JPH0550128A - Method for predicting rolling temperature of steel sheet in hot rolling - Google Patents

Abstract

PURPOSE:To evaluate the temperature at a necessary position in the direction of a plate thickness by predicting not only an average temperature but also the temperature distribution in the thickness direction of a steel plate through a simple calculation with high accuracy concerning a method for predicting the rolling temperature of a hot rolled stock such as a TMCP steel plate, etc., on line in the rolling process. CONSTITUTION:A 1st temperature distribution in the thickness direction of a steel sheet controlled only by the cooling mode of rolling process and a 2nd temperature distribution in the thickness direction of the steel sheet showing a recuperative behavior of heat in the steel sheet are intended to be obtained respectively as a boundary value problem of an initial value derived of simultaneous partial differential equations based on a heat contuction equation. For that purpose, a weak expression from is used for these simultaneous partial differential equations and these simultaneous partial differential equations results in the simultaneous ordinary differential equation series of time. The simultaneous ordinary differential equations are solved to find the 1st and 2nd temperature distributions, the predictive model of an on-line rolling temperature at a temperature field formed when the steel sheet having a prescribed initial temperature distribution is cooled under a specified cooling mode is created by combining the 1st temperature distribution and the 2nd temperature distribution and the rolling temperature in the thickness direction of the steel sheet in the rolling process is predicted in accordance with this model.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for predicting a rolling temperature of a hot rolled steel sheet such as a TMCP steel sheet online in a rolling process.

[0002]

2. Description of the Related Art In recent years, demands for strength, toughness, weldability, etc., which are important characteristics of thick plate products, have become more and more strict with the increase in size of steel structures and the severer usage environment.

Therefore, TMCP (Thermo Mechanical Con
trol Process) is applied and online cooling is performed in the rolling process to produce high-tensile steel sheets (hereinafter referred to as TMCP steel sheets; for example, accelerated cooling steel sheets, direct-quenched steel sheets) with excellent toughness and weldability. ..

For stabilization of the material of these TMCP steel plates and improvement of plate thickness accuracy and flatness (that is, for shape control, plate thickness control, and controlled rolling of hot-rolled steel plates), prediction of rolling temperature in rolling process Improving the accuracy of is an extremely important factor.

[0005]

For this reason, various online models have been conventionally constructed in order to predict the rolling temperature of the hot-rolled steel sheet, but there are problems as described below.

The thermal history of the steel sheet from extraction of the heating furnace to completion of rolling is calculated by rolling temperature simulation by the difference method, and a simple prediction formula for the average temperature is prepared based on the average temperature obtained from the thermal history. Since the basic form of the simple prediction formula of the average temperature is not based on the heat conduction equation, it cannot follow the dynamic cooling form in the rolling line including ordinary rolling and controlled rolling.

In addition, in order to secure an appropriate reduction amount in a temperature range required in a rolling line as in controlled rolling, the steel sheet cooling device is used to cool the steel sheet during rolling. It is important not only to set the average temperature to the target temperature but also to prevent the surface temperature from overcooling, but with the conventional means, it is impossible to control the surface temperature of the steel sheet because only the average temperature can be predicted. is there.

The conventional estimation of the surface temperature is as follows.
It is assumed that the temperature distribution in the plate thickness direction is represented by the power of the position in the plate thickness direction, but at that time, the order n of the power of the plate in the plate thickness direction is fixed, so the predicted average temperature Can not be converted to high precision.

The order n of the power to the power calculated by the rolling temperature simulation by the difference method is from the higher order of 30th order or higher to the 1st to 3rd order depending on various cooling modes of the rolling line, plate thickness during rolling, and the like. Since it changes dynamically from rough rolling to finish rolling, in order to perform such conversion with high accuracy, it is necessary to accurately estimate the order n of the power, but with a fixed order, only the form is converted. It's just done.

In mill setting during rolling, the surface temperature cannot be predicted even if the temperature is measured during rolling, or even if it is predicted, highly accurate estimation cannot be performed for the reasons described above. It was also not possible to check or correct the average temperature of the above with high accuracy.

For the above reasons, in recent years, there has been a case where temperature prediction and actual temperature calculation in a rolling line are performed using a difference model, but since the calculation load becomes large, it is naturally necessary to perform the prediction calculation. There is a limit, and in the temperature calculation including actual calculation, a very large-scaled computer is required in terms of capacity and capacity.

The present invention has been made in view of such a situation, and enables not only the average temperature but also the temperature distribution in the plate thickness direction of the steel plate to be estimated with high accuracy by a simple calculation. It is an object of the present invention to provide a method for predicting the rolling temperature of a steel sheet in hot rolling, which enables the temperature evaluation at the required position of.

[0013]

In order to achieve the above object, the method for predicting the rolling temperature of a steel sheet in hot rolling according to the present invention is a first method in the thickness direction of a steel sheet governed only by the cooling mode in the rolling process. And the second temperature distribution in the thickness direction of the steel sheet, which represents the recuperative behavior in the steel sheet, as the solution of the initial value boundary value problem consisting of simultaneous partial differential equations based on the heat conduction equation. , By using a weak representation form for the simultaneous partial differential equations to reduce the simultaneous partial differential equations to a system of simultaneous ordinary differential equations in time, and solve the simultaneous ordinary differential equations to obtain the first and second temperature distributions. After the determination, the on-line rolling temperature prediction model for the temperature field formed in the plate thickness direction of the steel plate when the steel plate having the predetermined initial temperature distribution is cooled under the predetermined cooling form is calculated using the first temperature distribution and the second The temperature of From building as obtained by superimposing the distribution, on the basis of the online rolling temperature prediction model, it is characterized by predicting the thickness direction of the rolling temperature in the rolling process of the steel sheet.

[0014]

In the method for predicting the rolling temperature of the steel sheet in the hot rolling of the present invention described above, the on-line rolling temperature prediction model in various cooling forms in the rolling process uses the weak expression of the heat conduction equation to Since it is constructed while giving a physical meaning based on the conduction equation, the temperature distribution in the steel plate thickness direction can be calculated with high accuracy by the model.

[0015]

EXAMPLE In the present invention, in order to construct a rolling temperature prediction in various cooling modes in a rolling process based on a heat conduction equation with high precision while having a physical meaning, a weak expression of the heat conduction equation is used. By using this, a new online rolling temperature prediction model that can calculate the temperature distribution in the plate thickness direction was newly constructed. The outline of the prediction model construction is described below. For the weak expression of the heat conduction equation, see BAFi
nlayson: The Methodof Weighted Residuals and Varia
tional Principle (1972, Academic Press), OCZienk
iewicz: The Finite Element Method (1977, McGraw-Hil
It is described in l).

By setting the following assumptions (a) to (d) as a premise for constructing the rolling temperature prediction model, the temperature prediction model in the rolling process relates to heat conduction in the plate thickness direction under each cooling mode. It is constructed by deriving the solution of the initial value boundary value problem.

(A) The temperature distribution in the plate thickness direction of the slab during extraction in the heating furnace is uniform. (b) The heat transfer coefficients of the upper and lower surfaces of the steel plate in the rolling process are the same. (c) Processing heat generated by plastic working during rolling is uniform in the plate thickness direction. (d) The plate thickness of the steel plate at the time of contact with the roll is the average thickness on the inlet and outlet sides.

Based on the above assumptions, the formulation of the prediction model will be described below. When a steel sheet having an initial temperature distribution φ ₀ (x) is cooled under a constant cooling mode, as shown in FIG. 1, the temperature field T (x, t) formed in the thickness direction of the steel sheet is It can be expressed in the form of equation (1) in which the solutions U and V of the initial value boundary value problem consisting of simultaneous partial differential equations (2) and (3) are superimposed. T (x, t) = U (x, t) + V (x, t) (1)

[0019]

[Equation 1]

In the above equations (2) and (3), λ, c,
ρ is the thermal conductivity, specific heat and density of the steel sheet, α is the heat transfer coefficient, h is the thickness of the steel sheet, T ₀ is the ambient temperature, t is the time,
x is the position in the plate thickness direction of the steel plate.

At this time, V represents the temperature distribution governed by the cooling mode, and U is the temperature distribution representing the recuperation behavior in the steel sheet.

In formulating U and V, the boundary conditions on the steel plate surface in the initial value boundary value problem (3) are expressed by the following formulas (4) and (5) in order to simplify the model. Approximated.

[0023]

[Equation 2]

It is assumed that the temperature distribution in the plate thickness direction of the steel plate in each cooling mode in the rolling process is expressed as a function of the power of the position x in the plate thickness direction. If the number of cooling processes in the previous history of the cooling process to be analyzed is k, the initial temperature distribution φ ₀ (x) can be displayed as in the following equation (6).

[0025]

[Equation 3]

At this time, the solutions U and V of the initial value boundary value problems (2) and (3) can be expressed as the following expressions (7) and (8).

[0027]

[Equation 4]

Next, by using the weak expression for the simultaneous partial differential equations (2) and (3), as shown below,

[Equation 5] Can be reduced to a system of simultaneous ordinary differential equations with time as an unknown function.

[0029]

[Equation 6]

[0030]

[Equation 7]

The simultaneous ordinary differential equations composed of equations (7) to (16) can be solved analytically with respect to the unknown function. Specifically, it becomes as shown in the following equations (17) to (37).

[0032]

[Equation 8]

[0033]

[Equation 9]

[0034]

[Equation 10]

[0035]

[Equation 11]

As described above, the solutions U and V of the initial value boundary value problems (2) and (3) were formulated, and a new rolling temperature prediction model capable of calculating the temperature distribution in the plate thickness direction was constructed.

That is, in this embodiment, the first temperature distribution V in the thickness direction of the steel sheet is governed only by the cooling mode in the rolling process.
And the second temperature distribution U in the thickness direction of the steel sheet that represents the recuperative behavior in the steel sheet, and the initial value boundary value problem consisting of simultaneous partial differential equations (2) and (3) based on the heat conduction equation. In order to obtain the solution of the simultaneous partial differential equations (2), (3), the partial partial differential equations (2), (3)
To a system of simultaneous ordinary differential equations (9) to (16).

Then, the simultaneous ordinary differential equations (9) to (16)
By solving the equations (17) to (37), the temperature distribution U,
After obtaining V, the online rolling temperature prediction for the temperature field T (x, t) formed in the steel plate thickness direction when the steel plate having the predetermined initial temperature distribution φ ₀ (x) is cooled under the predetermined cooling mode. The model is constructed by superimposing the temperature distributions U and V, and the rolling temperature in the plate thickness direction in the rolling process of the steel sheet is predicted based on this rolling temperature prediction model.

Here, the temperature change behavior of the steel sheet in a series of steps from the extraction of the heating furnace to the completion of the finish rolling is performed using a rolling temperature simulation model based on the difference method and an online rolling temperature prediction model newly constructed by this embodiment. Calculate using and compare accuracy.

The calculation conditions for this precision comparison calculation are shown in the table below.

[Table 1]

Further, the heat transfer coefficient α _R in contact with the roll being rolled is given by the following equation.

[Equation 12] Where λ _R , c _R and ρ _R are the thermal conductivity of the roll,
Specific heat, density, R is roll diameter, r is rolling reduction, h ₀ is inlet side thickness, and v is rolling speed.

Further, the following equations were used to calculate the amount ΔT of increase in steel plate temperature due to heat generated by plastic working of rolling and the average thickness h _m .

[Equation 13] Here, h ₁ is DegawaAtsu, is p _m is the average rolling pressure.

Regarding the changes with time of the average temperature, the surface temperature and the central temperature of the steel sheet in the rolling process, the accuracy of the prediction method according to the present embodiment performed based on the above table and each formula and the difference model capable of performing highly accurate calculation The comparison result is shown in FIG.

As is apparent from FIG. 2, the calculation results obtained by the online rolling temperature prediction model of this embodiment are almost the same as the calculation results obtained by the differential model throughout the entire process. From this, it is understood that the estimation accuracy of the prediction model of the present embodiment is almost the same as the estimation accuracy of the difference model.

As described above, according to the method of this embodiment, the temperature distribution V governed by the cooling form in the rolling process, which is obtained by using the weak expression of the heat conduction equation, and the cooling form under the cooling form. In addition to the temperature distribution U representing the recuperation behavior in the steel sheet, the temperature increase amount ΔT due to the heat generated by the plastic working due to rolling is taken into consideration, so that the temperature prediction equivalent to that of the differential model capable of reproducing the temperature change in the strict rolling line can be performed. It was realized by extremely simple calculation, and its high effectiveness was confirmed.

Further, it becomes possible to highly accurately estimate the temperature distribution in the plate thickness direction of the steel sheet, which could not be predicted by the simple formula until now, under any cooling mode in the rolling process.

Further, the temperature prediction calculation by the model of the present embodiment can be performed with a calculation amount of about 1/10 of the temperature prediction calculation by the difference model, and the time required for temperature prediction can be greatly shortened.

[0048]

As described in detail above, according to the method for predicting the rolling temperature of a steel sheet in hot rolling according to the present invention, an online rolling temperature predicting model in various cooling modes in the rolling process can be used as a heat conduction equation model. By using the weak expression, it is constructed while giving a physical meaning based on the heat conduction equation, so that the model can calculate not only the average temperature but also the temperature distribution in the plate thickness direction with extremely simple calculation with high accuracy. There is an effect that it can be calculated and a reliable temperature evaluation at a required position in the plate thickness direction can be realized.

[Brief description of drawings]

FIG. 1 is a graph showing an example of temperature distribution in a plate thickness direction of a steel plate for explaining a method for predicting a rolling temperature of a steel plate in hot rolling as an embodiment of the present invention.

FIG. 2 is a graph showing a temperature predicted value by the method of the present embodiment and a temperature predicted value by the difference method in comparison.

Claims (1)

[Claims] 1. A method of predicting a rolling temperature of a steel sheet in hot rolling, comprising: a first temperature distribution in the thickness direction of the steel sheet, which is governed only by a cooling mode in a rolling process; In order to obtain the second temperature distribution in the plate thickness direction of the steel sheet, which represents the thermal behavior, as the solution of the initial value boundary value problem consisting of the simultaneous partial differential equations based on the heat conduction equation, the weak partial differential equations are weakened. The simultaneous partial differential equations are reduced to a system of simultaneous ordinary differential equations in time by using the expression form, and the first and second temperature distributions are obtained by solving the simultaneous ordinary differential equations. An online rolling temperature prediction model for a temperature field formed in the thickness direction of the steel sheet when the steel sheet having a distribution is cooled under a predetermined cooling form is calculated by using the first temperature distribution and the second temperature distribution. After constructing as a superposed with a cloth, based on the online rolling temperature prediction model, the rolling temperature of the steel sheet in hot rolling characterized by predicting the rolling temperature in the sheet thickness direction in the rolling process of the steel sheet Temperature prediction method.