JP2017227350A - Refractory wear management device of electric furnace, refractory wear management system of electric furnace, refractory wear management method of electric furnace, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To highly accurately monitor wear of a refractory of an electric furnace, which melts scraps with arc discharge.SOLUTION: A refractory wear management device of an electric furnace is configured to: analyze an inverse unsteady-state heat transfer problem on the basis of temperatures measured at thermocouples 6a-6i in each temperature sampling time, to derive relationship between heat flux and time on a furnace wall inner surface 5a (hot spots 8a, 8b, 8c); and from the result, derive a time integration value of heat flux in a period corresponding to single operation to output it.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a refractory wear management apparatus for an electric furnace, a refractory wear management system for an electric furnace, a refractory wear management method for an electric furnace, and a program, and more particularly, to a furnace wall of an electric furnace for melting scrap by arc discharge. It is suitable for use for managing the state of the refractory material to be constructed.

  In an electric furnace (arc melting furnace), for each charge (ch), raw materials such as scrap are charged into the furnace, and the raw materials are melted and melted by an arc generated from an arc electrode to obtain a molten metal and molten slag. . Since the furnace wall of such an electric furnace is exposed to high temperature, it is comprised using refractory materials, such as a refractory brick.

  However, even if the refractory is used to form the furnace wall, the refractory is worn and reduced in thickness due to repeated operations. One of the causes is that arcs generated from a plurality of arc electrodes repel each other, the arcs head toward the inner peripheral surface of the furnace wall, and the refractory is locally heated. In particular, at the timing when the raw material charged in the furnace is melted, the refractory is subjected to a huge amount of radiant heat locally, and wear of the refractory proceeds rapidly. Therefore, it is important to manage the wear state of the refractory from the viewpoints of ensuring safe operation and extending the life of the refractory.

As a technique for grasping the state of wear of the refractory constituting the furnace wall of the electric furnace, there are techniques described in Patent Documents 1 and 2.
In Patent Document 1, a temperature sensor is arranged inside the refractory, and the remaining thickness of the refractory is calculated from the relationship between the temperature measured by the temperature sensor and the temperature obtained in advance and the amount of wear of the refractory. Is estimated. Patent Document 1 also discloses that the remaining thickness of the refractory is estimated from the temperature measured by the temperature sensor and the thermal conductivity of the refractory.

  In Patent Document 2, a temperature sensor is arranged inside the refractory to measure the temperature inside the refractory, and the time when the temperature shows the maximum value / minimum value and the start time / output end time It is disclosed that the refractory is worn out when the delay time is calculated and the calculated delay time is equal to or shorter than the reference time. Patent Document 2 also discloses that the delay time is calculated by comparing the time when the temperature measured by the temperature sensor shows the maximum value / minimum value with the energization start time / energization end time. Yes.

JP-A-8-94264 Japanese Patent Laid-Open No. 3-223658

Hon, Y.C. and Wei, T., "The method of fundamental solution for solving multidimensional inverse heat conduction problems", Comput. Model. In Eng. And Sci., 7 (2005), no.2, 119-132 P.C.Hansen, "Regularization Tools. A matlab Package for Analysis and Solution of Discrete Ill-Posed Problems", http://www.imm.dtu.dk (2008), 1-36 G.H.Golub, C.F.Van Loan, "Matrix Computations 3rd edition", The Johns Hopkins University Press (1996), 69-73

  In the method of estimating the wear amount of the refractory from the measured temperature inside the refractory disclosed in Patent Document 1, in order to obtain a certain relationship between the temperature and the wear amount of the refractory, a furnace is used. It is premised that the temperature of the wall inner surface is the same, and the temperature inside the refractory is steady, or the temperature histories until the temperature is measured are the same. Further, in the method of estimating the remaining thickness of the refractory from the measured temperature inside the refractory and the thermal conductivity of the refractory disclosed in Patent Document 1, the temperature of the furnace wall inner surface is known, and the refractory The premise is that the internal temperature is steady. However, in normal operation, there are naturally temperature fluctuations within one charge, and there are various temperature transition patterns between charges. In such a non-stationary situation, any of the above estimation methods can be used. However, the preconditions are broken and good estimation accuracy cannot be obtained.

  Further, the delay time from the energization start time and energization end time of the time indicating the minimum value and maximum value of the internal temperature of the refractory disclosed in Patent Document 2 is calculated, and the remaining refractory is calculated from this delay time. In the method of estimating the thickness, there is a problem that the time indicating the minimum value / maximum value of the temperature inside the refractory does not necessarily correspond to the start / end of energization. For example, normally, at the start of energization, there is almost no heat input on the inner surface of the furnace wall due to the influence of undissolved scrap, and it does not affect the temperature of the refractory, so it does not correspond to the minimum value. In addition, the input power during operation is finely controlled, and even if the energization is not terminated, depending on the relationship with the refractory temperature when the input power is lowered, the heat may turn into heat dissipation on the inner surface of the furnace wall, and this change is maximum. May correspond to a value. In addition, the technique described in Patent Document 2 cannot dynamically manage the amount of refractory wear during operation (that is, the amount of refractory wear during times other than the start and end of one charge operation). .

  The present invention has been made in view of the above-described problems, and an object of the present invention is to enable high-precision monitoring of wear of refractories constituting a furnace wall of an electric furnace for melting scrap by arc discharge. And

  The refractory wear management device for an electric furnace according to the present invention is a refractory wear management device for an electric furnace that manages the wear of the refractory constituting the furnace wall of the electric furnace that melts scrap by arc discharge generated at an arc electrode. Measured at a plurality of temperature detection ends arranged at different positions in the thickness direction of the furnace wall of the electric furnace between the inside of the furnace wall of the electric furnace and the outer peripheral surface of the furnace wall of the electric furnace. Heat flux deriving means for deriving the relationship between heat flux and time on the inner peripheral surface of the furnace wall of the electric furnace by performing unsteady heat transfer inverse problem analysis based on the measured temperature, and the heat flux deriving means The heat flux integrating means for deriving the time integral value of the heat flux in a period corresponding to one operation based on the relationship between the heat flux on the inner peripheral surface of the furnace wall of the electric furnace and the time derived by And derived by the heat flux integrating means The information includes a time integral value of the heat flux in the period corresponding to the operation of the one, and having and an output means for outputting as an index for evaluating the wear of the refractories.

  In the refractory wear management system for an electric furnace of the present invention, the refractory wear management apparatus for the electric furnace and the output means output information including a time integral value of heat flux in a period corresponding to the one operation. And a suppression measure executing means for taking measures for suppressing the wear of the refractory based on an instruction from an operator.

  The refractory wear management method for an electric furnace according to the present invention is a refractory wear management method for an electric furnace for managing wear of a refractory constituting a furnace wall of an electric furnace for melting scrap by arc discharge. Based on the temperatures measured at the temperature detection ends arranged at a plurality of positions where the positions in the thickness direction of the furnace wall of the electric furnace are different from the inside of the furnace wall and the outer peripheral surface of the furnace wall of the electric furnace A heat flux deriving step for deriving the relationship between heat flux and time on the inner peripheral surface of the furnace wall of the electric furnace by heat flux deriving means by performing an unsteady heat transfer inverse problem analysis, and the heat flux deriving step Based on the relationship between the heat flux on the inner peripheral surface of the furnace wall of the electric furnace and the time derived by the above, the time integral value of the heat flux in a period corresponding to one operation is derived by the heat flux integrating means. Heat flux integration step, and the heat flux integration An output step of outputting information including a time integral value of heat flux in a period corresponding to the one operation derived by the process as an index for evaluating wear of the refractory, and the output After the information including the time integral value of the heat flux in the period corresponding to the one operation is output by the process, the suppression measure that takes measures to suppress the wear of the refractory based on the instruction from the operator And an execution step.

  The program of the present invention causes a computer to function as each means of the refractory wear and tear management apparatus for the electric furnace.

  ADVANTAGE OF THE INVENTION According to this invention, the abrasion of the refractory material which comprises the furnace wall of the electric furnace which melt | dissolves scrap by arc discharge can be monitored with high precision. Therefore, the maintenance cost of the refractory can be reduced while maintaining the productivity in the electric furnace.

It is a figure which shows an example of schematic structure of a refractory wear management system with the top view of an electric furnace. It is a figure which shows an example of schematic structure of a refractory wear management system with sectional drawing of an electric furnace. It is a figure which shows an example of a functional structure of a refractory material wear management apparatus. It is a figure which shows an example of the input electric power (voltage x electric current) with respect to an arc electrode. It is a figure which shows an example of the temperature of a furnace wall refractory. It is a figure which shows an example of the heat flux of a furnace wall inner surface. It is a figure which shows an example of the relationship between the thickness of the spraying material before the operation start (the remaining spray thickness before the operation start) and the thickness of the spray material after the operation ends (the remaining spray thickness after the operation ends). It is a figure which shows an example of the heat flux of a hot spot, and the gradient (change amount of the heat flux per unit time) of the heat flux of a hot spot. It is a figure which shows an example of the relationship between the wear amount of the furnace wall refractory in each charge (ch), and the time integral value (cumulative heat flux) of the heat flux of the furnace wall inner surface in the said charge. When the thickness of the spray material before the start of operation (the remaining spray thickness before the start of operation) is less than 30 mm, the amount of wear of the furnace wall refractory in each charge (ch) and the heat flux on the inner surface of the furnace wall at that charge It is a figure which shows an example of the relationship with time integral value (cumulative heat flux) of. When the thickness of the spray material before the start of operation (the remaining spray thickness before the start of operation) is 120 mm or more, the amount of wear of the furnace wall refractory at each charge (ch) and the heat flux on the inner surface of the furnace wall at that charge It is a figure which shows an example of the relationship with time integral value (cumulative heat flux) of. It is a flowchart explaining an example of operation | movement of a refractory material wear management apparatus. It is a flowchart explaining an example of the process (preliminary preparation step) by a heat flux deriving unit. It is a flowchart explaining an example of the process (temperature information sampling step) by a heat flux deriving unit. It is a flowchart explaining an example of the process (memory operation step) by a heat flux deriving unit. It is a flowchart explaining an example of the process (heat flux calculation step) by a heat flux deriving unit.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
[Schematic configuration of electric furnace and position of temperature detection end]
1 and 2 are diagrams for explaining an example of a schematic configuration of an electric furnace 1 and a refractory wear management system of the electric furnace 1. FIG. 1 shows a plan view of the electric furnace 1, and FIG. 2 shows a cross-sectional view taken along line AA of FIG. In FIG. 1, the illustration of the upper lid 2 shown in FIG. 2 is omitted for convenience of explanation. In the following description, the refractory wear management system of the electric furnace 1 is referred to as a refractory wear management system as necessary.

  1 and 2, in this embodiment, the electric furnace 1 includes an upper lid 2 and three electric furnaces installed at equal angular intervals (120 ° intervals) around the central axis S of the electric furnace 1 in the furnace. Arc electrodes 3 a to 3 c, a furnace bottom electrode 4 provided at the bottom of the electric furnace 1, and a furnace wall 5 are provided.

  The furnace wall 5 is comprised using refractories, such as a refractory brick and a refractory cement. The outer peripheral surface of the furnace wall 5 is covered with an iron skin constituting the furnace frame. In the present embodiment, the case where the thickness of the refractory constituting the furnace wall 5 is 450 mm will be described as an example. In the following description, the refractory constituting the furnace wall 5 is referred to as “furnace wall refractory” as necessary.

  As shown in FIG. 1, a plurality of thermocouples 6a to 6i are embedded in the furnace wall refractory. In the present embodiment, the coordinates of the points on the furnace wall inner surface 5a are set to 0 mm, and the thermocouples 6a to 6i are embedded at three points where the coordinates on the straight line perpendicular to the furnace wall inner surface 5a are 150 mm, 300 mm, and 450 mm. . Here, the furnace wall inner surface 5a is a surface of the inner peripheral surface of the furnace wall that may be directly subjected to radiant heat generated by arc discharge in the electric furnace 1, that is, directly to molten steel or scrap in the electric furnace 1. It is a surface that may touch. In this embodiment, since the thickness of the furnace wall refractory is 450 mm, the point on the straight line perpendicular to the furnace wall inner surface 5 a is 450 mm is a point on the outer peripheral surface of the furnace wall 5.

  The thermocouples 6a to 6c, 6d to 6f, and 6g to 6i are straight lines that are orthogonal to the central axis S of the electric furnace 1 and that pass through the central axes of the arc electrodes 3a, 3b, and 3c, respectively. , 7c. In the following description, such a straight line is referred to as a “right angle axis” as necessary.

  Further, intersections between the right-angle axes 7a, 7b, and 7c and the furnace wall inner surface 5a are referred to as hot spots 8a, 8b, and 8c. Since there is one hot spot for each arc electrode, if there are a plurality of arc electrodes, the same number of hot spots exist. In the electric furnace 1 of this embodiment, since there are three arc electrodes 3a, 3b, 3c, there are three hot spots 8a, 8b, 8c. The thermocouples 6a to 6c, 6d to 6f, and 6g to 6i are aligned with the hot spots 8a, 8b, and 8c on the perpendicular axes 7a, 7b, and 7c, respectively. In other words, the center-of-gravity position, which is the average of the positions of the thermocouples 6a to 6c, 6d to 6f, and 6g to 6i in a row, is on the orthogonal axes 7a, 7b, and 7c passing through the hot spots 8a, 8b, and 8c, respectively. be able to.

  The height positions of the hot spots 8a, 8b and 8c, in other words, the thermocouples 6a to 6c, 6d to 6f and 6g to 6i in a line on the perpendicular axes 7a, 7b and 7c with respect to the hot spots 8a, 8b and 8c. It is preferable that the height position be above the molten metal surface of the molten steel 10 when all the scrap 9 has melted. Furthermore, of these height positions, when scrap 9 melts, the height position that directly receives greater radiant heat as the radiant heat generated by arc discharge (in other words, the furnace wall refractory is assumed to be heavily worn out. The height position of the hot spots 8a, 8b, and 8c is preferably the height position.

  When arranging the rows of thermocouples 6a to 6c, 6d to 6f, 6g to 6i at the same height and rotated by 45 ° around the central axis S of the electric furnace 1 on the furnace wall inner surface 5a, The time change of the heat flux on the furnace wall inner surface 5a calculated as described later became slow. Further, the rows of thermocouples 6a to 6c, 6d to 6f, and 6g to 6i are arranged at the same height on the furnace wall inner surface 5a at a position rotated by 60 ° around the central axis S of the electric furnace 1. Similarly, in the case, the time change of the heat flux on the furnace wall inner surface 5a became slow. Therefore, the time integral value of the heat flux of the furnace wall inner surface 5a calculated as described later is not correctly derived, and the wear of the furnace wall refractory (whether or not the furnace wall refractory is worn and whether the furnace wall refractory is worn or not) The degree of wear) could not be correctly determined. Therefore, when taking measures to reduce the input power as a measure for suppressing the wear of the furnace wall refractory, the input power may not be adjusted to an appropriate value. If the input power cannot be adjusted to an appropriate value, not only will the power efficiency be reduced, but the radiant heat received by the furnace wall inner surface 5a from the arc electrodes 3a, 3b, and 3c will not be properly controlled, so that more heat load will be applied. . For this reason, the wear of the furnace wall refractory becomes severe, and the life of the furnace wall refractory may be shortened.

  Therefore, the rows of the thermocouples 6a to 6c, 6d to 6f, and 6g to 6i are on the perpendicular axes 7a, 7b, and 7c passing through the hot spots 8a, 8b, and 8c above the molten steel surface as described above. It has been found that the arrangement is most effective in both improving the power efficiency and extending the life of the furnace wall refractory.

  In the present embodiment, the example in which the thermocouples 6a to 6c, 6d to 6f, and 6g to 6i are arranged in a row with respect to the hot spots 8a, 8b, and 8c has been described. However, the positional relationship of a plurality of thermocouples arranged for each hot spot 8a, 8b, 8c is not limited to a one-dimensional column. For example, a plurality of thermocouples may be embedded in the furnace wall 5 two-dimensionally or three-dimensionally, that is, as a group of thermocouples.

  Here, the group of thermocouples is preferably arranged in the vicinity of the right axis 7a, 7b, 7c. Specifically, as shown in FIG. 1, L is the distance from the central axis of the arc electrodes 3a, 3b, 3c to the hot spots 8a, 8b, 8c corresponding to the arc electrodes 3a, 3b, 3c. The groups of thermocouples for hot spots 8a, 8b, 8c corresponding to each arc electrode 3a, 3b, 3c must be within an area of 0.2 L vertically and horizontally from the right axis 7a, 7b, 7c, respectively. Is preferred. The up and down directions are directions parallel to the central axis S of the electric furnace 1, and the left and right directions are directions perpendicular to the up and down directions (circumferential direction of the furnace wall 5). The vertical and horizontal distances are linear distances measured parallel to the furnace wall working surface 5a. That is, the group of thermocouples is installed inside the furnace wall refractory so as to enter a rectangular parallelepiped region having a rectangular surface with a side of 0.4 L centered on the hot spots 8a, 8b, and 8c. If there is a group of thermocouples outside this rectangular parallelepiped region, the heat flux at the hot spots 8a, 8b, 8c, where the wear is severe, cannot be calculated correctly, and the furnace wall refractory is worn out (the furnace wall refractory is worn out). This is because it may be difficult to correctly determine whether or not it has occurred and the degree of wear of the furnace wall refractory. The group of thermocouples is preferably located close to the hot spots 8a, 8b, 8c, so the group of thermocouples is within an area of 0.1L vertically and horizontally from the right axis lines 7a, 7b, 7c. Is more preferable.

In the present embodiment, L = 1500 mm. Therefore, a group of thermocouples is embedded in the furnace wall refractory so as to be within an area of 0.2 × 1500 = 300 mm within each of the vertical axis 7a, 7b, and 7c.
Moreover, it is preferable that the center-of-gravity position, which is the average of the positions of a plurality of thermocouples forming a group, is on the right-angle axes 7a, 7b, 7c passing through the hot spots 8a, 8b, 8c.

  In the present embodiment, since there are three arc electrodes 3a, 3b, 3c, there are three hot spots 8a, 8b, 8c corresponding to the arc electrodes 3a, 3b, 3c. If one-dimensional arrays (or two-dimensional or three-dimensional groups) of thermocouples 6a to 6c, 6d to 6f, and 6g to 6i are arranged in these three places, the wear of the furnace wall refractory (furnace wall) Whether or not the refractory is worn and the degree of wear of the furnace wall refractory can be determined more finely. Specifically, since the degree of wear of the furnace wall refractory differs at these three locations, the place where the wear of the furnace wall refractory is most severe can be quickly identified, and measures to suppress the wear of the furnace wall refractory Can be taken quickly.

When the number of arc electrodes arranged in the electric furnace 1 is one, the central axis S of the electric furnace 1 coincides with the central axis of the arc electrode, and the radiant heat generated by the arc discharge is given to the furnace wall inner surface 5a. The influence is highly uniform, and the places where the influence of heat is likely to appear locally, such as the hot spots 8a, 8b, and 8c, are not clear. Therefore, the height positions of the plurality of thermocouples only need to be above the molten metal surface of the molten steel 10 when the scrap 9 has all melted away.
Moreover, in this embodiment, although the thermocouple was used as a temperature detection end, it does not prevent using other temperature detection ends, such as a radiation thermometer. In the present embodiment, three thermocouples 6a to 6c, 6d to 6f, and 6g to 6i are arranged for one hot spot 8a, 8b, and 8c, respectively. However, among the inside of the furnace wall 5 (furnace wall refractory) of the electric furnace 1 and the outer peripheral surface of the furnace wall 5 of the electric furnace 1, a plurality of positions including the inside of the furnace wall 5 of the electric furnace 1, If a plurality of temperature detection ends are arranged at a plurality of positions where the thickness direction of the furnace wall 5 of the electric furnace 1 is different, the number of temperature detection ends for one hot spot is not limited to three. That is, the plurality of positions may be positions only inside the furnace wall 5 of the electric furnace 1 or positions of the inside and the outer peripheral surface of the furnace wall 5 of the electric furnace 1 (in other words, the plurality of positions are And a position excluding the position of the furnace wall inner surface 5a).

[Refractory wear and tear management system]
As shown in FIG. 2, the refractory material wear management system of the present embodiment includes a refractory material wear management device 101, a temperature sampling device 102, an input power control device 103, and a power input device 104.

The temperature sampling device 102 acquires the temperature measured by the thermocouples 6a to 6i at each temperature sampling time that repeatedly arrives at a predetermined period.
The refractory wear management apparatus 101 performs various arithmetic processes and the like to be described later so that the operator can determine whether or not the furnace wall refractory is worn (whether or not the furnace wall refractory is worn and the degree of wear of the furnace wall refractory). Output information used as an index for evaluation. Details of the refractory wear management apparatus 101 will be described later.

The input power control device 103 controls the operation of the power input device 104 based on an instruction from the operator.
The power input device 104 supplies power to the arc electrodes 3 a, 3 b, 3 c and the furnace bottom electrode 4 in accordance with control by the input power control device 103.

<Refractory material wear management apparatus 101>
The refractory wear management apparatus 101 performs an unsteady heat transfer inverse problem analysis on the basis of the temperatures measured by the thermocouples 6a to 6i at each temperature sampling time, and thereby the furnace wall inner surface 5a (hot spots 8a, 8b, 8c). ) Is calculated, and the time integral value of the heat flux is calculated from the result.

  FIG. 3 is a diagram illustrating an example of a functional configuration of the refractory wear and tear management apparatus 101. The hardware of the refractory wear management apparatus 101 is realized by using, for example, an information processing apparatus including a CPU, a ROM, a RAM, an HDD, and various interfaces, a PLC (Programmable Logic Controller), or dedicated hardware. be able to.

  The refractory wear and tear management apparatus 101 includes a heat flux deriving unit 110, a heat flux integrating unit 120, and an output unit 130. Below, an example of the function which these each part has is demonstrated.

<< Heat flux derivation unit 110 >>
The heat flux deriving unit 110 calculates the temperature and heat flux at the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) from the temperatures measured by the thermocouples 6a to 6i at each temperature sampling time. Below, an example of the method of calculating the temperature and heat flux in the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) will be described.

<<< Solution of unsteady heat conduction equation and calculation of heat input flux >>>
In this embodiment, the heat flux in the furnace wall inner surface 5a is calculated from the temperature measured by the thermocouples 6a to 6i by the heat transfer inverse problem analysis using the interpolation function that satisfies the unsteady heat conduction equation. It is calculated by the gradient in the normal direction of the furnace wall inner surface 5a. In the following description, the temperature measured by the thermocouples 6a to 6i is referred to as “temperature information” as necessary.
The transient heat conduction equation is expressed as follows: the temperature of the furnace wall inner surface 5a is T, the density of the furnace wall refractory is ρ, the specific heat of the furnace wall refractory is C, the heat conductivity in the x direction of the furnace wall refractory is k _x , y The thermal conductivity in the direction is represented by k _y , and the thermal conductivity in the z direction is represented by k _z .

The position vector is (x, y, z), the time is t, and an extrapolation function F with parameters x, y, z, and t giving exact solutions to the unsteady heat conduction equation, parameter α _{j, i} , and reference position A function that gives an exact solution of the unsteady heat conduction equation using the vector (x ^j , y ^j , y ^j ), the reference time t ⁱ , the number of reference position vectors N _j , and the number of reference times N _i is given by (2).

(X ^k , y ^k , y ^k ) is a temperature information measurement position vector, t ^l is a temperature sampling time, temperature information measured at the temperature information measurement position is a _{k, l} , and parameter α _{j, i} is This is determined using the simultaneous equations of (3).

  The extrapolation function F (x, y, z, t) is given by the following equation (4).

As shown in FIG. 1, in the present embodiment, in the electric furnace 1, a furnace wall refractory having a thickness of 450 mm is provided on the outer peripheral surface of the furnace wall 5 and at a depth of 150 mm and 300 mm from the outer peripheral surface of the furnace wall 5. The thermocouples 6a to 6c, 6d to 6f, and 6g to 6i were embedded and attached in a straight line at the positions. That is, the number N _k of temperature information measurement positions is set to “3” (N _k = 3). There is only one hot spot that is subject to calculation of the heat flux, and the heat flux is calculated individually for each of the hot spots 8a, 8b, and 8c. Below, an example of the method of calculating the heat flux in the hot spot of one place of the furnace wall inner surface 5a from the temperature information inside a furnace wall refractory is demonstrated. Here, it is assumed that the thickness direction of the furnace wall refractory is x, the coordinate of the furnace wall inner surface 5a is x = 0 mm, and the coordinate of the outer surface of the furnace wall 5 is x = 450 mm. Moreover, since the furnace wall refractory has isotropic thermal conductivity, the thermal conductivity is represented by k. The heat flux is calculated by estimating a one-dimensional temperature distribution in the thickness direction of the furnace wall refractory using a one-dimensional heat conduction equation. That is, the unsteady heat conduction equation corresponding to the equation (1) is the following equation (5).

  Further, the extrapolation function F corresponding to the equation (4) is the following equation (6).

An expression corresponding to the expression (2) representing the temperature at an arbitrary position x and time t is the following expression (7). Here, x ^j and t ⁱ are a reference position and a reference time, respectively.

The expression (7) is based on the idea that a virtual heat source exists at the reference time t ⁱ at the reference position x ^j and the influence of the virtual heat source affects the temperature at the position x and the time t. To do. Therefore, the reference time t ⁱ is a time past the time t. The function representing the effect of the virtual heat source is ^{F (x-x k, t} -t l). The parameter α _{j, i} represents a weight given to the influence of the virtual heat source. If this weight can be determined, the temperature at time t at position x can be estimated. However, if the reference time t ⁱ is set to a very close past, F (x− ^{k k} , t−t ^l ) becomes a sharp function and the error increases.

N _k temperature information measurement positions are provided, and when the temperature sampling is performed N _l times, the influence weight from the reference time t ⁱ at the reference position x ^j is obtained. Here, the number of the reference positions x ^j is the number of N _j number, the reference time t ⁱ is N _i number. That is, N _j × N _i parameters α _{j, i} are obtained using N _k × N _l pieces of temperature information.
The method for obtaining the parameter α _{j, i} may be basically determined so that the measured temperature information is correctly reproduced. The temperature information measured at the position x ^k and time t ^l is a _{k, l} . Since T (x ^k , t ^l ) = a _{k, l} , the following simultaneous equation (8) with the parameter α _{j, i} as an unknown is obtained.

In equation (8), values other than the parameter α _{j, i} are known. Equation (8) is a basic simultaneous equation that determines the parameter α _{j, i} . However, it is not guaranteed that a solution can always be obtained from the simultaneous equations (8). In addition, there may be cases where a stable solution cannot be obtained due to random measurement errors entering the temperature information.

  If the right side of the equation (8) is expressed again by using the function F using the equation (6), the simultaneous equations of the equation (8) become the following equation (9).

The right side of equation (9) indicates that if parameter α _{j, i} is determined, an estimated value of temperature information at temperature information measurement position x ^k and temperature sampling time t ¹ is given. Therefore, the right side of the equation (9) can be expressed only by T _{k, l} and subscripts k, l. That is, the simultaneous equations of equation (9) are as shown in equation (10) below. However, T _{k, l} is expressed by the following equation (11).

Here, the number N _j of the reference position x ^j, with match the number N _k of temperature information measuring position, if the number N _i of the reference time t ⁱ is equal to the number N _j of the sampling time j, with unknown The number N _j × N _{i of a} certain parameter α _{j, i} matches the number of equations N _k × N _l , and in principle, the simultaneous equations of equation (10) can be solved. However, depending on how the reference position x ^j and the reference time t ⁱ are taken, N _j × N _i does not necessarily match N _k × N _{l, and it} is not always possible to obtain a solution of simultaneous equations of equation (10). Even if the number N _j × N _i of the parameter α _{j, i} that is the unknown is matched with the number N _k × N _{1 of the} equation, it is not guaranteed that a stable solution can be obtained. Such a problem is called “ill-posed problem” as described in Non-Patent Documents 1 and 2.

Here, in order to express the simultaneous equations of the equations (10) and (11) in a concise manner, the double subscript pairs (k, l) and (j, i) are respectively converted into one subscript s and p. replace. This is possible, for example, by the following method. N _j × N _i = Q, N _k × N _l = R, and s = N _l (k−1) +1 (k = 1, 2,..., N _k , l = 1, 2,. , N _l ), the double subscript (k, l) can be replaced with a single subscript s (s = 1, 2,..., R). Similarly, if p = N _i (j−1) + i (j = 1, 2,..., N _j , i = 1, 2,..., N _i ), double subscript (j , I) can be replaced with one subscript p (p = 1, 2,..., Q).

That is, T _{k, l} and a _{k, l} , which are matrix components of N _k rows and N _l columns, can be represented by R-dimensional vector components T _s and a _s , and matrix components of N _j rows and N _i columns. Α _{j, i} can be represented by a Q-dimensional vector component α _p , and F (x ^k −x ^j , t ¹ −t ⁱ ) is represented by a matrix component F _{s, p} of R rows and Q columns. Will be. That is, T _{k, l} = T _s , a _{k, l} = a _s , α _{j, i} = α _p , F (x ^k −x ^j , t ^l −t ⁱ ) = F _{s, p} . These vectors are represented by T, a, and α, and the matrix is represented by F. At this time, the expressions (10) and (11) can be expressed as the following expressions (12) and (13), respectively.

Here, a _s is a measured value, F _{s, p} is a function value, and is a known value. That is, there is a problem of obtaining a coefficient α _p that correctly gives a measured value of temperature information. As described above, the number of unknowns Q and the number of equations R generally do not match. In this case, equation (12) cannot be solved. That is, it is called “ill-posed problem”. Non-Patent Documents 1 and 2 describe a method called “regularization method” that handles such a problem.
Basically, the coefficient α _p is determined so that the sum of squares of errors between the measured value a _s and the estimated value T _s is minimized. The total sum of such errors is expressed by the following equation (14).

The coefficient α _p may be determined so as to minimize the value of the equation (14). However, according to Non-Patent Document 2, there are many cases where a stable solution cannot be obtained even with such a method. According to Non-Patent Document 2, a stable solution can be obtained if the amount to be minimized is the following equation (15). However, r is a positive constant and varies depending on the problem. Here, 2.25 × 10 ⁻⁶ was adopted as r.

The method for obtaining the coefficient α _p that minimizes the equation (15) is described in Non-Patent Documents 1 and 2. According to these Non-Patent Documents 1 and 2, a technique called “Singular Value Decomposition” is used. According to “Singular Value Decomposition”, as shown in Non-Patent Document 3, an arbitrary matrix of R rows and Q columns can be displayed as a product of three square matrices. Of these three square matrices, one is a matrix in which only the diagonal component is not 0, and the other two are their own transposed matrices, that is, the matrix in which the row component and the column component are interchanged. It is represented by a matrix (orthogonal matrix) that is an inverse matrix. Therefore, if singular value decomposition is applied to the matrix F, it is guaranteed that the three square matrices satisfying the following expression (16) uniquely exist. That is, there are matrices Σ, W, and V that satisfy the following expression (16).

  Here, Σ is a matrix in which only the diagonal component is not 0, and W and V are the orthogonal matrices. V ′ is a transpose matrix of V. Where W is an R-order square matrix, V is a Q-order square matrix, Σ is an R-row Q-column matrix, and the number of diagonal components is the smaller number U of R and Q. . That is, U is expressed by the following equation (17).

Here, if the n-th diagonal component of the matrix Σ is denoted as σ _n , and the components of the matrix W and V in the s-row and n-column are denoted as w _{s, n} and v _{s, n} respectively, It can be written as (18).

Substituting equation (18) into F _{s, p} in equation (15), a coefficient α _p that minimizes the value of equation (15) is obtained. According to Non-Patent Document 1 and Non-Patent Document 2, such a problem is obtained as in the following equation (19).

Here, r is a constant and varies depending on the thermal characteristics of the temperature measurement object. When r = 0, the solution minimizes the value of equation (16), but the temperature in that case is an unstable temperature that varies greatly between the temperature information measurement positions. In the present embodiment, a stable solution was obtained by setting the value of r in the range of 1.0 × 10 ^{−6 to} 5.0 × 10 ⁻⁶ , and the temperature could be estimated correctly. It is also possible to determine the optimum value of r by cutting out a small amount of the same test piece as the target refractory and conducting a small-scale preliminary test at the laboratory level. In the above description, the number N _k × N _l = R of the temperature information measurement data related to the calculation of the parameter α _{j, i} and the number N _j × N _i = Q of the reference position data are included even when they are different. However, in consideration of calculation accuracy, it is preferable that the two coincide. That is, it is preferable that P = Q. If further calculation accuracy is taken into consideration, the number of temperature information measurement positions and the number of reference positions may be the same, and the number of temperature sampling data and the number of reference times for calculating the parameters α _{j, i} may be the same. preferable.

The obtained coefficient α _p is substituted into the equation (13), the subscript p is returned to the subscripts j and i, and the subscript s is returned to the subscripts k and l. In other words, subscript j is obtained by adding 1 to the quotient obtained by dividing p by N _i, the remainder obtained by the division becomes subscript i. The subscript k is obtained by adding 1 to the quotient obtained by dividing s by N _l , and the remainder obtained by the division becomes the subscript l.

Further, the heat input flux can be calculated as follows.
Let (x ₀ , y ₀ , z ₀ ) be the coordinates of the heat input flux estimated point on the furnace wall inner surface 5a, and b be outward on the furnace wall inner surface 5a at the heat input flux estimated point, that is, from the furnace wall inner surface 5a to the molten steel. The unit normal vector facing side, K is a matrix composed of thermal conductivity, and the following equation (20), which is the inner product of the unit normal vector b and the temperature gradient at the heat input flux estimation point, is entered. A heat flux q is given.

  Here, ∇ is a gradient vector operator, and K is expressed by the following equation (21).

In this embodiment, the thermocouples 6a to 6c, 6d to 6f, and 6g to 6i for measuring temperature information are arranged one-dimensionally, and the thermocouples 6a to 6c, 6d to 6f, and 6g to 6i are embedded. Since the thermal conductivity of the refractory is isotropic, k _x = k _y = k _z = k. That is, when the coordinate of the heat input flux estimation point is set to x ₀ , the equation (20) becomes the following equation (22) when the equation (7) is used.

  As described above, the heat input flux at a predetermined position is calculated from the temperature information.

[Temperature sampling time interval and reference time interval]
In the present embodiment, the temperature sampling device 102 samples temperature information at N _k positions N _l times at a time interval Δ ₁ from the temperature sampling start time τ ₁ . Using the sampled temperature information, the heat flux deriving unit 110 obtains the coefficient α _p from the equation (20) and obtains the parameter α _{j, i} in the equation (2). That is, the heat flux deriving unit 110 performs calculation for obtaining the coefficient α _p only after the temperature sampling is started and after the N _l- th temperature sampling is completed. Thereafter, the heat flux deriving unit 110 calculates the coefficient α _p for each progress of temperature sampling. As described above, the coefficient α _p , that is, the parameter α _{j, i,} is determined by the fact that the virtual heat source existing at the N _i reference times t ⁱ at the N _j reference positions x ^j is arbitrary at any coordinates. It can be thought of as representing the weight of the effect on temperature over time. Therefore, it is preferable to consider the reference time t ⁱ as a past time. That is, the reference time t ⁱ may preferably be from past time tau ₂ is N _i number in _{τ 2 + (N i -1)} Δ 2 until the time interval delta _2. That is, the temperature sampling time t ¹ and the reference time t ⁱ are expressed by the following equation (23).

Further, in the present embodiment, since one dimension is considered, the influence from the past heat source shown in the formula (2) or (11) is F (x ^k −x ^j , t ^l −t ^i. ), And is expressed as the following equation (24).

When the temperature sampling of N _l times is completed, the heat flux deriving unit 110 uses the interpolation function F of the equation (4) or (6) from the above equation, [Solution of unsteady heat conduction equation and heat input flow] The matrix F is subjected to singular value decomposition to obtain a coefficient, an estimated temperature, and a heat flux.

Although the reference time t ⁱ does not hinder the calculation even if it is not updated as a fixed time in the past, it is preferable to update the reference time t ^{i in} order to improve the calculation accuracy. For example, when the number of temperature sampling exceeds the number N _i of the reference times t ⁱ , the reference time is updated at the time interval Δ ₂ . However, the reference time t ⁱ of the computation of the coefficients alpha _{j, i,} it is necessary that the reference is the time t ⁱ of the parameter alpha _j, past than the sampling time of temperature information according to calculation of _i. Temperature sampling number N _l, if both greater than N _i, the temperature sampling count may be represented by the residue system of N _l or N _i. That is, using an appropriate number M ₁ or M ₂ , M ₁ N _l + l (M ₁ = 1, 2,..., L = 1, 2,..., N _l ) or M ₂ N _i + i (M ₂ = 1, 2,..., i = 1, 2,..., N _i ). In this case, the temperature information sampling time t ^l and the reference time t ⁱ are expressed by the following equation (25).

  In this case, the extrapolation function is expressed as the following equation (26).

If it is possible to predict how much scrap starts to melt after the temperature measurement is started, the M ₁ and M ₂ can be determined in advance. Therefore, if F shown in the equation (26) is calculated in advance for each of M ₁ and M _{2 and} singular value decomposition (Singular Value Decomposition) is performed for each F, temperature estimation is performed in a short time. Can be done. Further, along with the progress of temperature sampling, F in the equation (26) may be obtained, singular value decomposition may be performed, and the coefficient α _p may be obtained. In this case, there is a concern that the number of calculation steps increases and calculation efficiency decreases.

Here, it is assumed that N ₁ = N _i and further Δ ₁ = Δ ₂ = Δ. That is, the number of reference times related to the calculation of the coefficient α _{j, i} is made equal to the number of temperature sampling times, and the time interval of progress of the temperature sampling is made equal to the time interval of progress of the reference time. At this time, since M ₁ = M ₂ , the expression (26) becomes the following expression (27).

  Expression (27) remains unchanged even if the temperature sampling progresses and the reference time is updated. Therefore, the heat flux deriving unit 110 obtains F shown in the equation (27), and performs in advance the singular value decomposition described in [Solving Unsteady Heat Conduction Equation and Calculation of Heat Input Flux]. The coefficient α may be obtained from the equation (19) for each progress of temperature sampling. Thereby, the number of calculation steps is significantly reduced, and the calculation time can be significantly reduced without degrading accuracy. Further, when the coefficient α is obtained in advance, the heat flux deriving unit 110 obtains the heat flux on the furnace wall inner surface 5a from the equation (20) or the equation (22).

<< Heat flux integrator 120 >>
The heat flux integrating unit 120 derives a time integral value of the heat flux in a period corresponding to one operation based on the heat flux at each temperature sampling time derived by the heat flux deriving unit 110.

  In the electric furnace 1, in order to suppress the wear of the furnace wall 5, the spraying material is sprayed onto the furnace wall inner surface 5 a using the time between operations in batch operation. The inventors statistically considered the amount of wear of the furnace wall refractory by spraying spray material on the furnace wall inner surface 5a with various thicknesses and operating the electric furnace 1 under the same other conditions. The knowledge obtained by the present inventors will be described. In addition, when it calls a furnace wall, a spraying material shall not be included.

<<< Knowledge obtained by the present inventors >>>
FIG. 4 is a diagram illustrating an example of input power (voltage × current) to the arc electrode 3a. FIG. 5 is a diagram illustrating an example of the temperature of the furnace wall refractory. Moreover, FIG. 6 is a figure which shows an example of the heat flux of the furnace wall inner surface 5a.

  In FIG. 5, a graph 501 shows a thermocouple embedded in a position where a coordinate on a straight line perpendicular to the furnace wall inner surface 5a is 150 mm, with the coordinates of a point on the furnace wall inner surface 5a (hot spot 8a) being 0 mm. 1 shows the temperature measured by the thermocouple 6a) shown in FIG. Similarly, a graph 502 shows a thermocouple embedded in a position where a coordinate on a straight line perpendicular to the furnace wall inner surface 5a is 300 mm, with the coordinates of a point on the furnace wall inner surface 5a (hot spot 8a) being 0 mm (shown in FIG. 1). The temperature measured with thermocouple 6b) is shown. The graph 503 shows the temperature measured with the thermocouple arrange | positioned on the furnace wall inner surface 5a (hot spot 8a). In FIG. 5, the value of the graph 503 is constant because the temperature on the furnace wall inner surface 5a (hot spot 8a) exceeds the upper limit of temperature measurement by the thermocouple (the disconnection of the thermocouple occurs). ). A graph 504 indicates the temperature of the furnace wall inner surface 5a (hot spot 8a) derived as described above using the graphs 501 and 502.

In FIG. 6, a graph 601 indicates the heat flux of the furnace wall inner surface 5 a (hot spot 8 a) derived as described above using the graphs 501 and 502.
As described above, since the electric furnace 1 is operated in a batch manner, as shown in FIG. 4, electric power is intermittently repeatedly supplied to the arc electrode 3a in each operation (in the example shown in FIG. An example of the number of operations being performed).

  As shown in FIG. 5, the calculated value (graph 504) and measured value (graph 503) of the temperature on the furnace wall inner surface 5a (hot spot 8a) are the same as those in the first half of each operation (the furnace wall inner surface 5a (hot spot 8a). In the period until the thermocouple arranged above breaks), they substantially coincide. Therefore, it is understood that the temperature of the furnace wall inner surface 5a (hot spot 8a) is derived with high accuracy by the heat flux deriving unit 110 as described above.

  Further, when the plot of FIG. 4 is compared with the graph 601 of FIG. 6, the timing at which the heat flux reaches a peak is later than the timing at which the power (voltage × current) peaks, and a time delay occurs. This is considered to be because the scrap existing in front of the furnace wall refractory is a shield for radiant heat from the arc electrode 3a until the scrap is melted off after the operation is started. Therefore, it can be seen that the furnace wall inner surface 5a (hot spot 8a) heat flux derived by the heat flux deriving unit 110 as described above reflects the state of the electric furnace 1 with high accuracy.

FIG. 7 is a diagram illustrating an example of the relationship between the thickness of the spray material before the start of operation (remaining spray thickness before the start of operation) and the thickness of the spray material after the end of operation (remaining spray thickness after the end of operation).
When the electric furnace 1 is operated by spraying the spray material as described above, the operation is started with the spray material remaining on the surface of the furnace wall refractory so as to suppress the wear of the furnace wall refractory as much as possible. Operation is performed. If the thickness of the spray material before the start of operation is sufficient, the spray material remains even after the operation is completed, and wear of the furnace wall refractory can be avoided. On the other hand, if the thickness of the spray material before the start of operation is not sufficient, it is expected that the thickness of the spray material becomes 0 (zero) during the operation and the wear of the furnace wall refractory progresses.

  In FIG. 7, a region i, a region ii, and a region iii are divided by a one-dot chain line. In the region i, since the thickness of the spray material before the start of operation is not sufficient, the thickness of the spray material becomes 0 (zero) until the operation is completed, and this corresponds to a state in which wear of the furnace wall refractory progresses. . On the other hand, the area iii corresponds to a state in which the spray material remains after the operation is completed because the spray material has a sufficient thickness before the operation is started, and wear of the furnace wall refractory can be avoided. Region ii is in an intermediate state between region i and region iii.

FIG. 8 shows the heat flux (FIG. 8A) of the furnace wall inner surface 5a (hot spot 8a) and the gradient of the heat flux of the furnace wall inner surface 5a (hot spot 8a) (the amount of change in heat flux per unit time, It is a figure which shows an example of 8 (b).
In FIG. 8A, a graph 801 is the heat flux of the furnace wall inner surface 5a (hot spot 8a). FIG. 8A shows the temperature (graph 802) of the furnace wall inner surface 5a (hot spot 8a) and the effective power (graph 803) for the arc electrode 3a. Moreover, in Fig.8 (a), the number attached | subjected on the graphs 801-803 is the thickness of the spraying material before the operation start in each operation (spray remaining thickness before the operation start) and after the operation end. It shows the thickness of the spray material (remaining spray thickness after the operation is completed) and the amount of wear of the furnace wall refractory. For example, in “62 → 3 (0)”, the thickness of the spray material before the operation start is 62 mm, the thickness of the spray material after the operation is 3 mm, and the amount of wear of the furnace wall refractory is 0 (zero). It shows that it is mm. “3 → 0 (−30)” is that the thickness of the spray material before the start of operation is 3 mm, the thickness of the spray material after the end of operation is 0 mm, and the amount of wear of the furnace wall refractory is 30 mm. (The thickness of the furnace wall refractory is reduced by 30 mm). Also, in two consecutive operations, the thickness of the spray material before the start of operation in the subsequent operation is thicker than the thickness of the spray material before the start of operation in the previous operation, between the two operations. Is sprayed onto the furnace wall inner surface 5a.

The refractory damage mechanism in the hot spot is considered as follows. The high temperature of the arc causes the refractory to melt or volatilize, which adds to the erosion of slag and fume. Furthermore, temperature changes in the furnace cause thermal spalling, and the formation of altered layers based on slag infiltration leads to structural spalling. It is also known that the atmosphere in the furnace affects the refractory erosion, and it is pointed out that the electromagnetic induction phenomenon on the lining surface is involved in the damage. Thus, since the damage mechanism is complicated, an effective index for evaluating the wear amount of the refractory during operation has not been found so far.
The inventors of the present invention have determined that the main factor of wear of the furnace wall refractory is the thermal load received by the furnace wall refractory, and have focused on the amount of time integration of the heat flux of the furnace wall inner surface 5a. Therefore, the wear amount of the furnace wall refractory was evaluated using the time integral value of the heat flux of the furnace wall inner surface 5a as an index.

Further, from the result shown in FIG. 7, when the thickness of the spray material before the start of operation becomes less than a certain value (about 30 mm in the example shown in FIG. 7), the effect of suppressing the heat load of the refractory is lost, and the furnace wall It is thought that the heat flux of the inner surface 5a rises rapidly. It has been found that this corresponds to the gradient of the heat flux of the furnace wall inner surface 5a. In the example shown in FIG. 8, as can be seen from FIG. 8 (a), when the thickness of the sprayed material after the end of the operation is 30 mm or more, no rapid increase in the heat flux of the furnace wall inner surface 5a is observed (FIG. 8 ( (See the numerical value at the tip of the arrow a) and graph 801). Further, FIG. 8B shows that the heat flux of the furnace wall inner surface 5a rapidly increases at the timing when the gradient of the heat flux of the furnace wall inner surface 5a becomes 60 kcal / m ² · Hr / s or more. .

  From this, the present inventors have found that it is preferable to set the timing of starting the calculation of the time integral value of the heat flux of the furnace wall inner surface 5a to the timing when the gradient of the heat flux of the furnace wall inner surface 5a exceeds the threshold value. Got. On the other hand, the timing at which the calculation of the time integral value of the heat flux of the furnace wall inner surface 5a is completed corresponds to the timing at which the operation ends. Here, a case where the timing at which the effective power with respect to the arc electrode becomes 0 (zero) is set as a timing at which the calculation of the time integral value of the heat flux of the furnace wall inner surface 5a is finished is taken as an example.

The present inventors examined the causal relationship between the time integral value of the heat flux of the furnace wall inner surface 5a as described above and the amount of wear of the furnace wall refractory.
FIG. 9 is a diagram showing an example of the relationship between the amount of wear of the furnace wall refractory in each charge (ch) and the time integral value (cumulative heat flux) of the heat flux of the furnace wall inner surface 5a in the charge. In addition, the amount of wear of the furnace wall refractory is the amount of decrease in the thickness of the furnace wall refractory when the state in which the furnace wall refractory is not worn is 0 (zero). A large value is shown in the negative direction (the value itself is small).

  In FIG. 9, the amount of wear of the furnace wall refractory in each charge (ch) and the heat flux of the furnace wall inner surface 5a at each charge (ch) are distinguished for each of the three groups of regions i, ii, and iii shown in FIG. The relationship with the time integral value (cumulative heat flux) is expressed. That is, in FIG. 9, the thickness of the spray material before the start of operation (the remaining spray thickness before the start of operation) d is 120 mm or more, 30 mm or more and less than 120 mm, and the case where it is less than 30 mm. write.

  As described with reference to FIG. 7, the degree of progress of wear of the furnace wall refractory varies depending on the thickness (regions i, ii, iii) of the spray material before the start of operation. Therefore, the present inventors, for each of the three groups of regions i, ii, and iii shown in FIG. 7, wear amount of the furnace wall refractory in each charge (ch) and the heat flow of the furnace wall inner surface 5a at the charge. We thought that these correlations could be clearly obtained by classifying the relationship with the time integral value (cumulative heat flux) of the bundle.

  FIG. 10 shows the relationship between the amount of wear of the furnace wall refractory in each charge (ch) and the time integral value (cumulative heat flux) of the heat flux of the furnace wall inner surface 5a in the charge shown in FIG. It is a figure which extracts and shows only the relationship in case the thickness (spray residual thickness before operation start) d before the operation start is less than 30 mm. FIG. 11 shows the relationship between the amount of wear of the furnace wall refractory in each charge (ch) shown in FIG. 9 and the time integral value (cumulative heat flux) of the heat flux of the furnace wall inner surface 5a at that charge. It is a figure which extracts and shows only the relationship in case the thickness (spray residual thickness before operation start) d before operation start is 120 mm or more.

  As described with reference to FIG. 7, when the thickness of the spray material before the start of operation (the remaining spray thickness before the start of operation) d is less than 30 mm, the progress of wear of the furnace wall refractory becomes remarkable. As shown in FIG. 10, when the thickness of the spray material before the start of operation (the remaining spray thickness before the start of operation) d is less than 30 mm, the time integral value (cumulative heat flux) of the heat flux of the furnace wall inner surface 5a is increased. Along with this, the amount of wear of the furnace wall refractory increases linearly in the negative direction (the value itself decreases).

  Further, as described with reference to FIG. 7, when the thickness of the sprayed material before the start of operation (the remaining spray thickness before the start of operation) d is 120 mm or more, the wear of the furnace wall refractory can be avoided. As shown in FIG. 11, when the thickness of the sprayed material before the start of operation (the remaining spray thickness before the start of operation) d is 120 mm or more, the time integral value (cumulative heat flux) of the heat flux of the furnace wall inner surface 5a is Regardless, the amount of wear of the furnace wall refractory is almost zero.

  As described above, when the thickness of the spray material is remarkably reduced, the present inventors have found that the amount of wear of the furnace wall refractory in each charge (ch) and the furnace wall inner surface 5a at that charge. The relationship with the time integral value (cumulative heat flux) of the heat flux can be approximated to a directly proportional relationship, and it has been found that both can be clearly associated.

  Based on the above knowledge, as described above, in the present embodiment, the heat flux integrating unit 120 performs one operation based on the heat flux at each temperature sampling time derived by the heat flux deriving unit 110. The time integral value of the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) in the corresponding period is derived.

<< Output unit 130 >>
The output unit 130 uses the information including the time integral value of the heat flux derived from the heat flux integrating unit 120 for a period corresponding to one operation to wear the furnace wall refractory (the furnace wall refractory is worn out). And the degree of wear of the furnace wall refractory) are output as information that serves as an index for the operator to evaluate. For example, the output unit 130 outputs information including a time integral value of the heat flux in a period corresponding to one operation and a time transition of the heat flux in the operation. As an output form of such information, for example, any one of storage in a storage medium or portable storage medium inside the refractory wear management apparatus 101, display on a computer display, and transmission to an external apparatus Can be taken.

  The operator determines that the wear of the furnace wall refractory has progressed when the time integral value of the heat flux in the period corresponding to one operation output by the output unit 130 exceeds a predetermined threshold value. Then, the input power control device 103 is operated to instruct to reduce the input power to the arc electrodes 3a, 3b, 3c or to stop the operation. About this threshold value, it can set suitably based on the upper limit of the amount of wear of a furnace wall refractory, and a management policy. The input power control device 103 controls the operation of the power input device 104 based on an instruction from the operator, and sets the input power to a positive value lower than the current value, or 0 (zero).

[Operation flowchart]
Next, an example of operation | movement of the refractory material wear management apparatus 101 is demonstrated, referring the flowchart of FIG.
First, in step S1201, the heat flux deriving unit 110 derives the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c). In addition, the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) is derived individually for each hot spot 8a, 8b, 8c.

  Next, in step S1202, the heat flux integrator 120 calculates the gradient of the heat flux (the amount of change in the heat flux per unit time) of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) derived in step S1201. Is derived.

  Next, in step S1203, the heat flux integrating unit 120 determines whether or not the gradient of the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) derived in step S1202 exceeds a threshold value. As a result of the determination, if the gradient of the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) does not exceed the threshold value, the process returns to step S1201, and the furnace wall inner surface 5a (hot spots 8a, 8b, 8c). Steps S1201 to S1203 are repeated until it is determined that the gradient of the heat flux exceeds the threshold value.

  And if the gradient of the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) exceeds the threshold value, the process proceeds to step S1204. In step S1204, the heat flux integrating unit 120 derives the time integral value of the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c).

  Next, in step S1205, the heat flux integrator 120 determines whether or not the effective power for the arc electrodes 3a, 3b, and 3c has become 0 (zero). If the effective power for the arc electrodes 3a, 3b, and 3c is not 0 (zero) as a result of this determination, the process returns to step S1204, and the effective power for the arc electrodes 3a, 3b, and 3c is 0 (zero). Until it is determined, the processes in steps S1204 and S1205 are repeated. In this case, the time integral value of the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) is continuously derived.

  If it is determined that the effective power for the arc electrodes 3a, 3b, and 3c is 0 (zero), the process proceeds to step S1206. At this time, as the time integral value of the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c), the gradient of the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) exceeds a threshold value. A value in a period until the effective power for the arc electrodes 3a, 3b, and 3c becomes 0 (zero) is obtained.

  In step S1206, the output unit 130 outputs information including the time integral value of the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) in the period corresponding to one operation in this way. .

  Next, in step S1207, the refractory material wear management apparatus 101 determines whether or not to end the operation of the electric furnace 1. This determination can be made by an operator operating the refractory wear management apparatus 101 and giving an instruction to end the operation of the electric furnace 1. As a result of this determination, if the operation of the electric furnace 1 is not terminated, the process returns to step S1201 and the processes of steps S1201 to S1207 are repeated until it is determined that the operation of the electric furnace 1 is terminated. And if it determines with complete | finishing operation of the electric furnace 1, the process by the flowchart of FIG. 12 will be complete | finished.

Next, an example of the process (step S1201) by the heat flux deriving unit 110 will be described with reference to the flowcharts of FIGS.
The heat flux deriving unit 110 mainly performs processing including a preparation step (FIG. 13), a temperature information sampling step (FIG. 14), a memory operation step (FIG. 15), and a heat flux calculation step (FIG. 16). Here, the interval between the temperature sampling times and the interval between the reference times are equally set to Δ. That is, it is assumed that there is only one matrix F that needs to be calculated in advance.

In the preliminary preparation step shown in FIG. 13, first, in step S1301, the heat flux deriving unit 110 inputs various parameters. The heat flux deriving unit 110 includes, for example, a reference position vector (x ^j , y ^j , y ^j ), the number of temperature information measurement positions N _k , the number of times of temperature sampling N _l , the number of reference positions x ^j is N _j , and the reference the number N _i, the temperature information measured position vector time ^{t i (x k, y k} , y k), the interval of temperature sampling time and the reference time delta, temperature sampling start time tau _1, past time tau _2, and out interpolation functions F (x, y, z, t), and inputs the thermal conductivity k _x of refractory, k _y, k _z, and the positive constant r.

Next, in step S1302, the heat flux deriving unit 110 derives the matrix component F _{s, p} from the interpolation function F composed of the equation (4) or (6). Specifically, the matrix component F _{s, p} is derived using the following equations (28) to (31).
F (x ^k −x ^j , y ^k −y ^j , z ^k −z ^j , t ^l −t ⁱ ) = F (x ^k −x ^j , y ^k −y ^j , z ^k −z ^j , τ ₂ − τ ₁ + (l−i) Δ) (28)
s = N _l (k−1) + l (k = 1, 2,..., N _k : l = 1, 2,..., N _l ) (29)
p = N _i (j−1) + i (j = 1, 2,..., N _j : i = 1, 2,..., N _i ) (30)
F _{s, p} = F (x ^k −x ^j , y ^k −y ^j , z ^k −z ^j , τ ₂ −τ ₁ + (l−i) Δ) (s = 1, 2,..., N _k × N ₁ = R: p = 1, 2,..., N _j × N _i = Q) (31)

Next, in step S1303, the heat flux deriving unit 110 performs singular value decomposition on the matrix component F _{s, p} and derives matrices W, V, and Σ that satisfy Expression (16) or Expression (18). The method of singular value decomposition can be realized by using a general method shown in Non-Patent Documents 1 to 3. When the advance preparation step of FIG. 13 is completed, the temperature information acquisition preparation state is entered. The timing for executing the preliminary preparation step in FIG. 13 may be any timing as long as it is before the temperature information sampling step in FIG. Prior to starting the flowchart of FIG. 12, the preparatory step of FIG. 13 may be executed.

After the preliminary preparation step of FIG. 13 is completed, the heat flux deriving unit 110 executes the temperature information sampling step of FIG.
First, in step S1401, the heat flux deriving unit 110 stands by until a start signal is received. This start signal is, for example, a signal from an external device or a signal generated by an operator's operation on the refractory material wear management apparatus 101.

When the start signal is received, the process proceeds to step S1402. In step S1402, the heat flux deriving unit 110 sets the start time t to “0 (zero)” (t = 0). The heat flux deriving unit 110 sets the counter variable c to “1” (c = 1).
Next, in step S1403, the heat flux deriving unit 110 stands by until the temperature sampling start time τ ₁ is reached. When the temperature sampling start time τ ₁ is reached, the process proceeds to step S1404.

In step S1404, the temperature sampling device 102 samples temperature information at _Nk temperature information measurement positions. That is, the temperature sampling device 102 acquires N _k pieces of temperature information in one temperature sampling. The heat flux deriving unit 110 temporarily stores the N _k pieces of temperature information acquired by the temperature sampling device 102 in this way in the buffer memory together with the counter variable c. Here, the buffer memory refers to an area for temporarily storing information.

Next, in step S1405, the heat flux deriving unit 110 calls a memory operation step. As a result, execution of processing by the memory operation step of FIG. 14 is started.
Next, in step S1406, the heat flux deriving unit 110 updates the counter variable c by adding “1” to the counter variable c.

Next, in step S1407, the heat flux deriving unit 110 determines whether an end signal has been received. This end signal is, for example, a signal from an external device or a signal generated by an operator's operation on the refractory material wear management apparatus 101. If it is determined that the end signal has not been received, the process returns to step S1403 and waits until the next sampling start time is reached. On the other hand, when the end signal is received, the processing according to the flowchart of FIG. 14 ends.
As described above, in the temperature information sampling step, the sampling of the temperature information, the update of the counter variable c, and the transmission of the temperature information and the counter variable are repeated every time the sampling start time is reached. This is continued until an end signal is received.

In each step S1405 in FIG. 14, the memory operation step in FIG. 15 is started each time the memory operation step is called ( _Nk pieces of temperature information and counter variable c are temporarily stored in the buffer memory). In the memory operation step, the buffer memory temperature information and the counter variable c are stored in the work memory. Here, the work memory refers to an area for accumulating information used for calculation of heat flux.

First, in step S1501 in particular, the heat flux deriving unit 110 determines whether or not the counter variable c, which is temporarily stored in the buffer memory is below the number N _l temperature sampling. As a result of the determination, if the counter variable c is below the number N _l temperature sampling, the process proceeds to step S1502. In step S1502, the heat flux deriving unit 110 uses the temperature information temporarily stored in the buffer memory as a _{k, c} (k = 1, 2,..., N _k , c = 1, 2). ,..., N _l ) are stored in the work memory. Further, the heat flux deriving unit 110 accumulates the counter variable c corresponding to the temperature information in the work memory. And the process by the flowchart of FIG. 15 is complete | finished.

On the other hand, if the counter variable c is not below the number N _l temperature sampling, the process proceeds to step S1503. In step S1503, the heat flux deriving unit 110 determines whether or not the counter variable c, which is temporarily stored in the buffer memory is equal to the number N _l temperature sampling. As a result of the determination, if the counter variable c is equal to the number N _l temperature sampling, the process proceeds to step S1504.

In step S1504, the heat flux deriving unit 110 converts the temperature information temporarily stored in the buffer memory into a _{k, c} (k = 1, 2,..., N _k , c = 1, 2). ,..., N _l ) are stored in the work memory. Further, the heat flux deriving unit 110 accumulates the counter variable c corresponding to the temperature information in the work memory. As a result, N _k × N _l pieces of temperature information a _{k, l} and the latest counter variable c are stored in the work memory.

  Therefore, in step S1505, the heat flux deriving unit 110 calls a heat flux calculation step. Thereby, execution of the process by the heat flux calculation step of FIG. 15 is started. And the process by the flowchart of FIG. 15 is complete | finished.

If it is determined in step S1503 that the counter variable c temporarily stored in the buffer memory is not equal to the number of times of temperature sampling N ₁ , that is, the counter variable c temporarily stored in the buffer memory is the temperature If it is the sampling number N _l or more, the process proceeds to step S1506.
In step S1506, the heat flux deriving unit 110 determines that N _k × N _l pieces of temperature information a _{k, l} (k = 1, 2,..., N _k , l = , N _l ), the oldest temperature information of l = 1 is deleted from the work memory, and l → l−1 is obtained for those where l ≧ 2, and a new a _{k, l} ( _{k = 1,2, ···, N k} , l = 1,2, ···, rewritten as N _l -1), and updates. Then, the heat flux deriving unit 110 accumulates the latest N _k pieces of temperature information temporarily stored in the buffer memory as a _{k, l} (l = N _l ) in the work memory, and further, the temperature information Is stored in the work memory. Then, it progresses to step S1505 and the heat flux derivation | leading-out part 110 calls a heat flux calculation step.
Thus, in the memory operation step, the work memory is updated each time the temperature information and the counter variable c are temporarily stored in the buffer memory. As a result, when N _k × N _l pieces of temperature information a _{k, l} are stored in the work memory, a heat flux calculation step is called.

Each time the heat flux calculation step is called in step S1505 in FIG. 15 (N _k × N _l pieces of temperature information a _{k, l} are updated in the work memory), the heat flux calculation step in FIG. 16 is started.
First, in step S1601, the heat flux deriving unit 110 stores N _k × N _l pieces of temperature information a _{k, l} (k = 1, 2,..., N _k , l = 1, 2,..., N _l ), the coefficient α _p is obtained by the equation (19). Then, the heat flux deriving unit 110 converts the subscript p to the subscripts _{j and i,} and derives the parameter α _{j, i} .

Next, in step S1602, the heat flux deriving unit 110 derives the latest data acquisition time t = τ ₁ + (c−1) Δ based on the counter variable c stored in the work memory.
Next, in step S1603, the heat flux deriving unit 110 calculates the heat flux q on the furnace wall inner surface 5a from the equation (20) or the equation (22). And the process by the flowchart of FIG. 16 is complete | finished.
It should be noted that in order to prepare for the case where there is a problem such as temperature sampling failure, it is possible to insert a step for providing redundancy between the steps, but no particular problem was found in this embodiment. .

[Summary]
As described above, in the present embodiment, by performing the unsteady heat transfer inverse problem analysis based on the temperatures measured by the thermocouples 6a to 6i at each temperature sampling time, the furnace wall inner surface 5a (hot spots 8a, 8b, The relationship between the heat flux and the time of 8c) is derived, and from the result, the time integral value of the heat flux in the period corresponding to one operation is derived and output. Therefore, the heat flux of the furnace wall inner surface 5a (hot spots 8a, 8b, 8c) can be derived in consideration of the temperature that changes in an unsteady manner. Moreover, the amount of wear of the furnace wall refractory in each charge can be clearly associated with the time integral value of the heat flux of the furnace wall inner surface 5a in the charge. Therefore, the wear of the refractory in the electric furnace can be monitored with high accuracy. Thereby, the maintenance cost of a refractory can be reduced, maintaining the productivity in an electric furnace.

[Modification]
In this embodiment, when deriving the time integral value of the heat flux of the furnace wall inner surface 5a, the timing for starting and ending the integration is not limited as long as it is a period corresponding to one operation. For example, the time when the operation is started may be set as the timing when the derivation of the time integral value of the heat flux of the furnace wall inner surface 5a is started. In addition, after starting the derivation of the time integral value of the heat flux of the furnace wall inner surface 5a, the time integral value of the heat flux of the furnace wall inner surface 5a is derived at the timing when a preset time assumed as the operation time has elapsed. It is good also as the timing which completes. The timing at which the effective power for the arc electrode becomes 0 (zero) as in the above-described embodiment may be set as the timing at which the derivation of the time integral value of the heat flux of the furnace wall inner surface 5a is terminated.

However, in the electric furnace 1 in operation, the heat flux of the furnace wall inner surface 5a may be negative. This embodiment is based on the idea that when the heat flux of the furnace wall inner surface 5a is positive, the refractory is subjected to a heat load and wears out. However, when the heat flux is negative, recovery of the refractory occurs. I don't get. Therefore, if the heat flux is integrated when the heat flux is negative, it becomes a factor that lowers the accuracy as an evaluation index of the amount of wear.
Therefore, it is preferable that the timing at which the gradient of the heat flux of the furnace wall inner surface 5a exceeds the threshold as in this embodiment be the timing at which the derivation of the time integral value of the heat flux of the furnace wall inner surface 5a is started.

  The timing at which the heat flux of the furnace wall inner surface 5a changes from a negative value to 0 (zero) or a predetermined positive value may be the timing at which the derivation of the time integral value of the heat flux of the furnace wall inner surface 5a is started.

  In addition, after starting the derivation of the time integral value of the heat flux of the furnace wall inner surface 5a, the time integral of the heat flux of the furnace wall inner surface 5a is the first time when the value of the heat flux of the furnace wall inner surface 5a becomes 0 (zero). It may be the timing when the derivation of the value is finished.

  Further, when the value of the heat flux of the furnace wall inner surface 5a becomes negative in the period for deriving the time integral value of the heat flux of the furnace wall inner surface 5a, the negative value is set to 0 (zero) and the furnace wall inner surface The time integral value of the heat flux of 5a may be derived.

  Moreover, in this embodiment, when the time integral value of the heat flux in the period corresponding to one operation exceeds a predetermined threshold value, the case where the input power to the arc electrodes 3a, 3b, 3c is reduced is taken as an example. I gave it as an explanation. However, if measures are taken to suppress the wear of the furnace wall refractory, measures to reduce the input power to the arc electrodes 3a, 3b, 3c are not necessarily taken. For example, by performing slag forming, a measure is taken so that the slag is positioned between the hot spots 8a, 8b, 8c and the arc electrodes 3a, 3b, 3c. You may take instead of or in addition to the measure to lower.

  Further, as shown in FIG. 10, an equation and a table indicating the relationship between the amount of wear of the furnace wall refractory and the time integral value of the heat flux of the furnace wall inner surface 5a are stored, and based on this relationship, the furnace The amount of wear of the furnace wall refractory may be derived and output from the time integral value of the heat flux of the wall inner surface 5a.

The embodiment of the present invention described above can be realized by a computer executing a program. Further, a computer-readable recording medium in which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. As the recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.
In addition, the embodiments of the present invention described above are merely examples of implementation in carrying out the present invention, and the technical scope of the present invention should not be construed as being limited thereto. Is. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features thereof.

  1: electric furnace, 2: upper lid, 3a-3c: arc electrode, 4: furnace bottom electrode, 5: furnace wall, 6a-6i: thermocouple, 7a, 7b, 7c: right angle axis, 8a-8c: hot spot , 9: scrap, 10: molten steel, 101: refractory wear management device, 102: temperature sampling device, 103: input power control device, 104: power input device, 110: heat flux deriving unit, 120: heat flux integrating unit, 130: Output unit

Claims (5)

A refractory wear management device for an electric furnace that manages the wear of the refractory constituting the furnace wall of an electric furnace that melts scrap by arc discharge generated at an arc electrode,
Temperature measured at temperature detection ends arranged at a plurality of different positions in the thickness direction of the furnace wall of the electric furnace among the inside of the furnace wall of the electric furnace and the outer peripheral surface of the furnace wall of the electric furnace A heat flux deriving means for deriving the relationship between the heat flux and the time on the inner peripheral surface of the furnace wall of the electric furnace by performing an unsteady heat transfer inverse problem analysis based on
The time integral value of the heat flux in a period corresponding to one operation is derived based on the relationship between the heat flux and the time on the inner peripheral surface of the furnace wall of the electric furnace derived by the heat flux deriving means. Heat flux integrating means to
Output means for outputting, as an index for evaluating wear of the refractory, information including a time integral value of the heat flux in a period corresponding to the one operation derived by the heat flux integrating means; An refractory wear management apparatus for an electric furnace, comprising:   The plurality of temperature detection ends are straight lines perpendicular to the central axis of the electric furnace, in the vicinity of the straight line passing through the central axis of the arc electrode, and from the molten steel surface when all of the scrap is melted The refractory wear management apparatus for an electric furnace according to claim 1, wherein the refractory wear management apparatus for an electric furnace according to claim 1 is disposed at an upper position. The refractory wear management device for an electric furnace according to claim 1 or 2,
After the information including the time integral value of the heat flux in the period corresponding to the one operation is output by the output means, a measure for suppressing the wear of the refractory based on the output result. And a refractory wear management system for an electric furnace, characterized by comprising: An electric furnace refractory wear management method for managing wear of a refractory constituting a furnace wall of an electric furnace for melting scrap by arc discharge,
Temperature measured at temperature detection ends arranged at a plurality of different positions in the thickness direction of the furnace wall of the electric furnace among the inside of the furnace wall of the electric furnace and the outer peripheral surface of the furnace wall of the electric furnace A heat flux deriving step of deriving the relationship between the heat flux and the time on the inner peripheral surface of the furnace wall of the electric furnace by the heat flux deriving means by performing an unsteady heat transfer inverse problem analysis based on
Based on the relationship between the heat flux on the inner peripheral surface of the furnace wall of the electric furnace derived from the heat flux deriving step and the time, the time integral value of the heat flux in the period corresponding to one operation is calculated as the heat flow. A heat flux integrating step derived by a flux integrating means;
An output step of outputting information including a time integral value of the heat flux in a period corresponding to the one operation derived by the heat flux integration step as an index for evaluating wear of the refractory. When,
After the output process outputs information including the time integral value of the heat flux in the period corresponding to the one operation, a measure for suppressing wear of the refractory based on the result of the output. A refractory wear management method for an electric furnace, comprising:   A program for causing a computer to function as each means of the refractory wear management apparatus for an electric furnace according to claim 1 or 2.

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