JPH07258752A - Method for controlling combustion in heating furnace for rolling - Google Patents

Abstract

PURPOSE:To calculate the furnace temp. to be set to a heating furnace for rolling by dissolving an unidimensional thermal conduction difference equation in the thickness direction of a slab within a range between skids and a two-dimensional thermal conduction difference equation in the thickness direction and in the longitudinal direction of the slab on the skid part. CONSTITUTION:At the time of controlling heating-up of the slab in the heating furnace for rolling, within a range between the skids, the unidimensional thermal conduction difference equation in the thickness direction of the slab is dissolved. Further, on the skid part, the two-dimensional thermal conduction difference equation in the thickness direction and the longitudinal direction of the slab simplified with the thermal conduction in the longitudinal direction of the slab by introducing a factor is dissolved. By this method, the future temp. distributions are predicted as to the slab between the skids and on the skid part in the furnace, these heating-up quality is evaluated, the furnace temp. to be set to the heating furnace for rolling is calculated and the heating-up quality of the slab is improved.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to combustion control (slab baking control) of a rolling heating furnace.

[0002]

2. Description of the Related Art Generally, the purpose of computer control of a heating furnace in a rolling mill is to heat a continuously charged slab to a target temperature determined by rolling conditions (product size, rolling temperature, etc.) and to demand the rolling line. It is to extract according to the pitch. Furthermore, in order to prevent uneven burning of the slab during extraction, it is desirable in terms of quality to soak the heat as much as possible. On the other hand, in order to reduce the fuel consumption, overheating should be avoided, and control that satisfies both the contradictory objectives of quality and energy saving is required.

To achieve this, an accurate slab temperature calculation model and furnace temperature setting model are required.
Here, the slab temperature calculation model is to calculate the current temperature of the slab from the atmosphere temperature in the furnace detected by the furnace temperature detector and the heat conduction equation.The calculation method is the temperature between the skids and the temperature of the skid part. A two-dimensional (slab thickness direction x slab longitudinal direction) heat conduction difference equation that can calculate the distribution with high accuracy is often used. The furnace temperature setting model is
It is a model to calculate the furnace temperature required to bake the slab from the current temperature to the extraction target temperature, and various calculation methods have been proposed, but in general, the slab baking simulation is performed under appropriate conditions, The baking result is evaluated to determine the set value. The baking simulation function requires a slab temperature rise prediction calculation model. Here, the slab temperature rise prediction calculation model requires repeated temperature rise prediction calculation until each slab is extracted for all slabs in the furnace, and if a two-dimensional heat conduction difference equation is to be solved, The amount of calculation is generally enormous, and the processing time cannot withstand online control. Therefore, in order to reduce the calculation time, use the one-dimensional heat conduction equation in the slab thickness direction, which has a small calculation load when solving it using a numerical calculation method, or the difference between the current temperature and the target temperature. It is common to limit the calculation load by limiting the neck slab to the calculation target slab in order to achieve baking of all slabs by baking the slab that is considered to be the most difficult to burn, such as the largest slab. Target.

[0004]

However, since the temperature distribution of the skid part cannot be calculated usually by the one-dimensional heat conduction equation, the skid part is successfully baked in the furnace temperature setting model using this for the slab temperature rise prediction model. I can't.

Further, when the slabs to be calculated are limited, and when the slabs in the furnace are of various types, waste slabs are likely to occur for slabs not to be calculated.

The present invention solves the above-mentioned drawbacks and makes it possible to predict the temperature distribution between skids and skid parts for all slabs in the furnace with a small amount of calculation, and a furnace temperature setting model using this It is an object of the present invention to provide a method for ensuring high quality baking excellent in heat uniformity not only in the thickness direction of the slab but also in the longitudinal direction of the slab.

[0007]

According to the present invention, the above-mentioned problems are solved by introducing a one-dimensional heat conduction difference equation in the slab thickness direction between skids and introducing a coefficient of heat conduction in the longitudinal direction of the slab for skid parts. By solving a simplified two-dimensional (slab thickness direction x slab longitudinal direction) heat conduction difference equation, the future temperature distribution between the skids of the slab in the furnace and in the thickness direction of the skid part is predicted, and their baking quality is evaluated. By doing so, the furnace temperature to be set in the rolling heating furnace (set furnace temperature) is calculated.

[0008]

The outline of the processing of the present invention is shown in FIG. 1 using the expression of the functional configuration. In the present invention, with respect to the slab in the furnace, it is assumed that the furnace temperature at the present time continues, and after predicting the slab temperature at the time of extraction assuming that the slab moves in the furnace at the planned extraction pitch, the set furnace The calculation of the temperature is linearized as a problem of minute fluctuations near the current furnace temperature, and is solved by a linear programming process that finds the optimum furnace temperature change amount of each combustion zone under the constraint condition of baking quality. In the slab temperature rise prediction, the temperature distribution is predicted not only between the skids but also up to the skid part.Therefore, the soaking degree between the skid and the skid part is one of the constraints of the baking quality when determining the optimal furnace temperature change amount. Can be taken into consideration, and it is possible to calculate the amount of change in furnace temperature that enables uniform baking not only in the slab thickness direction but also in the slab longitudinal direction. In addition, the optimum set furnace temperature is calculated for all slabs in the furnace, and the final set furnace temperature is output as a weighted average value of those slabs, so that even when there are many types of slabs in the furnace , It is possible to bake them on average or with priorities.

[0009]

EXAMPLES Examples of a rolling heating furnace combustion control method according to the present invention will be described below. FIG. 2 shows a general rolling heating furnace and a computer 6 for carrying out the present invention, and a calculation function is shown in a block of the computer 6.
The fuel flow rate control device 2 controls the fuel flow rate by using the set furnace temperature calculated by the computer 6 as a target value, so that the slab continuously charged into the heating furnace 1 is rolled under the rolling conditions (product size, rolling temperature). Etc.) to a target temperature determined by.

The computer (combustion control function) 6 includes a current slab temperature calculation function 7 and a set furnace temperature calculation function 8. The current slab temperature calculation function 7 calculates the difference between the two-dimensional heat conduction equation based on the furnace temperature information from the furnace temperature detector 3 and the slab information (reactor position, slab size, etc.) from the slab information function 5. By using the method, the temperature distribution of the slab at that time is calculated accurately. The set furnace temperature calculation function 8 receives the calculation result of the current slab temperature calculation function 7 (slab current temperature) and calculates the furnace temperature required to bake from the current temperature to the target temperature until the slab is extracted. Then, the set furnace temperature is set in the fuel flow rate control device 2.

The present invention finally obtains the set furnace temperature, and the furnace temperature required for baking the slab to the target value is calculated according to the flow of FIG. 3 below. In the present invention, with respect to the in-furnace slab, assuming that the furnace temperature at the present time continues, after predicting the slab temperature at the time of extraction as the slab moves in the furnace at the planned extraction pitch,
The calculation of the set furnace temperature is linearized as a problem of minute fluctuations in the vicinity of the current furnace temperature, and is solved by a linear programming process that finds the optimum furnace temperature change amount of each combustion zone under the constraint condition of baking quality.

Referring to FIG. 3, first, in step 1, assuming that the furnace temperature at the present time continues, assuming that the slab moves in the furnace at a planned extraction pitch, the slab temperature distribution at the time of extraction is determined as follows. Predict for all slabs. Here, the slab temperature distribution prediction will be described. As shown in FIG. 4, the temperature is calculated at a total of 10 points including 5 points in the thickness direction between skids and 5 points in the thickness direction of the skid portion. However,
These calculation points exist between the skids in the center of the slab longitudinal direction between the adjacent fixed skids, and in the slab width direction in the slab width direction, both the skids and the skid part exist in the center of the slab width.

As a calculation method, for the skids, a one-dimensional four-division model considering only the thickness direction in the heat conduction difference equation is used, and for the skids, the heat conduction in the longitudinal direction of the slab is simplified by introducing a coefficient. A two-dimensional model (4 divisions in the thickness direction) is used. The calculation formula is shown below.

Skid temperature calculation formula: A general one-dimensional differential equation of heat conduction in the slab thickness direction (divided in four in the thickness direction). Top surface: H1 (t + Δt) = H1 (t) + (2 × Kd × Δt) / (ρ × Δx ² ) × {(Δx / Kd) × QU−Φ1 (t) + Φ2 (t)} 1/4 Above: H2 (t + Δt) = H2 (t) + (Kd × Δt) / (ρ × Δx 2) × {Φ1 (t) -2 × Φ2 (t) + Φ3 (t)} center: H3 (t + Δt) = H3 (t ) + (Kd × Δt) / (ρ × Δx ² ) × {Φ2 (t) -2 × Φ3 (t) + Φ4 (t)} ¼ Bottom: H4 (t + Δt) = H4 (t) + (Kd × Δt) / (ρ × Δx ² ) × {Φ3 (t) -2 × Φ4 (t) + Φ5 (t)} Lower surface: H5 (t + Δt) = H5 (t) + (2 × Kd × Δt) / (ρ × Δx ² ) × {Φ4 (t) −Φ5 (t) + (Δx / Kd) × QL} QU = σ × ΦCGH × {(TG + 273) ⁴ − (Φ1 (t) +273) ⁴ } QL = σ × ΦCGL × {(TG + 273) ⁴ − (Φ5 (t) +273) ⁴ }.

Skid part temperature calculation formula: A simple two-dimensional heat conduction difference equation in which a general two-dimensional heat conduction difference equation of the slab thickness direction × slab longitudinal direction is simplified by introducing a coefficient of heat conduction in the slab longitudinal direction. . That is, as shown in FIG. 5, when considering heat conduction in the longitudinal direction of the slab to the lattice points of the skid portion, in the case of a general two-dimensional heat conduction difference equation, the lattice point temperature next to the skid portion is required. However, instead of this, the temperature calculation of the grid point between the skid part and the skid is omitted by utilizing the grid point temperature between the skids by introducing the coefficient. The lower surface formula considers heat dissipation from the skid rail (divided in the thickness direction).

Top surface: HS1 (t + Δt) = HS1 (t) + (2 × Kd × Δt) / (ρ × Δx ² ) × {(Δx / Kd) × QUS−ΦS1 (t) + ΦS2 (t)} + ( 2 × Kd × Δt) / (ρ × Δy ² ) × {(Φ1 (t) −ΦS1 (t)) × αSKID} 1/4 Above: HS2 (t + Δt) = HS2 (t) + (2 × Kd × Δt ) / (Ρ × Δx ² ) × {ΦS1 (t) -2 × ΦS2 (t) + ΦS3 (t)} + (2 × Kd × Δt) / (ρ × Δy ² ) × {(Φ2 (t) -ΦS2 (t)) × αSKID} Center: HS3 (t + Δt) = HS3 (t) + (2 × Kd × Δt) / (ρ × Δx ² ) × {ΦS2 (t) -2 × ΦS3 (t) + ΦS4 (t) } + (2 × Kd × Δt) / (ρ × Δy ² ) × {(Φ3 (t) −ΦS3 (t)) × αSKID} ¼ bottom: HS4 (t + Δt) = HS4 (t) + (2 × Kd × Δt) / (ρ × Δx ² ) × {ΦS3 (t) -2 × ΦS4 (t) + ΦS5 (t)} + (2 × Kd × Δt) / (ρ × Δy ² ) × {(Φ4 (t ) −ΦS4 (t)) × αSKID} Lower surface: HS5 (t Δt) = HS5 (t) + (2 × Kd × Δt) / (p × Δx 2) × {ΦS4 (t) -ΦS5 (t) + (Δx / Kd) × ((1.0-SB) × QS + SB × QW )} + (2 × Kd × Δt) / (ρ × Δy ² ) × {(Φ5 (t) −ΦS5 (t)) × αSKID} QUS = σ × ΦCGH × {(TG + 273) ⁴ − (ΦS1 (t) +273) ⁴ } QLS = σ × ΦCGL × {(TG + 273) ⁴ − (ΦS5 (t) +273) ⁴ } QS = QLS × βSDW QW = (TW-ΦS5 (t)) × HK.

Hi (t): heat content at time t Φi (t): conversion temperature at time t HSi (t): heat content at skid part at time t ΦSi (t): conversion temperature at skid part t : Specific gravity Δx: Dividing distance in slab thickness direction Δy: Dividing distance in slab thickness direction Δt: Dividing time ΦCGH: Overall heat absorption rate of upper combustion zone ΦCGL: Overall heat absorption rate of lower combustion zone TG: Current atmospheric temperature in furnace QU: Above skid Amount of heat transfer to the surface QL: Amount of heat transfer to the lower surface between skids QUS: Amount of heat transfer to the upper surface of the skid part QLS: Amount of heat transfer to the lower surface of the skid part QW: Amount of heat transfer from the skid rail TW: Cooling Water temperature HK: Heat transmission coefficient SB: Equivalent skid rail width αSKID: Heat transfer coefficient between skids → skid part βSDW: Influence coefficient of skid shadow.

[0018]

[Equation 1]

In step 2, the furnace temperature is ΔT from the current furnace temperature.
Assuming that only _Fi (i: combustion zone number) has changed, the slab temperature distribution during extraction is predicted for all slabs in the furnace in the same manner as in step 1.

In step 3, the constraint conditions (1), (2), and
∂T _Smj / ∂T which is the linearization coefficient used in equation (3)
_Fi , ∂T _Sscj / ∂T _Fi , and ∂T _Snsj / ∂T _Fi are obtained for all slabs in the furnace using the slab extraction temperature distribution when the furnace temperature calculated in step 2 _slightly changes. ∂T _Smj /
∂T _Fi , ∂T _Sscj / ∂T _Fi , ∂T _Snsj / ∂T _Fi are the i-th
This is the rate of change due to changes in the combustion zone.

[Average temperature in the thickness direction between skids during extraction] T _Smj ⁰ + Σ (∂T _Smj / ∂T _Fi ) · ΔT _Fi ≧ T _Sj aim ・ ・ ・ (1) [Surface temperature during skids during extraction] And the central temperature] T _Sscj ⁰ + Σ (∂T _Sscj / ∂T _Fi ) ・ ΔT _Fi ≧ T _Sscj aim ・ ・ ・ (2) [Difference between the skids during extraction and the thickness direction average temperature] T _Snsj ⁰ + Σ (∂T _Snsj / ∂T _Fi ) · ΔT _Fi ≧ T _Snsj aim (3).

Here, T _Smj ⁰ , T _Sscj ^0, and T _Snsj ⁰ are the average temperature in the thickness direction between the skids during extraction, the difference between the surface temperature and the central temperature between the skids during extraction, and It is the difference between the skids during extraction and the average temperature in the thickness direction of the skid part, T _Sj aim, T
_Sscj aim and T _Snsj aim are respective target values.

In step 4, the constraint condition (1) expression,
Under the equations (2) and (3), the furnace temperature change amount ΔT _Fi that minimizes the objective function Z of the equation (4) is obtained for all in-reactor slabs; Z = Σ _Wi · ΔT _Fi (4) Here, w _i is a coefficient, and by setting w ₁ > w ₂ > w ₃ > w ₄ , it is possible to perform post-loading type energy saving-oriented baking.

In step 5, the furnace temperature change amount ΔT _Fi calculated for each slab up to step 4 is weighted averaged for each combustion zone, and a value obtained by adding this to the set furnace temperature at the present time is set as the set furnace temperature, and the flow rate is set. Output to the control device 2.

[0025]

As described above, according to the present invention, in predicting the temperature distribution of a slab, the heat conduction in the longitudinal direction of the slab between the skids and the skid portion is simplified by introducing a coefficient to reduce the number of calculation points, and the slab with a small calculation load. The temperature distribution of the part required for the evaluation of baking quality is calculated. Therefore, it is possible to calculate the temperature distribution between the skids and the skid part necessary for the slab baking quality evaluation with a processing time that can be practically used for online control, and with the furnace temperature setting model using this Therefore, it is possible to secure high quality baking excellent in heat uniformity not only in the thickness direction of the slab but also in the longitudinal direction of the slab.

Since the set furnace temperature is calculated for all slabs in the furnace and the weighted average value is output, even if different slabs such as dimensions and target extraction temperature are mixed in the furnace, they are averaged. It is possible to bake with a certain priority or priority.

[Brief description of drawings]

FIG. 1 is a block diagram showing an outline of processing of the present invention by using a functional configuration expression.

FIG. 2 is a block diagram showing a general rolling heating furnace and a computer 6 for carrying out the present invention thereto, and a calculation function is shown in the block of the computer 6.

FIG. 3 is a flowchart showing the processing contents of setting furnace temperature calculation and output of the computer 6 shown in FIG.

FIG. 4 is an enlarged perspective view of one slab in the heating furnace 1 shown in FIG. 2, showing a calculation target portion of slab temperature distribution prediction in the embodiment of the present invention.

5 is a plan view showing a distribution of temporary vacancies in temperature calculation in a vertical cross section in the thickness direction of the slab shown in FIG.

[Explanation of symbols]

1: Heating furnace 2: Fuel flow control device 3: Furnace temperature detector 4: Combustion burner 5: Slab information function 6: Computer (furnace temperature setting function) 7: Current slab temperature calculation function 8: Set furnace temperature calculation function

Claims (1)

[Claims] 1. A method for controlling baking of a slab in a rolling heating furnace, wherein a one-dimensional heat conduction difference equation in the slab thickness direction between the skids and a coefficient of the heat conduction in the longitudinal direction of the slab for the skid part are introduced. By solving a simplified two-dimensional heat conduction difference equation in the slab thickness direction and the slab longitudinal direction, by predicting the future temperature distribution between the skids of the in-reactor slab and the skid part and evaluating their baking quality, A rolling furnace heating furnace combustion control method, which comprises calculating a furnace temperature to be set in the rolling heating furnace.