JPS62127422A - Method for determining temperature rising curve of material in heating furnace - Google Patents

Abstract

PURPOSE:To accurately control extracting temp. of each material and save fuel, by using respective means from the first to the seventh arithmetic means for calculating variation of furnace temp. with the lapse of time to determine temp. rising curve of material in hot rolling line. CONSTITUTION:Average temp., etc., at material extraction in present state fuel flow rate are calculated by the fourth arithmetic means due to results of the respective first, second and third arithmetic means. The first means calculates variation with the lapse of time in furnace temp. due to fuel flow rate, the second means calculates that in temp. of furnace wall inside due to furnace temp., and the third means calculates that in temp. in material due to furnace temp. Fuel flow rate of each control zone is varied from present state flow rate by a fixed value to calculate min. temp., etc., at material extraction, and linearizing coefft. is calculated by the fifth arithmetic means due to this and result of the fourth means. Next, the most suitable fuel flow rate is calculated by the sixth arithmetic means using the coefft., etc. Temp. rising curve to material extraction is calculated by the seventh arithmetic means due to the most suitable flow rate.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a method for determining a heating pattern of a material that minimizes fuel consumption in temperature control of a heating furnace in a hot rolling line.

[Conventional technology]

Conventionally, as a method for determining the temperature rise curve online for temperature control of this type of heating furnace, for example, Japanese Patent Application Laid-Open No. 56-Y
As shown in the sss34 publication, in order to perform nonlinear fuel minimization, a dual-valve linear model is used: a model that calculates the material temperature from the furnace temperature, and a model that calculates the fuel flow rate from the furnace temperature and material temperature. Then, linearization is performed by changing the furnace temperature in steps and using the perturbation simulation method (a method in which the linearization coefficient is determined by performing simulations in the standard state and perturbed state), and the temperature rise curve of the material is determined from the results. method is adopted.

[Problem that the invention seeks to solve]

In the conventional method for determining material temperature rise curves for heating furnaces as described above, the number of furnace temperature calculation zones is generally greater than the number of zones in which fuel flow rate can be controlled. There was a problem in that the furnace temperature and temperature rise curve were not always in a realizable pattern.

In addition, when determining the linearization coefficient and temperature increase pattern, the simulation is performed by ignoring heat loss to the furnace wall, furnace wall temperature distribution, etc., and changing the furnace temperature in steps without considering the furnace response delay. As a result, there was a problem that a temperature rise curve was determined which was far from the actual temperature rise trend of the material and the furnace condition.In addition, the influence of extraction pauses (interruptions) during unsteady operation caused optimization problems. Because it was not incorporated into the logic, there was no operation to lower the furnace temperature setting that would normally be done manually, which caused the problem of worsening the fuel consumption rate.

This invention was made in order to solve the above-mentioned problems, and it is possible to determine a temperature rise curve that is feasible and corresponds to the actual conditions, and that lowers the set furnace temperature during unsteady operation with extraction pauses. The purpose of this study is to obtain a method for determining the material temperature rise curve of a heating furnace.

[Means for solving problems]

The method for determining a material temperature rise curve for a heating furnace according to the present invention includes a model that calculates the furnace temperature using an unsteady heat balance formula based on the fuel flow rate, a model that calculates the furnace wall temperature distribution based on the furnace temperature,
and a model that calculates material temperature based on the furnace temperature.In order to minimize the fuel, we use perturbation method simulation and use that changes the fuel flow rate in steps, and LP (linear programming). ) The temperature rise curve is determined by incorporating the influence of fuel flow rate and unsteady operation into the evaluation function of the method.

[Effect]

In this invention, three nonlinear models including the furnace wall temperature distribution are used, and a so-called perturbation method simulation is used to determine the temperature rise curve in order to perform fuel minimization. It is also possible to determine a temperature increase curve that matches the actual state and that lowers the set furnace temperature during non-regular operation with extraction paused.

〔Example〕

The zero furnace temperature calculation model to explain the principle of the present invention is constructed as follows.

As shown in Figure 1, the heating furnace is divided into n (l) parts in the furnace length direction.
Establish the following heat balance equation for each divided mesh.
@ t = Qe ... Sensible heat of fuel and air 6,
...Fuel calorific value +01+1"pF"
gl+1 ... Calorific value of exhaust gas from upstream i pg gi ... Calorific value of exhaust gas to downstream
... Radiation from other mesh furnace temperatures... Radiation from the furnace wall"2 (Twi-"gi"C3(Tei-"pi)...
Convection to furnace walls and materials - QW□ ...Skid cooling water loss...
・(1) Here, H is the amount of emitted *A per unit flow rate of fuel, Cpg is the exhaust gas specific heat, Gi is the number of divisions in the exhaust gas flow rate of each mesh,
m is the number of slabs 0. The above equation (1) can be transformed as follows if the fuel flow rate W is given and the furnace wall temperature and slab temperature are known.

+ Σ B fist T +a (1
= 1es fist H) ik gk i φ conflict Q (2) Tore is s n7c simultaneous nonlinear differential equations, but 1
Using the temperature distribution in the furnace 5 steps ago as a starting value, discretize it with respect to time and converge using Newton's method etc., then
You can easily calculate a new temperature distribution inside the furnace.

Furthermore, the material temperature model can be expressed as follows using the well-known two-dimensional heat conduction equation.

The boundary conditions on the surface are where X represents the material thickness direction, Y represents the material width direction,
d and d2 represent the material thickness and the inside of the material, respectively.

Also, aB, λ8. r is the specific heat of each material.

These are thermal conductivity and specific gravity, and q8 is the surface heat flux of the material, which can be expressed by the following formula.

qs= Σ to 3u ((7g1+273)'-(Ts,
+273)'11=1''03(Ts6-Tge)
---(6) Equation (8) can be solved by a normal difference method using the boundary condition of Equation (4).

As shown in FIG. 1, the furnace wall temperature model can be expressed as follows using a one-dimensional heat conduction equation only in the thickness direction within the mesh for each division in the longitudinal direction of the furnace.

The boundary condition on the inner surface of the furnace is number + 02 (Tg soil - Tw) ・ ・
・(η The boundary condition on the outer surface of the furnace is here, X is the furnace wall thickness direction, d is the furnace wall thickness, Cw・
rW, λ7 represent the specific heat, thermal conductivity, and specific gravity of the furnace wall, HOUT is the external thermal conductivity, and 〒1□1 is the external temperature. By using the boundary condition in 8), it becomes possible to solve the problem using an ordinary difference equation.

By using the above three models in combination, if the fuel flow rate is given, the current values of the furnace temperature, material temperature, and furnace wall temperature are used as initial values, and the furnace temperature, material temperature, furnace wall temperature, and the three The future temperature of can be calculated.

Next, a method for determining a temperature increase curve for a material that minimizes fuel consumption will be explained based on FIG. 2. Note that (1) is the 15th step of determining the heating curve, and (2) is the 2nd stop of the aircraft.

(8) is a similar fifth stop, and (4) is a similar fourth stop.

(6) is the furnace temperature calculation model, (6) is the furnace wall temperature calculation model, (γ) is the material temperature calculation model, (8) is the calculation of the furnace temperature at the material passage position, and (9) is the minimum temperature and uniform heating degree. calculation, (to)
is the calculation of the linearization coefficient, α is the calculation of linear programming (I, P), and (2) is the calculation that determines the temperature rise curve until the material is extracted.

First, as the first 5top (1), the current flow rate WK
. Therefore, by repeatedly using the five models (5), (6), and (γ), the time until all materials are extracted, the minimum temperature T8° during extraction of each material, and the soaking degree (
(maximum temperature - minimum temperature) ΔT, O and the material average temperature T5□ at the outlet side position of the calculation zone in the furnace. can be calculated.

Next, as the 25th top (2), by changing the fuel flow rate by ΔWK'' in 5 tops for each fuel flow rate control zone, each material is extracted at each flow rate change in the same way as the 1st 5top (1). Minimum temperature; K, soaking degree Δ
TK, the material average temperature TbK at each zone exit position can be calculated.

Next, as the 3rd 5th top (8), calculate the following linearization coefficient (101). By the procedure of the 2nd 5th top (2), the extraction special material minimum temperature, soaking degree, and each The average temperature in each calculation zone when the material passes can be linearized as follows.

Here, KMAX is the number of fuel flow control bands, and p
p and p are IKl when the flow rate is changed respectively.
2K 31 is the linearization coefficient, given by:

(y,ni-,;,0) To Pl: □　　　　　・Φ・Scream ΔwK0 Also, each fuel flow rate is calculated by assuming that ΔWx is the amount of change in each control band. w = w +ΔWK K It can be expressed as

The constraints in determining the temperature rise curve are as follows due to metallurgical constraints of the material and constraints on furnace operation.

"biMIN≦Tbi≦Tl)l MAX"KMIN
≦WK ≦”KMAX where subscripts MIN, MA
X indicates each lower limit value and upper limit value.

The optimization evaluation function is fuel minimization, and the effect of unsteady operation, that is, the extension of each reactor zone time, is incorporated into the following equation.

The minimization of 2〇〇) under the constraint condition of K=1 can be obtained using the ordinary linear programming (LP) calculation αη formula.

The flow rate of the above solution is the optimal flow rate "kopt" for each material, and linear programming (LP) is performed based on this flow rate as the 4th and 5th top.
By substituting into the calculation value, it is possible to calculate the temperature rise curve of the material until extraction.

Next, heating furnace control based on an embodiment of the present invention will be explained with reference to FIG.

In Figure 3, a heating furnace (1
01) includes a combustion burner (105) and a furnace temperature detector (1).
04) is arranged, and the flow rate is controlled by the fuel flow rate controller (103) so as to reach the set temperature for each control zone set by the furnace temperature setting means (106). (
1o2) is a material information means, which instructs the furnace temperature setting means (106) with material information such as the dimensions, weight, extraction temperature, and conveyance information of the material in the furnace.

The furnace temperature setting means (106) consists of a current temperature calculation means (a), a heating curve determination means (21), and a set furnace temperature calculation means, and is activated periodically. Current temperature calculation method
is calculated using the furnace temperature calculation model (6), furnace wall temperature calculation model (6), and material temperature calculation model (7) based on the material information.
Calculate the current material temperature. Temperature rise curve determining means (3))
As described in the description of this invention, the temperature rise curve for each material is determined under fuel minimization.

The set furnace temperature calculation means) compares the target temperature rise curve for each material with the current temperature, calculates the furnace temperature for each control zone, and instructs the fuel flow rate controller (103) to set the furnace temperature. .

〔Effect of the invention〕

As explained above, according to the present invention, the furnace temperature calculation means,
Using three nonlinear models: a furnace wall calculation method and a material temperature calculation method, and providing an evaluation function that takes unsteady operation into consideration, a perturbation method simulation is used to determine the temperature rise curve in order to perform fuel minimization. This makes it possible not only to determine a temperature rise curve for the material that is feasible and in line with the actual conditions, but also to determine a temperature rise curve that will reduce the set furnace temperature even during unsteady operation. . Therefore, the extraction temperature of each material can be precisely controlled and the fuel consumption rate can be reduced.

[Brief explanation of drawings]

Fig. 1 is a schematic diagram showing the zone division of the furnace temperature calculation, Fig. 2 is an explanatory diagram to explain the method for determining the temperature rise curve of the material that minimizes the amount of fuel, and Fig. 5 is an example of the present invention. FIG. 1 is an overall configuration diagram showing an example. (5): Furnace temperature calculation model (6): Furnace wall temperature calculation model (7): Material temperature calculation model (company): Current temperature calculation means tzll: Temperature rise curve calculation means C @ Two-stage setting furnace temperature calculation means 101 ): Heating furnace (103): Fuel flow rate controller (104): Furnace temperature detector (105): Combustion burner (106): Furnace temperature setting means

Claims (1)

[Claims] In heating control of a continuous heating furnace having a plurality of control zones, a first calculating means for calculating the time change in the furnace temperature using an unsteady heat balance formula based on the fuel flow rate, and calculating the time change in the furnace wall internal temperature from the furnace temperature. A second calculation means for calculating the temporal change in the material internal temperature from the furnace temperature, a third calculation means for calculating the temporal change in the material internal temperature from the furnace temperature, and the first, second, and third calculation means are used to extract the material at the current fuel flow rate in each control zone. a fourth calculation means for calculating the average temperature, the degree of soaking, and each furnace temperature when the material passes;
, the fuel flow rate in each control zone is changed by a certain constant value from the current flow rate using the third calculation means, and the lowest temperature at the time of extraction of the material,
A fifth calculation means calculates the uniform temperature and the average temperature when passing through each calculation zone, and calculates a linearization coefficient around the current flow rate based on this and the result of the fourth calculation means, and the furnace operation is performed using the coefficients. Under the above constraint conditions, the fuel required to bake the material is minimized, and the influence of the stoppage is incorporated into the optimization evaluation function in consideration of unsteady operation when there is a scheduled stoppage (interruption) of extraction. A method for determining a material temperature rise curve for a heating furnace, comprising a sixth calculation means for calculating a fuel flow rate, and a seventh calculation means for determining a temperature rise curve until the material is extracted based on the fuel flow rate.