JP7705038B2 - Heat calculation program and heat treatment device - Google Patents

Description

The present invention relates to a thermal calculation program and a thermal processing device.

Technology for performing thermal calculations using computer simulations has been known for some time. This technology can be applied to various structures, including building materials (see, for example, Patent Document 1) and insulated containers (see, for example, Patent Document 2).

Patent No. 6482970 Patent No. 6465582

The above-mentioned thermal calculations can also be applied, for example, to estimating the temperature inside a heat treatment device (i.e., a vacuum carburizing furnace) for vacuum carburizing using a hydrocarbon gas at high temperature and reduced pressure. For example, a controller can estimate the temperature inside the furnace and use the estimated value to control the temperature inside the furnace in real time.

However, the methods disclosed in Patent Documents 1 and 2 are premised on solving a heat diffusion equation (or a heat conduction equation), and while the thermal calculations are highly accurate, they take a correspondingly long time to perform. As a result, the problem of impairing the real-time nature of temperature control arises.

In addition, to ensure real-time temperature control, it is desirable to perform thermal calculations using a method that requires less calculations to find a steady-state solution, for example, a differential equation following Fourier's law. However, as the temperature difference between the temperature on one side of the insulating wall and the temperature on the opposite side (hereinafter also referred to as the "temperature difference between the two wall surfaces") increases, another problem occurs in that Fourier's law is "broken" and the calculation accuracy decreases. In particular, in heat treatment equipment such as a vacuum carburizing furnace, the temperature difference between the two wall surfaces can reach approximately 1000°C, and the above-mentioned decrease in calculation accuracy becomes more noticeable.

The present invention was made in consideration of these problems, and its purpose is to provide a thermal calculation program and a thermal processing device that can suppress the decrease in calculation accuracy caused by the temperature difference between both wall surfaces of an insulating wall when performing thermal calculations based on Fourier's law.

The thermal calculation program in the first aspect of the present invention causes a computer to execute a correction step of correcting a heat flux obtained according to Fourier's law for a thermal structural model describing the state of an insulated wall including a thermal insulating material by multiplying or dividing the heat flux by a correction function having as an argument a constant volume specific heat ratio, which is the ratio of the constant volume specific heat at a position on the surface of the thermal insulating material to the constant volume specific heat at a position in the thickness direction of the thermal insulating material, and a calculation step of obtaining a steady-state solution of the thermal structural model using the corrected heat flux.

In the thermal calculation program according to the second aspect of the present invention, in the calculation step, a constraint is imposed on the thermal structural model so that the temperature difference between the temperature on one surface of the insulating wall and the temperature on the opposite surface is 500°C or more.

In the thermal calculation program according to the third aspect of the present invention, a constraint is imposed on the thermal structure model so that the heat transfer function, which takes as an argument the temperature difference between the temperature on one surface of the insulating wall and the temperature of the outside air in contact with the one surface, is an odd function.

In the thermal calculation program according to the fourth aspect of the present invention, the correction function is an identity function of the constant volume specific heat ratio.

The heat treatment device according to the fifth aspect of the present invention is a device comprising a device body for treating the surface of a workpiece and a controller for controlling the device body, the device body comprising an insulating wall including a heat insulating material and arranged to surround the workpiece, and a heater for heating the inside of a heating chamber formed by the insulating wall, the controller corrects the heat flux obtained according to Fourier's law for a thermal structural model describing the state of the insulating wall by multiplying or dividing the heat flux by a correction function having as an argument a constant volume specific heat ratio, which is the ratio of the constant volume specific heat at a position on the surface of the insulating material to the constant volume specific heat at any position in the thickness direction of the insulating material, and obtains a steady-state solution of the thermal structural model using the corrected heat flux, calculates an estimate of the temperature inside the heating chamber from the steady-state solution, and performs heating control on the heater using the obtained estimate.

According to the present invention, when performing thermal calculations based on Fourier's law, it is possible to suppress the decrease in calculation accuracy caused by the temperature difference between both wall surfaces of an insulating wall.

1 is a schematic cross-sectional view of a heat treatment apparatus according to an embodiment of the present invention. 4 is a flowchart showing an example of a temperature control operation by the controller of FIG. 1 . 3 is a detailed flowchart showing a method for estimating the temperature inside the furnace shown in step SP14 of FIG. 2. FIG. 2 is a diagram illustrating an example of a thermal structure model simulating the internal structure of a furnace body. FIG. 13 is a diagram illustrating an example of a correction function. FIG. 13 is a diagram showing an example of the shape of a heat transfer function. FIG. 13 is a diagram showing an example of an effect of improving calculation accuracy by correcting heat flux.

Hereinafter, an embodiment of the present invention will be described with reference to the attached drawings. In order to facilitate understanding of the description, the same components in each drawing are denoted by the same reference numerals as much as possible, and duplicate descriptions will be omitted.

[Overall configuration of heat treatment apparatus 10]
1 is a schematic cross-sectional view of a heat treatment apparatus 10 according to an embodiment of the present invention. The heat treatment apparatus 10 includes a vacuum carburizing furnace 12 (corresponding to an "apparatus main body"), a controller 14 (corresponding to a "computer"), a heating power source 16, and temperature sensors 18 and 20.

The vacuum carburizing furnace 12 is a device for performing vacuum carburizing using a hydrocarbon gas at high temperature and reduced pressure. The vacuum carburizing furnace 12 includes a furnace body 22 that houses the workpiece W, which is the object to be treated, and a frame body 24 that is attached to the inside of the furnace body 22. Inside the frame body 24, a relatively large hollow rectangular insulating member 26, a relatively small hollow rectangular insulating member 28, and a plurality of insulating members 30 for connecting the insulating member 26 to the insulating member 28 are provided. The insulating members 26, 28, and 30 are made of an insulating material such as a ceramic fiberboard. The two insulating members 26 and 28 are provided at a distance from each other, forming a space layer 32 that functions as an insulating layer.

The interior of the furnace body 22 is surrounded by a hollow insulating member 30 to form a carburizing chamber 36 for performing vacuum carburizing. A hearth 38 is provided in the furnace body 22, extending from its lower portion into the carburizing chamber 36. The workpiece W is placed on the upper end of the hearth 38 in a tray or basket (not shown).

Multiple heat radiation pipes 40 (corresponding to "heaters") are attached to the upper part of the furnace body 22 so as to extend toward the inside of the carburizing chamber 36. Each heat radiation pipe 40 is provided in a position that broadly covers the range from the upper end to the lower end of the carburizing chamber 36. This allows the space defined by the carburizing chamber 36 to be heated approximately evenly. The inside of the carburizing chamber 36 is set to a high temperature, for example, exceeding 900°C.

Multiple gas introduction nozzles 42 are provided on the top and sides of the furnace body 22 so as to face the position of the workpiece W. By introducing hydrocarbon gas from a gas supply mechanism (not shown) through the gas introduction nozzles 42 into the carburizing chamber 36, the surface of the workpiece W can be carburized.

An exhaust pipe 44 is provided at the bottom of the furnace body 22, connecting the carburizing chamber 36 to the outside of the vacuum carburizing furnace 12. The pressure inside the carburizing chamber 36 can be adjusted by operating a vacuum pump (not shown) to exhaust air from the exhaust port 46.

The controller 14 is a computer having a processor 50 and a memory 52, which controls the operation of each part of the vacuum carburizing furnace 12. The controller 14 reads and executes the programs and data stored in the memory 52 to synchronously or in parallel execute: [1] supply control for supplying hydrocarbon gas into the carburizing chamber 36, [2] pressure control for adjusting the pressure in the carburizing chamber 36, and [3] heating control for heating the carburizing chamber 36. To control these operations, a flow rate sensor, a pressure sensor (none of which are shown), and temperature sensors 18 and 20 are connected to the controller 14.

The processor 50 acquires temperature signals from the temperature sensors 18 and 20, and uses the measured temperatures to calculate an estimate of the temperature inside the carburizing chamber 36 (hereinafter also referred to as the "furnace temperature"). The processor 50 then controls the heating of each heat sink tube 40 by turning the heating power source 16 on and off based on the estimate it has calculated. Here, the temperature sensor 18 is provided at a position in contact with the top of the furnace body 14, and the temperature sensor 20 is provided at a position on the periphery of the vacuum carburizing furnace 12.

[Operation of controller 14]
<Overview of temperature control operation>
The heat treatment apparatus 10 in this embodiment is configured as described above. Next, the operation of the heat treatment apparatus 10, more specifically, an example of a temperature control operation by the controller 14 will be described with reference to the flow chart of FIG.

In step SP10 of FIG. 2, the controller 14 determines whether or not to continue temperature control in the carburizing chamber 36. If temperature control is to be continued (step SP10: YES), the controller 14 proceeds to the next step SP12.

In step SP12, the controller 14 determines whether or not the execution timing for temperature control has arrived. If the execution timing has not yet arrived (step SP12: NO), the controller 14 returns to step SP10 and sequentially repeats steps SP10 and SP12 until the execution timing arrives. On the other hand, if the execution timing has arrived (step SP12: YES), the controller 14 proceeds to the next step SP14.

In step SP14, the controller 14 estimates the current temperature inside the furnace. This estimation method will be described in detail later with reference to Figures 3 to 6.

In step SP16, the controller 14 controls the heating of each heat sink tube 40 by turning on or off the heating power source 16 based on the estimated value of the furnace temperature calculated in step SP14. Specifically, the controller 14 uses a known method including so-called PID control to control the temperature so that the furnace temperature transitions according to a predetermined temperature sequence.

Then, the process returns to step SP10, and the controller 14 sequentially repeats the operations of steps SP10 to SP16. If the controller 14 does not want to continue controlling the temperature inside the carburizing chamber 36 (step SP10: NO), it ends the operation of the flowchart shown in FIG. 2.

<Estimation of furnace temperature>
Next, a method for estimating the temperature inside the furnace in step SP14 (FIG. 2) will be described in detail with reference to the flow chart of FIG. 3 and FIG.

In step SP20 of FIG. 3, the controller 14 acquires temperature signals from the temperature sensors 18 and 20 and measures the outer wall temperature and the outside temperature of the furnace body 22, respectively.

In step SP22, the controller 14 determines a combination of the thermal structural model and solution method for the furnace body 14. This "thermal structural model" refers to a mathematical model that describes the state of the insulating wall, including the insulating material. The "solution method" of the model includes the type of equation, constraint conditions, how to find the solution, how to assign initial values, convergence conditions, etc.

4 is a diagram showing a schematic example of a thermal structure model simulating the internal structure of the furnace body 22. More specifically, this diagram shows a cross section of an insulating wall formed by stacking three sheets of insulating material. For example, a coordinate axis (X-axis) is defined in the direction from the inside to the outside of the furnace body 22. With respect to the position on the coordinate axis (unit: m), "inside the furnace" corresponds to the high temperature side and "outside the furnace" corresponds to the low temperature side. Parameters required to determine the steady-state heat transfer coefficients _h1 , _h2 (unit: W/ ^m2 ·K) and temperature distribution T (unit: °C) include: [1] thermal conductivity of the insulation _λ1 - _λ3 (unit: W/m2·K), [2] thickness of the insulation _l1 - _l3 (unit: m), [3] surface area of the insulation A (unit: ^m2 ), [4] high-temperature side fluid temperature Th (unit: °C), [5] low-temperature side fluid temperature Tc (unit: °C), [6] high-temperature side wall temperature Twh (unit: °C), and [7] low-temperature side wall temperature Twc (unit: °C).

In step SP24 of FIG. 3, the controller 14 provides an initial value for the temperature distribution to be calculated. For example, when solving a nonlinear differential equation using the Newton-Raphson method (hereinafter also simply referred to as "Newton's method"), it is desirable to provide an initial value that is as close as possible to a steady-state solution so as not to be trapped in a so-called local solution.

In step SP26, the controller 14 updates the temperature distribution given in step S24 using a successive approximation method including Newton's method. The controller 14 may update the temperature for each position sequentially from the high temperature side to the low temperature side using a "forward difference method", or may update the temperature for each position sequentially from the low temperature side to the high temperature side using a "backward difference method". The position interval (ΔX) may be set to various values, such as 1 mm intervals or 5 mm intervals. As described below, the corrected heat flux is used to update the temperature distribution.

In step SP28, the controller 14 determines whether or not a predetermined convergence condition is satisfied after the update of step SP26. One example of the convergence condition is that the difference in heat flux entering and leaving the insulating wall becomes a small value. If it is determined that the convergence condition is still not satisfied (step SP28: NO), the controller 14 returns to step SP26 and sequentially repeats steps SP26 and SP28 until the convergence condition is satisfied. On the other hand, if it is determined that the convergence condition is satisfied (step SP28: YES), the controller 14 proceeds to the next step SP30.

In step SP30, the controller 14 determines the temperature distribution and heat transfer coefficient finally found in step SP26 as the steady-state solution, and estimates the temperature inside the furnace using the obtained temperature distribution. In this way, the controller 14 ends the flowchart in FIG. 3 (step SP16 in FIG. 2).

<Characteristics of the thermal calculation method>
Next, the features of the heat calculation method in this embodiment will be described with reference to FIGS.

(1. Improvement of Fourier's Law)
One example of an equation used in thermal calculations is the heat diffusion equation. However, while the use of the heat diffusion equation increases the accuracy of the thermal calculation, it also takes longer to calculate. In other words, it is difficult to ensure real-time performance, making it unsuitable for online temperature control.

Therefore, in order to reduce the amount of calculation required to obtain a steady-state solution, it is possible to perform thermal calculations using a differential equation according to "Fourier's law". Specifically, Fourier's law is given by the following equation (1). Note that Q corresponds to heat flux (unit: W/ ^m2 ), A corresponds to the surface area of the insulating wall (unit: ^m2 ), λ corresponds to thermal conductivity (unit: W/m·K), and T corresponds to temperature (unit: K).

However, as the temperature difference between the two walls of the insulating wall increases, Fourier's law breaks down, and another problem occurs in that the accuracy of the thermal calculation decreases when the temperature difference exceeds approximately 500°C. In particular, in a heat treatment device 10 such as a vacuum carburizing furnace 12, the temperature difference between the two walls often exceeds 800°C, and the above-mentioned decrease in calculation accuracy becomes more noticeable.

Therefore, by improving Fourier's law shown in equation (1), calculation accuracy almost equivalent to that of the heat diffusion equation can be obtained. The heat flux Q can be calculated according to the following equation (2).

As can be seen from equations (1) and (2), the heat flux Q calculated according to Fourier's law is multiplied by the correction function f(·) to obtain the corrected heat flux Q. This correction function is a continuous function that satisfies f(1) = 1, and has various functional shapes, such as a polynomial function or an exponential function. From the viewpoint of achieving both improved calculation accuracy and reduced calculation volume, it is more preferable that the correction function is an identity function (y = x).

The argument of the correction function, rCv, is the ratio of specific heats at constant volume (hereinafter referred to as the "specific heat ratio at constant volume") and is a dimensionless physical quantity. Specifically, rCv is calculated according to the following formula (3).

Here, Cp(.) is the specific heat at constant pressure, and ρ(.) is the density. Furthermore, Tb is the surface temperature of the insulation material, and T corresponds to the temperature at any position in the thickness direction of the insulation material. In other words, the "specific heat ratio at constant volume" is the ratio of the specific heat at constant volume at any position in the thickness direction of the insulation material to the specific heat at constant volume at a position on the surface of the insulation material.

Figure 5 is a diagram showing an example of a correction function. The horizontal axis of the graph indicates the position in the thickness direction (unit: mm), and the vertical axis of the graph indicates the value of the correction function (unit: dimensionless). Here, the position of the surface on the high temperature side is X=0, and the position of the surface on the low temperature side is X=D. As can be seen from the graph in this figure, in the case of forward differential, the isochoric specific heat at any position is normalized by the isochoric specific heat at X=0. In other words, the correction function has a property that the value is 1 at X=0 and gradually increases as X increases. On the other hand, in the case of backward differential, the isochoric specific heat at any position is normalized by the isochoric specific heat at X=D. In other words, the correction function has a property that the value is 1 at X=D and gradually decreases as X decreases.

In this way, by correcting the heat flux using a correction function that uses the constant volume specific heat ratio as an argument, it is possible to reflect the difference in "specific heat" in Fourier's law. As a result, the decrease in calculation accuracy caused by the temperature difference between both wall surfaces of an insulated wall is suppressed.

(2. Shape of Heat Transfer Function)
6 is a diagram showing an example of the shape of a heat transfer function. The horizontal axis of the graph indicates the temperature difference (unit: °C), and the vertical axis of the graph indicates the heat flux (unit: W/m ² ). This "temperature difference" means the value obtained by subtracting the surface temperature (Twc) from the external temperature (Tc). The entire heat transfer function Qout is expressed, for example, as the sum of a first function indicating "radiative heat transfer" and a second function indicating "convective heat transfer".

Here, assuming that the heat flux Qin on the input side is constant, the steady-state solution of the temperature distribution is when the heat flux Qout on the output side is balanced. Therefore, when finding a steady-state solution using Newton's method, it is desirable that the heat transfer function of the heat flux Qout is a monotonically increasing function, as shown in Figure 6. For this reason, a constraint may be imposed so that the heat transfer function is an odd function, or a constraint may be imposed so that it is a composite function that connects multiple even functions divided into positive and negative sides.

<Effect of heat flux correction>
7 is a diagram showing an example of the effect of improving calculation accuracy by correcting the heat flux. This graph shows the temperature distribution obtained by thermal calculation. That is, the horizontal axis of the graph indicates the position in the thickness direction (unit: mm), and the vertical axis of the graph indicates the temperature (unit: ° C.). The "Comparative Example (without correction)" corresponds to the steady-state solution of the temperature distribution obtained using equation (1). On the other hand, the "Example (with correction)" corresponds to the steady-state solution of the temperature distribution obtained using equation (2).

As can be seen from this figure, a divergence occurs between the two graphs, mainly around the area where the temperature gradient changes abruptly (X = 80 to 100 mm). In contrast, the steady-state solution of the temperature distribution obtained using the heat diffusion equation generally coincides with the graph of the "Example". In other words, by correcting the heat flux, the decrease in calculation accuracy is suppressed even when heat calculations are performed using Fourier's law.

As described above, in the thermal calculation program and method of this embodiment, one or more computers (here, controller 14) execute a correction step (SP26 in FIG. 3) for correcting the heat flux obtained according to Fourier's law by multiplying or dividing the heat flux by a correction function whose argument is the constant volume specific heat ratio, which is the ratio of the constant volume specific heat at a position on the surface of the insulation to the constant volume specific heat at any position in the thickness direction of the insulation, and a calculation step (SP28) for finding a steady-state solution of the thermal structure model using the corrected heat flux.

In this way, by correcting the heat flux using a correction function that uses the constant volume specific heat ratio as an argument, it is possible to reflect the difference in "specific heat" in Fourier's law. As a result, the decrease in calculation accuracy caused by the temperature difference between both wall surfaces of an insulated wall is suppressed.

In addition, in the calculation step, a constraint condition may be imposed on the thermal structure model so that the temperature difference between the temperature on one surface of the insulating wall and the temperature on the opposite surface is 500°C or more. As this temperature difference increases, the degree to which Fourier's law is violated tends to increase, and therefore the effect of maintaining calculation accuracy by correction using the correction function becomes more pronounced.

A constraint may also be imposed on the thermal structure model so that the heat transfer function, whose argument is the temperature difference between the temperature on one surface of the insulating wall and the temperature of the outside air in contact with that surface, is an odd function. Making the heat transfer function symmetric about the origin improves the convergence of the steady-state solution.

The correction function may also be an identity function of the constant volume specific heat ratio. This makes it easier to improve the calculation accuracy while reducing the amount of calculation.

The heat treatment apparatus 10 in this embodiment also includes an apparatus body (here, vacuum carburizing furnace 12) that treats the surface of the workpiece (here, workpiece W), and a controller 14 that controls the vacuum carburizing furnace 12. The vacuum carburizing furnace 12 includes an insulating wall (here, insulating members 26, 28, 30) that includes a heat insulating material and is arranged to surround the workpiece W, and a heater (here, heat dissipation tube 40) that heats the inside of a heating chamber (here, carburizing chamber 36) formed by the insulating wall.

The controller 14 then corrects the heat flux by multiplying or dividing by a correction function that uses the constant volume specific heat ratio as an argument, obtains a steady-state solution of the thermal structure model using the corrected heat flux, calculates an estimate of the temperature inside the carburizing chamber 36 from the steady-state solution, and uses the obtained estimate to control the heating of the heat sink tube 40. This reduces the amount of calculation required to obtain the steady-state solution compared to estimating the temperature inside the carburizing chamber 36 using a thermal diffusion equation, making it easier to ensure real-time temperature control.

[Modification]
The present invention is not limited to the above-described embodiment, and can be freely modified without departing from the spirit and scope of the present invention. Alternatively, the respective configurations may be arbitrarily combined without causing any technical contradiction.

In the above embodiment, the temperature sensors 18, 20 are used to measure the outer wall temperature and the external temperature to estimate the temperature inside the carburizing chamber 36, but the arrangement of the temperature sensors is not limited to this form. For example, a heat-resistant temperature sensor may be provided inside the carburizing chamber 36 to estimate the temperature of the workpiece W. Also, if the external temperature of the vacuum carburizing furnace 12 is kept within a known control range, the configuration of the temperature sensor 20 may be omitted.

In the above embodiment, the controller 14 constituting part of the heat treatment device 10 executes the heat calculation program, but the configuration of the device is not limited to this. For example, a general-purpose computer independent of the vacuum carburizing furnace 12 may execute the heat calculation program for the purpose of computer simulation.

10...Heat treatment device, 12...Vacuum carburizing furnace (device body), 14...Controller (computer), 26, 28, 30...Insulating member, 36...Carburizing chamber (heating chamber), 50...Processor, 52...Memory, W...Work (processed object)

Claims (5)

A correction step of correcting a heat flux obtained according to Fourier's law with respect to a thermal structural model describing a state of an insulating wall including a thermal insulating material by multiplying or dividing the heat flux by a correction function having as an argument a constant volume specific heat ratio, which is the ratio of the constant volume specific heat at a position on the surface of the insulating material to the constant volume specific heat at an arbitrary position in the thickness direction of the insulating material;
A calculation step of obtaining a steady-state solution of the thermal structural model using the corrected heat flux;
A thermal calculation program characterized by causing a computer to execute the above. The thermal calculation program according to claim 1, characterized in that in the calculation step, a constraint condition is imposed on the thermal structural model so that the temperature difference between the temperature on one side of the insulating wall and the temperature on the opposite side is 500°C or more. The thermal calculation program according to claim 1 or 2, characterized in that a constraint condition is imposed on the thermal structure model so that a heat transfer function, which takes as an argument the temperature difference between the temperature on one surface of the insulating wall and the temperature of the outside air in contact with the one surface, is an odd function. The thermal calculation program according to any one of claims 1 to 3, characterized in that the correction function is an identity function of the constant volume specific heat ratio. A heat treatment apparatus comprising an apparatus body for treating a surface of a workpiece and a controller for controlling the apparatus body,
The device body includes:
A heat insulating wall including a heat insulating material and arranged to surround the object to be treated;
A heater for heating a heating chamber formed by the heat insulating wall;
Equipped with
The controller:
With respect to a thermal structural model describing the state of the insulating wall, a heat flux obtained according to Fourier's law is corrected by multiplying or dividing the heat flux by a correction function having as an argument a constant volume specific heat ratio, which is the ratio of the constant volume specific heat at a position on the surface of the insulating material to the constant volume specific heat at an arbitrary position in the thickness direction of the insulating material;
determining a steady-state solution of the thermal structural model using the corrected heat flux;
a heat treatment apparatus comprising: a heat treatment unit for controlling heating of the heater by calculating an estimated value of a temperature in the heating chamber from the steady-state solution and using the estimated value thus obtained.

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