JP2554414B2 - Prediction method of rolling temperature of steel sheet in hot rolling - Google Patents

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 stringent 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-strength steel sheets with excellent toughness and weldability (hereinafter referred to as TMCP steel sheets; for example, accelerated cooling steel sheets, direct-quenched steel sheets). .

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

[0005]

For this reason, various online models have been constructed so far in order to predict the rolling temperature of the hot-rolled steel sheet, but there were the following problems.

The thermal history of the steel sheet from extraction of the heating furnace to completion of rolling is calculated by rolling temperature simulation using 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 for 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 amount of reduction in the temperature range required in the rolling line as in the case of 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, since the order n of the power of the plate in the plate thickness direction is fixed, the predicted average temperature Can not be converted to high precision.

The order n of the power to be calculated by the rolling temperature simulation by the difference method is from the higher order of 30th order or more to the 1st to 3rd order depending on various cooling modes of the rolling line, the 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 the 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 the rolling line are performed using the 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 the actual calculation, a very large-scale computer is required in terms of capacity and capacity.

The present invention has been made in view of the above circumstances, and enables not only the average temperature but also the temperature distribution in the plate thickness direction of a 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 recuperation 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. , The weak partial expression is used 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 online rolling temperature prediction model for the temperature field formed in the sheet thickness direction of the steel sheet under each cooling mode in the rolling process was superposed with the first temperature distribution and the second temperature distribution. things and From building Te, the online rolling
Rolling temperature in the plate thickness direction calculated by the temperature prediction model
The amount of temperature rise due to rolling plastic working heat is added to the distribution.
Is used to predict the rolling temperature in the plate thickness direction in the rolling process of the steel plate.

[0014]

[Function] As is well known, heating furnace extraction to finish rolling is completed.
In the hot rolling process up to
(High-pressure water scale breaker) cooled state, rough rolling completed
Cooling state by shower water cooling after completion, stop shower water cooling
Immediately after cooling, for each pass of rough rolling or finish rolling
Various cooling modes such as the cooling state due to roll contact in
There is. In the method for predicting the rolling temperature of the steel sheet in the hot rolling of the present invention described above, each cooling type as described above in the rolling process is used.
The on-line rolling temperature prediction model in the state is constructed while having a physical meaning based on the heat conduction equation by using the weak expression of the heat conduction equation. Can be calculated with high accuracy.

[0015]

EXAMPLES In the present invention, in order to construct a rolling temperature prediction in various cooling modes in a rolling process based on the heat conduction equation with high precision while having a physical meaning, a weak expression of the heat conduction equation is used. An online rolling temperature prediction model that can calculate the temperature distribution in the sheet thickness direction was newly constructed by using it. 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) and 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 a 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 entrance and exit 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.

When 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. Now, if the number of cooling steps in the previous history of the cooling step to be analyzed is k, the initial temperature distribution φ ₀ (x) can be taught as in the following equation (6). Where the expression
Μ _i and A _i in (6) are the i-th in the hot rolling process.
For cooling process (for example, shower water cooling process after rough rolling is completed)
Generated temperature distribution (equation (2), (3) in the initial value boundary value problem)
Of the solution U and V) of A _i (1
-X / μ _i ) ⁿ function with the position x in the plate thickness direction as a variable
It is a constant determined by approximating. Also, n
Is a predetermined order (positive integer) and can be set arbitrarily
In the embodiment described later, n = 2 is set.
I have. This order n expresses the temperature distribution in the plate thickness direction to be obtained.
Function that represents the basic temperature distribution for
It is the order of a function having x as a variable).

[0025]

(Equation 3) Here, μ _i ≦ h / 2, and T _a is the value when the heating furnace is extracted.
This is a temperature distribution (constant value) in the plate thickness direction of the slab. That
Then, the initial temperature distribution φ ₀ (x) is obtained as follows.
Here, the order n is set to n = 2, for example.
First, the initial temperature distribution φ ₀ (x) in the first cooling step is
From the assumption (a) described above, T _a is obtained. Second cooling step
Initial temperature distribution φ ₀ (x) at
If the generated temperature distribution is approximated by A ₁ (1−x / μ ₁ ) ² ,
It becomes T _a + A ₁ (1−x / μ ₁ ) ² . And the third
The initial temperature distribution φ ₀ (x) in the cooling process is the second cooling process
Approximate the temperature distribution generated at A ₂ (1−x / μ ₂ ) ²
Then, T _a + A ₁ (1−x / μ ₁ ) ² + A ₂ (1−x / μ 1
₂ ) It becomes ² . Similarly, in the k + 1th cooling step
The initial temperature distribution φ ₀ (x) is generated in the kth cooling step.
If the temperature distribution is approximated by A _k (1−x / μ _k ) ² , T _a
+ ΣA _i (1−x / μ _i ) ² , i = 1, ..., k,
In this way, the initial temperature distribution φ ₀ (x) can be obtained.
Become.

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) It 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]

From the 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 the present embodiment, the first temperature distribution V in the steel plate thickness direction governed only by the cooling mode in the rolling process.
And the second temperature distribution U in the thickness direction of the steel sheet, which 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, respectively. In order to obtain the solution of, the weak partial form of the simultaneous partial differential equations (2) and (3) is used to solve the simultaneous partial differential equations (2) and (3).
To a system of simultaneous ordinary differential equations (9) to (16).

Then, the simultaneous partial differential equations (9) to (16)
By solving the equations (17) to (37), the temperature distribution U,
After obtaining V, an online rolling temperature prediction model for the temperature field T (x, t) formed in the steel sheet thickness direction under each cooling mode is constructed by superimposing the temperature distributions U and V, Calculated by this online rolling temperature prediction model
Heat generated during plastic working of rolling in a specified rolling temperature distribution in the plate thickness direction
By adding the amount of temperature rise due to , the rolling temperature in the plate thickness direction in the rolling process of the steel plate is predicted.

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 finish rolling is performed by 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 results of this precision comparison calculation are shown in the table below. Further, the order n of the equation (6) is n = 2.

[Table 1]

The heat transfer coefficient α _{R at the time} of contact with the roll during rolling 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 sheet 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 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 online pressure constructed by using the weak expression of the heat conduction equation is used.
The temperature distribution V governed by the cooling form in the rolling process and the temperature distribution U representing the reheat behavior in the steel sheet under the cooling form, which were obtained from the rolling temperature prediction model, were used to determine the plastic deformation of rolling.
By adding the temperature rise amount ΔT due to heat, it is possible to realize the temperature prediction equivalent to the difference model capable of reproducing the temperature change on the strict rolling line 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 a simple formula until now under an arbitrary 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 prediction 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 steel sheet thickness direction for explaining a method for predicting a rolling temperature of a steel sheet 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)

(57) [Claims] 1. A method for 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 composed of the simultaneous partial differential equations based on the heat conduction equation, the weak partial differential equations are weakened. By using the expression form, the simultaneous partial differential equations are reduced to a system of simultaneous ordinary differential equations in time, and the first and second temperature distributions are obtained by solving the simultaneous ordinary differential equations, and then, in the rolling process. build online rolling temperature prediction model, as obtained by superimposing a second temperature distribution and the first temperature distribution of the temperature field formed in the thickness direction of the steel plate under each cooling form of After it was calculated by the online rolling temperature prediction model
In the rolling temperature distribution in the plate thickness direction, the temperature due to the plastic working heat of rolling
A method of predicting a rolling temperature of a steel sheet in hot rolling, comprising predicting a rolling temperature in a sheet thickness direction in the rolling step of the steel sheet by adding a degree of increase in degree .