JPH0535713A - Analyzing method for temperature distribution of conductive material due to conduction heating - Google Patents

Abstract

PURPOSE:To attain the accurate and efficient analysis of the temperature distribution of a conductive material due to inductive heating by considering the temperature change of the electromagnetic physical property value of an analyzing subject. CONSTITUTION:The temperature characteristic curve data on the electromagnetic/thermal physical property value of the steel stock are inputted to a computer together with the initial temperature of the steel stock. Then the time interval of the transient temperature field analysis is inputted together with the start conditions of the metastable electromagnetic field analysis and the end time of the transient temperature field analysis. Then the conductivity and the permeability are obtained from the initial temperature of the steel stock, and the metastable electromagnetic field analysis is carried out. Thus the Joule heat is calculated. Then the heat conductivity is obtained together with the heat capacity per unit accumulation and the heat transmittance. The transient temperature field analysis is repeated based on the obtained heat conductivity/transmittance and the Joule heat while the heat capacity and the heat transmittance are updated. Then the new conductivity and permeability of the steel stock are obtained based on the relevant temperature. Based on these coductivity and permeability, the metastable electromagnetic field analysis is carried out again and the Joule heat is calculated again for repetition of the transient temperature field analysis.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for analyzing a temperature distribution of a conductive material, which is an object to be heated, by analyzing an induction electromagnetic field by an induction heating device using a computer, for example, in a hot rolling process. It is suitable for application when analyzing the temperature distribution of a conductive material due to electromagnetic induction heating.

[0002]

2. Description of the Related Art First, a method of numerically analyzing transient and quasi-stationary induction electromagnetic fields will be described.

Numerical analysis method of transient induction electromagnetic field is described, for example, in Takayoshi Nakata and Norio Takahashi "Finite Element Method in Electrical Engineering", Morikita Publishing, p. 211, and numerical analysis of induction electromagnetic field in quasi-stationary case. For information on how to do "IEEE Transa
ctions on Magnetics "Vol.25, No.5, p.4153 (1989), respectively.

As the basic equation of the induction electromagnetic field, the following series of equations or equivalent equations obtained by converting these with other variables are used.

[0005]

[Equation 1]

[0006]

[Equation 2]

[0007]

[Equation 3]

[0008]

[0009]

[Equation 4]

[0010]

In these formulas, letters with an arrow symbol at the head
Is a vector that has all x, y, and z components (the same applies below.
Mr. However, the arrow symbol at the head is omitted in the text of the specification.
To do. ). In addition, A: vector potential [Vs /
m], φ: Scalar potential [V], J₀: Forced power
Flow density [A / m²], J_e: Eddy current density [A / m²],
E: electric field [V / m], B: magnetic flux density [Wb / m²],
σ: conductivity [S / m], μ: permeability [H / m], t: hour
The interval [s]. Of these physical quantities, vector potatoes
Initial A, scalar potential φ, forced current density J
₀, Eddy current density J _e, Electric field E and magnetic flux density B are all coordinates
(X, y, z) and a function of time t (hereinafter, "physics"
We call it "variable". ). Also, the electromagnetic property values σ and μ are tensor
Is expressed as a 3 × 3 matrix, and
Is a function that depends on. That is,

[0012]

[Equation 5]

It can be expressed as However, T = T (x,
y, z): Absolute temperature [K].

The above-mentioned [Equation 1] is Maxwell's equation, and [Equation 2] is a current continuity equation. In the transient analysis, the above physical variables are applied to the target area, and the necessary equations are solved while updating the time.

On the other hand, when the time change has quasi-stationarity such as an AC field, the time derivative can be replaced by a complex number, and the eddy current density J _e and the electric field E among the above physical variables are expressed by the following equations. be able to.

[0016]

[Equation 6]

However, ω: angular frequency [rad / s], j:
It is an imaginary unit.

The average value of Joule heat generated by the induced current is

[0019]

[Equation 7]

Is given by The unit is [W / m ² ].

Next, a method of analyzing transient and steady temperature fields will be described.

These analysis methods are described, for example, in "Computer analysis of heat and flow", edited by Nippon Mechanics, Corona Publishing Co., Ltd.,
It is described in detail on page 55, 1986 edition.

The basic equation of the transient temperature field is generally given by the following equation.

[0024]

[Equation 8]

Where κ: thermal conductivity [W / (m · K)],
Q: calorific value per unit time and unit volume [W / m ³ ],
C: Heat capacity per unit volume [J / (K · m ³ )].

When the temperature field is transient, it can be calculated in the same manner as in the case of the electromagnetic field described above. On the other hand, in the stationary case, the time derivative on the right side of the above [Equation 8] is set to 0 and solved.
That is,

[0027]

[Equation 9]

[0028] The heat exchange on the boundary is considered by the following equation.

[0029]

[Equation 10]

However, T _b : temperature of the boundary surface [K], n: vector of normal direction of the boundary surface, q: heat flow density [W / m ² ] passing through the boundary surface, α: heat transfer coefficient [W / (M ² · K)],
η: Stefan-Boltzmann constant 5.67 × 10
^-8 [W / (m ² · K ⁴ )], T _e : external temperature [K].

The above-mentioned thermal property values κ, α and C also depend on temperature,

[0032]

[Equation 11]

It is expressed as follows.

The state of induction heating can be investigated by combining the method of analyzing the induction electromagnetic field and the method of analyzing the temperature field described above. There are the following three conventional combination methods.

[Mathematical formula-see original document] By solving the equations [Equation 1], [Equation 2], [Equation 3] or their equivalents, the average Joule heat can be calculated, for example, by the following equation:

[0036]

[Equation 12]

[Equation 1]
1], the temperature is calculated from [Equation 8] and [Equation 10], and from that temperature [Equation 1], [Equation 2], [Equation 3] A series of processes for updating the electric conductivity σ and the magnetic permeability μ are repeatedly solved.

[Equation 1], [Equation 2], [Equation 6] or equations equivalent thereto are solved, the Joule heat of [Equation 7] is calculated only once, and this is used as an invariant heat source. 8], [Equation 10] and [Equation 11] are used to calculate only the temperature momentarily. The electromagnetic property values are not updated. An example of this is the document "IEEE Transactions on Magnetics" Vo
l.MAG-23, No.5, p.3296 (1987).

By solving [Equation 1], [Equation 2], [Equation 6] or an equation equivalent thereto, the Joule heat of [Equation 7] is calculated only once, and this is used as an invariant heat source. 9]
Is used to calculate only the steady state temperature distribution. The electromagnetic and thermal properties cannot be updated. An example of this is
Reference "Proceedings of the 5th Eddy Current Seminar"
28-30 Mar. (1988) at Rutherford Appleton Laborator
y, Oxford, UK, RAL-88-099.

[0040]

However, each of the above-mentioned conventional methods has the following problems.

According to the method (1), the temperature distribution can be obtained with high accuracy, but an enormous calculation time is required because both the electromagnetic field and the temperature field are calculated at each time. That is, in the temperature field, the only variable is the temperature T, whereas the electromagnetic field has three times the variables A _x , A _y , A _Z of the vector potential A and the scalar potential φ, and the calculation area is generally Since it is larger than the temperature field, the calculation time was about ten to several thousand times that of the temperature field.

According to the method (1), the initial temperature distribution can be obtained fairly accurately, but the electromagnetic property values of the conductive material, which is the material to be heated, such as the temperature changes of the conductivity σ and the magnetic permeability μ are taken into consideration. Since there was no such error, the error increased with the passage of time.

The method (1) gives a solution in the shortest calculation time among these three calculation methods, but has the worst accuracy,
In most cases, there was a large deviation from the actual phenomenon.

Therefore, an object of the present invention is to overcome the enormous calculation time of the above-mentioned method and the inaccuracy of the method, and to analyze the temperature distribution of the conductive material by induction heating accurately and efficiently. Is to provide a method that can.

[0045]

In order to solve the above-mentioned problems, in the present invention, a computer is used to analyze an induction electromagnetic field by an induction heating device to calculate Joule heat of a conductive material which is a heated object. Then, in the method of analyzing the temperature distribution of the conductive material based on the Joule heat, (a) inputting temperature characteristic curve data of electromagnetic property value and thermal property value of the conductive material, respectively; ) Inputting an initial temperature of the conductive material; (c) Inputting a time interval of transient temperature field analysis; (d) Inputting start conditions of quasi-stationary electromagnetic field analysis; (e) Transient temperature A step of inputting an end time of the field analysis; (f) a quasi-stationary electromagnetic field analysis is performed using the electromagnetic physical property value of the conductive material obtained according to temperature, and Joule heat due to an induced current of the conductive material is calculated. Calculate And (g) the thermal property value of the conductive material obtained according to the temperature and the Joule heat calculated in step (f) are used to perform a transient temperature field analysis to obtain a temperature distribution of the conductive material. And a step of calculating
(H) It is determined whether or not the starting condition for the quasi-stationary electromagnetic field analysis input in step (d) is satisfied, and if the starting condition is satisfied, the step (g) is used according to the temperature calculated in step (g). After updating the electromagnetic property value of the conductive material based on the temperature characteristic curve data of the electromagnetic property value of the conductive material input in a), the process returns to step (f) to satisfy the starting condition. If there is not, the step to proceed to the next step; (i) It is judged whether or not the end time of the transient temperature field analysis input in step (e) has come, and if not, the step According to the temperature calculated in (g), the thermal property value of the conductive material is updated based on the temperature characteristic curve data of the thermal property value of the conductive material input in step (a). After, the flow returns to step (g), steps and proceed to the next step if it becomes the end time; and a step of outputting (j) the temperature distribution data of said calculated conductive material.

The steps (a), (b), (c), (d) and (e) for inputting the various data and conditions described above may be in any order.

[0047]

In the present invention, the transient temperature field analysis is performed on the conductive material which is the material to be heated, and the temperature distribution is obtained.
For example, the same transient temperature field analysis is performed for each material that constitutes a heating device such as an induction heating device, and the change in the electromagnetic field due to the temperature change is calculated accurately to obtain the temperature distribution of the conductive material more accurately. You can

According to the method of the present invention, unlike the above-described conventional method, it is necessary to consider at least the change in the electromagnetic property value of the analysis object, instead of calculating the electromagnetic field at each time. Only when there is an electromagnetic field calculation to update the Joule heat. Therefore, compared to the conventional method,
The number of calculations of the electromagnetic field can be significantly reduced, which in turn can significantly reduce the overall calculation time. Moreover, unlike the previously described and methods described above, it is possible to perform an analysis that also considers the temperature change of the electromagnetic properties of the analysis target, so the accuracy of the analysis is significantly higher than those methods. To improve.

In order to achieve this object, in the present invention, the starting condition for the quasi-stationary electromagnetic field analysis is input, and only when the starting condition is satisfied, the quasi-stationary electromagnetic field analysis is performed to update the Joule heat. There is. It is the simplest to use the time interval as the starting condition. That is, a time interval that is a predetermined multiple of the time interval of the transient temperature field analysis is used as the starting condition for the quasi-stationary electromagnetic field analysis, and when the transient temperature field analysis is repeated a predetermined number of times, the quasi-stationary electromagnetic field analysis is performed and the Joule heat is updated. is there. In this case, the time interval of the transient temperature field analysis and the time interval used as the starting condition of the quasi-stationary electromagnetic field analysis are not arbitrarily determined, and the temperature characteristics of the conductive material and each material of the heating device to be analyzed are It should be determined in consideration of the performance (calculation speed, etc.) of the computer (computer) to be used, the target total calculation time, the required analysis accuracy, and the like. In particular,
The time interval used as the starting condition for the quasi-stationary electromagnetic field analysis is
Considering the degree of change of electromagnetic property value or thermal property value due to temperature in the analysis target, the value should be set to a value that maximizes accuracy and calculation efficiency.

As a starting condition for this quasi-stationary electromagnetic field analysis, in addition to the above-mentioned time interval, for example, the reached temperature of the analysis target, the temperature change width, etc. can be used. For example, if the ultimate temperature to be analyzed is used as the starting condition, enter multiple set temperatures as the starting conditions, and perform quasi-stationary electromagnetic field analysis when the temperature obtained by calculating the temperature field exceeds each set temperature. To do. In this case, as the set temperature input as the starting condition, it is preferable to select a temperature at which the electromagnetic property value or the thermal property value of the analysis target changes relatively greatly. When the temperature change width is used as the starting condition, the temperature rise obtained by the calculation of the temperature field is
The quasi-stationary electromagnetic field analysis is performed when the change width input in advance is exceeded.

Further, the starting condition of the quasi-stationary electromagnetic field analysis can be set for each conductive material or each material of the heating device to be analyzed. In this case, when an analysis target satisfies the conditions for starting the quasi-stationary electromagnetic field analysis, quasi-stationary electromagnetic field analysis is performed only for that analysis target, and the results are used to
Continue the transient temperature field analysis for all analysis targets.

The reason why sufficient analysis accuracy can be obtained by the method of the present invention is that the rate of change of the electromagnetic field with time (the angular frequency ω in the alternating field) is generally the rate of change of the temperature field ∂T /
This is because quasi-stationaryness of the electromagnetic field with respect to the temperature field may be assumed because it is sufficiently large with respect to ∂t≈Q / C and the change of the electromagnetic field due to temperature change is sufficiently slow.

FIG. 1 shows the procedure of the analysis method according to the present invention.

[0054]

EXAMPLES The present invention will be described below with reference to examples.

FIG. 2 shows an example of a simple induction heating device having axial symmetry. An alternating forced current flows in one annular induction coil 1 in the coil at the same current density in the circumferential direction, and induction heats a steel material 2 as a material to be heated. Other numbers in the figure indicate the lengths of each part of the apparatus and the material to be heated, and the unit is all millimeters. In this embodiment, the current density is 3.33 × 10 ¹⁰ [A / m ² ] and the frequency is 80.
[KHz].

FIG. 3 shows a temperature characteristic curve of electric conductivity σ of the steel material used as the material to be heated. The electrical conductivity σ is isotropic, and its temperature characteristic is also isotropic. In addition, in this embodiment,
The temperature characteristic curve of the magnetic permeability μ of the steel material to be heated is given by the following formula [Equation 13] as a temperature characteristic curve of the relative magnetic permeability μ _s . Note that μ _s = μ / μ ₀ (μ ₀ : permeability of vacuum 1.
2566 × 10 ^-8 [H / m]).

[0057]

[Equation 13]

The relative permeability μ _s was also isotropic, and its temperature characteristic was also isotropic.

FIG. 4 shows a temperature characteristic curve of the thermal conductivity κ of the steel material, and FIG. 5 shows a temperature characteristic curve of the heat capacity C of the steel material per unit volume. The temperature characteristic curve of the heat transfer coefficient α is given by the following equation.

[0060]

[Equation 14]

The temperature characteristic curves described above are all obtained by experiments conducted by the present inventors or equations based thereon. In addition, in FIG. 3, FIG. 4 and FIG. 5, the temperature is expressed in degrees Celsius [° C.].

First, as shown in the flow chart of FIG. 1, the electromagnetic property values (conductivity σ and relative permeability μ _s ) and thermal property values (heat conductivity κ, heat capacity C per unit volume) of the above-mentioned steel material. And the temperature characteristic curve data of the heat transfer coefficient α) were input to the computer, respectively, and further the initial temperature of the steel material 2 was input. In this embodiment, the temperature field analysis of the induction coil 1 which is a heating device is not performed.

Then, the time interval of the transient temperature field analysis, the starting condition of the quasi-stationary electromagnetic field analysis, and the end time of the transient temperature field analysis were input.

In this embodiment, the initial temperature of the steel material 2 is 303 [K] and the time interval of transient temperature field analysis is 0.001.
[S], quasi-stationary electromagnetic field analysis starting condition is time interval 0.1
[S] was set to be single, and the end time of the transient temperature field analysis was set to 3.0 [s].

Next, the data shown in FIG.
Based on the above, the electric conductivity σ and the magnetic permeability μ (= μ _s · μ ₀ ) are obtained from the input initial temperature of the steel material 2, and these are substituted into [Equation 1], [Equation 2] and [Equation 6]. Then, a quasi-stationary electromagnetic field analysis was performed, and the average Joule heat was calculated from [Equation 7].

Next, based on the data shown in FIGS. 4 and 5 and [Equation 14], the thermal conductivity κ, the heat capacity C per unit volume and the heat transfer coefficient α are obtained from the initial temperature of the steel material 2, respectively, and And the Joule heat described above in [Equation 8] and [Equation 10]
Substituting into, the transient temperature field analysis was performed and the temperature distribution was obtained. This transient temperature field analysis is performed while updating the thermal conductivity κ, the heat capacity C per unit volume and the heat transfer coefficient α for each time.
I went 0 times.

Then, based on the temperature when the transient temperature field analysis was performed 100 times, the conductivity σ and the magnetic permeability μ of the steel material 2 were newly obtained from the data shown in FIG. Using these, quasi-stationary electromagnetic field analysis was performed again, and Joule heat, which is a heat source, was calculated again. Then, the transient temperature field analysis was continued using this new Joule heat.

This series of repeated calculations was performed until the end time of 3.0 [s].

FIG. 6 shows the results of isothermal lines showing the temperature distribution of the steel material 2 obtained by the above-described analysis method.
On the other hand, the actually measured temperature measured by the thermocouple inserted in the steel material 2 is shown at the measurement points indicated by black circles. All numerical values in the figure are degrees Celsius. Further, since the device used in this example has an axial symmetry, the display of the result was performed only on the 1/4 part of the steel material 2. As is apparent from FIG. 6, the analysis method of the present embodiment can obtain a temperature distribution extremely close to the actually measured value.

For comparison, FIG. 7 shows the result calculated by the conventional analysis method described above. The calculation result is the same as in FIG.
It is indicated by an isotherm, and the actual measurement value at the measurement point indicated by a black circle is specified. All numbers are in degrees Celsius. In this conventional method, since the reduction of the electric conductivity σ and the magnetic permeability μ of the steel material 2 at a high temperature is not taken into consideration, the Joule heat is estimated to be larger than it actually is, and the steel material temperature is generally higher. Also, there is a difference in the size of the high temperature region.

As is clear from the results described above,
In the analysis method of the present embodiment, the steel material 2 accompanying the temperature change is used.
By considering the degree of change in the electromagnetic property value of, it is possible to reduce the number of calculations of the electromagnetic field while maintaining the analysis accuracy, and it is possible to reduce the calculation cost.

Further, according to the method of this embodiment, even if the analysis result is not good and the reanalysis can be performed, it is not necessary to input various data at the beginning. For example, the starting condition of the quasi-stationary electromagnetic field analysis is It is possible to easily improve the analysis accuracy simply by changing the time interval.

In the present embodiment, the conductivity σ and the magnetic permeability μ are treated as isotropic, but the same analysis can be performed when these are anisotropic. That is, in the anisotropic case, the conductivity σ and the magnetic permeability μ
Are calculated for each coordinate axis direction, and the same update procedure as described above is performed for them. For example, for the conductivity σ, the conductivity σ _x , σ _y , σ _z (tensor σ for each coordinate axis direction)
It is sufficient to obtain temperature characteristic curves for each of the three diagonal components of 1) and update them in accordance with the temperature.

Further, in the above-mentioned embodiments, the case where the steel material is heated has been described, but the present invention can be applied to the case where the non-ferrous metal such as aluminum, titanium and copper and various alloys are induction-heated. is there.

[0075]

According to the method of the present invention, the number of times the electromagnetic field is calculated can be reduced as compared with the case where the electromagnetic field and the temperature field are calculated every time, so that the total calculation time can be greatly shortened. it can. In addition, since it is possible to perform the analysis in consideration of the temperature change of the electromagnetic property value of the object to be analyzed, it is possible to obtain practically sufficient analysis accuracy. Then, by the method of the present invention, it is possible to analyze the temperature distribution when the conductive material such as steel material is induction-heated fairly accurately, and whether or not the desired temperature distribution can be obtained under the specified heating conditions is accurately determined. As can be seen, the present invention is very suitable for application to the design of an induction heating device, operation simulation, and the like.

[Brief description of drawings]

FIG. 1 is a flowchart showing a procedure of the present invention.

FIG. 2 is a schematic configuration diagram of an induction heating device for explaining an embodiment of the present invention.

FIG. 3 is a graph showing a temperature characteristic curve of electric conductivity of steel material.

FIG. 4 is a graph showing a temperature characteristic curve of thermal conductivity of steel.

FIG. 5 is a graph showing a temperature characteristic curve of heat capacity per unit volume of steel material.

FIG. 6 is a schematic diagram showing a temperature distribution of a steel material obtained by an analysis method according to an example of the present invention.

FIG. 7 is a schematic diagram showing a temperature distribution of a steel material obtained by a conventional analysis method.

[Explanation of symbols]

 1 induction coil 2 steel

─────────────────────────────────────────────────── ───

[Procedure amendment]

[Submission date] June 2, 1992

[Procedure Amendment 1]

[Document name to be amended] Statement

[Correction target item name] 0009

[Correction method] Change

[Correction content]

[0009]

[Equation 4]

[Procedure Amendment 2]

[Document name to be amended] Statement

[Name of item to be corrected] 0019

[Correction method] Change

[Correction content]

[0019]

[Equation 7]

[Procedure 3]

[Document name to be amended] Statement

[Correction target item name] 0036

[Correction method] Change

[Correction content]

[0036]

[Equation 12]

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Yoshio Hirano 1618 Ida, Nakahara-ku, Kawasaki City, Nippon Steel Corporation Advanced Technology Research Laboratories (72) Inventor Keiji Iwata 1618, Ida, Nakahara-ku, Kawasaki-shi Nippon Steel Incorporated company Advanced Technology Research Institute

Claims (1)

Claim: What is claimed is: 1. A computer is used to analyze an induction electromagnetic field by an induction heating device to calculate Joule heat of a conductive material, which is a heated object, and the conductive material is calculated based on the Joule heat. In the method of analyzing the temperature distribution of (a), the steps of: (a) inputting temperature characteristic curve data of electromagnetic property values and thermal property values of the conductive material; and (b) inputting an initial temperature of the conductive material. And (c) a step of inputting a time interval of the transient temperature field analysis, (d) a step of inputting a starting condition of the quasi-stationary electromagnetic field analysis, and (e) a step of inputting an end time of the transient temperature field analysis, (F) performing a quasi-stationary electromagnetic field analysis using the electromagnetic property value of the conductive material obtained according to the temperature, and calculating Joule heat due to the induced current of the conductive material; and (g) depending on the temperature. Asked And a step of calculating a temperature distribution of the conductive material by performing a transient temperature field analysis using the thermal property value of the conductive material and the Joule heat calculated in step (f), and (h) step (d) It is determined whether or not the starting condition of the quasi-stationary electromagnetic field analysis input in step S3 is satisfied, and if the starting condition is satisfied, the temperature input in step (a) is input according to the temperature calculated in step (g). After updating the electromagnetic property value of the conductive material based on the temperature characteristic curve data of the electromagnetic property value of the conductive material, the process returns to step (f), and if the starting condition is not satisfied, the next step Step (i), (i) It is determined whether or not the end time of the transient temperature field analysis input in Step (e) has been reached. If it is not the end time, go to Step (g). The thermal property value of the conductive material is updated based on the temperature characteristic curve data of the thermal property value of the conductive material input in step (a) according to the calculated temperature. Returning to g), when the end time is reached, the method proceeds to the next step, and (j) outputs the calculated temperature distribution data of the conductive material.