JP6620610B2 - Method for estimating surface heat flux of heat-treated members - Google Patents

Description

  The present invention relates to a method for estimating the surface heat flux of a heat treatment member during heat treatment such as cooling or heating of a heat treatment member such as steel.

  In the steel manufacturing process, measure the cooling capacity, for example, to add a spray to improve cooling equipment that cools high-temperature steel, to change sprays to reduce cooling unevenness, and to examine new cooling equipment. It is important to improve productivity and yield.

  In order to know the cooling capacity, an experiment is usually performed. In the experiment, cooling water is injected into the high-temperature steel material, the temperature change of the steel material at that time is recorded, and the cooling capacity is calculated using that. Here, the “cooling capacity” is a relationship between the “surface heat flux” meaning the amount of heat removed from the surface of the member to be cooled and the “surface temperature” at that time. (Hereinafter, “surface heat flux” may be simply referred to as “heat flux”.)

  However, there is currently no method for directly measuring the surface heat flux or the surface temperature of a member to be cooled that is water-cooled. Therefore, in the experiment, first, the temperature change of the inside of the high-temperature steel material being cooled or the surface opposite to the surface being cooled is measured, and then the surface heat flux and surface that can reproduce the temperature change. The relationship with temperature is estimated by calculating backwards or trial and error.

  However, in order to perform this back calculation, a large amount of calculation time is conventionally required. Therefore, even if an experiment is performed, the result cannot be quickly utilized for improving the cooling process. Further, even if a large number of measurement points are taken in order to obtain a detailed distribution of the cooling capacity, the data processing cannot be performed, so that it is difficult to know the detailed cooling capacity distribution. Therefore, a method capable of performing this reverse calculation at high speed is desired.

  For example, Non-Patent Document 1 describes that in order to obtain the surface temperature and heat flux of an object to be cooled, convergence calculation (repetitive calculation) is performed to change the heat flux so as to coincide with the experimental results. In order to perform the convergence calculation, it is necessary to determine how the heat flux is changed in the direction in which the calculation converges. As a means for determining the direction, the surface heat flux of the temperature at the measurement point is determined. The use of dependency (∂T / ∂q) is disclosed.

  In addition, in the process of calculating the surface heat flux as described in Non-Patent Document 1, it is necessary to use the temperature distribution inside the object to be cooled. However, Patent Document 1 describes the temperature distribution as an unsteady state. The use of results obtained by numerical analysis is disclosed.

  Patent Document 2 shows an example in which a secant method is used for convergence calculation (repetition calculation) for obtaining a solution of a polynomial. A model expression expressing an arbitrary physical phenomenon is approximated by series expansion (polynomial approximation), and the expression It is disclosed that the calculation time can be shortened by solving Newton method, Secant method or the like.

Japanese Patent No. 3769164 Japanese Patent Laid-Open No. 7-191965

Beck, J. V., Litkouhi, B., and St. Clair Jr, C. R., “Efficient Sequential Solution of the Nonlinear Inverse Heat Conduction Problem,” Numerical HeatTransfer, Part A: Applications, Vol. 5 (1982), pp. 275-286.

  However, the analysis method described in Patent Document 1 has a large calculation load, and cannot be used for quick process improvement by quick calculation. In addition, the secant method described in Patent Document 2 shows how to solve a general polynomial, and there is no method for calculating heat flux using this method.

  This invention is made | formed in view of such a viewpoint, and it aims at providing the method of calculating | requiring a heat flux accurately, reducing calculation load using the measured value of the temperature of a heat processing member.

  In order to solve the above problem, the present invention provides a step of actually measuring a temperature history during heat treatment of a heat treatment member and two different types of heat fluxes to perform heat conduction analysis on the heat treatment member, A step of calculating each numerical analysis value, and an odd power of the difference between the actual measurement value of the temperature history and the numerical analysis value as a target function, and performing a convergence calculation of the target function by a solution method, Provided is a method for estimating the surface heat flux of a heat treatment member, wherein the value of the heat flux when the objective function converges is the surface heat flux when the measured value is measured.

  The solution solving method may be a secant method or a bisection method. The target function may be a difference between the actual measurement value and the numerical analysis value.

  The heat treatment member may be a steel material, and the heat treatment may be cooling in a steel manufacturing process.

  According to the present invention, it is possible to reduce the calculation load and accurately obtain the heat flux.

It is a flowchart which shows the process concerning embodiment of this invention. It is a flowchart which shows the conventional process. It is a figure explaining the image of the conventional convergence calculation. It is a figure explaining the image of the convergence calculation concerning embodiment of this invention. It is a figure explaining the image of the convergence calculation concerning different embodiment of this invention. The conditions of an Example are shown, (a) is a figure which shows the outline of steel materials, (b) is a graph which shows a time-dependent change of temperature, (c) is a graph which shows a time-dependent change of a heat flux. It is a graph which shows the result of Example 1, (a) is the calculation result by the example of this invention, (b) is the calculation result by a prior art example. It is a graph which shows the result of Example 2, (a) is a calculation result by the example of this invention, (b) is a calculation result by a prior art example.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the following description of the present specification, “surface heat flux” is simply referred to as “heat flux”. Further, in the present embodiment, a method for estimating the heat flux of the steel material during cooling in the steel material manufacture using the heat treatment member as a steel material will be described.

  First, a conventional calculation method for estimating a heat flux during cooling of a steel material will be described with reference to a flowchart of FIG.

(Process B1)
A steel cooling experiment is conducted to measure the temperature history of the steel.

ただし、
Ｔ：熱伝導解析における温度の数値解析値
ｑ：表面熱流束 (Process B2)
Appropriate heat flux is given and heat conduction analysis is performed for several steps. This heat conduction analysis is preliminarily performed in order to investigate the relationship between the heat flux and the temperature, and is performed for a plurality of patterns by changing the value of the heat flux. And from the result obtained by this heat conduction analysis, the relationship of the temperature change of the steel material with respect to the provided heat flux is calculated | required by Formula (1).

However,
T: Numerical analysis value of temperature in heat conduction analysis q: Surface heat flux

(Process B3)
Furthermore, an appropriate heat flux is given, and heat conduction analysis is performed for several steps.

ここで、

ただし、
Ｙ：実験により得られた温度の実測値
Ｔ：熱伝導解析における温度の数値解析値
ｑ：表面熱流束
ｒ：熱伝導解析を行うステップ数（数値計算の時間ステップ） (Process B4)
The measured value of the temperature of the steel material obtained by the experiment in the step B1 is compared with the numerical analysis value of the temperature of the steel material obtained by the heat conduction analysis in the step B3, and the difference is calculated. Furthermore, using the relationship between the temperature change of the steel material with respect to the heat flux obtained by Equation (1), the applied heat flux is corrected by Equation (2) so that the difference between the measured value and the numerical analysis value can be reduced. To do.

here,

However,
Y: Actual measurement value of temperature obtained by experiment T: Numerical analysis value of temperature in heat conduction analysis q: Surface heat flux r: Number of steps for performing heat conduction analysis (time step of numerical calculation)

(Process B5)
If the correction amount Δq in the process B4 is sufficiently small with respect to a preset reference, it is determined that the process has converged and the process proceeds to the process B6, and if large, the process returns to the process B3.

(Process B6)
It is considered that the heat flux given when the correction amount Δq in step B4 is sufficiently small with respect to a preset reference reproduces the instantaneous heat flux at the time of the experiment. When the required time is not calculated, the process returns to step B3, and the heat flux for the next time is obtained. When the required time has been calculated, the process ends.

In the conventional method as described above, in the convergence calculation, the heat flux q that gives the temperature T that minimizes the target function F shown in Expression (3) is calculated by repeated calculation.

  An image of this repeated calculation is shown in FIG. As shown in FIG. 3, from the coordinate (q (1), F (1)) to the coordinate (q (2), F (2)) and then the coordinate (q ( 3), F (3))... And the calculation is repeated until the target function F is minimized, that is, until it becomes smaller than the threshold δ (F <δ). This threshold δ is an arbitrary value that F is considered to have converged, and is set in advance. However, the minimum value of the target function F is unknown, and it is also unknown whether there is a value smaller than the threshold value δ set as the convergence condition.

  Next, a calculation method according to the embodiment of the present invention in the case of estimating the heat flux at the time of cooling the steel material will be described with reference to the flowchart of FIG.

(Process A1)
A steel cooling experiment is conducted to measure the temperature history of the steel.

ただし、
Ｙ：実験により得られた温度の実測値
Ｔ：熱伝導解析における温度の数値解析値
ｒ：熱伝導解析を行うステップ数（数値計算の時間ステップ） (Process A2)
Appropriate heat flux is given, and heat conduction analysis is performed for several steps (time step of numerical calculation). This analysis is performed twice with two different heat flux values (q (1) and q (2)) set. And about these two analysis results, the measured value of the temperature of the steel material obtained by the experiment and the numerical analysis value of the temperature of the steel material obtained by the heat conduction analysis are compared, and the temperature difference S is expressed by the formula ( 4).

However,
Y: Actual measurement value of temperature obtained by experiment T: Numerical analysis value of temperature in heat conduction analysis r: Number of steps for conducting heat conduction analysis (time step of numerical calculation)

(Process A3)
Using the result obtained in step A2, the heat flux q (3) at which the temperature difference between the actual measurement value and the numerical analysis value becomes zero is calculated by linear interpolation using the secant method.

(Process A4)
The temperature difference S (3) is calculated using the heat flux q (3) obtained in step A3.

(Process A5)
If the temperature difference S (3) obtained in step A4 is sufficiently small with respect to a preset reference, the process proceeds to step A6. If the temperature difference is larger than a preset standard, two sets of data obtained in the process so far are picked up two sets in which the temperature difference between the measured value and the numerical analysis value is close to zero (step A7). Return to step A3.

(Process A6)
It is considered that the heat flux given when the temperature difference between the actual measurement value and the numerical analysis value obtained in step A4 is sufficiently small reproduces the instantaneous heat flux at the time of the experiment. And when calculation of required time is not performed, it returns to process A2 and calculates | requires the heat flux of the next time continuously. When the required time is calculated, the process ends.

In the present invention, the reverse calculation corresponds to the calculation of the heat flux q such that the target function S shown in Expression (5) is set to be zero by repeated calculation.

  That is, in the present invention, the temperature history of the steel material calculated by applying the heat flux given as the numerical analysis value is compared with the temperature history of the steel material obtained by actual measurement, and the heat flow is reduced so that the difference is reduced. Determine the bunch.

  An image of the iterative calculation of this embodiment is shown in FIG. For example, assuming that strong cooling was performed, a large heat flux q (1) was given as an estimated value, the temperature history of the steel material was calculated from the heat flux, and then it was assumed that weak cooling was performed. The small heat flux q (2) is given as an estimated value, and the temperature history of the steel material is calculated from the heat flux. The temperature history of the steel material obtained by actual measurement is considered to be intermediate between these calculated values. Therefore, it is considered that the heat flux closer to the temperature history of the steel material obtained by actual measurement can be calculated by interpolating so as to eliminate the difference. Alternatively, even when the temperature history measured is not in the middle of the estimated value, by performing extrapolation so that the difference approaches 0, the correct heat flux is similarly set as the next estimated value based on the actually measured value. Obtainable. In this embodiment, as shown in FIG. 4, by using linear interpolation from coordinates (q (1), S (1)) and coordinates (q (2), S (2)), the target S = It is possible to obtain the heat flux q (3) satisfying 0 at once. More precisely, a heat flux q satisfying | S | <δ is obtained with respect to a preset value δ that S is considered to have converged.

  Note that the iterative calculation method used in this embodiment is generally known as a secant method. In the present embodiment, the secant method is applied to the convergence calculation by setting the target function S for convergence as a temperature difference between the actual measurement value Y and the numerical analysis value T. In this way, by applying the secant method to the problem of obtaining the surface heat flux by back calculation, it is possible to perform back calculation equivalent to the conventional one by greatly reducing the calculation time by reducing the calculation load.

  In the above formula (5), the target function S is set to the first power of the temperature difference between the actual measurement value and the numerical analysis value. However, the target function S may be an odd power other than the first power. When the temperature difference is large, the target function S is further away from 0, and the temperature difference with respect to the target function S can be weighted.

  In the above embodiment, only the secant method has been described as the iterative calculation method. However, a dichotomy method is also known as the iterative calculation method. FIG. 5 shows an image of calculation when the bisection method is used as an embodiment of a different iterative calculation method.

  First, a heat flux q that satisfies S <0 and a heat flux q that satisfies S> 0 are appropriately determined by actually conducting a heat conduction analysis. Let q and S at this time be (q (1), S (1)), (q (2), S (2)), respectively.

  Next, S (3) when q (3) = (q (1) + q (2)) / 2 is obtained. Further, when S (3)> 0, S (4) is obtained as q (4) = (q (1) + q (3)) / 2, and S (3) <0 as shown in FIG. In this case, S (4) is obtained as q (4) = (q (2) + q (3)) / 2. By repeating this, q satisfying S = 0 (more accurately, | S | <δ) is found.

  As described above, the present invention makes it possible to repeatedly calculate a calculation system using only a solution method such as a secant method or a bisection method from only input information of experimentally measured values and numerical analysis values as output information. By doing so, the heat flux can be calculated backward with a small number of iterations, and the heat flux can be estimated at high speed with the same accuracy as existing methods while reducing the calculation load.

  The temperature measurement during the experiment may be performed by any temperature detection means such as a thermocouple or thermography. Moreover, although the said embodiment demonstrated the cooling of a steel plate as object, heating is the same also in the point of calculating | requiring the surface heat flux of steel materials, and it can be used also for calculating | requiring the heat flux by heating. Furthermore, it can be similarly performed when heating and cooling are repeated.

  As mentioned above, although preferred embodiment of this invention was described, this invention is not limited to this example. It is obvious for those skilled in the art that various changes or modifications can be conceived within the scope of the technical idea described in the claims. It is understood that it belongs to.

  In order to verify the effect of the present invention, the following numerical analysis was performed.

First, assuming the cooling of the high-temperature steel material 1 having a thickness of 28 mm as shown in FIG. 6A, a heat transfer coefficient of 5000 W / (m ² · K) is given to the surface of the steel plate with an initial temperature of 850 ° C. The cooling process was determined by numerical analysis. The back surface of the steel material 1 is in a thermally insulated state. This numerical analysis can be performed by any means such as commercially available calculation software.

  The temperature change of the steel material 1 was recorded as a temperature measuring point 2 at a position 1.5 mm from the surface. FIG. 6 (b) shows the change over time in the temperature as the analysis result, and FIG. 6 (c) shows the change over time in the surface heat flux. The temperature change in FIG. 6B corresponds to Y in the above equations (2) and (4).

  And the back calculation of the heat flux which can implement | achieve the temperature change of FIG.6 (b) was performed by the calculation method (invention example) concerning the above-mentioned embodiment of this invention, and the conventional calculation method (conventional example). FIG. 7A shows the calculation result according to the example of the present invention, and FIG. 7B shows the calculation result according to the conventional example. The result obtained by the example of the present invention was sufficiently close to the actual heat flux shown in FIG. 6C, and it was shown that the accuracy was equal to that of the conventional example. The time required for this calculation is 25 in the example of the present invention, assuming that the conventional example is 100, and the time can be greatly reduced.

  Although the temperature change in Example 1 is a numerical analysis value, noise such as a measurement error occurs in the actual measurement value. For this reason, the actual measurement value is usually analyzed after passing through a noise filter. Therefore, by adding random noise in the range of ± 2 ° C. to the temperature change of Example 1, and further giving a temperature change obtained by moving average in 1 second before and after this, the example of the present invention and the conventional example are the same as Example 1. The surface heat flux was calculated back by way of example. FIG. 8A shows the calculation result according to the example of the present invention, and FIG. 8B shows the calculation result according to the conventional example. Also in this case, as in Example 1, it was shown that the example of the present invention is sufficiently close to the actual heat flux shown in FIG. The time required for this calculation is 100 for the conventional example of the first embodiment. The conventional example of the present embodiment is 800, and the present invention example is 25, which is the same as the first embodiment. I was able to.

  The present invention can be applied to estimation of the heat flux of an object to be measured in secondary cooling of a continuous casting machine in an iron and steel manufacturing process, accelerated cooling equipment such as hot rolling and thick plates, heat treatment equipment for various steel materials, etc. It can be used for improvement studies on productivity improvement and yield improvement, and development of design methods for new equipment.

1 Steel 2 Temperature measuring point

Claims (4)

Measuring the temperature history during heat treatment of the heat treatment member;
Two different heat fluxes are given, a heat conduction analysis is performed on the heat treatment member, and a numerical analysis value of the temperature history is calculated,
A target function is an odd power of the difference between the measured value of the temperature history and the numerical analysis value, and a convergence calculation of the target function is performed by a solution method.
A method of estimating a surface heat flux of a heat treatment member, wherein a value of a heat flux when the target function converges is a surface heat flux when the measured value is measured. The method for estimating the surface heat flux of the heat treatment member according to claim 1, wherein the solving method is a secant method or a bisection method. The method for estimating the surface heat flux of the heat treatment member according to claim 1, wherein the target function is a difference between the actual measurement value and the numerical analysis value. The said heat processing member is steel materials, The said heat processing is cooling in a steel manufacturing process, The estimation method of the surface heat flux of the heat processing member as described in any one of Claims 1-3 characterized by the above-mentioned.

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