Numerical analysis program and heat treatment device

Abstract

To provide a numerical analysis program and a heat treatment device with which it is possible to suppress an increase in the required time of analysis processing due to the complexity of a three-dimensional shape that the object to be analyzed has.SOLUTION: A computer performs the analysis processing of an object by acquiring the three-dimensional shape of the object to be analyzed, dividing the three-dimensional space that includes the object into a plurality of elements, finding the density occupied by the object in a unit space composed of the elements, calculating a density distribution that indicates the density per element position, finding a physical quantity of the elements correlating to the heat transfer characteristic by using the density distribution, constructing each element a heat transfer equation that includes the physical quantity, and solving the heat transfer equation for each element. When the physical quantity represents an exchange amount of radiant heat between the object and the outside of the object, the computer calculates a change amount of the object's surface area using the difference between a first density corresponding to a first element and a second density corresponding to a second element which is adjacent to the first element, and finds the exchange amount of radiant heat using the change amount.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a numerical analysis program for performing a numerical analysis on an object having a three-dimensional shape, and a heat treatment apparatus. [Background technology]

[0002] Conventionally, techniques for performing numerical analysis using computer simulations have been known. For example, Patent Document 1 discloses a method for analyzing the mechanical properties of an object using the finite element method. More specifically, this document uses a method for setting a coordinate system for each element, taking into account the anisotropic direction and / or the orientation of the curved surface of the object, so as to prevent the construction of a characteristic value matrix from becoming complicated. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent No. 6447454 Summary of the Invention [Problem to be solved by the invention]

[0004] In a typical finite element method, an object is divided into elements according to the contours of its three-dimensional shape. For example, by reducing the size of the elements, it is possible to represent more complex three-dimensional shapes. However, this results in a huge number of element divisions, and the positional relationships between the elements become more complex, which creates the problem of longer calculation times required for analysis.

[0005] The present invention has been made in consideration of such problems, and its purpose is to provide a numerical analysis program and a heat treatment apparatus that can suppress an increase in the time required for analysis processing due to the complexity of the three-dimensional shape of the object to be analyzed. [Means for solving the problem]

[0006] A numerical analysis program in a first aspect of the present invention causes a computer to execute the following steps: an acquisition step for acquiring the three-dimensional shape of an object to be analyzed; a division step for dividing a three-dimensional space including the object into a plurality of elements; a calculation step for determining the density of the volume of the object within a unit space formed by the elements and calculating a density distribution indicating the density at each position of the elements; a construction step for determining a physical quantity correlated to the heat transfer characteristics of the elements using the calculated density distribution and constructing a heat transfer equation including the physical quantity for each element; and an analysis step for performing an analysis process of the object by solving the constructed heat transfer equation for each element, wherein the physical quantity is the amount of radiant heat exchanged between the object and the outside of the object; and in the construction step, a change in surface area of ​​the object is calculated using the difference between a first density corresponding to a first element and a second density corresponding to a second element adjacent to the first element, and the amount of change is used to determine the amount of radiant heat exchanged.

[0007] In the numerical analysis program according to the second aspect of the present invention, in the division step, when the density is expressed as a percentage, the three-dimensional space is divided so that one or more of the calculated densities are intermediate values ​​between 0% and 100%.

[0008] In the numerical analysis program according to a third aspect of the present invention, the division step defines a cylindrical coordinate system whose coordinate axes are the extension direction of the object, and divides the three-dimensional space into cylindrical elements that are coaxial with the coordinate axes, and the calculation step calculates the density distribution that indicates the density for each radial position and each axial position in the cylindrical coordinate system.

[0009] A heat treatment apparatus according to a fourth aspect of the present invention is an apparatus comprising an apparatus main body for performing heat treatment on a workpiece, and a controller for controlling the apparatus main body, wherein the apparatus main body comprises a heat insulating wall provided so as to surround the object as the workpiece, and a heater for heating the inside of a heating chamber formed by the heat insulating wall, and the controller includes an acquisition step for acquiring a three-dimensional shape of the object, a division step for dividing a three-dimensional space including the object into a plurality of elements, a calculation step for determining the density of the volume of the object within a unit space formed by the elements and calculating a density distribution showing the density for each position of the elements, and a calculation step for calculating a density distribution using the calculated density distribution. The method executes a construction step of determining a physical quantity correlated with the heat transfer characteristics of the element and constructing a heat transfer equation including the physical quantity for each element, and a control step of performing an analysis process for the object by solving the heat transfer equation for each element thus constructed and controlling the heating of the heater using the obtained analysis results, wherein the physical quantity is the amount of radiant heat exchanged between the object and the outside of the object, and in the construction step, a change in surface area of ​​the object is calculated using the difference between a first density corresponding to a first element and a second density corresponding to a second element adjacent to the first element, and the amount of change is used to determine the amount of radiant heat exchanged. [Effects of the Invention]

[0010] According to the present invention, it is possible to prevent an increase in the time required for analysis processing due to the complexity of the three-dimensional shape of the object to be analyzed. [Brief explanation of the drawings]

[0011] [Figure 1] 1 is a schematic cross-sectional view of a vacuum carburizing furnace as a heat treatment apparatus according to an embodiment of the present invention. [Figure 2] 2 is a flowchart showing an example of a numerical analysis operation performed by the controller of FIG. 1. [Figure 3] FIG. 1 is a diagram showing a three-dimensional shape of a part that is an example of an analysis target. [Figure 4] FIG. 10 is a diagram illustrating a first example of a method for calculating a density distribution. [Figure 5]FIG. 10 is a diagram illustrating a second example of a method for calculating a density distribution. [Figure 6] FIG. 10 is a diagram showing the effect obtained by introducing a density distribution. [Figure 7] FIG. 10 is a diagram illustrating an example of a method for determining a soaking time. DETAILED DESCRIPTION OF THE INVENTION

[0012] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. To facilitate understanding of the description, the same components in the drawings will be denoted by the same reference numerals as much as possible, and duplicated descriptions will be omitted.

[0013] [Overall Configuration of Heat Treatment Device 10] 1 is a schematic cross-sectional view of a heat treatment apparatus 10 according to one embodiment of the present invention. The heat treatment apparatus 10 includes a vacuum carburizing furnace 12 (corresponding to the "apparatus main body"), a controller 14 (corresponding to the "computer"), a heating power source 16, and temperature sensors 18 and 20.

[0014] The vacuum carburizing furnace 12 is an apparatus 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 (corresponding to the "object to be heated") and a frame 24 attached to the inside of the furnace body 22. Inside the frame 24, there are provided a relatively large, hollow, rectangular parallelepiped insulating member 26, a relatively small, hollow, rectangular parallelepiped insulating member 28, and a plurality of insulating members 30 for connecting the insulating member 26 to the insulating member 28. 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 spaced apart to form a space 32 that functions as an insulating layer.

[0015] A carburizing chamber 36 for vacuum carburizing is formed inside the furnace body 22, surrounded by a hollow insulating member 30. A hearth 38 is provided in the furnace body 22, extending from the bottom thereof toward the inside of the carburizing chamber 36. A workpiece W is placed on the upper end of the hearth 38.

[0016] A number of heat radiation pipes 40 (corresponding to "heaters") are attached to the top of the furnace body 22 so as to extend inward into the carburizing chamber 36. Each heat radiation pipe 40 is provided in a position that covers a wide area from the top to the bottom of the carburizing chamber 36. This allows the space defined by the carburizing chamber 36 to be heated almost uniformly. The interior of the carburizing chamber 36 is set to a high temperature, for example, exceeding 900°C.

[0017] A plurality of gas introduction nozzles 44 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) into the carburizing chamber 36 through the gas introduction nozzles 44, the surface of the workpiece W can be carburized.

[0018] An exhaust pipe 46 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 an exhaust port 48.

[0019] The controller 14 is a computer that has a processor 50, memory 52, and operation panel 54, and controls the operation of each part of the vacuum-carburizing furnace 12. The controller 14 reads and executes programs and data stored in the memory 52 to synchronously or in parallel perform the following operations: [1] supply control for supplying hydrocarbon gas into the carburizing chamber 36, [2] pressure control for adjusting the pressure inside the carburizing chamber 36, and [3] heating control for heating the inside of 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. Here, the temperature sensor 18 is located in contact with the top of the furnace body 22, and the temperature sensor 20 is located on the periphery of the vacuum-carburizing furnace 12.

[0020] The processor 50 acquires temperature signals from the temperature sensors 18, 20 and uses the measured temperatures to calculate estimated values ​​for the temperature inside the carburizing chamber 36 and the temperature of the workpiece W. The processor 50 determines the set conditions for the heat treatment of the workpiece W (hereinafter also referred to as "heat treatment conditions") based on the estimated values ​​calculated by itself. The processor 50 controls the heating of each heat sink pipe 40 by controlling the thyristor of the heating power source 16.

[0021] The memory 52 stores setting conditions for the heat treatment of the workpiece W (i.e., heat treatment conditions) and information on a heat transfer model that describes heat transfer within the furnace body 22 (hereinafter also referred to as "model information"). The model information includes: [1] "shape information" regarding the three-dimensional shape of the object; [2] "arrangement information" regarding the definition of the three-dimensional coordinate system and the arrangement of elements; [3] "temperature information" regarding temperature constraint conditions; and [4] "physical property information" regarding the physical properties of the object.

[0022] [Controller 14 Operation] <1. Temperature control operation> The heat treatment apparatus 10 in this embodiment is configured as described above. Next, the first operation of the heat treatment apparatus 10, more specifically, the temperature control operation by the controller 14, will be outlined.

[0023] First, the controller 14 calculates various control times included in the heat treatment conditions. Here, "control time" refers to the time involved in controlling each step constituting a series of heat treatments, such as [1] the "heating time" required to reach the target temperature for carburizing, [2] the "soaking time" required to soak at the target temperature, or [3] the "heating time" which is the sum of the heating time and the soaking time.

[0024] Next, the controller 14 sets the heat treatment conditions including the calculated control time. After starting the heat treatment, the controller 14 performs a series of temperature control operations (e.g., feedback control or feedforward control regarding temperature) on the heat radiation pipe 40 in accordance with the set heat treatment conditions. By executing these control steps, a temperature increase process, a soaking process, a carburizing process, a diffusion process, a furnace cooling process, a quenching and soaking process, and an oil cooling process are performed in sequence.

[0025] <2. Numerical analysis operation> Next, the second operation by the heat treatment apparatus 10, more specifically, the numerical analysis operation by the controller 14, will be described with reference to the flowchart of FIG. 2 and FIGS.

[0026] (SP10: Acquisition step) In step SP10 of FIG. 2, the controller 14 acquires model information including the three-dimensional shape of the object to be analyzed.

[0027] FIG. 3 is a diagram showing the three-dimensional shape of a part 60, which is an example of the part to be analyzed. This part 60 is, for example, a gear shaft composed of a shaft portion 62 and a first gear portion 64 formed on the shaft portion 62. The shaft portion 62 includes a shaft body 66 and a second gear portion 68 provided on the tip side of the shaft body 66. The first gear portion 64 has a plurality of teeth 70 (12 in this example) and is provided at an intermediate position on the shaft body 66. Thus, the part 60 is approximately isotropic with respect to the axis A, but has a relatively complex three-dimensional shape.

[0028] (SP12: Split Step) 2, the controller 14 divides the three-dimensional spaces 80 and 90 containing the object (i.e., the part 60) into a plurality of elements 82 and 92. A specific example of the division method will be described later with reference to FIGS.

[0029] (SP14: Calculation step) In step SP14, the controller 14 calculates the density (i.e., density distributions 86, 96) for each position of the elements 82, 92 divided in step SP12. This "density" corresponds to the proportion of the volume of the object within the unit space formed by the elements 82, 92. The density can take various values ​​within the range of [0, 1]. When expressing the density as a percentage, a value of "0" corresponds to 0% and a value of "1" corresponds to 100%. Furthermore, the density value may be a continuous value or a discrete value with three or more levels.

[0030] Fig. 4 shows a first example of a method for calculating a density distribution 86. More specifically, Fig. 4(A) shows an example of a method for dividing a three-dimensional space 80, and Fig. 4(B) shows an example of the calculation result of the density distribution 86. In the first example, the three-dimensional space 80 is divided into a plurality of elements 82 based on an orthogonal coordinate system (x, y, z), and the density distribution 86 corresponds to a two-dimensional map of density with (y, z) as a variable.

[0031] 4(A) schematically shows a cross-sectional shape 84 of the first gear portion 64 with respect to the axis A shown in FIG. 3. As can be seen from this figure, a three-dimensional space 80 is divided into a plurality of elements 82 according to a predetermined rule, without depending on the outline of the cross-sectional shape 84. Each element 82 is prismatic and extends in the X-axis direction.

[0032] In the density distribution 86 of Figure 4(B), the vertical axis of the graph indicates the position on the y-axis (unit: mm), and the horizontal axis of the graph indicates the density D (unit: dimensionless). As can be seen from this figure, the density distribution 86 changes in value depending on the position on the y-axis. Specifically, the density D increases as the position y approaches the axis A, while the density D decreases as the position y moves away from the axis A.

[0033] Fig. 5 is a diagram showing a second example of a method for calculating a density distribution 96. More specifically, Fig. 5(A) shows an example of a method for dividing a three-dimensional space 90, and Fig. 5(B) shows an example of the calculation result of the density distribution 96. In the second example, the three-dimensional space 90 is divided into a plurality of elements 92 based on a cylindrical coordinate system (r, θ, z), and the density distribution 96 corresponds to a two-dimensional map of density with (r, z) as a variable.

[0034] 5(A), like FIG. 4(A), schematically shows a cross-sectional shape 94 of the first gear portion 64 with respect to the axis A shown in FIG. 3. As can be seen from this figure, a three-dimensional space 90 is divided into a plurality of elements 92 according to a predetermined rule, regardless of the outline of the cross-sectional shape 94. Each element 92 is cylindrical or columnar and is arranged coaxially.

[0035] In the density distribution 96 of FIG. 5(B), the vertical axis of the graph represents the radial position r (unit: mm), and the horizontal axis of the graph represents the density D (unit: dimensionless). As can be seen from this figure, the density distribution 96 changes in value depending on the position r. Specifically, in the range of 0≦r≦R1, the density D is constant (D=1). In the range of r>R1, the density D rapidly decreases as the position r increases, and in the range of r>R2, the density D is constant (D=0). Here, r=R1 corresponds to the bottom position of the tooth 70 (FIG. 3), and r=R2 corresponds to the top position of the tooth 70 (FIG. 3).

[0036] (SP16: Construction Steps) 2, the controller 14 uses the density distributions 86 and 96 calculated in step SP14 to construct a heat transfer equation for each element 82 and 92 that describes the heat transfer characteristics in the three-dimensional spaces 80 and 90. For example, the heat transfer equation in the cylindrical coordinate system (r, θ, z) shown in FIG. 5 is expressed by the following equation (1):

[0037]

number

[0038] Typically, when performing numerical calculations, the partial differential equation shown in equation (1) is transformed into a difference equation by approximating it with a difference. Examples of transformation methods include the explicit method, the implicit method, and the ADI (Alternating Direction Implicit) method. Here, by multiplying a physical quantity correlated with the heat transfer characteristics of elements 82 and 92 by density, the density distributions 86 and 96 can be reflected in the difference equation. Examples of such physical quantities include surface area, volume, thermal conductivity, and heat flux.

[0039] Furthermore, the amount of change in the surface area of ​​the component 60 can be calculated using density distribution 96, which uses (r, z) as a variable. For element 92 at position (r, z), assuming that the density is D(r, z) and the width is (Δr, h), and that the radiation distance between the component 60 and another object (radiation source) is sufficiently long, the amount of change in surface area ΔS can be approximately calculated using the following equation (2):

[0040]

number

[0041] By integrating this change ΔS along the radial or axial direction, the surface area of ​​the part 60 can be calculated for each position without directly using the three-dimensional shape of the part 60. In other words, the effect of heat exchange by radiation can be reflected for each element 92. Furthermore, if the shape information of the part 60 includes the number, shape, or orientation of the teeth 70, the amount of heat exchange by radiation may be corrected according to this shape information. For example, in the case of radiation, the amount of heat exchange may be relatively increased as the angle between the heat incident angle and the tooth height direction becomes smaller, and may be relatively decreased as the angle becomes larger.

[0042] (SP18: Analysis Step) 2, the controller 14 simultaneously or coupledly solves the heat transfer equations for the elements 82 and 92 constructed in step SP16, thereby obtaining a transient or steady-state solution for the temperature distribution in the three-dimensional spaces 80 and 90.

[0043] Figure 6 shows the effect obtained by introducing a density distribution. The horizontal axis of the graph indicates elapsed time (unit: minutes), and the vertical axis of the graph indicates temperature (unit: °C). The dotted curve shows the analysis results using a conventional division method, and corresponds to the "standard (3D-FEM)" calculation accuracy. Here, the element shape is a "tetrahedron," and the part 60 (Figure 3) is divided into multiple elements based on its contour shape. In this case, each value of the density distribution is binarized as 1 (all present) or 0 (absent).

[0044] The "Reference Example (2D-FEM)" shown by the two-dot chain line corresponds to the analysis results obtained by using the division method shown in FIG. 5(A) while binarizing (1 or 0) the density distribution 96 shown in FIG. 5(B) using a threshold value of D=0.5. In other words, smoothing the three-dimensional shape of the part 60 results in the construction of a heat transfer model for a part with missing teeth 70. As a result, the curve for the "Comparative Example" shows a faster temperature rise and faster arrival at the target temperature To than the "Reference" curve, and the deviation between the two (i.e., the calculation error) is larger.

[0045] On the other hand, the "Example" shown by the solid line corresponds to the analysis results obtained using the division method shown in Fig. 5(A) and the density distribution 96 shown in Fig. 5(B). The curve of the "Example" roughly coincides with the curve of the "Reference" during the time period until the target temperature To is reached, and sufficient calculation accuracy is obtained.

[0046] (SP20: Decision Step) In step SP20 of FIG. 2, the controller 14 determines the heat treatment conditions from the analysis results obtained in step SP18.

[0047] FIG. 7 is a diagram showing an example of a method for determining the soaking holding time. The horizontal axis of the graph indicates the elapsed time (unit: minutes), and the vertical axis of the graph indicates the temperature (unit: °C). The three curves indicate the temperatures at different positions P1, P2, and P3 within the workpiece W. As understood from the drawing content of FIG. 1, since there are differences in the degree of heat transfer depending on the position within the workpiece W, the shapes of the curves are different. When defining the arrival times at the target temperatures at positions P1, P2, and P3 as t1, t2, and t3, respectively, the magnitude relationship of t1 < t2 < t3 is satisfied. In this case, the maximum value of the time difference (t3 - t1) may be determined as the soaking holding time.

[0048] [Summary of the Embodiment] As described above, in the numerical calculation program and method in this embodiment, one or more computers (here, the controller 14) perform an acquisition step (SP10 in FIG. 2) of acquiring the three-dimensional shape of an object to be analyzed (here, the component 60), a division step (SP12) of dividing the three-dimensional spaces 80 and 90 including the component 60 into a plurality of elements 82 and 92, a calculation step (SP14) of obtaining the density occupied by the volume of the component 60 in the unit space formed by the elements 82 and 92 and calculating density distributions 86 and 96 indicating the density at each position of the elements 82 and 92, and an analysis step (SP18, SP20) of performing an analysis process of the component based on the finite element method using the calculated density distributions 86 and 96.

[0049] In this way, by obtaining the density occupied by the volume of the component 60 in the unit space formed by the elements 82 and 92 and calculating the density distributions 86 and 96, a pseudo-intermediate volume representation independent of the three-dimensional shape of the component 60 becomes possible, and the design freedom regarding the shape or arrangement of the elements 82 and 92 is increased. For example, by dividing the three-dimensional spaces 80 and 90 so as to improve the calculation efficiency, it is possible to suppress an increase in the required time for the analysis process due to the complexity of the three-dimensional shape of the component 60.

[0050] Furthermore, in the dividing step, when the density is expressed as a percentage, the controller 14 may divide the three-dimensional spaces 80 and 90 so that one or more calculated densities are intermediate values ​​between 0% and 100%. This makes it easier to express the outline of the part 60 more simply, and the number of elements can be reduced accordingly.

[0051] Furthermore, the controller 14 may further execute a construction step (SP16 in FIG. 2) in which the controller 14 uses the calculated density distribution to determine physical quantities correlated with the heat transfer characteristics in the elements 82, 92, and constructs heat transfer equations including the physical quantities for each of the elements 82, 92. In this case, the controller 14 performs analysis processing of the part 60 in the analysis step by simultaneously or coupledly solving the heat transfer equations constructed for each of the elements 80, 90.

[0052] Furthermore, when the physical quantity is the amount of radiant heat exchanged between the component 60 and the outside of the component 60, the controller 14 may calculate a change ΔS in the surface area of ​​the component 60 in the construction step using the difference between a first density corresponding to a first element and a second density corresponding to a second element adjacent to the first element, and use the change ΔS to determine the amount of radiant heat exchanged.

[0053] Furthermore, in the dividing step, the controller 14 may define a cylindrical coordinate system whose coordinate axes are the extension direction of the part 60, divide the three-dimensional space 90 into cylindrical elements 92 that are coaxial with the coordinate axes, and in the calculating step, calculate a density distribution 96 that indicates the density for each radial position (r) and each axial position (z) in the cylindrical coordinate system. By introducing a cylindrical coordinate system whose coordinate axes are the extension direction of the part 60, high-speed and high-precision analysis processing can be performed on an object that is isotropic or has high rotational symmetry (for example, a gear shaft).

[0054] Heat treatment apparatus 10 also includes an apparatus main body (here, vacuum carburizing furnace 12) that performs heat treatment on the workpiece, and a controller 14 that controls vacuum carburizing furnace 12. Vacuum carburizing furnace 12 includes insulating walls (here, insulating members 26, 28, 30) that are arranged to surround the object (here, component 60) that is the workpiece, and a heater (here, heat dissipation pipe 40) that heats the inside of a heating chamber (here, carburizing chamber 36) formed by the insulating walls.

[0055] The controller 14 then acquires the three-dimensional shape of the part 60, divides the three-dimensional space 80, 90 containing the part 60 into a plurality of elements 82, 92, determines the density of the volume of the part 60 within the unit space formed by the elements 82, 92, calculates density distributions 86, 96 that indicate the density for each position of the elements 82, 92, performs an analysis process of the part 60 based on the finite element method using the calculated density distributions 86, 96, and controls the heating of the heat sink tube 40 using the obtained analysis results.

[0056] Similar to the above-described effect, this configuration can reduce the calculation time required for analysis regardless of the complexity of the three-dimensional shape of the part 60. In particular, when heat treatment is performed on a wide variety of parts 60, heating control suitable for various situations can be performed, thereby improving production efficiency.

[0057] [Variations] The present invention is not limited to the above-described embodiment, and can be freely modified without departing from the spirit of the present invention. Alternatively, the respective configurations may be arbitrarily combined within the scope of the present invention without causing any technical contradiction.

[0058] In the above embodiment, the three-dimensional space 80, 90 is divided into rectangular parallelepiped elements 80 or cylindrical elements 90, but the method of dividing the elements is not limited to this. For example, the shape, size, arrangement, or a combination thereof of the elements may be changed as needed.

[0059] In the above embodiment, the controller 14 constituting part of the heat treatment apparatus 10 executes the numerical analysis program, but the configuration of the apparatus is not limited to this. For example, a general-purpose computer independent of the vacuum carburizing furnace 12 may execute the thermal calculation program for the purpose of computer simulation.

[0060] In the above embodiment, the case where a computer performs thermal calculations has been described, but the application of numerical calculations is not limited to this. This numerical calculation can be applied to any field problem described by partial differential equations, such as structural analysis, fluid analysis, and electromagnetic field analysis. [Explanation of symbols]

[0061] 10...heat treatment device, 12...vacuum carburizing furnace, 14...controller (computer), 26, 28, 30...thermal insulating member, 36...carburizing chamber, 50...processor, 52...memory, 60...part (object), 80, 90...three-dimensional space, 82, 92...elements, 86, 96...density distribution, W...work (processed object), SP10...acquisition step, SP12...division step, SP14...calculation step, SP16...construction step, SP18...analysis step

Claims

1. an acquisition step of acquiring a three-dimensional shape of an object to be analyzed; a division step of dividing a three-dimensional space including the object into a plurality of elements; a calculation step of determining the density of the volume of the object within a unit space formed by the elements and calculating a density distribution indicating the density for each position of the elements; a construction step of calculating a physical quantity correlated with the heat transfer characteristics in the element using the calculated density distribution, and constructing a heat transfer equation including the physical quantity for each element; an analysis step of performing an analysis process of the object by solving the heat transfer equation for each of the constructed elements; on the computer, the physical quantity is the amount of radiant heat exchanged between the object and the outside of the object, A numerical analysis program characterized in that in the construction step, a change in surface area of ​​the object is calculated using the difference between a first density corresponding to a first element and a second density corresponding to a second element adjacent to the first element, and the amount of radiant heat exchange is determined using the change.

2. 2. The numerical analysis program according to claim 1, wherein in the division step, when the density is expressed as a percentage, the three-dimensional space is divided so that one or more of the calculated densities are intermediate values ​​between 0% and 100%.

3. In the dividing step, a cylindrical coordinate system is defined in which the extension direction of the object is defined as a coordinate axis, and the three-dimensional space is divided into cylindrical elements coaxial with the coordinate axis; 3. The numerical analysis program according to claim 1, wherein the calculation step calculates the density distribution indicating the density for each radial position and each axial position in the cylindrical coordinate system.

4. A heat treatment apparatus comprising: an apparatus main body that performs heat treatment on a workpiece; and a controller that controls the apparatus main body, The device body includes: a heat insulating wall provided to surround the object to be treated; a heater for heating the inside of a heating chamber formed by the heat insulating wall; Equipped with The controller acquiring a three-dimensional shape of the object; a division step of dividing a three-dimensional space including the object into a plurality of elements; a calculation step of determining the density of the volume of the object within a unit space formed by the elements and calculating a density distribution indicating the density for each position of the elements; a construction step of calculating a physical quantity correlated with the heat transfer characteristics in the element using the calculated density distribution, and constructing a heat transfer equation including the physical quantity for each element; a control step of performing an analysis process of the object by solving the heat transfer equation for each of the constructed elements, and performing heating control on the heater using the obtained analysis result; Run the physical quantity is the amount of radiant heat exchanged between the object and the outside of the object, A heat treatment apparatus characterized in that in the construction step, the change in surface area of ​​the object is calculated using the difference between a first density corresponding to a first element and a second density corresponding to a second element adjacent to the first element, and the amount of radiant heat exchanged is determined using the change.

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