same as that for the non-uniform distribution of slag channel / liquid slag / solid slag thickness. The quantitative evaluation method includes the following steps: Step 1: Preprocessing of slag channel / liquid slag / solid slag thickness data; (1) Discretize the billet and place it at a certain height below the meniscus. h Discrete exists on Individual slag / liquid slag / solid slag data, defined as follows: , i The range of values ​​for is 1, 2, 3… ; (2) Data sorted from smallest to largest, and data re-sorted from smallest to largest, is defined as follows: ,but Define the proportion of each data point to the sum of all data points as ; ,make ,but ; Step 2: Construct the Lorentz curves for the thickness distribution of slag channel / liquid slag / solid slag; (1) Let , ,definition ; will point ( , Plot on a rectangular coordinate system, starting from point (0, 0), according to... i Connect each point in increasing order. , The Lorentz curve is an approximate curve formed by the distribution characteristics of the thickness of the slag channel / liquid slag / solid slag. The Lorentz curve will present a common form and two extreme forms due to the distribution characteristics of the thickness of the slag channel / liquid slag / solid slag. The extreme forms are the absolutely uniform distribution form and the absolutely non-uniform distribution form, which correspond to the normal distribution, absolutely uniform distribution and absolutely non-uniform distribution of the thickness of the slag channel / liquid slag / solid slag, respectively. Apart from the common form, the two extreme forms only exist in theory. (2) When the thickness of the slag channel / liquid slag / solid slag Absolutely uniform distribution (i.e.) When the Lorentz curve is transformed into a straight line L, the curve becomes a straight line L. (3) When the thickness of the slag channel / liquid slag / solid slag The Lorenz curve is the curve of the normal distribution. (4) When the thickness of the slag channel / liquid slag / solid slag When the distribution is absolutely non-uniform, the Lorentz curve transforms into a broken line PolyL, where absolutely non-uniform distribution refers to the distribution of all non-uniform curves except for the following: All values ​​except the maximum value are 0; Step 3: Calculate the non-uniform distribution coefficient; (1) Define the line L and the broken line PolyL as forming a right angle. The coordinates of point A are (0,0), which is the origin of the rectangular coordinate system; the coordinates of point B are (n,1); and the coordinates of point C are (n,0). for area, Let L be the area of ​​the closed figure formed by the line L and the line L; then the formula for calculating the non-uniform distribution coefficient is: When the temperature is absolutely non-uniformly distributed, the Lorentz curve coincides with the broken line PolyL. The maximum value is equal to When the temperature is absolutely uniformly distributed, the Lorentz curve coincides with the straight line L, then... The minimum value is equal to 0; that is... , where 0 represents an absolutely uniform distribution and 1 represents an absolutely non-uniform distribution; Step 4: Evaluation of the non-uniformity of thickness distribution in the crystallizer slag channel / liquid slag / solid slag; Change the height of the first step h After determining the size, repeating steps one, two, and three will yield the non-uniformity distribution coefficient after changing the crystallizer height; repeating the height change... h Then, the non-uniformity distribution coefficient of slag channel / liquid slag / solid slag thickness at all heights of the billet under the meniscus can be obtained; the change of the non-uniformity distribution coefficient indicates the change of non-uniformity of slag channel / liquid slag / solid slag thickness in the casting direction, thus achieving the purpose of evaluating the non-uniform distribution of slag channel / liquid slag / solid slag thickness.

2. The quantitative evaluation method for non-uniform distribution in a continuous casting crystallizer metallurgical process according to claim 1, characterized in that, The evaluation method described herein is applicable to the evaluation of the non-uniformity of the metallurgical behavior of slabs, square billets, round billets, irregularly shaped billets, or other continuously cast billets.

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