JP2017125754A - Heat conductivity calculation method for treatment object, and heat treatment method for treatment object using the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a heat conductivity calculation method for a treatment object capable of taking heat conductivity in multiple locations into account in order to highly accurately compute a calculated value of a distortion value of heat treatment simulation.SOLUTION: A heat conductivity calculation method for a treatment object implements: a step S1 for measuring a first cooling curve that gives a temporal change of an interface temperature between a first surface and a fluid and a second cooling curve that gives a temporal change of an interface temperature between a second surface and the fluid, regarding the first surface and the second surface of a test piece formed from a tabular body modelling the treatment object; a step S2 for setting a heat conduction equation based on the measured first cooling curve and second cooling curve and identifying heat conductivity of an interface with the fluid on the first surface and heat conductivity of an interface with the fluid on the second surface; a step S3 for estimating temperature distribution within the test piece based on the identified heat conductivity; and a step S6 for finally identifying the heat conductivity when a difference between the estimated temperature distribution and a measurement is settled within a predetermined range.SELECTED DRAWING: Figure 11

Description

  The present invention relates to a heat transfer coefficient calculation method for a processing target and a heat processing method for the processing target using the same.

  Conventionally, with the widespread use of heat treatment simulations, it has become possible to calculate the hardness at the time of quenching of steel, quenching distortion, and the like by CAE computer simulation. The simulation requires various physical property data such as mechanical properties of metal materials, metallurgical phase change, and heat transfer coefficient of the coolant. Among these, with respect to the physical properties of metal materials, the physical properties have been acquired through various studies and compiled into a database.

On the other hand, with respect to the heat transfer coefficient of the coolant, for example, a method of calculating the heat transfer coefficient from a cooling curve measured by a heat treatment oil cooling test of JIS K2242 is known (for example, Patent Document 1 and Patent Document 2). .
By utilizing the heat treatment simulation, it was confirmed that the calculated value of the simulation and the actually measured value substantially coincided with each other regarding the hardness at the time of quenching the steel.
Then, when heat-treating the heat treatment object using a predetermined heat treatment oil, the cooling curve of the heat treatment object by the coolant is measured in advance, the heat transfer coefficient of the coolant is identified based on the cooling curve, and the identified heat transfer The effect of obtaining a heat treatment target having a desired hardness can be obtained by cooling the heat treatment target while controlling the temperature of the coolant based on the rate.

Japanese Patent Application Laid-Open No. 07-146264 JP 2006-266751 A

In the techniques described in Patent Document 1 and Patent Document 2, the heat treatment object is considered to have the same heat transfer coefficient, and the cooling condition for the heat treatment object is determined based on the obtained heat transfer coefficient. Was.
In this case, with respect to hardness, the calculated value and the actually measured value coincide with each other, but with respect to the quenching distortion, there is a problem that the calculated value and the actually measured value do not coincide with each other.

  An object of the present invention is to provide a heat transfer coefficient calculation method for a treatment target that can match a calculated value of a distortion value of a heat treatment simulation with an actual measurement value, and a heat treatment method for a treatment target using the method.

A heat treatment method for a processing target according to the present invention is a heat transfer coefficient calculation method for a processing target in which the processing target is cooled by a fluid, and includes the following steps.
1st process: The 1st cooling curve which gives the time change of the interface temperature between the 1st surface and the fluid about each of the 1st surface of the test piece which consists of a plate-like object which imitates the treating object, and the 2nd surface And a second cooling curve that gives a temporal change in the interface temperature between the second surface and the fluid.
Second step: Based on the measured first cooling curve and second cooling curve, a heat conduction equation represented by the following equation (1) is set, and is represented by the following equations (2) and (3). Based on the boundary condition and the initial condition expressed by Equation (4), the heat transfer coefficient h ₁ at the interface with the fluid on the first surface and the heat transfer at the interface with the fluid on the second surface. The rate h ₂ is identified.
Third step: A temperature distribution inside the test piece is estimated based on the identified heat transfer coefficient h ₁ and heat transfer coefficient h ₂ .
Fourth step: The heat transfer coefficients h ₁ and h ₂ are corrected based on the estimated temperature distribution, and the steps from the first step are repeated, and the difference between the estimated temperature distribution and the measured value is within a predetermined range. Then, the final identification of the heat transfer coefficients h ₁ and h ₂ is performed.

ｘ：第１表面から第２表面に至る厚み方向位置（ｍ，０≦ｘ≦板状体の厚さＬ）
ｔ：時間（ｓ）
Ｔ（ｘ，ｔ）：任意の時間における任意の厚み方向位置の温度（Ｋ）
α：熱拡散率（ｍ^２／ｓ）

x: Position in the thickness direction from the first surface to the second surface (m, 0 ≦ x ≦ thickness L of the plate-like body)
t: Time (s)
T (x, t): Temperature (K) at an arbitrary position in the thickness direction at an arbitrary time
α: Thermal diffusivity (m ² / s)

ｋ_１：第１表面の熱伝導率（Ｗ／（ｍ・Ｋ））

k ₁ : thermal conductivity of first surface (W / (m · K))

ｋ_２：第２表面の熱伝導率（Ｗ／（ｍ・Ｋ））

k ₂ : thermal conductivity of the second surface (W / (m · K))

[Equation 4]
T = F (x) (t = 0, 0 ≦ x ≦ L) (4)
T: Initial temperature distribution in the thickness direction of the specimen (K)

  According to the present invention, it is possible to realize a heat transfer coefficient calculation method for a processing target that can match a calculated value of a distortion value of a heat treatment simulation with an actually measured value.

  In the heat treatment method of the present invention, the heat transfer coefficient is identified using the heat transfer coefficient calculation method of the process object, and then the posture of the process object is changed and the heat transfer of the process object is performed again. Estimate the temperature distribution using the rate calculation method.If the temperature distribution of the processing target increases, change the orientation of the processing target in the reverse direction.If the temperature distribution of the processing target decreases, change the orientation of the processing target in the same direction. Further changes to

In the present invention,
In the step of measuring the cooling curve of the first surface and the cooling curve of the second surface,
The test piece includes a first hole penetrating from the center in the thickness direction of the outer peripheral end surface of the test piece to the center of the first surface, and the second surface from the center in the thickness direction of the outer peripheral end surface of the test piece. A second hole penetrating in the center of the
It is preferable to measure the interface temperature between the first surface and the fluid and the interface temperature between the second surface and the fluid by inserting a thermocouple into each of the first hole and the second hole.

  According to the present invention, temperature measurement can be performed at a position very close to the interface between the fluid and the object to be processed, so that highly accurate measurement can be performed.

The schematic diagram showing the structure of the metal surface temperature measuring apparatus which concerns on embodiment of this invention. The side view showing the structure of the to-be-measured body in the said embodiment. The side view and top view showing the structure of the test piece in the said embodiment. The schematic diagram for demonstrating identification of the heat transfer rate in the said embodiment. The graph for demonstrating identification of the heat transfer rate in the said embodiment. The graph for demonstrating identification of the heat transfer rate in the said embodiment. The graph showing the cooling curve of the test piece in the said embodiment. The graph showing the relationship between the temperature and heat transfer coefficient in the embodiment. The graph showing the temperature distribution for every time of the test piece in the said embodiment. The schematic diagram showing the attitude | position and position change of the test piece in the said embodiment. The flowchart for demonstrating the effect | action in the said embodiment.

Hereinafter, an embodiment of the present invention will be described.
[1] Configuration of Surface Temperature Measuring Device FIG. 1 shows a metal surface temperature measuring device according to an embodiment of the present invention. The surface temperature measuring device includes a heating electric furnace 1 as a heater, a cooling container 2 to be processed, a measurement object 3, a thermometer 4 and a recorder 4A.
The heating electric furnace 1 is for heating the object to be measured 3 to a predetermined temperature (about 800 ° C.), and a non-dielectric type which does not form a strong magnetic field or an alternating magnetic field in the furnace is used. The cooling container 2 is a container for storing a coolant to be inspected, for example, lubricating oil, and is disposed below the measurement object 3. The thermometer 4 has a thermocouple portion, and the measurement unit is incorporated in the measured object 3 to measure the temperature of the measured object surface. The recorder 4A records the temperature measured by the thermometer 4.

FIG. 2 shows a side view of the measured object 3. The measured object 3 includes a support 5 that can be moved up and down by a moving means 3A (FIG. 1), and a test piece 6 that is rotatably supported by the support 5. In the following description, the surface 6C of the test piece 6 will be described as the first surface of the present invention, and the back surface 6D will be described as the second surface of the present invention.
As shown in FIG. 3, the test piece 6 is made of a metal disk-like body. Holes 6 </ b> A and 6 </ b> B are formed on the circumferential side surface serving as the outer peripheral end surface, and the thermocouple 7 is inserted. ing.
The test piece 6 is made of SUS303 having a diameter of 35 mm and a thickness of 10 mm.
The hole 6A penetrates from approximately the center of the circumferential side surface to the surface 6C of one test piece 6, and the hole 6B penetrates from the approximately center of the circumferential side surface to the other back surface 6D. Near the surface of the holes 6A and 6B, a thermocouple serving as a temperature detector of the thermocouple 7 is arranged on the outermost surface, and it is possible to measure the temperature of the portion very close to the interface between the front surface 6C and the rear surface 6D and the cooling fluid. It has become.

[2] Identification of heat transfer coefficients h ₁ and h ₂ The introduction of the above-described equations (1) to (4) and the identification of the heat transfer factors h ₁ and h ₂ are obtained as follows.
Now, as shown in FIG. 4, the heat conduction equation of an infinite flat plate of thickness L that is cooled by the refrigerant with the temperature T = 0 from the front surface 6C and the rear surface 6D of the test piece 6 with the heat transfer coefficients h1 and h2 is It is represented by the following formula (5).

０≦ｘ≦Ｌ，ｔ＞０

0 ≦ x ≦ L, t> 0

  The boundary condition is expressed by the following formulas (6) and (7).

ｘ＝０，ｔ＞０

ｘ＝Ｌ，ｔ＞０

x = 0, t> 0

x = L, t> 0

  The initial condition can be expressed by the following formula (8).

ｔ＝０，０≦ｘ≦Ｌ

t = 0, 0 ≦ x ≦ L

  In order to solve this, the temperature T, which is a function of an arbitrary location x in the thickness direction and time t, is variable-separated as in the following equation (9).

  When the variables are separated in this way, the eigenvalue problem is solved by using the orthogonal relationship of trigonometric functions, and the solution shown in the following equation (10) is derived.

Here, N (β _m ) is the following formula (11).

  Since T is the initial temperature F (x) when t → 0, the following equation (12) is derived.

０＜ｘ＜Ｌ

0 <x <L

  As an eigenfunction, the following equation (13) is obtained.

  Therefore, the eigenvalue representing the heat transfer coefficient is represented by the following formula (14).

  The norm is represented by the following equation (15).

here,
α: Thermal Diffusivity (m ² / s)
k: Thermal conductivity (W / m · K)
c: Specific heat (Specific Heat, J / kg · K)
ρ: Density (Density, kg / m ³ )
h: Heat transfer coefficient (W / m ² · K)
Then, H ₁ = h ₁ / k ₁ and H ₂ = h ₂ / k ₂ (m ⁻¹ ).

The identification of the heat transfer coefficients h ₁ and h ₂ is obtained by the following procedure.
First, when the measured value of the temperature of the front surface 6C of the test piece 6 at the elapsed time t is T _m1 (i) and the temperature of the back surface 6D is T _m2 (i), the measured value at the elapsed time t + Δt is
T _m1 (i + 1), ΔT ₁ = T _m1 (i + 1) −T _m1 (i)
T _m2 (i + 1), ΔT ₂ = T _m2 (i + 1) −T _m2 (i)
It becomes.
The predicted values of the heat transfer rates h ₁ and h ₂ identify the temperature change rates (cooling rates) ΔT ₁ / Δt and ΔT ₂ / Δt of the front surface 6C and the back surface 6D of the test piece 6 with respect to the minute time Δt shown in FIG. Used as a guide for the initial value of the process.

The above-described equation (14) indicates the relationship between the eigenvalue β _m and H ₁ and H ₂ . Assuming that H ₁ = H ₂ = 100, the relationship of equation (14) is shown in FIG.
When H ₁ ≠ H ₂ , for the eigenvalue β _m , Equation (13) was calculated until m = 60.
Using ΔT ₁ / ΔT ₂ ∝H ₁ / H ₂ as a guide value, first, H ₁ and H ₂ are provisionally obtained, and then the difference between the temperature measurement result and the temperature calculation value is set to 0. The provisional H ₁ and H ₂ on both sides are corrected so as to be 02 ° C. or lower, and the final H ₁ and H ₂ are identified.
FIG. 7 shows the cooling curve used, FIG. 8 shows the heat transfer coefficient at each identified temperature, and FIG. 9 shows the temperature distribution of the test piece 6 over time.

The specific heat transfer coefficient is calculated by three subroutines as follows.
[2-1] Eigenvalue Calculation Subroutine The eigenvalue β _m is calculated from the relationship of the following formula (16) by setting the plate thickness L, the temperature dependence α, and the thermal conductivity k.

Specifically, the left side is decreased from a large value, and a plurality of, for example, 60 β _m ^{* s} matching the right side are found.
At this time, H ₁ and H ₂ used first are substituted with values as shown in FIG.
Thereafter, H ₁ and H ₂ that match the measured values are obtained by a temperature comparison subroutine described later.
First, when the value on the left side of the equation (16) is decreased at a certain value interval and the value on the right side of the equation (16) becomes negative after passing through the matching point, the value interval is changed. If it passes by 1/10 and passes again, the value interval is again reduced by 1/10 and this is repeated to find the intersection.

Next, T ^* (x ^* , t) is calculated based on the following formula (17) using the obtained 60 eigenvalues β _m (m = 1 to 60). For m → ∞, 60 sums are calculated using 60 found β _m ^* .

[2-2] Temperature comparison subroutine between calculated value and measured value Of the calculated temperatures, the surface temperature calculated value is compared with the surface temperature measured value, and H ₁ and H ₂ are changed until they match the measured value. 60 β _m ^{* s} that match H ₁ and H ₂ are calculated, T ^* (x ^* , t) is calculated again by Equation (17), and the temperature is compared with the measured value.
As the eigenfunction, equation (18) is used.

Note that F (x ^* ) dx ^* in the equation (17) is calculated using the initial temperature distribution, and the integral is a trapezoidal numerical integration.

[2-3] Subroutine for reading the cooling curve First, initial conditions are set, and a temperature interval for reading data from the cooling curve is set. The temperature when the temperature interval is subtracted from the initial temperature at this time is read from the cooling curve. At the same time, the time is read and the time interval is calculated.
For the first time, the temperature at each point in the plate thickness direction, that is, the cooling start temperature is set as an initial condition.
Next, the data read from the cooling curve is input to the eigenvalue calculation subroutine and the calculation value / measurement value comparison subroutine described below.

The heat transfer coefficient result identified by the eigenvalue calculation subroutine, the initial temperature of the front surface 6C, the initial temperature of the back surface, the temperature of the front surface 6C after Δt, and the temperature of the back surface 6D are recorded.
At this time, in Equation (10), the temperature distribution in the plate thickness direction is calculated.
Record the calculated temperature distribution at each point in the thickness direction.
The temperature distribution at each point is set as the next initial condition.
The temperature data of the temperature interval is read from the cooling curve in the same manner as described above, and the data is input to the subroutine for calculating the eigen value, the subroutine for comparing the calculated value and the measured value, and the identified heat transfer coefficient and the decreased temperature are recorded. Here, the temperature at each point in the plate thickness direction is set as an initial condition one after another.

In identifying the heat transfer coefficients h ₁ and h ₂ of the front surface 6C and the back surface 6D, a set (h ₁ , λn), (h ₂ , λn) composed of a certain heat transfer coefficient h ₁ , h ₂ and its series solution λn. ) And a series (h ₁ , λn), (h) in which series solutions λn corresponding to these heat transfer coefficients h ₁ and h ₂ are sequentially substituted into eigenfunctions to give a temperature calculation value close to the temperature measurement value. ₂ , λn) are selected, and a regression equation is obtained from the relationship between these pairs (h ₁ , λn), (h ₂ , λn) and the calculated temperature, and a temperature measurement value is obtained from this regression equation. The heat transfer coefficients h ₁ and h _{2 to be given} and the series solution λxn are obtained, and this set is substituted into the eigenfunction, and the heat transfer coefficient h is calculated so that the temperature calculation value calculated by the substitution matches the temperature measurement value. _1, to identify and correct the _{h 2.}
By using commercially available heat treatment simulation software using the obtained heat transfer coefficients h ₁ and h ₂ of the two surfaces, it is possible to accurately calculate the heat treatment strain when cooling unevenness occurs.
Examples of commercially available heat treatment simulation software include Deform-HT (Yamanaka Gokin Co., Ltd.), COSMAP (idea map of limited company), DANTE (Dante Solutions, Incorporated (USA)) and the like.

[3] Posture control and action of processing object The temperature distribution inside the test piece 6 obtained as described above is performed for various postures as shown in FIG. 10, and the temperature distribution for each posture is grasped. To do.
During actual cooling of the processing target, the processing target is first cooled in a certain posture, and the internal temperature distribution of the processing target at that time is estimated, and if the difference in internal temperature distribution exceeds a predetermined threshold, this is Change the posture in the direction to cancel.

Specifically, this is performed based on the flowchart shown in FIG.
First, the test piece 6 is put into the cooling container 2 in a predetermined posture, the surface temperatures of the front surface 6C and the back surface 6D of the test piece 6 are measured, and the first cooling curve of the front surface 6C and the second cooling curve of the back surface 6D are obtained. Measure (step S1: first step).
Next, the heat transfer coefficients h ₁ and h ₂ of the front surface 6C and the back surface 6D are identified based on the first cooling curve and the second cooling curve (step S2: second step).
Based on the identified heat transfer coefficients h ₁ and h ₂ , the temperature distribution inside the test piece 6 is estimated (step S3: third step).

It is determined whether or not the difference between the calculated value of the estimated temperature distribution and the measured value is equal to or less than a predetermined range (step S4: fourth step).
If it is not below the predetermined range, the heat transfer coefficients h ₁ and h ₂ are corrected (step S5: fourth step), and steps S1 to S3 are repeated.
When the temperature falls below the predetermined range, the heat transfer coefficients h ₁ and h ₂ are finally identified (step S6).
When the final identification of the heat transfer coefficients h ₁ and h ₂ is completed, the posture of the test piece 6 is changed, and the steps S1 to S3 are repeated, but it is determined whether the temperature distribution before and after the posture change is reduced ( Step S7) When the position becomes smaller, the posture is changed in the same direction (Step S8). When the position becomes larger, the posture is changed in the opposite direction (Step S9), and Steps S1 to S4 are performed. repeat.

[4] Effects of the Embodiment According to the present embodiment as described above, the following effects are obtained.
The temperature distribution inside the test piece 6 is estimated by using different thermal conductivities of the front surface 6C and the back surface 6D of the test piece 6, and the posture and position in the cooling fluid are changed. Etc. can be reduced.
Further, the hole 6A reaching the front surface 6C and the hole 6B reaching the back surface 6D are formed in the test piece 6, so that the temperature is measured by the thermocouple 7 at a position very close to the interface between the test piece 6 and the fluid. Therefore, highly accurate measurement can be performed.

[5] Modifications of Embodiments The present invention is not limited to the above-described embodiments, and includes the following modifications.
In the above-described embodiment, the disk-shaped test piece 6 is used. However, the present invention is not limited to this, and a square plate-shaped test piece may be used. It is not limited.
In addition, other structures and the like may be adopted as long as the object of the present invention can be achieved.

  DESCRIPTION OF SYMBOLS 1 ... Electric furnace for heating, 2 ... Cooling container, 3 ... Object to be measured, 4 ... Thermometer, 4A ... Recording meter, 5 ... Support body, 6 ... Test piece, 6A ... Hole, 6B ... Hole, 6C ... Surface, 6D ... back surface, 7 ... thermocouple, S1 ... step, S2 ... step, S3 ... step, S4 ... step, S5 ... step, S6 ... step, S7 ... step, S8 ... step, S9 ... step

Claims (3)

A method for calculating a heat transfer coefficient of a processing target, wherein the processing target is cooled by a fluid, and includes the following steps.
1st process: The 1st cooling curve which gives the time change of the interface temperature between the 1st surface and the fluid about each of the 1st surface of the test piece which consists of a plate-like object which imitates the treating object, and the 2nd surface And a second cooling curve that gives a temporal change in the interface temperature between the second surface and the fluid.
Second step: Based on the measured first cooling curve and second cooling curve, a heat conduction equation represented by the following equation (1) is set, and is represented by the following equations (2) and (3). Based on the boundary condition and the initial condition expressed by Equation (4), the heat transfer coefficient h ₁ at the interface with the fluid on the first surface and the heat transfer at the interface with the fluid on the second surface. The rate h ₂ is identified.
Third step: A temperature distribution inside the test piece is estimated based on the identified heat transfer coefficient h ₁ and heat transfer coefficient h ₂ .
Fourth step: The heat transfer coefficients h ₁ and h ₂ are corrected based on the estimated temperature distribution, and the steps from the first step are repeated, and the difference between the estimated temperature distribution and the measured value is within a predetermined range. Then, the final identification of the heat transfer coefficients h ₁ and h ₂ is performed.

x: Position in the thickness direction from the first surface to the second surface (m, 0 ≦ x ≦ thickness L of the plate-like body)
t: Time (s)
T (x, t): Temperature (K) at an arbitrary position in the thickness direction at an arbitrary time
α: Thermal diffusivity (m ² / s)

k ₁ : thermal conductivity of first surface (W / (m · K))

k ₂ : thermal conductivity of the second surface (W / (m · K))
[Equation 4]
T = F (x) (t = 0, 0 ≦ x ≦ L) (4)
T: Initial temperature distribution in the thickness direction of the specimen (K)   The heat transfer coefficient of the processing target according to claim 1 is changed again after the heat transfer coefficient is identified using the heat transfer coefficient calculation method of the processing target according to claim 1 and then the posture of the processing target is changed. The temperature distribution is estimated using a calculation method, and when the temperature distribution of the processing target becomes large, the posture of the processing target is changed in the reverse direction, and when the temperature distribution of the processing target becomes small, the processing target A heat treatment method of a processing object, wherein the posture is further changed in the same direction. In the heat processing method of the process target of Claim 2,
In the step of measuring the cooling curve of the first surface and the cooling curve of the second surface,
The test piece includes a first hole penetrating from the center in the thickness direction of the outer peripheral end surface of the test piece to the center of the first surface, and the second surface from the center in the thickness direction of the outer peripheral end surface of the test piece. A second hole penetrating in the center of the
The interface temperature between the first surface and the fluid and the interface temperature between the second surface and the fluid are measured by inserting a thermocouple into each of the first hole and the second hole. Heat treatment method to be treated.

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