KR20080053709A - Cooling analysis model for hot rolled steel sheet and method of estimating properties of hot rolled steel sheet using the same - Google Patents

Cooling analysis model for hot rolled steel sheet and method of estimating properties of hot rolled steel sheet using the same Download PDF

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KR20080053709A
KR20080053709A KR1020060125596A KR20060125596A KR20080053709A KR 20080053709 A KR20080053709 A KR 20080053709A KR 1020060125596 A KR1020060125596 A KR 1020060125596A KR 20060125596 A KR20060125596 A KR 20060125596A KR 20080053709 A KR20080053709 A KR 20080053709A
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steel sheet
rolled steel
hot rolled
section
cooling
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KR1020060125596A
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KR100851868B1 (en
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이중형
이재곤
김홍준
임영록
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주식회사 포스코
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B1/00—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations
    • B21B1/22—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length
    • B21B1/24—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length in a continuous or semi-continuous process
    • B21B1/26—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length in a continuous or semi-continuous process by hot-rolling, e.g. Steckel hot mill
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B1/00—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations
    • B21B1/22—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length
    • B21B1/30—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length in a non-continuous process
    • B21B1/32—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length in a non-continuous process in reversing single stand mills, e.g. with intermediate storage reels for accumulating work
    • B21B1/34—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length in a non-continuous process in reversing single stand mills, e.g. with intermediate storage reels for accumulating work by hot-rolling
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B13/00—Metal-rolling stands, i.e. an assembly composed of a stand frame, rolls, and accessories
    • B21B13/02—Metal-rolling stands, i.e. an assembly composed of a stand frame, rolls, and accessories with axes of rolls arranged horizontally
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/16—Control of thickness, width, diameter or other transverse dimensions
    • B21B37/18—Automatic gauge control
    • B21B37/20—Automatic gauge control in tandem mills
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B3/00—Rolling materials of special alloys so far as the composition of the alloy requires or permits special rolling methods or sequences ; Rolling of aluminium, copper, zinc or other non-ferrous metals
    • B21B2003/001—Aluminium or its alloys
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B13/00—Metal-rolling stands, i.e. an assembly composed of a stand frame, rolls, and accessories
    • B21B13/02—Metal-rolling stands, i.e. an assembly composed of a stand frame, rolls, and accessories with axes of rolls arranged horizontally
    • B21B2013/025—Quarto, four-high stands
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B15/00—Arrangements for performing additional metal-working operations specially combined with or arranged in, or specially adapted for use in connection with, metal-rolling mills
    • B21B15/0007—Cutting or shearing the product
    • B21B2015/0014—Cutting or shearing the product transversely to the rolling direction
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B15/00—Arrangements for performing additional metal-working operations specially combined with or arranged in, or specially adapted for use in connection with, metal-rolling mills
    • B21B15/0007—Cutting or shearing the product
    • B21B2015/0021—Cutting or shearing the product in the rolling direction
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B2271/00—Mill stand parameters

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  • Mechanical Engineering (AREA)
  • Control Of Metal Rolling (AREA)

Abstract

A cooling analysis method of a hot rolled steel sheet that is faster and more stable than an existing cooling analysis method of the hot rolled steel sheet is provided, and a method for estimating properties of the hot rolled steel sheet using the cooling analysis method of the hot rolled steel sheet is provided. A method for estimating properties of a hot rolled steel sheet comprises: a first step(11) of dividing the total length of a hot rolled steel sheet into at least two minute sections in the longitudinal direction to measure and calculate cooling information; a second step(12) of measuring cooling information of a finishing delivery temperature measuring section and a coiling temperature measuring section in the divided minute sections; a third step(13) of setting an initial value of a heat transfer correcting coefficient; a fourth step(14) of calculating a phase transformation of the hot rolled steel sheet; a fifth step(15) of obtaining an analytic solution by a cooling analysis method; a sixth step(16) of obtaining a difference between a temperature at the coiling temperature section measured in the second step and a temperature of the coiling temperature section calculated by the analytic solution of the fifth step; and a seventh step(17) of confirming whether the second to sixth steps have been performed by a final minute section divided in the first step. The method comprises the step of repeatedly performing the fourth to sixth steps if the temperature difference is higher than 1 deg.C in the sixth step. The method further comprises the step of adjusting and renewing the heat transfer correcting coefficient if the temperature difference is higher than 1 deg.C in the sixth step. The method comprises the step of repeatedly performing the second to sixth steps with respect to a next minute section in the seventh step if a process of estimating properties of the hot rolled steel sheet is not proceeded by the final minute section divided in the first step.

Description

열연강판의 냉각해석방법 및 이를 이용한 재질예측방법 {COOLING ANALYSIS MODEL FOR HOT ROLLED STEEL SHEET AND METHOD OF ESTIMATING PROPERTIES OF HOT ROLLED STEEL SHEET USING THE SAME}COOLING ANALYSIS MODEL FOR HOT ROLLED STEEL SHEET AND METHOD OF ESTIMATING PROPERTIES OF HOT ROLLED STEEL SHEET USING THE SAME}

도 1은 본 발명의 일 실시예에 따른 냉각해석방법 유도과정이다.1 is a cooling analysis method induction process according to an embodiment of the present invention.

도 2는 본 발명의 일 실시예에 따른 재질예측방법의 순서도이다.2 is a flow chart of a material prediction method according to an embodiment of the present invention.

도 3은 열연강판 하부의 냉각이력 그래프이다.3 is a cooling history graph of the bottom of the hot rolled steel sheet.

도 4는 열연강판 중심부의 냉각이력 그래프이다.4 is a cooling history graph of the center of the hot rolled steel sheet.

도 5는 열연강판 상부의 냉각이력 그래프이다.5 is a cooling history graph of the top of the hot rolled steel sheet.

본 발명은 열연강판의 냉각해석방법 및 이를 이용한 재질예측방법에 관한 것이다. 더 상세하게는, 냉각해석방법의 계산 시간을 줄여, 짧은 시간내에 정확한 예측이 가능한 냉각해석방법 및 이를 이용한 재질예측방법에 관한 것이다.The present invention relates to a method for cooling analysis of a hot rolled steel sheet and a material prediction method using the same. More specifically, the present invention relates to a cooling analysis method capable of accurate prediction within a short time and a material prediction method using the same, by reducing the calculation time of the cooling analysis method.

열연강판의 권취온도예측을 위한 종래의 냉각해석방법은 공냉과 수냉을 고려한 단순냉각방법 및 이를 반복해서 적용하는 회귀모형이 있다. 그러나 단순냉각방법로는 권취온도의 정확한 예측이 어려웠으므로, 근래에 1차 또는 2차 열전달 방정 식을 이용한 유한차분법(FDM)을 기초로 한 냉각해석방법이 개발되었다. Conventional cooling analysis methods for the prediction of the coiling temperature of hot rolled steel include a simple cooling method considering air cooling and water cooling, and a regression model repeatedly applying the same. However, it was difficult to accurately estimate the winding temperature by simple cooling method. Recently, a cooling analysis method based on finite difference method (FDM) using first- or second-order heat transfer equations has been developed.

대다수 열연강판의 재질예측방법에 적용되고 있는 냉각해석방법도 1차 유한차분법을 기초로 하고 있다. 이와 같이 유한차분법은 온도해석에 있어 널리 사용되고 있지만, 수치해석적 방법을 사용하므로 해의 수렴성 문제와 해를 계산하는데 장시간이 걸리는 문제점이 있다. 냉각해석방법을 이용하여 열연강판의 전체가 아닌 특정한 지점의 냉각이력을 구하기 위해서도, 열 전달계수를 보정해가며 많은 반복계산을 해야 한다. 따라서 열연강판 전장의 재질예측을 하기 위해서는 냉각모델을 수백에서 수천번까지 반복해서 계산해야 한다. 그러므로 재질예측모델의 경우 해의 계산시간이 길어지는 점이 더욱 큰 문제점이 된다. The cooling analysis method applied to the material prediction method of most hot rolled steel sheets is also based on the first finite difference method. As described above, the finite difference method is widely used in temperature analysis, but there is a problem in that it takes a long time to solve a solution convergence problem and a solution because a numerical method is used. In order to obtain the cooling history of a specific point instead of the entire hot rolled sheet by using the cooling analysis method, many iterative calculations have to be made while the heat transfer coefficient is corrected. Therefore, in order to predict the material of the hot rolled sheet, the cooling model needs to be repeatedly calculated hundreds to thousands of times. Therefore, in the case of the material prediction model, the longer the calculation time of the solution is, the more problematic.

전술한 문제점을 해결하기 위하여, 기존 열연강판의 냉각해석방법에 비하여 빠르고 안정적인 냉각해석방법을 제공한다. 또한, 이를 이용한 열연강판의 재질예측방법을 제공한다. In order to solve the above problems, it provides a fast and stable cooling analysis method compared to the cooling analysis method of the existing hot rolled steel sheet. In addition, it provides a method of predicting the material of the hot rolled steel sheet using the same.

본 발명의 일 실시예에 따른 열연강판의 냉각해석방법은 다음의 수학식을 만족한다. Cooling analysis method of the hot rolled steel sheet according to an embodiment of the present invention satisfies the following equation.

Figure 112006091564409-PAT00008
Figure 112006091564409-PAT00008

여기서,

Figure 112006091564409-PAT00009
는
Figure 112006091564409-PAT00010
이고, f(y)는 초기온도조건,
Figure 112006091564409-PAT00011
는 비열용량(specific heat), H는 열연강판의 두께, y는 두께 변수, t는 시간,
Figure 112006091564409-PAT00012
는 발열량,
Figure 112006091564409-PAT00013
은 강판 상부의 부열유속,
Figure 112006091564409-PAT00014
는 강판 하부의 부열유속, T(y,t)는 온도분포, 그리고 k는 상수이다.here,
Figure 112006091564409-PAT00009
Is
Figure 112006091564409-PAT00010
F (y) is the initial temperature condition,
Figure 112006091564409-PAT00011
Is the specific heat, H is the thickness of the hot rolled steel, y is the thickness variable, t is the time,
Figure 112006091564409-PAT00012
Is calorific value,
Figure 112006091564409-PAT00013
Sub-heat flow rate at the top of the steel sheet,
Figure 112006091564409-PAT00014
Is the sub-heat flux at the bottom of the steel sheet, T (y, t) is the temperature distribution, and k is a constant.

또한, 본 발명의 일 실시예에 따른 열연강판의 재질예측방법은 ⅰ) 구간을 나누어 냉각 정보를 측정 및 계산하기 위하여 열연강판의 전장을 길이방향으로 2이상의 미소구간으로 나누는 제1단계, ⅱ) 나누어진 미소구간 중에서 다듬질압연(finishing rolling) 출측(FDT) 구간 및 권취온도(Coiling Temperature, CT) 측정위치 구간의 냉각정보를 측정하는 제2단계, ⅲ) 열전달 보정계수(h(n))의 초기값을 설정하는 제3단계, ⅳ) 상기 열연강판에 해당구간의 상변태를 계산하는 제4단계, ⅴ) 제1항의 냉각해석모델로 해석해를 구하는 제5단계, ⅵ) 상기 제2단계에서 측정한 CT구간 온도와 상기 제5단계의 해석해에서 계산된 CT구간 온도의 차를 구하는 제6단계, 및 ⅶ) 상기 제1단계에서 나눈 마지막 구간까지 상기 제2단계 내지 제6단계가 수행되었는지 확인하는 제7단계를 포함한다. In addition, the material prediction method of the hot-rolled steel sheet according to an embodiment of the present invention is the first step of dividing the overall length of the hot-rolled steel sheet into two or more minute sections in the longitudinal direction in order to measure and calculate cooling information by dividing the section iii) The second step of measuring cooling information in the finishing rolling exit (FDT) section and the coiling temperature (CT) measurement position section among the divided microsections, i) of the heat transfer correction coefficient (h (n)) A third step of setting an initial value, i) a fourth step of calculating the phase transformation of the section on the hot-rolled steel sheet, i) a fifth step of obtaining an analysis by the cooling analysis model of claim 1, and i) the measurement in the second step. A sixth step of obtaining a difference between the CT section temperature and the CT section temperature calculated in the analysis solution of the fifth step; and iii) confirming whether the second to sixth steps are performed until the last section divided in the first step. Including the seventh step .

여기서, 열연강판의 재질예측방법은 제6단계에서의 온도차가 1℃ 보다 큰 경우에, 제4단계 내지 제6단계를 반복하여 수행할 수 있다. 또한, 열연강판의 재질예측방법은 6단계에서의 온도차가 1℃ 보다 큰 경우에, 열전달 보정계수를 조절하여 갱신하는 단계를 더 포함할 수 있다. 또한, 열연강판의 재질예측방법은 제7단계에서 제1단계에서 나눈 마지막 구간까지 재질예측이 진행되지 않은 경우에는, 열연강판의 길이방향으로 다음 구간에 대하여 전술한 제2단계 내지 제6단계를 다시 수행할 수 있다. Here, the method of predicting the material of the hot rolled steel sheet may be performed by repeating the fourth to sixth steps when the temperature difference in the sixth step is greater than 1 ° C. In addition, the material prediction method of the hot rolled steel sheet may further include the step of updating by adjusting the heat transfer correction coefficient when the temperature difference in step 6 is greater than 1 ℃. In addition, if the material prediction method of the hot rolled steel sheet does not proceed from the seventh step to the last section divided in the first step, the second step to the sixth step for the next section in the longitudinal direction of the hot rolled steel sheet You can do it again.

이하, 첨부한 도면을 참고로 하여 본 발명이 속하는 기술 분야에서 통상의 지식을 가진 자가 용이하게 실시할 수 있도록 본 발명의 실시예를 상세히 설명한다. 그러나 본 발명은 여러 가지 상이한 형태로 구형될 수 있으며, 이하에서 설명하는 실시예에 한정되지 않는다. 그리고 본 명세서 및 도면에서 동일한 부호는 동일한 구성요소를 나타낸다. Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art may easily implement the present invention. As those skilled in the art would realize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. Like reference numerals in the present specification and drawings denote like elements.

도 1은 본 발명의 일 실시예에 따른 냉각해석방법을 유도하는 과정을 설명하기 위하여, 열연강판(F) 두께방향의 단면 및 그 경계조건을 나타낸다. 도 1에서의 열연강판(F)은 런아웃테이블(Run Out Table)을 통과하는 과정에 있는 것이다. 즉, 열연강판(F)은 다듬질압연 출측(FDT)에서부터 권취온도 측정위치(CT)까지의 구간에 위치할 수 있다. 1 is a cross-sectional view of the hot rolled steel sheet F in the thickness direction and a boundary condition thereof to explain a process of inducing a cooling analysis method according to an exemplary embodiment of the present invention. The hot rolled steel sheet F in FIG. 1 is in the process of passing through a run out table. That is, the hot rolled steel sheet F may be located in a section from the finishing rolled-out side FDT to the winding temperature measuring position CT.

먼저, 냉각해석계산을 용이하게 하기 위하여, FDT구간에서 CT구간 사이를 n개의 미소구간으로 나눈다. 여기서 n은 2이상의 자연수일 수 있으나, 정확한 계산을 위하여는 큰 값이 될 수 있다. 도 1의 확대원은 나누어진 미소구간의 하나를 자세하게 나타낸다. First, in order to facilitate the cooling analysis calculation, the FDT section is divided into n minute sections between the CT sections. N may be a natural number of 2 or more, but may be a large value for accurate calculation. The enlarged circle in Fig. 1 shows one of the divided minute sections in detail.

열연강판(F)은 상, 하 비대칭적인 냉각조건 속에서 런아웃테이블을 통과한다. 따라서 열연강판(F)은 두께 방향을 따라 서로 다른 온도 분포를 보이고, 이를 반영하기 위하여 열연강판(F)의 두깨방향으로 하단의 값을 0으로 하고, 상단의 값을 H로 하는 두께변수y를 설정한다. 여기서 H는 열연강판(F) 전체 두께이다. 또한, 열연강판 상부 및 하부의 냉각조건이 다르므로, 강판 상부의 열 유속을

Figure 112006091564409-PAT00015
, 강판 하부의 열 유속을
Figure 112006091564409-PAT00016
로 둔다. 그러면 열연강판(F)의 두께방향에 따른 발열량 및 온도분포는 두께상수y에 의존하게 되므로, 발열량을
Figure 112006091564409-PAT00017
, 온도분포를 T(y,t)로 할 수 있다. The hot rolled steel sheet F passes through the runout table in asymmetrical cooling conditions. Therefore, the hot rolled steel sheet (F) shows a different temperature distribution along the thickness direction, in order to reflect this, the thickness value y having the bottom value as 0 and the top value as H in the thickness direction of the hot rolled steel sheet (F). Set it. Where H is the total thickness of the hot rolled steel sheet (F). In addition, since the cooling conditions of the upper and lower parts of the hot rolled steel sheet are different,
Figure 112006091564409-PAT00015
Heat flux at the bottom of the steel sheet
Figure 112006091564409-PAT00016
Leave it as. Then, the calorific value and the temperature distribution along the thickness direction of the hot rolled steel sheet F depend on the thickness constant y.
Figure 112006091564409-PAT00017
The temperature distribution can be T (y, t).

그리하면 열연강판(F)의 두께방향위치 및 시간을 변수로 하여 1차원 비정상 열전달 구성 방정식을 세울 수 있다. 방정식은 아래의 수학식1과 같다. Then, one-dimensional abnormal heat transfer constitutive equations can be established by using the thickness direction position and time of the hot-rolled steel sheet F as variables. The equation is shown in Equation 1 below.

Figure 112006091564409-PAT00018
Figure 112006091564409-PAT00018

여기서, k는 상수이고,

Figure 112006091564409-PAT00019
는 비열용량(specific heat)이다. Where k is a constant,
Figure 112006091564409-PAT00019
Is the specific heat.

수학식 1은 열연강판(F) 상부 및 하부의 비대칭적인 냉각조건을 만족하여야 한다. 따라서 아래의 수학식2 및 수학식3과 같은 경계조건이 적용된다.Equation 1 should satisfy the asymmetric cooling conditions of the top and bottom of the hot rolled steel sheet (F). Therefore, boundary conditions as shown in Equations 2 and 3 below are applied.

Figure 112006091564409-PAT00020
Figure 112006091564409-PAT00020

Figure 112006091564409-PAT00021
Figure 112006091564409-PAT00021

또한, 시간이 0일 때의 초기조건을 아래의 수학식4과 같이 설정한다. In addition, an initial condition when the time is 0 is set as shown in Equation 4 below.

Figure 112006091564409-PAT00022
Figure 112006091564409-PAT00022

다음으로 전술한 수학식 1 내지 수학식 4를 관련된 제차구성방정식(homogeneous problem)으로 변환한다. 수학식 2 내지 수학식 4에 초기값과 경계값이 주어져 있으므로 고유함수전개(eigenfunction expansion)을 통해서 편미분방정식의 해를 구할 수 있다. Next, the above-described equations (1) to (4) are converted into related homogeneous problems. Since the initial values and the boundary values are given in Equations 2 to 4, the partial differential equations can be solved through eigenfunction expansion.

다음으로 고유함수의 직교성(orthogonality) 및 그린의 정리(Green's theorem)을 적용하면 아래의 수학식5와 같은 열연강판(F)의 두께방향위치 및 시간에 따른 온도값을 나타내는 해를 구할 수 있다. Next, by applying the orthogonality of the eigenfunction and Green's theorem, a solution representing the temperature value according to the thickness direction position and time of the hot-rolled steel sheet F as shown in Equation 5 below can be obtained.

Figure 112006091564409-PAT00023
Figure 112006091564409-PAT00023

여기서,

Figure 112006091564409-PAT00024
는
Figure 112006091564409-PAT00025
이고,
Figure 112006091564409-PAT00026
는 초기온도조건,
Figure 112006091564409-PAT00027
는 비열용량(specific heat), H는 열연강판의 두께, y는 두께 변수, t는 시간,
Figure 112006091564409-PAT00028
는 발열량,
Figure 112006091564409-PAT00029
은 강판 상부의 부열유속,
Figure 112006091564409-PAT00030
는 강판 하부의 부열유속,
Figure 112006091564409-PAT00031
는 온도분포, 그리고 k는 상수를 의미한다.here,
Figure 112006091564409-PAT00024
Is
Figure 112006091564409-PAT00025
ego,
Figure 112006091564409-PAT00026
Is the initial temperature condition,
Figure 112006091564409-PAT00027
Is the specific heat, H is the thickness of the hot rolled steel, y is the thickness variable, t is the time,
Figure 112006091564409-PAT00028
Is calorific value,
Figure 112006091564409-PAT00029
Sub-heat flow rate at the top of the steel sheet,
Figure 112006091564409-PAT00030
Is the subheat rate at the bottom of the steel sheet,
Figure 112006091564409-PAT00031
Is the temperature distribution and k is the constant.

런아웃테이블에서는 계속적으로 경계조건 및 공정조건이 변화하게 되므로, 전술한 미소구간에 대해 미소시간(Δt)을 단위로 하여 냉각해석이 진행된다. 따라서, 열연강판(F) 전장에 대한 냉각해석을 위해서는 수학식5가 반복해서 적용될 수 있다. 미소시간(Δt)을 증가시키면 계산의 반복횟수가 줄어들어서 계산속도가 개선된다. 그러나 기존의 유한차분법을 이용한 방법은 미소시간이 증가함에 따라 해의 불안정성도 같이 커지므로, 미소시간을 증가시키는데 한계가 있다. 반면에 본 발명의 일 실시예에 따른 냉각해석방법은 미소시간에 대한 제한조건이 없으므로, 미소시간을 증가시켜 해석을 수행하여도 해의 정밀도 및 신뢰성이 유지된다. 따라서 열연강판(F) 전장에 대해서 냉각해석을 수행하는 경우, 수학식5를 적용하는 횟수가 줄어들게 되므로, 종래의 방법에 비하여 보다 짧은 시간에 해석해를 구할 수 있다. In the runout table, the boundary condition and the process condition continuously change, and thus the cooling analysis is performed in the minute time interval? T as a unit for the above-mentioned minute section. Therefore, Equation 5 may be repeatedly applied for cooling analysis of the hot rolled steel sheet (F) electric field. Increasing the micro time Δt decreases the number of iterations of the calculation and improves the calculation speed. However, the conventional finite difference method has a limitation in increasing the micro time because the instability of the solution increases as the micro time increases. On the other hand, since the cooling analysis method according to an embodiment of the present invention does not have a limitation on the micro time, the solution accuracy and reliability are maintained even when the micro time is increased and the analysis is performed. Therefore, when the cooling analysis is performed on the entire length of the hot rolled steel sheet (F), since the number of times to apply the equation (5) is reduced, it is possible to obtain an analysis solution in a shorter time than the conventional method.

이하에서는 도 2를 통하여 전술한 냉각해석방법을 이용한 재질예측방법을 자세히 설명한다. Hereinafter, a material prediction method using the aforementioned cooling analysis method will be described in detail with reference to FIG. 2.

도 2는 본 발명의 일 실시예에 따른 재질예측방법을 순서도로 나타낸다. 먼저, 제1단계(11)는 열연강판의 전장을 길이방향으로 n개의 미소구간으로 나눈다. n은 2 이상의 자연수일 수 있으나, 정밀도를 높이기 위하여 큰 숫자일 수 있다. 열연강판이 런아웃테이블 위에서 냉각되는 과정에서는 계속적으로 경계조건 및 공정조건이 변한다. 따라서 이러한 변화를 고려하기 위하여 열연강판을 미소구간으로 나누어 미소시간단위로 재질예측을 수행한다. 2 is a flowchart illustrating a material prediction method according to an embodiment of the present invention. First, the first step 11 divides the entire length of the hot rolled steel sheet into n minute sections in the longitudinal direction. n may be a natural number of 2 or more, but may be a large number to increase precision. As the hot rolled steel sheet cools on the runout table, boundary conditions and process conditions continuously change. Therefore, in order to consider such a change, the hot rolled steel sheet is divided into minute sections and material prediction is performed in minute time units.

다음으로, 제2단계(12)는 나누어진 미소구간 중에서 FDT구간 및 CT구간의 냉각정보를 측정한다. FDT구간의 냉각정보는 냉각해석방법의 초기조건으로 사용되며, CT구간의 냉각정보는 냉각해석으로 구한 해석해와 비교하는데 사용된다. 다음으로, 제3단계(13)는 열전달 보정계수(h(n))의 초기값을 설정한다. 열전달 보정계수는 실제 측정된 열전달 값과 계산된 열전달 값의 차이를 줄이기 위해서 도입한 계수이다. 계산된 열전달 값과 실측된 열전달 값의 차이로 인해서, 계산된 CT구간의 온도와 실측된 CT구간의 온도간에 차이가 발생한다. 따라서 열전달 보정계수를 계산에 더 추가하여 실측값과 계산값의 차이를 줄일 수 있다. 열전달 보정계수는 CT구간의 온도차이를 고려하여 수정할 수 있으므로, 초기값은 1로 설정할 수 있다. Next, the second step 12 measures cooling information of the FDT section and the CT section among the divided minute sections. The cooling information of the FDT section is used as the initial condition of the cooling analysis method, and the cooling information of the CT section is used to compare with the analysis solution obtained by the cooling analysis. Next, the third step 13 sets an initial value of the heat transfer correction coefficient h (n). The heat transfer correction coefficient is a coefficient introduced to reduce the difference between the actual measured heat transfer value and the calculated heat transfer value. Due to the difference between the calculated heat transfer value and the measured heat transfer value, a difference occurs between the calculated CT section temperature and the measured CT section temperature. Therefore, the heat transfer correction coefficient can be added to the calculation to reduce the difference between the measured value and the calculated value. Since the heat transfer correction coefficient can be corrected in consideration of the temperature difference in the CT section, the initial value can be set to 1.

다음으로, 제4단계(14)는 열연강판의 상변태를 계산한다. 열연강판이 런아웃테이블에서 냉각되면서, 오스테나이트로부터 펄라이트, 페라이트, 또는 마르텐사이트 등으로 열연강판의 상(phase)변태가 발생한다. 상변태로 인해서 잠열이 방출되거나 흡수될 수 있다. 따라서 열연강판 전장의 재질을 정확하게 예측하기 위해서는 도 1에서 설명한 열연강판의 냉각해석 결과뿐만 아니라, 상변태도 계산하여 잠열의 출입을 고려하여야 한다. 다음으로, 제5단계(15)는 도 1에서 설명한 냉각해석방법을 이용하여 열연강판의 두께 및 시간에 따른 온도값을 나타내는 해를 구한다. 여기서 구한 해를 이용하면 CT구간의 냉각정보를 계산할 수 있다. 도 1에서 냉각해석 해를 구하는 방법을 자세하게 설명하였으므로 여기서는 그 자세한 설명을 생략한다. Next, the fourth step 14 calculates the phase transformation of the hot rolled steel sheet. As the hot rolled steel sheet is cooled in the runout table, phase transformation of the hot rolled steel sheet occurs from austenite to pearlite, ferrite, or martensite. Phase transformation can cause latent heat to be released or absorbed. Therefore, in order to accurately predict the material of the electric field of the hot rolled steel sheet, not only the cooling analysis result of the hot rolled steel sheet described in FIG. 1 but also the phase transformation should be calculated to consider the entry and exit of latent heat. Next, the fifth step (15) is obtained by using the cooling analysis method described in Figure 1 to obtain a solution representing the temperature value of the thickness and time of the hot-rolled steel sheet. Using the solution, we can calculate the cooling information of the CT section. Since the method for obtaining the cooling analysis solution was described in detail in FIG. 1, the detailed description thereof will be omitted.

다음으로, 제6단계(16)는 측정한 CT구간의 온도와 도 1의 냉각해석방법을 이용하여 계산한 CT구간의 온도를 비교한다. 여기서, 계산한 온도와 측정한 온도의 차이가 1℃ 미만인 경우 다음 단계로 진행하고, 1℃ 이상인 경우 상변태를 계산하는 단계로 돌아간다. 이때, 열전달 보정계수를 조건에 맞도록 수정하여 갱신한다. 즉, 온도차이가 1℃ 이상인 경우 계속해서 열전달 보정계수를 수정하면서, 상변태 계산 단계 및 냉각해석 단계를 반복 수행한다. 이와 같은 과정을 통해서, 계산값이 실제 측정값에 수렴할 수 있으므로, 열연강판의 재질을 더욱 정확하게 예측할 수 있다. 다음으로, 제7단계(17)는 첫 단계에서 나눈 미소구간 전체에 대해서 예 측을 진행하였는지 확인한다. 만약 그렇지 않다면, 다시 제2단계로 돌아가서 다음 미소구간에 대해서 전술한 제2단계 내지 제6단계의 예측을 반복해서 진행한다. 이와 같은 방법으로, 계속해서 반복하여 열연강판 전장에 대해서 재질예측(18)을 수행할 수 있다. Next, the sixth step 16 compares the measured temperature of the CT section with the temperature of the CT section calculated using the cooling analysis method of FIG. Here, if the difference between the calculated temperature and the measured temperature is less than 1 ℃ proceeds to the next step, and if it is more than 1 ℃ return to the step of calculating the phase transformation. At this time, the heat transfer correction coefficient is corrected and updated to meet the condition. That is, when the temperature difference is 1 ° C. or more, the phase transformation calculation step and the cooling analysis step are repeatedly performed while continuously modifying the heat transfer correction coefficient. Through this process, since the calculated value can converge to the actual measured value, the material of the hot rolled steel sheet can be predicted more accurately. Next, the seventh step (17) checks whether the prediction for the entire microdivision divided in the first step has been made. If not, the process returns to the second step again and repeats the above-described prediction of the second to sixth steps for the next minute section. In this manner, the material prediction 18 can be performed continuously and repeatedly on the hot rolled steel sheet electric field.

이하에서는 도 3 내지 도 5을 통하여 본 발명의 일 실시예에 따른 냉각해석방법의 효과를 설명한다.  Hereinafter, the effects of the cooling analysis method according to an embodiment of the present invention through FIGS. 3 to 5.

도 3 내지 도 5는 런아웃테이블상에서의 열연강판의 길이 또는 시간에 따른 열연강판의 두께에 따른 각 부분의 온도변화를 나타낸다. 도 3 내지 도 5는 순서대로 열연강판 하부의 온도변화, 열연강판 중심부의 온도변화, 및 열연강판 상부의 온도변화에 대한 그래프이다. 열연강판은 런아웃테이블을 일정한 속도로 통과하므로, 일정한 지점의 시간에 따른 온도변화와 열연강판의 길이에 따른 온도변화가 동일한 그래프를 나타낸다. 3 to 5 show the change in temperature of each part according to the thickness of the hot-rolled steel sheet over time or length of the hot-rolled steel sheet on the runout table. 3 to 5 are graphs of the temperature change of the bottom of the hot rolled steel sheet, the temperature change of the center of the hot rolled steel sheet, and the temperature change of the hot rolled steel sheet in order. Since the hot rolled steel sheet passes through the runout table at a constant speed, the temperature change according to the time of a certain point and the temperature change according to the length of the hot rolled steel sheet are the same.

사용된 열연강판은 탄소함량 0.11%이고, 두께가 3.23mm이며, 런아웃테이블에서의 이동속도는 900m/분이다. 또한, FDT에서의 온도는 900℃ 이고, CT에서의 온도는 600℃이다. The hot rolled steel sheet used was 0.11% carbon, 3.23 mm thick, and the moving speed in the runout table was 900 m / min. In addition, the temperature in FDT is 900 degreeC, and the temperature in CT is 600 degreeC.

도 3 내지 도 5의 그래프에서 본 발명의 일 실시예에 따른 방법의 결과를 실시예로 표시하였고, 기존의 유한차분법을 이용한 방법의 결과를 비교예로 표시하였다. 도 3 내지 도 5의 그래프에서 알 수 있듯이, 비교예와 실시예의 결과는 열연강판의 상부, 중간부, 및 하부에서 모두 동일하다. 그러나 실시예는 비교예에 비해 30%정도 단축된 계산시간을 나타내므로, 비교예에 비하여 같은 결과를 빠른 시 간에 얻을 수 있다. 3 to 5 show the results of the method according to an embodiment of the present invention as an example, and the results of the conventional method using a finite difference method as a comparative example. As can be seen in the graphs of FIGS. 3 to 5, the results of the comparative examples and the examples are the same in all of the upper, middle and lower portions of the hot rolled steel sheet. However, since the Example shows a calculation time reduced by about 30% compared to the Comparative Example, the same result can be obtained faster than the Comparative Example.

본 발명의 일 실시예에 따른 열연강판의 냉각해석방법은 해석해를 이용하므로, 종래의 방법에 비하여 해가 더욱 안정적으로 수렴한다. Since the cooling analysis method of the hot rolled steel sheet according to the embodiment of the present invention uses an analysis solution, the solution converges more stably than the conventional method.

또한, 미소시간을 증가시켜 해석을 수행하여도 해의 정밀도 및 신뢰성이 유지되므로, 계산의 반복횟수가 줄어들어 전체 계산속도가 향상된다. In addition, even if the analysis is performed by increasing the micro time, the accuracy and the reliability of the solution are maintained, so that the number of iterations of the calculation is reduced and the overall calculation speed is improved.

또한, 각각의 계산과정에서도 경계조건 및 공정조건을 단순화하여 각각의 계산속도도 향상된다. In addition, the calculation speed is also improved by simplifying boundary conditions and process conditions in each calculation process.

또한, 적용이 간편하여 다른 곳으로의 이식이 용이하다.In addition, it is easy to apply and thus easy to transplant to other places.

본 발명의 일 실시예에 따른 열연강판의 재질해석방법은 전술한 냉각해석방법을 이용하여, 열연강판의 전장예측에 계산속도 및 계산의 안정성이 향상된다. In the material analysis method of the hot rolled steel sheet according to the embodiment of the present invention, the calculation speed and stability of the calculation are improved in the electric field prediction of the hot rolled steel sheet by using the aforementioned cooling analysis method.

또한, 더욱 빠른 시간에 보다 정확한 계산을 재질예측을 수행하므로, 생산된 열연강판의 신뢰성이 높아지며, 제조원가가 절감된다. In addition, since the material prediction is performed in a more accurate calculation at a faster time, the reliability of the produced hot rolled steel sheet is increased, and the manufacturing cost is reduced.

Claims (5)

열연강판의 냉각해석방법에 있어서,In the cooling analysis method of the hot rolled steel sheet, 하기의 수학식을 만족하는 열연강판의 냉각해석방법. Cooling analysis method of the hot rolled steel sheet satisfying the following equation.
Figure 112006091564409-PAT00032
Figure 112006091564409-PAT00032
 여기서,
Figure 112006091564409-PAT00033
는
Figure 112006091564409-PAT00034
이고,
Figure 112006091564409-PAT00035
는 초기온도조건,
Figure 112006091564409-PAT00036
는 비열용량(specific heat), H는 열연강판의 두께, y는 두께 변수, t는 시간,
Figure 112006091564409-PAT00037
는 발열량,
Figure 112006091564409-PAT00038
은 강판 상부의 부열유속,
Figure 112006091564409-PAT00039
는 강판 하부의 부열유속,
Figure 112006091564409-PAT00040
는 온도분포, 그리고 k는 상수이다.here,
Figure 112006091564409-PAT00033
Is
Figure 112006091564409-PAT00034
ego,
Figure 112006091564409-PAT00035
Is the initial temperature condition,
Figure 112006091564409-PAT00036
Is the specific heat, H is the thickness of the hot rolled steel, y is the thickness variable, t is the time,
Figure 112006091564409-PAT00037
Is calorific value,
Figure 112006091564409-PAT00038
Sub-heat flow rate at the top of the steel sheet,
Figure 112006091564409-PAT00039
Is the subheat rate at the bottom of the steel sheet,
Figure 112006091564409-PAT00040
Is the temperature distribution, and k is a constant. 구간을 나누어 냉각 정보를 측정 및 계산하기 위하여 열연강판의 전장을 길이방향으로 2이상의 미소구간으로 나누는 제1단계;Dividing the entire length of the hot-rolled steel sheet into two or more minute sections in the longitudinal direction to measure and calculate cooling information by dividing the sections; 상기의 나누어진 미소구간 중에서 다듬질압연(finishing rolling) 출측(FDT) 구간 및 권취온도(Coiling Temperature, CT) 측정위치 구간의 냉각정보를 측정하는 제2단계;A second step of measuring cooling information of a finishing rolling exit (FDT) section and a coiling temperature (CT) measurement position section among the divided minute sections; 열전달 보정계수(h(n))의 초기값을 설정하는 제3단계;A third step of setting an initial value of the heat transfer correction coefficient h (n); 상기 열연강판에 상변태를 계산하는 제4단계;A fourth step of calculating a phase transformation on the hot rolled steel sheet; 제1항의 냉각해석방법으로 해석해를 구하는 제5단계; A fifth step of obtaining an analysis solution by the cooling analysis method of claim 1; 상기 제2단계에서 측정한 CT구간 온도와 상기 제5단계의 해석해에서 계산된 CT구간 온도의 차를 구하는 제6단계;A sixth step of obtaining a difference between the CT section temperature measured in the second step and the CT section temperature calculated in the analysis solution of the fifth step; 상기 제1단계에서 나눈 마지막 미소구간까지 상기 제2단계 내지 제6단계가 수행되었는지 확인하는 제7단계;A seventh step of confirming whether the second to sixth steps are performed until the last minute section divided in the first step; 를 포함하는 열연 강판의 재질예측방법.Material prediction method of hot rolled steel sheet comprising a. 제2항에 있어서,The method of claim 2, 상기 6단계에서의 온도차가 1℃ 보다 큰 경우에, If the temperature difference in the six steps is greater than 1 ℃, 상기 제4단계 내지 제6단계를 반복해서 수행하는 열연강판의 재질예측방법.Method of predicting the material of the hot rolled steel sheet to repeat the fourth step to sixth step. 제3항에 있어서,The method of claim 3, 상기 6단계에서의 온도차가 1℃ 보다 큰 경우에, If the temperature difference in the six steps is greater than 1 ℃, 상기 열전달 보정계수를 조절하여 갱신하는 단계를 더 포함하는 열연강판의 재질예측방법.The method of predicting the material of the hot rolled steel sheet further comprising the step of updating by adjusting the heat transfer correction coefficient. 제1항에 있어서,The method of claim 1, 상기 7단계에서, In step 7, 상기 제1단계에서 나눈 마지막 미소구간까지 재질예측이 진행되지 않은 경우, 다음 미소구간에 대하여 상기 제2단계 내지 제6단계를 반복해서 수행하는 열연강판의 재질예측방법.When the material prediction does not proceed to the last minute section divided in the first step, the material prediction method of hot rolled steel sheet is performed by repeating the second step to the sixth step for the next minute section.
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