JP2020012654A - Die temperature calculation method and die temperature calculation system - Google Patents

Abstract

To provide a die temperature calculation method and a die temperature calculation system capable of more easily simulating a die temperature distribution.SOLUTION: The die temperature calculation method includes: a first calculating step of calculating a temperature of each partial area included in a partial area of one row including a plurality of partial areas along a row direction; and a second calculating step of calculating a temperature of each partial area included in a partial area of one column including a plurality of partial areas along a column direction. The first calculation step and the second calculation step are alternately performed a plurality of times. In the second and subsequent first calculation steps, among the temperatures of the partial areas included in the partial area of one row for which the temperature is calculated, the temperature of the partial area calculated in the previous second calculation step is presumed to be an initial temperature of the partial area. In the second and subsequent second calculation steps, among the temperatures of the partial areas included in the partial area of one column for which the temperature is calculated, the temperature of the partial area calculated in the previous first calculation step is presumed to be an initial temperature of the partial area.SELECTED DRAWING: Figure 24

Description

  The present invention relates to a technique for extruding a metal or an alloy, and particularly to grasping a temperature distribution of a die used for an extrusion process.

  In order to achieve high-precision and high-quality extrusion in metal or alloy extrusion, it is essential to specify the influence of an extrusion die on an extruded profile.

  It is known that the temperature distribution of a die affects the accuracy of an extruded profile, particularly the wall thickness. Therefore, it is important to understand the temperature distribution of the die. 2. Description of the Related Art Conventionally, a method of simulating a temperature distribution of a die by performing a finite element method (FEM) analysis has been known (for example, Non-Patent Document 1).

"Investigation on Wall Thickness Variations of Aluminum Alloy Extruded Profiles," by Takayuki Hayashi, Altopia, Japan, Karos Publications, July 15, 2017, Vol. 47, July 2017, p. 9-16

  However, since the FEM analysis requires advanced technology and dedicated equipment (including software), the operable environment is extremely limited. For this reason, there has been a demand for a method and the like that can more easily simulate the temperature distribution of a die.

  The present invention has been made in view of such a problem, and has as its object to provide a die temperature calculation method and a die temperature calculation system that can more easily simulate the die temperature distribution.

  A method for calculating the temperature of a die according to an aspect of the present invention is a method for calculating the temperature of a die that simulates a temperature distribution of a die used for extrusion of a target to be extruded, which is a metal or an alloy. Setting a virtual model of a cross-section in a row direction with respect to a center portion of the die in which the extrusion port to be extruded is arranged, with the extrusion direction being a column direction and a direction orthogonal to the extrusion direction being a row direction; and A step of setting a two-dimensional matrix-like divided model including a plurality of partial regions in the row direction and the column direction; and a first position where the extrusion target pressed against the die in the extrusion direction exists. A second location where the object to be extruded extruded from the die exists, and a space inside the die on the extrusion direction side with respect to the second location. A third location, a fourth location which is a space on the end side of the die on the extrusion direction side, and a space on the outer peripheral side of the die located on the opposite side to the second location and the third location. Obtaining the temperature of the fifth location, the heat input to the die at the first location and the second location, and the heat release from the die at the third location, the fourth location and the fifth location. Calorific value, and a temperature distribution calculating step of calculating the temperature of each partial region included in the divided model, wherein the temperature distribution calculating step is performed at the second location on the inner peripheral side of the die. From the heat input to the third location on the inner peripheral side of the die, the amount of heat released from the outer peripheral side of the die to the fifth location, and a predetermined initial temperature of each partial region. Included in one line based on A first calculation step of calculating the temperature of the partial region, a heat input amount from the first location on one end side of the die, and a heat release amount from the other end side of the die to the fourth location, which are predetermined. A second calculating step of calculating the temperature of each partial area included in one column based on the initial temperature of each partial area, wherein the first calculating step and the second calculating step are each performed a plurality of times. The first calculation step and the second calculation step are performed alternately, and in the second and subsequent first calculation steps, of the temperatures of the partial areas of one row for calculating the temperature, The temperature of the partial area calculated in the second calculation step is set as the initial temperature of the partial area, and in the second and subsequent second calculation steps, the temperature of each of the partial areas of one row for which the temperature is calculated is calculated. The temperature of the partial area calculated in the previous first calculation step is The initial temperature of the partial area is set as the initial temperature.

  As one embodiment of the present invention, in a later step of the first calculation step and the first second calculation step, the temperature of the partial area calculated in the earlier step is determined by the partial area. It is preferable to set the above initial temperature.

  As one aspect of the present invention, in the temperature distribution calculation step at each of two different timings before and after the predetermined time when it is assumed that a predetermined time has elapsed, the initial temperature of each partial region at a later timing is equal to the earlier temperature. It is preferable that the temperature is the temperature of each partial region calculated in the temperature distribution calculating step at the timing.

  A temperature calculation system for a die according to an aspect of the present invention includes a temperature information acquisition device that acquires temperature information of a die used for extrusion of an extrusion target that is a metal or an alloy, and an extrusion process for an extrusion target that is a metal or an alloy. An information processing device for simulating a temperature distribution of a die to be used, and a temperature calculation system for the die, wherein the temperature information acquisition device is configured to push the extrusion target pressed against the die in an extrusion direction of the extrusion target. A first temperature information obtaining unit that obtains temperature information of a first location where there is, a second temperature information obtaining unit that obtains temperature information of a second location where the extrusion target extruded from the die exists, and the second location A third temperature information acquisition unit that acquires temperature information of a third location that is a space inside the die on the extrusion direction side with respect to the extrusion direction; A fourth temperature information acquisition unit that acquires temperature information of a fourth location, which is a space on the side of the end, and a space on the outer peripheral side of the die located on the opposite side to the second location and the third location. A fifth temperature information acquisition unit configured to acquire temperature information of a fifth point, wherein the information processing apparatus sets a pushing direction of the extrusion target in the die as a column direction, and sets a direction orthogonal to the pushing direction as a row direction. A two-dimensional matrix including a plurality of partial regions in the row direction and the column direction in the virtual model, in which a virtual model of a cross section in the row direction with respect to a center portion of the die in which the extrusion target of the extrusion target is arranged is set. And a heat input amount from the second location on the inner peripheral side of the die and a heat release amount to the third location on the inner peripheral side of the die. To the point A calculating unit for calculating a heat quantity and calculating a temperature of each partial region included in the divided model, wherein the calculating unit is configured to calculate a temperature from an inner peripheral side of the die including the second location and the third location. The temperature of each partial region included in one row based on the heat input amount and the heat release amount, the heat release amount from the outer peripheral side of the die including the fifth portion, and the predetermined initial temperature of each partial region. A first calculation step of calculating a heat input amount from one end of the die including the first location, a heat release amount from the other end side of the die including the fourth location, and predetermined portions. Performing a second calculation step of calculating the temperature of each partial area included in one row based on the initial temperature of the area, a plurality of times, and alternately performing the first calculation step and the second calculation step In the first and second calculation steps for the second and subsequent times, one line for calculating the temperature Of the temperatures of the respective partial regions, the temperature of the partial region calculated in the previous second calculation step is set as the initial temperature of the partial region, and in the second and subsequent second calculation steps, the temperature is calculated. The temperature of the partial area calculated in the first calculation step before the temperature of each partial area of the row is set as the initial temperature of the partial area.

  According to the aspect of the present invention, it is possible to more easily simulate the temperature distribution of the dice.

FIG. 1 is a block diagram illustrating a main configuration of the temperature calculation system according to the embodiment. FIG. 2 shows an image diagram of direct extrusion of a metal or an alloy by an extrusion device. FIG. 3 is a diagram showing a die having a wide channel shape and its temperature measurement points (P1 to P4). FIG. 4 is a schematic cross-sectional view of a die for describing a method of entering a temperature sensor into the temperature measurement point shown in FIG. FIG. 5 is a diagram showing a measurement result of a temperature history and an FEM analysis result of each measurement point of three billet continuous extrusions. FIG. 6 is a diagram showing the measured values of the wall thickness of portions A, B, and C of the extruded front end material and the rear end material in the continuous extrusion of ten billets. FIG. 7 is a diagram showing a schematic diagram of two-dimensional heat conduction. FIG. 8 is a diagram showing a one-dimensional graphical representation of external heat and unsteady heat conduction of a solid. FIG. 9 is a diagram showing a model for calculating the heat conduction of the dice by the Fourier theoretical formula and the difference method. FIG. 10 is a diagram showing a calculation model of the difference method based on heat input and heat radiation in a one-dimensional case. FIG. 11 is a table showing the heat transfer coefficient, the ambient temperature, and the equivalent distance when heat transfer is converted to heat conduction, which is the boundary condition between F1 and F4. FIG. 12 is a diagram showing an FEM analysis model. FIG. 13 is a diagram showing a temperature distribution diagram of an FEM analysis result after a lapse of 300 seconds. FIG. 14 is a diagram illustrating a comparison between the difference method calculation result and the FEM analysis result after a lapse of 300 seconds. FIG. 15 is a table showing the heat transfer coefficient, ambient temperature, and equivalent distance when heat transfer is converted to heat conduction, which are the five boundary conditions of FIG. FIG. 16 is a diagram showing a temperature distribution diagram of an FEM analysis result after a lapse of 300 seconds. FIG. 17 shows the temperature distribution in the X direction of each row element as a result of the FEM analysis. FIG. 18 is a diagram illustrating a result of a temperature distribution in the X direction of each row element by the difference method after a lapse of 300 seconds. FIG. 19 is a diagram illustrating a comparison between the difference method calculation result of the 1-row element and the 5-row element and the FEM analysis result. FIG. 20 is a diagram showing a method of calculating the heat transfer in the left, right, up, and down directions devised. FIG. 21 is a diagram showing a devised method of calculating the heat transfer in the left, right, up and down directions. FIG. 22 is a diagram showing a devised method of calculating the left, right, up, and down heat transfer. FIG. 23 is a diagram showing a devised method of calculating left and right and up and down heat transfer. FIG. 24 is a diagram showing an X-direction temperature distribution of each row element by the devised difference calculation method. FIG. 25 is a diagram showing a comparison between the calculation results of the 1-line element and the 5-line element of the devised difference method and the FEM analysis results. FIG. 26 is a diagram showing the relationship between the elapsed time and the temperature history of the element E11 near the bearing and the outer peripheral side element E15 of the die during extrusion processing by the difference method calculation.

  Hereinafter, embodiments according to the present invention will be described with reference to the drawings, but the present invention is not limited thereto. The components of the embodiments described below can be appropriately combined. In some cases, some components may not be used. In addition, components in the embodiments described below include components that can be easily assumed by those skilled in the art, components that are substantially the same, and components that are in an equivalent range.

  FIG. 1 is a block diagram illustrating a main configuration of a temperature calculation system 1 according to the embodiment. The temperature calculation system 1 includes a temperature information acquisition device 60 and an information processing device 70. The temperature information acquisition device 60 acquires temperature information of each part of the extrusion device 100. The temperature information acquisition device 60 includes a first temperature information acquisition unit 61, a second temperature information acquisition unit 62, a third temperature information acquisition unit 63, a fourth temperature information acquisition unit 64, and a fifth temperature information acquisition unit 65.

  FIG. 2 shows an image of direct extrusion of a metal or an alloy by the extrusion device 100. Note that the image shown in FIG. 2 is an image of a cross section when the die 2 having a cylindrical outer shape is cut along the central axis of the cylinder. FIG. 2 illustrates the extrusion apparatus 100 during the extrusion of the billet 3. The die 2 is a mold used for extruding a metal or an alloy. The billet 3 is a metal or an alloy serving as a base of the extruded shape member 3a processed using the die 2, and is, for example, aluminum or an alloy containing aluminum. The stem 4 presses the billet 3 against the die 2. Dummy block 5 is provided between billet 3 and stem 4. The container 6 supports the billet 3 pressed against the die 2 from the outer peripheral side of the billet 3. The shape and size of the space inside the container 6 correspond to the shapes and sizes of the billet 3, the stem 4, and the dummy block.

  The first temperature information acquisition unit 61 detects the temperature at the first point FP1. The second temperature information acquisition unit 62 detects the temperature at the second point FP2. The third temperature information acquisition unit 63 detects the temperature at the third point FP3. The fourth temperature information acquisition unit 64 detects the temperature at the fourth point FP4. The fifth temperature information acquisition unit 65 detects the temperature at the fifth point FP5.

  The first temperature information acquisition unit 61, the second temperature information acquisition unit 62, the third temperature information acquisition unit 63, the fourth temperature information acquisition unit 64, and the fifth temperature information acquisition unit 65 have at least 100 ° C. to 550 ° C. ] Can be detected. As a specific configuration example of the first temperature information acquisition unit 61, the second temperature information acquisition unit 62, the third temperature information acquisition unit 63, the fourth temperature information acquisition unit 64, and the fifth temperature information acquisition unit 65, a thermocouple is used. However, the temperature sensor is not limited to this, but may be any temperature sensor that functionally satisfies the above requirements.

  The first point FP1 corresponds to a first location where an extrusion target pressed against the die 2 in the extrusion direction exists. The second point FP2 corresponds to a second location where the extrusion target extruded from the die 2 exists. The third point FP3 corresponds to a third location that is a space inside the die 2 on the extrusion direction side with respect to the second location. The fourth point FP4 corresponds to a fourth location which is a space on the end side of the die 2 on the extrusion direction side. The fifth point FP5 corresponds to a fifth location which is a space on the outer peripheral side of the die 2 located on the opposite side of the second portion and the third portion. In other words, the second point FP2 and the third point FP3 are located on the inner peripheral side of the die 2 facing the extruded profile 3a to be extruded.

  The temperature at the first point FP1 is used to calculate the heat input F0 from the metal processing heat in the die chamber. The temperature at the second point FP2 is used to calculate the heat input F1 from the metal friction heat of the bearing of the die 2. The temperature at the third point FP3 is used to calculate the heat radiation F2 from the interface between the die escape portion and the air. The temperature at the fourth point FP4 is used to calculate heat radiation F3 from contact with the tool system at the rear of the die. The temperature at the fifth point FP5 is used to calculate the heat radiation F4 from the contact with the die stack. The heat input F0, the heat input F1, the heat radiation F2, the heat radiation F3, and the heat radiation F4 will be described later.

  The information processing device 70 includes a calculation unit 71, a storage unit 72, an input unit 73, an output unit 74, an interface 75, and the like. The arithmetic unit 71 has an arithmetic device such as a CPU (Central Processing Unit), and reads and executes a software program and data corresponding to the processing content from the storage unit 72 to execute various processes. The arithmetic processing corresponding to the function is performed. The storage unit 72 has a main storage device and an auxiliary storage device, and stores a software program and data read by the calculation unit 71. As a specific configuration example of the main storage device, there is a semiconductor memory functioning as a RAM (Random Access Memory). Specific examples of the configuration of the auxiliary storage device include a hard disk drive (HDD), a solid state drive (SSD), a flash memory, and a read only memory (ROM).

  The input unit 73 includes one or more input devices such as a keyboard, a mouse, and a microphone, and receives an input from a user who operates the information processing device 70. The output unit 74 includes at least one of a display device such as a liquid crystal display and an audio output device such as a speaker, and performs an output according to the processing content of the information processing device 70. The interface 75 is an interface that allows the temperature information acquisition device 60 to be connected to the information processing device 70. The interface 75 is a bus interface such as a USB (Universal Serial Bus), but may be any interface that corresponds to the output interface of the temperature information acquisition device 60. In other words, the relationship between the output interface of the temperature information acquisition device 60 and the interface 75 is provided so as to be the relationship of the interface capable of interconnecting and transmitting data.

  In the embodiment, data input from the temperature information acquisition device 60 to the interface 75 is digital data. The first temperature information acquisition section 61, the second temperature information acquisition section 62, the third temperature information acquisition section 63, the fourth temperature information acquisition section 64, and the fifth temperature information acquisition section 65 are sensors capable of outputting digital data. Alternatively, the analog temperature output from the first temperature information acquisition unit 61, the second temperature information acquisition unit 62, the third temperature information acquisition unit 63, the fourth temperature information acquisition unit 64, and the fifth temperature information acquisition unit 65 A configuration may be adopted in which the information is converted into digital data by an analog / digital conversion circuit provided in the temperature information acquisition device 60 and output.

  The storage unit 72 of the embodiment stores a simulation program 72P. The simulation program 72P includes, for example, a spreadsheet software program and spreadsheet data that can be used by the software program. The spreadsheet data includes a calculation formula and data in accordance with an algorithm for the arithmetic unit 71 executing the spreadsheet software program to execute a temperature calculation method of the die 2 described later.

  Hereinafter, the temperature calculation method of the die 2 and matters related to the temperature calculation method will be described with reference to FIGS.

  In the extrusion process, a change in the temperature distribution of the die 2 directly affects the size of the opening of the die and the thickness of the profile, so that examination is important. In this paper, we introduce the unsteady heat conduction analysis of the die 2 by Fourier's theoretical formula and the difference method calculation, and the calculation method of the die temperature distribution. In the two-dimensional heat conduction analysis, a difference calculation method with high calculation accuracy was developed by considering the influence of heat conduction from two directions.

(1. Introduction)
In recent years, in order to improve fuel efficiency by reducing the weight of vehicles, the application of aluminum extruded shapes to fields such as automobiles and vehicles is expanding. Along with this, the required performance, accuracy, and quality required of the extruded shape member 3a have been enhanced year by year. In order to achieve high-precision and high-quality extrusion, it is indispensable to investigate and take measures on the influential factors that affect the shape and dimensions of the profile.

  The accuracy of the extruded profile 3a, particularly the variation of the wall thickness, is often caused by a change in force during extrusion and a change in temperature of the die 2 and the tool system. In the extrusion process, a change in the temperature distribution of the die 2 directly affects the die opening (wall thickness of the profile). Therefore, it is important to study the temperature distribution of the die 2.

  This paper introduces the transient heat conduction analysis of die 2 in the extrusion process and the calculation method of die temperature distribution by Fourier's theoretical formula and difference method calculation.

(2. Thickness variation problem in extrusion)
During extrusion, the force factor, the container seal force 7 (see FIG. 2), the metal pressure 8 in the die 2 (see FIG. 2), and the thermal factor, the temperature distribution in the die 2, change over time.

  As an example, a description will be given of the results of temperature change and wall thickness change of the die 2 having a wide channel shape.

  FIG. 3 and FIG. 4 show the die 2 of the wide channel shape and its temperature measurement points (P1 to P4). FIG. 5 shows the measurement results of the temperature history and the FEM analysis results at each measurement point of the continuous extrusion of three billets. As shown in FIG. 5, the temperature of P3 and P4 near the bearing of the die 2 increases due to the heat generated by the plastic working during the extrusion. On the other hand, due to heat transfer to the die stack and the like, the temperatures of P1 and P2 on the outer periphery of the die 2 decrease. The temperature difference between the portion near the bearing and the outer peripheral portion increases from the tip of the extrusion to the trailing end of the extrusion. Further, as the number of extruded billets increases, the temperature difference increases.

  FIG. 4 is a schematic cross-sectional view of the die 2 for explaining a method of entering the temperature sensor into the temperature measurement points P1 and P3 shown in FIG. Further, i1 in FIG. 4 is 8 [mm]. Further, i2 in FIG. 4 is 10 [mm]. In FIG. 4, in order to measure the temperatures at the temperature measurement points P1 and P3, holes H1 and H2 are provided in the die 2 and the temperature sensor is made to enter. Although not shown, the mechanism of temperature measurement at the temperature measurement points P2 and P4 is the same as that at the temperature measurement points P1 and P3. In the temperature measurement at the first point FP1 using the first temperature information acquisition unit 61 and the temperature measurement at the second point FP2 using the second temperature information acquisition unit 62, the temperature measurement at the temperature measurement points P1 and P3 is also performed. For this purpose, a hole is made in the die 2 and at least one of the die 2 and the billet 3 is opened to allow the temperature sensor to enter.

  FIG. 6 shows the measured values of the wall thickness of portions A, B, and C of the extruded front end material and the rear end material in the continuous extrusion of ten billets. The thickness of each extruded billet tends to decrease from the leading end material to the trailing end material. Even between billets, the wall thickness becomes thinner as the number of extrusions increases. Thus, it is considered that the thickness variation between the rear end of the extrusion tip and the billet is due to the load and the temperature change in the die 2.

(3. Calculation of Fourier theoretical formula and difference method)
As described above, the temperature of the die 2 that changes with time during the extrusion process affects the opening of the die 2 and causes the thickness of the profile to fluctuate. Here, in order to quantitatively examine the temperature distribution and the temperature change inside the die 2, a calculation was performed using a Fourier theoretical formula and a difference method.

FIG. 7 shows a schematic diagram of two-dimensional heat conduction. During the time dt, write the equations of heat dQ ₁ stored in the rectangular inside from the top of the heat conduction and the Y-direction due to heat conduction to the bottom from the left in the X direction to the right as shown in equation (1).

  Here, T is temperature, and λ is thermal conductivity.

  The temperature (T) is determined by measurement or setting. The thermal conductivity (λ) is a constant determined by the composition of the die 2, for example. Further, ∂ is a code representing partial differentiation. The X direction corresponds to the row direction. The Y direction corresponds to the column direction.

On the other hand, during the time dt, the amount of heat dQ ₂ required internal temperature change becomes Equation (2). Here, C is specific heat, and ρ is density.

  The specific heat (C) and the density (ρ) are constants determined by the composition of the die 2, for example.

From Equations (1) and (2), the internal temperature change due to heat conduction becomes Equation (3).

Here, if a = λ / Cρ, equation (3) becomes equation (4).

  Equation (4) is a Fourier differential equation. To solve this double partial differential equation, the difference method is an effective method.

  FIG. 8 shows a schematic solution of one-dimensional external heat and unsteady heat conduction of a solid. Here, the graphical solution method and the difference method calculation of the unsteady heat conduction will be described.

First, regarding the heat conduction calculation inside the solid, the temperature calculation points (T ₁ , T ₂ , T ₃ ...) At a certain time t inside are divided at equal intervals Δx. As shown in FIG. 8, after the lapse of temperature _{T 2} is time Δx time _t, by heat conduction between the T 1, _{T 3,} the _{T 2A.} Calculation of the difference method of the temperature change is represented by Expression (5).

Therefore, the relationship between the temperature T _{2A at} time t + Δt and the temperatures T ₁ , T ₂ , and T ₃ at time t is represented by Expression (6). Here, it is assumed that M = (Δx) ² / aΔt.

  Next, calculation of heat transfer from the external heat to the solid will be described. The heat transfer calculation from the external heat to the solid is converted into the heat conduction calculation and examined. At this time, the heat conduction calculation is performed using an equivalent distance calculated from the heat transfer coefficient and the heat conductivity.

As shown in FIG. 8, the temperature of the external heat is T _f , the heat transfer coefficient between the external heat and the solid surface is α, the initial temperature of the solid surface is T ₀ , and the thermal conductivity of the solid is λ.

The equation for calculating the heat flux q from the external heat to the solid surface by the heat transfer is given by equation (7).

On the other hand, when heat conduction is considered, the equation for calculating the heat flux q from external heat to the solid surface is represented by Expression (8).

From equations (7) and (8), the equation of equation (9) can be written.

When the heat transfer from the external heat to the solid surface is converted into the heat conduction according to the equation (9), the equivalent distance dx between the external heat and the solid surface is obtained from the heat transfer coefficient and the thermal conductivity according to the equation (10). .

When calculating the heat transfer from the outside using the finite difference method, as shown in FIG. 8, the external atmosphere temperature point T _f is located at a position equivalent to λ / α from the solid surface, and Δx / 2 from the solid surface. It is necessary to provide a T- ₁ point at the position. The value of T _-1 can be calculated from the linear relationship between the x-coordinate of the solid surface point T ₀ and the external point T _f . If the value of T ₋₁ is obtained, T _{1A at} time t + Δt can be calculated from T ₋₁ , T ₁ , and T _{2 at} time t as in equation (6). Once T _1A is determined, the surface T _0A (temperature of t ₀ at t + Δt) can be calculated from the linear relationship between T _1A and T ₋₁ .

  In this way, the temperature at each calculation point inside the solid is calculated at the set time steps. Further, the temperature change at each calculation point is defined as the initial temperature of the heat transfer calculation in the next time step, and the temperature change is calculated. We conduct unsteady heat transfer analysis of external heat and solids, and solids by repeatedly calculating time steps. The repetitive calculation can be performed by an operation or the like by the operation unit 71 using a spreadsheet software program.

Note that the ambient temperature (T _f ) outside the die 2 is determined by the first temperature information acquisition unit 61, the second temperature information acquisition unit 62, the third temperature information acquisition unit 63, the fourth temperature information acquisition unit 64, or the fifth temperature information. The information is acquired by the information acquiring unit 65. The initial surface temperature of the die 2 (T ₀ ) is a predetermined initial temperature of the die 2 (for example, 450 ° C.). The die 2 is heated to the initial temperature before starting the extrusion.

(4. Calculation of heat conduction of die during extrusion)
(4.1 Heat conduction calculation of die)
FIG. 9 shows a model for calculating the heat conduction of the die 2 by the Fourier theoretical formula and the difference method. The heat input and the heat radiation of the die 2 during the extrusion process are the heat input F0 from the metal processing heat in the die chamber, the heat input F1 from the metal frictional heat of the bearing of the die 2, and the interface between the die escape portion and the air. Heat radiation F2, heat radiation F3 from contact with the tool system at the rear of the die, and heat radiation F4 from contact with the die stack are defined.

  Hereinafter, when simply described as F0, it indicates the heat input F0. In addition, when simply described as F1, it indicates the heat input F1. In addition, when simply described as F2, it refers to heat radiation F2. In addition, when simply described as F3, it indicates the heat radiation F3. In addition, when simply described as F4, it means the heat radiation F4.

  FIG. 9 illustrates a divided model in which 5 × 5 partial areas are set in a matrix direction (X direction × Y direction) as a virtual model of the dice. The dice virtual model shown in FIG. 9 and FIGS. 20, 21, 22, and 23 described below is, for example, a virtual model of a cross section 2V of the dice 2 shown in FIG. Also, different numbers (11 to 15, 21 to 25, 31 to 35, 41 to 45, 51 to 55) are assigned to different partial areas for the purpose of distinguishing between them. The tens place of this number indicates the position in the X direction, and the ones place indicates the position in the Y direction.

  The heat input F0 shown in FIG. 9 and FIG. 20, FIG. 21, FIG. 22, and FIG. 23, which will be described later, has “11”, “12”, “13”, and “14” in partial regions arranged at one end in the Y direction. , "15" function as heat input to the partial regions for five rows. The heat radiation F3 shown in FIG. 9 is obtained from five rows of partial areas in which “51”, “52”, “53”, “54”, and “55” are added to partial areas arranged at one end in the Y direction. Function as heat radiation. The heat input F1 shown in FIG. 9 functions as heat input to a partial region of one row in which “11” is added to a partial region arranged at one end in the X direction. The heat radiation F2 illustrated in FIG. 9 functions as heat radiation from a partial region of one row in which “21”, “31”, “41”, and “51” are added to a partial region arranged at one end in the X direction. . The heat radiation F4 shown in FIG. 9 is a partial area for one row in which “15”, “25”, “35”, “45”, and “55” are added to partial areas arranged at the other end in the X direction. Functions as heat radiation from

  The heat input F0 corresponds to the heat input to the die 2 at the first location. The heat input F1 corresponds to the heat input to the die 2 at the second location. The heat radiation F2 corresponds to heat radiation from the die 2 at the third location. The heat radiation F3 corresponds to the heat radiation from the die 2 at the fourth location. The heat radiation F4 corresponds to the heat radiation from the die 2 at the fifth location.

  The illustrated analysis model is divided into 5 rows × 5 columns, and has a total of 25 elements.

(4.2 One-dimensional heat conduction calculation in the horizontal direction)
First, in the case of the one-dimensional case shown in FIG. 10, the calculation of the heat input of F1 from the left and the heat release of F4 to the right will be considered. The shape of the model is a square 100 × 100 mm.

The initial temperature of the die 2 is 450 ° C., the thermal conductivity is 30 W / (m · ° C.), the specific heat is 460 J / (kg · ° C.), and the density is 7800 kg / m ³ . The model is a planar model.

  FIG. 11 shows the heat transfer coefficient, the ambient temperature, and the equivalent distance when heat transfer is converted to heat conduction, which is the boundary condition between F1 and F4. The calculation time is 300 s. The calculation time interval of the difference method is 6 s, and the number of calculation steps is 50.

  Note that 300 s means 300 seconds (s: second). 6s refers to 6 seconds (s).

  FEM analysis of unsteady heat transfer was performed to study the calculation accuracy of the difference method. For the FEM analysis of the unsteady heat transfer, general-purpose FEM analysis software Ansys18.0 (registered trademark) was used. FIG. 12 shows an FEM analysis model. The elements have a division size of 5 mm and a total of 400 elements.

  FIG. 13 shows a temperature distribution diagram of the FEM analysis result after a lapse of 300 s. The temperature decreases from left to right. FIG. 14 shows a comparison between the difference method calculation result and the FEM analysis result after a lapse of 300 s. It turns out that both are in agreement. Therefore, in the case of the one-dimensional case, it can be understood that the calculation accuracy of the difference method is high in the heat transfer analysis under two thermal boundary conditions from the left and right.

[4.3 Two-dimensional horizontal and vertical heat conduction analysis]
As shown in FIG. 9, the heat conduction of the die 2 is in the horizontal direction and the vertical direction. Here, similarly, a heat transfer analysis of the five boundary conditions in FIG. 9 will be examined using a square 100 × 100 mm model. The length of the bearing part is 20 mm.

  FIG. 15 shows the equivalent distance when the heat transfer coefficient, the ambient temperature, and the heat transfer are converted to heat conduction, which are the five boundary conditions of FIG. The calculation time is 300 s. The calculation time interval of the difference method is 6 s, and the number of calculation steps is 50. Similarly, in order to examine the calculation accuracy of the difference method, FEM analysis of unsteady heat transfer was performed.

The ambient temperature (T _f ) shown in FIG. 15 is a temperature acquired by the temperature information acquisition device 60. Boundary No. The atmosphere temperature of “F0” (T _f = 520 [° C.]) is acquired by the first temperature information acquisition unit 61. Boundary No. The atmosphere temperature of “F1” (T _f = 550 [° C.]) is acquired by the second temperature information acquisition unit 62. Boundary No. The atmosphere temperature of “F2” (T _f = 200 [° C.]) is acquired by the third temperature information acquisition unit 63. Boundary No. The atmosphere temperature of “F3” (T _f = 200 [° C.]) is acquired by the fourth temperature information acquisition unit 64. Boundary No. The atmosphere temperature of “F4” (T _f = 100 [° C.]) is acquired by the fifth temperature information acquisition unit 65. That is, the heat input F0 in the embodiment is heat conduction to the die 2 caused by the temperature detected at the first location. The heat input F1 is heat conduction to the die 2 caused by the temperature detected at the second location. The heat radiation F2 is heat conduction to the die 2 generated by the temperature detected at the third location. The heat radiation F3 is heat conduction to the die 2 caused by the temperature detected at the fourth location. The heat radiation F4 is heat conduction to the die 2 generated by the temperature detected at the fifth location.

  FIG. 16 shows a temperature distribution diagram of the FEM analysis result after a lapse of 300 s. FIG. 17 shows the temperature distribution in the X direction of each row element as a result of the FEM analysis. Heat input from the metal F0 in the chamber and the bearing F1 increases the temperature near the bearing. On the other hand, due to the heat radiation of F4 on the outer periphery of the die 2, F2 of the escape portion, and F3 of the back die portion, the temperature decreases from the inside of the die 2 to the outside and from the upper surface of the die 2 to the lower surface.

  FIG. 18 shows the result of the temperature distribution in the X direction of each row element by the difference method after 300 s has elapsed. The temperature calculation value of each time step by the two-dimensional difference method is a value obtained by superimposing the temperature calculation results in the X direction and the Y direction.

  A comparison between the temperature calculation result of each row element by the difference method in FIG. 18 and the FEM analysis result in FIG. 17 shows that there is a difference between the two. FIG. 19 shows a comparison between the difference method calculation result of the 1-row element and the 5-row element and the FEM analysis result. From FIG. 19, the difference method calculation result of the right element in one row is about 36 ° C. lower than the FEM analysis result. On the other hand, the result of the difference method calculation of the right element in the fifth row is about 25 ° C. higher overall than the result of the FEM analysis. As described above, in the two-dimensional case, it is understood that the accuracy is not good simply by superimposing the temperature calculation results in the X and Y directions.

  The cause of the discrepancy between the difference method calculation result and the FEM analysis result is considered to be due to the setting of the initial temperature of the calculation. Here, the calculation method of the difference method was reconsidered. The method of this embodiment is based on the recalculated difference method.

  FIGS. 20 to 23 show a method of calculating the heat transfer in the left, right, up, and down directions devised. When calculating the die temperature in the time step, first, as shown in FIG. 20, first, the heat conduction is calculated by the boundary conditions F1 and F4 between the elements 11 and 15 in the first row. Next, in the second step, heat conduction is calculated between the elements 11 and 51 in the first column of FIG. 21 by the boundary conditions F0 and F3. At this time, the initial temperature value of the element 11 is set as the temperature value after the calculation in the first step. Thereafter, when calculating the heat conduction of the element in the second row in the third step in FIG. 22, the initial temperature value of the element 21 is set to the temperature value after the calculation in the first column in the second step. Thereafter, when calculating the heat conduction of the elements in the second column in the fourth step of FIG. 23, the initial temperature values of the elements 12 and 22 are the temperature values after the calculation in the first step and the third step, respectively. Similarly, when calculating the heat conduction of the 3rd to 5th row elements and the 3rd to 5th column elements, the value calculated in the previous row and column is defined as the initial temperature and calculated by the above method. According to this calculation method, it is considered that the influence of the temperature change of the heat conduction in the X and Y directions is taken into consideration, which leads to an improvement in calculation accuracy.

  In addition, "the heat conduction by the boundary conditions F1 and F4 between the element 11 and the element 15 in the first row" means "the heat input F1 from the metal frictional heat of the bearing of the die and the heat radiation from the contact with the die stack". The heat conduction occurring in the partial area (element 11, element 12, element 13, element 14, element 15) in the first row set in the dice virtual model due to the influence of F4. Further, "the heat conduction by the boundary conditions F0 and F3 between the element 11 and the element 51 in the first row" means "the contact between the heat input F0 from the metal working heat in the die chamber and the tool system at the rear of the die". From the heat radiation F3 of the die, the heat conduction occurring in the partial area (element 11, element 21, element 31, element 41, element 51) of the first row set in the virtual model of the dice.

For example, the equivalent distance (λ / α [mm]) shown in FIG. 15 is applied to “λ / α” shown in FIG. The ambient temperature (T _f [° C.]) shown in FIG. 15 is applied to “T _f ” shown in FIG. The heat transfer coefficient α [(W / m 2 · ° C.)] is used to derive the equivalent distance (λ / α [mm]). At least one of the heat transfer coefficient α [(W / m 2 · ° C.)] and the equivalent distance (λ / α [mm]) depends on conditions such as the specific configuration of the extrusion device 100 and the environment in which the extrusion device 100 is placed. It is given as a derived default value.

  If the virtual model of the dice is a square model of 100 × 100 mm, Δx shown in FIG. 8 is 20 mm. Δx / 2 is 10 mm. That is, Δx is １ ／ of the dimension of the virtual model in the X direction (or Y direction).

As a specific example, the initial temperature and the calculated initial temperature in the partial area for one row in which the partial areas marked with “11”, “12”, “13”, “14”, and “15” in FIG. The temperature will be described. Boundary No. Since the ambient temperature _Tf of “F1” is “550”, “550” is substituted for _Tf in FIG. The initial value of _{T 0} in FIG. 8 is as described above, the die 2 initial temperature (e.g., 450 [℃]). Thus, where "450" is substituted for the _{T 0} it is. Also, the boundary No. is added to “λ / α” in FIG. “15” of the equivalent distance λ / α of “F1” is substituted. Since the virtual model of the dice is a square model of 100 × 100 mm, “10” is substituted for “Δx / 2”. These values imputed _{T f, T 0, λ /} α, by [Delta] x / 2, calculating unit 71 calculates the _{T -1} corresponding to "F1" in FIG. 15. This T _-1 is from the “11” side in the partial region for one row in which the partial regions with “11”, “12”, “13”, “14”, and “15” are arranged in the X direction. Of heat input F1.

Each _{T 1,} T 2, _{T 3} in FIG. 8, "11" in FIG. 20, "12", is the initial temperature of the partial regions are designated by "13". This initial temperature is the initial temperature of the die 2. In this specific example, “450” is assigned to each of T ₁ , T ₂ , and T ₃ . Although not shown, T ₄ and T ₅ are actually set as the initial temperatures of the partial areas to which “14” and “15” are added. In this specific example, “450” is also assigned to T ₄ and T ₅ .

Furthermore, although not shown in FIG. 8, T _7, which corresponds to heat dissipation F4 from "15" side is set. T ₇ is calculated by the same mechanism as the calculation of T _-1 corresponding to heat input F1 described above. That is, the boundary No. Since the ambient temperature _Tf of “F4” is “100”, “100” is substituted for _Tf in FIG. The initial value of _{T 0} in FIG. 8 is as described above, the die 2 initial temperature (e.g., 450 [℃]). Thus, where "450" is substituted for the _{T 0} it is. Also, the boundary No. is added to “λ / α” in FIG. “120” of the equivalent distance λ / α of “F4” is substituted. Since the virtual model of the dice is a square model of 100 × 100 mm, “10” is substituted for “Δx / 2”. These values imputed _{T f, T 0, λ /} α, by [Delta] x / 2, calculating unit 71 calculates the _{T -1} corresponding to "F4" in Figure 15. Is _{T -1} corresponding to the "F4", are treated as _{T 7.} The initial value of _{T 6} between _{T 5} and _{T 7} is the same as the initial value of _{T 0.}

Based on T ₋₁ , T ₀ , T ₁ , T ₂ , T ₃ , T ₄ , T ₅ , T ₆ , T ₇ determined in this way, and T _−1A , T _0A , T _1A , T _2A , T _3A , T _4A , T _5A , T _6A and T _7A are calculated. In the embodiment, it is assumed that _Tf in FIG. 15 is constant. It is assumed that the _three values used in the calculation of T2A in equation (6) can be expressed as (T ₁ , T ₂ , T ₃ ). In this case, the three values used for calculating T _1A are (T ₋₁ , T ₁ , T ₂ ) and do not include T ₀ . T _0A is obtained based on the linear relationship between T _1A and T ₋₁ . Further, T- _1A is obtained by calculating the slope of the line segment (difference between _Tf and _T0A ) connecting _Tf and _T0A used in the calculation of T- ₁ and the ratio of λ / α to Δx / 2. Required based on. _Tf is the ambient temperature _Tf of “F1”.

As described above, in the first calculation (first first calculation step) described above, the calculation unit 71 determines the portions indicated by “11”, “12”, “13”, “14”, and “15” in FIG. region is calculated _T -1A corresponding to one row of partial areas arranged in the X _{direction, T 0A, T 1A, T} 2A, T 3A, T 4A, T 5A, the _{T 6A} and _{T 7A.} Here, T _1A is the temperature after the elapse of t [s] in the partial area “11”. _T2A is the temperature after the elapse of t [s] in the partial region of "12". _T3A is the temperature after the elapse of t [s] in the partial region of "13". _T4A is the temperature after elapse of t [s] in the partial region of "14". _T5A is the temperature after the elapse of t [s] in the partial region “15”.

Next, the calculation unit 71 determines that the partial areas marked with “11”, “21”, “31”, “41”, and “51” in FIG. to _{T -1A, T 0A, T 1A} , T 2A, T 3A, T 4A, T 5A, the processing for calculating the _{T 6A} and _{T 7A} performed. Here, the heat input from the “11” side is the heat input F0. Therefore, the boundary No. substituted in the above description is not limited to the above. The ambient temperature _Tf of the “F1” and the boundary No. The equivalent distance λ / α of “F1” is set to the boundary No. The ambient temperature _Tf of “F0” and the boundary No. The value is substituted by substituting for the equivalent distance λ / α of “F0”, and the arithmetic unit 71 calculates “F0” in FIG. 15 by using T _f , T ₀ , λ / α, and Δx / 2 to which these values are substituted. _Is calculated. This T- ₁ is from the “11” side in the partial region for one row in which the partial regions with “11”, “21”, “31”, “41”, and “51” are arranged in the Y direction. Of heat input F0.

In a similar mechanism, T ₆ corresponding to the heat radiation F3 from "51" side, the boundary was assigned in the above description No. The ambient temperature _Tf and the boundary No. of “F4” The equivalent distance λ / α of “F4” is set to the boundary No. The ambient temperature _Tf of the “F3” and the boundary No. By substituting values by substituting the equivalent distance λ / α of “F3”, and using these values substituted T _f , T ₀ , λ / α, and Δx / 2, the arithmetic unit 71 calculates “F0” in FIG. _Is calculated. Is _{T -1} corresponding to the "F3", are treated as _{T 7} corresponding to the heat radiation F3 from "51" side.

And T _-1, T ₇ which was thus determined, "21" in FIG. 21, "31", "41", the partial area "51" are assigned one column of partial areas arranged in the Y-direction Is calculated based on the initial values T ₂ , T ₃ , T ₄ , and T ₅ of “1” and the temperature T _1A of “11” calculated in the “first first calculation step”. The “first second calculation step” performed after the “calculation step” is performed. Specifically, the arithmetic unit 71 is replaced with a temperature T _1A of the "initial second calculation step", was calculated T ₁ in the "initial first calculation step", "11". That is, the arithmetic unit 71, the _T -1, _{T 7} shown in FIG. 8, is substituted for _{T -1, T 7} corresponding to the heat radiation F3 corresponding to heat input F0. In addition, the arithmetic unit 71 substitutes the initial temperature of the die 2 for T ₀ , T ₂ , T ₃ , T ₄ , and T ₅ . The arithmetic unit 71, the T _1, substitutes the temperature T _1A of the calculated by "initial first calculation step", "11". Based on T ₋₁ , T ₁ , T ₂ , T ₃ , T ₄ , T ₅ , and T ₆ determined in this way and the above-described equation (6), T _−1A , T _0A , T _1A , _T2A , _T3A , _T4A , _T5A , _T6A and _T7A are calculated. Here, the temperature T _1A of “11” is recalculated. That is, when the same partial area value is calculated in the first calculation step and the second calculation step, the value of the step performed later is adopted.

Next, the arithmetic unit 71 determines that the partial areas marked with “21”, “22”, “23”, “24”, and “25” in FIG. to _{T -1A, T 0A, T 1A} , T 2A, T 3A, T 4A, T 5A, the processing for calculating the _{T 6A} and _{T 7A} performed. Here, the heat radiation from the “12” side is the heat radiation F2. Therefore, the boundary No. substituted in the above description is not limited to the above. The ambient temperature _Tf of the “F1” and the boundary No. The equivalent distance λ / α of “F1” is set to the boundary No. The ambient temperature _Tf of the “F2” and the boundary No. By substituting values by substituting the equivalent distance λ / α of “F2”, and using these values _Tf , T ₀ , λ / α, and Δx / 2, the calculation unit 71 calculates “F2” in FIG. _Is calculated. This T _-1 is from the "21" side in the partial region for one row in which the partial regions to which "21", "22", "23", "24", and "25" are attached are arranged in the X direction. Of the heat radiation F2. Incidentally, T ₇ corresponding to the heat radiation F4 is the same as T ₇ in the first operation is already already calculated (initial first calculation process).

And T _-1, T ₇ that definite in this way, "22", "23", "24", one line of partial areas arranged partial region "25" is attached is in the x-direction in FIG. 22 Based on the initial values T ₂ , T ₃ , T ₄ , and T _{5 of the above} and the temperature T _2A of “21” calculated in the “first second calculating step”, the arithmetic unit 71 calculates the “first second The “second calculation step” performed after the “calculation step” is performed. Specifically, the arithmetic unit 71, in the "second first calculation step", substituting T ₁ at a temperature T _2A of the calculated by "initial second calculation step", "21". That is, the arithmetic unit 71, the _T -1, _{T 7} shown in FIG. 8, is substituted for _{T -1, T 7} corresponding to the heat radiation F4 corresponding to the heat radiation F2. In addition, the arithmetic unit 71 substitutes the initial temperature of the die 2 for T ₀ , T ₂ , T ₃ , T ₄ , and T ₅ . The arithmetic unit 71, the T _1, substitutes the temperature T _2A of the calculated by "initial second calculation step", "21". Based on T ₋₁ , T ₀ , T ₁ , T ₂ , T ₃ , T ₄ , T ₅ , T ₆ , T ₇ determined in this way, and T _−1A , T _0A , T _2A , T _3A , T _4A , T _5A , T _6A and T _7A are calculated.

Next, the arithmetic unit 71 determines that the partial areas marked with “12”, “22”, “32”, “42”, and “52” in FIG. to _{T -1A, T 1A, T 2A} , T 3A, T 4A, T 5A, the processing for calculating the _{T 6A} and _{T 0A} performed. Here, the heat input from the “12” side is the already calculated heat input F0. The heat radiation from the “52” side is the already calculated heat radiation F3.

T _-1 was definite in this _way, a T _6, "32" in FIG. 23, "42", the initial value T for one column of partial areas partial area "52" is attached are arranged in the Y-direction ₃ , T ₄ , T ₅ , the temperature T _2A of “12” calculated in the “first calculation step” and the temperature T _{2A of} “22” calculated in the “second calculation step” , The calculation unit 71 performs a “second calculation step”. That is, the arithmetic unit 71 substitutes T _-1 corresponding to the heat input F3 and T ₆ corresponding to the heat radiation F3 into T _-1 and T ₇ shown in FIG. In addition, the calculation unit 71 substitutes the initial temperature of the die 2 for T ₃ , T ₄ , and T ₅ . The calculation unit 71 substitutes the temperature T _2A of “12” calculated in the “first first calculation step” for T ₀ and T ₁ . The arithmetic unit 71, the T _2, substitutes the temperature T _2A of "22" calculated by the "second first calculating step". Based on T ₋₁ , T ₀ , T ₁ , T ₂ , T ₃ , T ₄ , T ₅ , T ₆ , T ₇ determined in this way, and T _−1A , T _0A , T _2A , T _3A , T _4A , T _5A , T _6A and T _7A are calculated.

Thereafter, although not shown, in the fifth operation (third first calculation step), the temperature T _{3A of the} partial region to which “31” and “32” have been calculated in the previous second calculation step is attached. , T _3A to the initial values T ₁ , T ₂ . In the sixth calculation (third second calculation step), the temperatures T _3A , T _3A and T _{3 of the} partial areas to which “13”, “23”, and “33” have been calculated in the previous first calculation step are added. _3A and T _3A are substituted for initial values T ₁ , T ₂ and T ₃ . In the seventh calculation (the fourth first calculation step), the temperatures T _4A , T _{4 of the} partial areas to which “41”, “42”, and “43” have been calculated in the previous second calculation step are attached. _4A and T _4A are substituted for initial values T ₁ , T ₂ and T ₃ . In the eighth operation (fourth second calculation step), the temperatures of the partial areas to which "14", "24", "34", and "44" have been calculated in the previous first calculation step are given. T _4A , T _4A , T _4A , and T _4A are substituted for initial values T ₁ , T ₂ , T ₃ , and T ₄ . In the ninth operation (fifth first calculation step), the temperatures of the partial areas to which “51”, “52”, “53”, and “54” calculated in the previous second calculation step are attached T _5A , T _5A , T _5A , and T _5A are substituted for initial values T ₁ , T ₂ , T ₃ , and T ₄ . In the tenth calculation (fifth second calculation step), “15”, “25”, “35”, “45”, and “55” that have been calculated in the previous first calculation step are added. The temperatures T _5A , T _5A , T _5A , T _5A , T _5A of the partial areas are substituted into initial values T ₁ , T ₂ , T ₃ , T ₄ , T ₅ .

As described above, the initial value of each partial region excluding the specially described “replacement with reference to the value of the previous calculation step” is the initial temperature of the die 2. Further, in the second and subsequent first calculation steps, the heat radiation (T ₋₁ ) from one end and the heat radiation (T ₇ ) from the other end are the already calculated heat radiation F2 and heat radiation F4. Further, the heat input (T ₋₁ ) from one end and the heat radiation (T ₇ ) from the other end in the second calculation step are the heat input F1 and the heat radiation F3 that have already been calculated.

  As described above, the calculation unit 71 calculates the heat input amount F1 from the second location on the inner peripheral side of the die 2 and the heat release amount F2 to the third location on the inner peripheral side of the die 2, and the fifth A first calculating step of calculating the temperature of each partial area included in one row based on the heat release amount F4 to the location and a predetermined initial temperature of each partial area; Each partial area included in one row based on the heat input F0 from one location, the heat release F3 from the other end of the die 2 to the fourth location, and the predetermined initial temperature of each partial area. And a second calculating step of calculating the temperature. Further, the first calculation step and the second calculation step are performed a plurality of times, respectively, with t being the same value. Further, the first calculation step and the second calculation step are performed alternately. Further, in the second and subsequent first calculation steps, the temperature of the partial area calculated in the previous second calculation step is used as the initial temperature of the partial area among the temperatures of the partial areas of one row for calculating the temperature. And Further, in the second and subsequent second calculation steps, the temperature of the partial area calculated in the first calculation step before that among the temperatures of the partial areas for one row for calculating the temperature is set to the initial temperature of the partial area. And

In the subsequent steps of the first first calculation step and the first second calculation step, the temperature of the partial area calculated in the previously performed step is set as the initial temperature of the partial area. In the above description, the first calculation step is performed first, but the second calculation step may be performed first. In such a case, the “first calculation step” (the first second calculation step) is performed. The temperature T _1A of the partial region “11” is substituted into the initial value T ₁ of the second partial region “11” (first calculation step).

  In the embodiment, as described above, the calculation time is 300 s. The calculation time interval of the difference method is 6 s, and the number of calculation steps is 50. Specifically, the timing at which the initial temperature is 450 [° C.] is set as the start time (0 s). The temperatures of the dies 2 in all the partial regions at this timing are the initial temperatures (450 [° C.]). The calculation unit 71 sets t = 6, repeats the first calculation step and the second calculation step as described above based on the above equation (6), and calculates the temperature of each partial area after a lapse of 6 s from the start time. Is calculated.

Next, the calculation unit 71 sets t = 6, sets the temperatures of the respective partial regions calculated based on the initial temperatures at the start time (0s) as initial temperatures (T ₁ , T ₂ ,...) = 6, and the first calculation step and the second calculation step are repeated as described above based on the above equation (6). As a result, the temperature of each partial area 12 seconds after the start time is calculated. Hereinafter, by repeating the process using the calculated temperature as the initial temperature by the number of calculation steps, the temperature of each partial region after the calculation time (300 s) and the temperature of each partial region up to the 6 second interval are calculated. Is done.

  In this manner, in the temperature distribution calculation process at each of two different timings before and after the predetermined time, which is assumed to elapse the predetermined time, the initial temperature of each partial region at the later timing is calculated by the temperature distribution calculation process at the previous timing. Is the temperature of each partial region calculated by

  FIG. 24 shows the temperature distribution in the X direction of each row element according to the devised difference calculation method. Comparing the result of temperature calculation by the difference method in FIG. 24 with the result of FEM analysis in FIG.

  FIG. 25 shows a comparison between the calculation results of the one-line element and the five-line element of the devised difference method and the FEM analysis results. Both agree. As described above, in the two-dimensional heat conduction analysis, the effect of the heat conduction from two directions is considered, so that a difference calculation method with high calculation accuracy is obtained.

24 and 25, the temperature distribution of the die 2 after 300 s derived by the temperature calculation method of the die 2 according to the embodiment is compared with the temperature distribution of the die 2 after 300 s derived by FEM analysis. ing. In FIGS. 24 and 25, the temperatures of the respective partial regions after 300 s are obtained by calculating the temperatures T _0A , T _1A , T _2A , T _3A , T _4A , T _5A , and T _5A calculated in the first calculation step and the second calculation step. It is represented by _T6A .

  Further, “1 row Y = 90” in FIG. 24 indicates that the partial areas denoted by “11”, “12”, “13”, “14”, and “15” in FIG. It corresponds to the partial area of the line. Further, “2 rows Y = 70” in FIG. 24 indicates that the partial areas denoted by “21”, “22”, “23”, “24”, and “25” in FIG. It corresponds to the partial area of the line. In addition, “3 rows Y = 50” in FIG. 24 indicates that the partial areas denoted by “31”, “32”, “33”, “34”, and “35” in FIG. It corresponds to the partial area of the line. In addition, “4 rows Y = 30” in FIG. 24 indicates that the partial areas denoted by “41”, “42”, “43”, “44”, and “45” in FIG. It corresponds to the partial area of the line. In addition, “5 rows Y = 10” in FIG. 24 indicates that the partial areas denoted by “51”, “52”, “53”, “54”, and “55” in FIG. It corresponds to the partial area of the line.

  The “one-line element” in FIG. 25 is equivalent to one line in which the partial areas denoted by “11”, “12”, “13”, “14”, and “15” in FIG. Corresponds to the partial region of The “five-row element” in FIG. 25 is equivalent to one row in which the partial areas denoted by “51”, “52”, “53”, “54”, and “55” in FIG. Corresponds to the partial region of “Difference method modification” in FIG. 25 indicates that this is the method for calculating the temperature of the die 2 according to the embodiment. Further, “FEM” in FIG. 25 indicates that it is a calculation result by the FEM analysis.

  FIG. 26 shows the relationship between the elapsed time and the temperature history of the element E11 near the bearing and the outer peripheral element E15 of the die 2 during extrusion processing by the difference method calculation. By using the calculation method devised this time, the temperature difference between the inside and the outside of the die 2 at the rear end of the extrusion destination can be quantitatively examined.

  In addition, E11 in FIG. 26 corresponds to the partial area indicated by “11” in FIG. 9 and the like. In addition, E15 in FIG. 26 corresponds to the partial area indicated by “15” in FIG. 9 and the like. FIG. 26 is a graph that draws a line connecting the temperatures of the partial regions at each timing from 0 s to 300 s with the calculation time interval of the difference method set to 6 s and the calculation step set to 50.

[Effects]
As described above, according to the present embodiment, it is possible to calculate the temperature of each partial region that is approximated by FEM analysis. That is, a highly accurate operation equivalent to that of the FEM analysis can be obtained regardless of the environment in which the FEM analysis can be performed. As described above, according to the embodiment, the temperature distribution of the die 2 can be more easily simulated, and a highly accurate calculation result equivalent to the FEM analysis can be obtained.

[Others]
The metal is not limited to aluminum. Further, the alloy is not limited to an alloy containing aluminum. The metal or alloy may be any metal or alloy to which extrusion using the die 2 can be applied.

  The above-mentioned “model shape (square, 100 mm × 100 mm)”, “length of bearing part (20 mm)”, “calculation time (300 s)”, “calculation time interval (6 s) of difference method”, “calculation step ( 50) "is merely an example, and the present invention is not limited to this, and can be changed as appropriate. The analysis model is not limited to 25 elements. The analysis model may be h × v in the matrix direction. h and v are natural numbers of 2 or more.

  The virtual model in the above-described embodiment is a plane model of the cross section of the die 2, but may be an axially symmetric model of the die 2.

  In the foregoing, various useful embodiments of the present invention have been shown and described. It is needless to say that the present invention is not limited to the various embodiments and modifications described above, but can be variously modified without departing from the gist of the present invention and the contents described in the appended claims. Not even.

DESCRIPTION OF SYMBOLS 1 Temperature calculation system 2 Die 2V Section 3 Billet 60 Temperature information acquisition device 61 First temperature information acquisition unit 62 Second temperature information acquisition unit 63 Third temperature information acquisition unit 64 Fourth temperature information acquisition unit 65 Fifth temperature information acquisition unit 70 information processing device 71 arithmetic unit

Claims (4)

A method for calculating a temperature of a die that simulates a temperature distribution of a die used for extrusion of a metal or an alloy to be extruded,
With the extrusion direction of the extrusion target in the die as a column direction, and a direction perpendicular to the extrusion direction as a row direction, a virtual model of a cross section in the row direction with respect to the center of the die in which the extrusion port of the extrusion target is arranged is set. The process of
Setting a two-dimensional matrix-shaped divided model including a plurality of partial regions in the row direction and the column direction in the virtual model;
A first location where the extrusion target is pressed against the die in the extrusion direction, a second location where the extrusion target is extruded from the die, and the extrusion location side with respect to the second location. A third location that is a space inside the die, a fourth location that is a space on the end side of the die on the extrusion direction side, and the third location that is opposite to the second location and the third location. A step of obtaining a temperature of a fifth location which is a space on the outer peripheral side of the die;
Calculating the heat input to the die at the first location and the second location, and the heat release from the die at the third location, the fourth location, and the fifth location;
Temperature distribution calculation step of calculating the temperature of each partial region included in the divided model,
The temperature distribution calculation step,
The heat input from the second location on the inner peripheral side of the die and the heat release to the third location on the inner peripheral side of the die, the heat release from the outer peripheral side of the die to the fifth location, A first calculation step of calculating the temperature of each partial area included in one row based on the determined initial temperature of each partial area;
One row based on the heat input from the first location at one end of the die, the heat release from the other end of the die to the fourth location, and a predetermined initial temperature of each partial area. A second calculation step of calculating the temperature of each partial region included in the minute,
Including
The first calculation step and the second calculation step are each performed a plurality of times,
The first calculation step and the second calculation step are performed alternately,
In the second and subsequent first calculation steps, of the partial area temperatures for one row for which the temperature is calculated, the temperature of the partial area calculated in the previous second calculation step is used as the initial value of the partial area. Temperature
In the second and subsequent second calculation steps, the temperature of the partial area calculated in the first calculation step earlier than the initial temperature of the partial area among the temperatures of the partial areas for one row for which the temperature is calculated is calculated. Characterized by temperature
Die temperature calculation method. Of the first calculation step and the second calculation step, in a later step, the temperature of the partial area calculated in the earlier step is set as the initial temperature of the partial area. Characterized by
The method for calculating a temperature of a die according to claim 1. In the temperature distribution calculating step at each of two different timings before and after the predetermined time, where the predetermined time is supposed to elapse, the initial temperature of each partial region at a later timing is calculated based on the temperature distribution calculating step at a previous timing. Characterized in that it is the temperature of each partial region calculated in
The method for calculating a temperature of a die according to claim 1. Temperature information acquisition device for acquiring temperature information of a die used for extrusion processing of a metal or alloy extrusion target, and information processing device for simulating temperature distribution of a die used for extrusion processing of a metal or alloy extrusion target A die temperature calculation system comprising:
The temperature information acquisition device,
A first temperature information acquisition unit configured to acquire temperature information of a first location where the extrusion target is pressed against the die in an extrusion direction of the extrusion target, and a second location where the extrusion target extruded from the die exists A second temperature information acquisition unit for acquiring temperature information of the third position, and a third temperature information acquisition unit for acquiring temperature information of a third location which is a space inside the die on the extrusion direction side with respect to the second location. Part, a fourth temperature information acquisition unit for acquiring temperature information of a fourth location which is a space on the end side of the die on the extrusion direction side, and located on the opposite side to the second location and the third location. A fifth temperature information acquisition unit that acquires temperature information of a fifth location that is a space on the outer peripheral side of the die,
The information processing device,
With the extrusion direction of the extrusion target in the die as a column direction, and a direction perpendicular to the extrusion direction as a row direction, a virtual model of a cross section in the row direction with respect to the center of the die in which the extrusion port of the extrusion target is arranged is set. And
In the virtual model, a two-dimensional matrix-like divided model including a plurality of partial regions in the row direction and the column direction is set,
The amount of heat input from the second location on the inner periphery of the die and the amount of heat radiation to the third location on the inner periphery of the die, and the amount of heat radiation from the outer periphery of the die to the fifth location are calculated. And
An arithmetic unit that calculates the temperature of each partial region included in the divided model,
The arithmetic unit includes:
A heat input amount and a heat release amount from the inner peripheral side of the die including the second location and the third location, a heat release amount from the outer peripheral side of the die including the fifth place, and predetermined partial regions A first calculation step of calculating the temperature of each partial region included in one row based on the initial temperature of the first position, the amount of heat input from one end of the die including the first position, and the fourth position. A second calculating step of calculating the temperature of each partial area included in one row based on the heat radiation amount from the other end of the die including the predetermined initial temperature of each partial area, Done several times,
Performing the first calculation step and the second calculation step alternately;
In the second and subsequent first calculation steps, of the partial area temperatures for one row for which the temperature is calculated, the temperature of the partial area calculated in the previous second calculation step is used as the initial value of the partial area. Temperature
In the second and subsequent second calculation steps, the temperature of the partial area calculated in the first calculation step earlier than the initial temperature of the partial area among the temperatures of the partial areas for one row for which the temperature is calculated is calculated. Characterized by temperature.
Die temperature calculation system.