JP2006205449A - Estimation method of internal temperature of heating target and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To simply and precisely estimate the temperature change in a heating target even in a case that the passage of heat from the peripheral surface almost vertical to the heating surface of the heating target is relatively large in the heat treatment of the heating target. <P>SOLUTION: This estimation method of the internal temperature of the heating target comprises a correction step for correcting the coefficient of heat diffusion which characterizes the heating target corresponding to an area ratio which expresses the ratio of the area of the heating surface of the heating target to the equivalent area of the side surface almost vertical to the heating surface of the heating target and an estimate step for estimating a temporal change in the temperature of the heating target using a unidimensional heat conduction equation, wherein the corrected coefficient of heat diffusion is a coefficient and the height direction of the heating target is an axis, and the boundary condition corresponding to a predetermined heating condition. The equivalent area of the side surface of the heating target is determined corresponding to the length of the peripheral side of the heating surface of the heating target and the height in the direction almost vertical to the heating surface of the heating target. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a method for predicting the internal temperature of an object to be heated, and more particularly to a method and a program for predicting a temperature change inside an object to be heated in a vulcanization process of the object to be heated with high accuracy using a one-dimensional heat conduction equation. .

Today, in bridges that are large structures, rubber bearings for bridges are provided between an upper structure such as a bridge and a lower structure such as a pier. The rubber bearing for bridge smoothly transmits the weight of the upper structure such as the bridge, the force acting on the upper structure, and the deformation of the upper structure due to temperature change to the lower structure. A rubber bearing for a bridge is a rubber product with a structure in which a metal layer and a rubber layer are laminated. Like a general rubber product, it is loaded into a product mold and heated by a press hot plate and vulcanized. Manufactured.
Many conventional bridge rubber bearings have a flat plate shape, and in the vulcanization process of the rubber bearing for bridges, heat is applied from these heating surfaces using two relatively wide opposing surfaces as heating surfaces. . The rubber support for bridges is a plate-like member, and the thickness in the direction substantially perpendicular to the heating surface in the vulcanization process is very thin. Therefore, in the vulcanization process, the inflow and outflow of heat from the side surface that is substantially perpendicular to the heating surface and surrounds the periphery of the rubber bearing for bridges is extremely small. As described above, for the rubber bearing for a bridge whose thickness in the direction substantially perpendicular to the heating surface is very small with respect to the area of the heating surface, the heating body is formed by heat conduction from the heating surface to the inside during the vulcanization process. The internal temperature-time change can be predicted with sufficient accuracy by a simple heat conduction calculation using a one-dimensional heat conduction equation.

  As described above, as an example of a method for predicting a change in temperature and time inside the flat plate member, in Patent Document 1 below, a one-dimensional heat conduction equation that performs a one-dimensional heat conduction analysis in the thickness direction of the flat plate member. A method for analyzing the temperature distribution of an object to be heated is disclosed. In the following Patent Document 1, when the temperature distribution of the thermal load applied in the molding process of these resin molded products is predicted for the thin-walled resin molded products, the surface of the thin-walled structure is utilized by utilizing the low thermal conductivity of the resin. Ignoring the heat conduction in the inward direction, the heat conduction analysis is performed only for the heat conduction in the thickness direction by a one-dimensional heat conduction analysis.

In Patent Document 1, a three-dimensional shape effect such as a corner portion or a rib base portion of a resin molded product made of a flat plate member is incorporated into a one-dimensional heat conduction analysis by thickness correction, and the resin temperature distribution is calculated. It is accurately predictable. In the following Patent Document 1, the microelement is a two-dimensional element such as a triangle or a quadrangle, heat conduction between adjacent microelements is omitted, and the amount of heat entering and exiting the surface of the flat plate member independently for each microelement. Is obtained by one-dimensional heat conduction analysis. In Patent Document 1, by incorporating a three-dimensional shape effect through wall thickness correction in this way, even in a one-dimensional heat conduction analysis, high precision is taken into account the effects of animal heat at corners and ribs. Analysis is possible.
Japanese Unexamined Patent Publication No. 07-52220

However, in recent years, even for rubber bearings for bridges, products with a large number of laminated rubber layers and metal layers inside the rubber bearings and a high height are increasing. For such products, the area of the side surface substantially perpendicular to the heating surface is relatively large, and heat inflow and outflow from the side surface cannot be ignored.
As described above, with respect to a vulcanized body having a shape in which the inflow and outflow of heat from the side surface cannot be ignored, the temperature change inside the vulcanized body cannot be calculated correctly by normal one-dimensional heat conduction calculation.
In the above-mentioned Patent Document 1, the three-dimensional shape effect of a resin molded product made of a flat plate member such as a corner portion and a rib root portion is incorporated into a one-dimensional heat conduction equation by thickness correction. The animal heat due to the three-dimensional shape effect such as the portion and the rib root portion can be predicted with high accuracy by a normal one-dimensional heat conduction analysis.
However, in the one-dimensional heat conduction calculation in Patent Document 1, it is possible to predict the influence of animal heat on the three-dimensional shape effect such as the thick-walled portion, but the inflow of heat from the side surface of the heated object and The outflow cannot be predicted. Therefore, there is a limit to the accuracy of predicting the internal temperature.

  As described above, for products in which the inflow and outflow of heat from the side cannot be ignored, the internal temperature history is predicted by calculating the internal temperature by three-dimensional heat conduction analysis using FEM or by actually measuring the temperature. It is also possible. However, since these methods require special knowledge, time, and cost, there is a problem that it is difficult to implement as daily routine work.

  In order to solve the above-described problem, the present invention provides a temperature of the heated object when a columnar heated object having two opposed surfaces is heated from at least one of the two opposed surfaces. A method for predicting a change in time, characterized by heat that characterizes the object to be heated according to an area ratio that represents a ratio of an area of the heating surface to an equivalent area of a side surface substantially perpendicular to the heating surface of the object to be heated. A correction step for correcting the diffusion coefficient, a one-dimensional heat conduction equation with the corrected heat diffusion coefficient as a coefficient, the axis being the height direction of the heated object, and a boundary condition according to a predetermined heating condition And a predicting step for predicting a temperature-time change of the heated body, and the equivalent area of the side surface is equal to the length of the periphery of the heated surface of the heated body and the heated surface of the heated body. It is determined according to the height in the substantially vertical direction. To provide an internal temperature estimation method of the thermal body.

Further, the heated body is a substantially rectangular parallelepiped or a substantially cubic body, the length of one side of the heating surface is a, the length of the other side of the heating surface substantially perpendicular to the one side is b, If the height in the direction substantially perpendicular to the heating surface is 1, the equivalent area S of the side surface is preferably expressed by the following formula (1).
S = 1 × (a + b) (1)

  In the correction step, the thermal diffusion coefficient is corrected by multiplying the thermal diffusion coefficient by a correction coefficient set according to the area ratio of the object to be heated. It is preferably set based on the correspondence relationship between the area ratio and the correction coefficient obtained in advance.

  Further, when the heated body is a laminated member in which a plurality of different plate-like members are laminated in the height direction, a thermal diffusion coefficient that characterizes the material of one plate-like member among the plurality of plate-like members. The height of each plate-like member is used as a thermal diffusion coefficient characterizing the object to be heated and according to the ratio of the thermal diffusion coefficient of each plate-like member to the heat diffusion coefficient of the one plate-like member. It is preferable to correct the thickness in each direction, and use the corrected total value as the height of the object to be heated.

The heated body is a laminated member in which n types of plate-like members B _m (m = 1, 2,... N) made of different materials are laminated in the height direction, and n types of plates one plate-like member the thermal diffusion coefficient alpha ₁ characterizing the material of B _1, wherein when used as a thermal diffusion coefficient characterizing the object to be heated, n kinds of plate-shaped members of each of the height of the Jo member B _m The total thickness in the direction is 1 _m (m = 1, 2,... N), and the thermal diffusion coefficient characterizing the material of each plate member is α _m (m = 1, 2,... N). ), _Where l _eq is the total value after correction, the l _eq is preferably represented by the following formula (2).

  In addition, this invention predicts the temperature time change of the said to-be-heated body at the time of heating the column-shaped to-be-heated body provided with two opposing surfaces from at least any one surface among the two opposing surfaces. A computer-executable program that characterizes the heated object according to an area ratio that represents a ratio of an area of the heating surface to an equivalent area of a side surface substantially perpendicular to the heating surface of the heated object. Using a procedure for correcting the coefficient, a one-dimensional heat conduction equation with the corrected thermal diffusion coefficient as a coefficient, the axis being the height direction of the heated object, and a boundary condition according to a predetermined heating condition, A procedure for predicting a temperature-time change of the heated object, and the equivalent area of the side surface is a length around the heating surface of the heated object and a height in a direction substantially perpendicular to the heating surface of the heated object. Of the object to be heated Also together to provide temperature prediction program.

According to the method for predicting the internal temperature of the heated object of the present invention, even if the heated object has a relatively large height in the direction substantially perpendicular to the heating surface, and the heat input / output from the side surface in the heat treatment is relatively large, It is possible to easily and accurately predict changes in temperature with time in the heated body.
For example, by setting the vulcanization process conditions in the vulcanization process based on the temperature change inside the heated object predicted by the method for predicting the internal temperature of the heated object, the optimum vulcanization conditions can be set. It becomes easy. Further, by performing the vulcanization treatment under the vulcanization conditions set as described above, the quality and stability of the vulcanized product produced by the vulcanization treatment are realized.

Hereinafter, a method for predicting an internal temperature of an object to be heated according to the present invention will be described in detail based on a preferred embodiment shown in the accompanying drawings.
FIG. 1 is a schematic configuration diagram of a temperature predicting device 10 (hereinafter referred to as device 10), which is an example of an internal temperature predicting device for an object to be heated, which implements the internal temperature predicting method for an object to be heated according to the present invention. .
The apparatus 10 is a rubber at a predetermined heating elapsed time in a vulcanization process of a bridge rubber support unvulcanized body 30 (hereinafter simply referred to as a rubber support 30) (see FIG. 2), which is a substantially columnar heated body. The temperature of the central portion of the support 30 is predicted with relatively high accuracy by a one-dimensional heat conduction equation.

The apparatus 10 represents the ratio of the area of the heating surface of the rubber bearing 30 to the equivalent area of the side surface substantially perpendicular to the heating surface of the rubber bearing 30 based on the shape data of the rubber bearing 30 input from input means (not shown). Equivalent area ratio calculating means 12 for calculating an equivalent area ratio of the rubber bearing 30;
According to the equivalent area ratio calculated by the equivalent area ratio calculating means 12, a correction coefficient setting means 14 for setting a correction coefficient k (the correction coefficient k will be described in detail later) and a correction coefficient setting means 14 are set. Using the correction coefficient k, the thermal diffusion coefficient correction means 15 for correcting the thermal diffusion coefficient described above, a one-dimensional heat conduction equation using the corrected thermal diffusion coefficient as a coefficient, and the heating condition of the rubber bearing 30 are A temperature information calculation unit 16 that performs a three-dimensional heat conduction analysis and calculates the temperature inside the rubber bearing 30 is provided. In addition, the apparatus 10 includes an input unit 18 that can accept instructions from the operator and various data. The input means 18 may be an input means such as a keyboard or a mouse that can input shape data in accordance with an operation by an operator, and shape data recorded on a predetermined recording medium such as a magnetic recording medium. It may be a predetermined reading means for reading. The apparatus 10 is a computer that includes a CPU 20 and a memory 22 therein, and each part functions by a program.

  FIG. 2 is a schematic configuration diagram illustrating the rubber support 30 and the vulcanization system 40 that vulcanizes the rubber support 30. The vulcanization system 40 sandwiches the upper and lower molds 42 for shaping the rubber support 30 from above and below, the side mold 44 for shaping the rubber support 30 from the side, and the upper and lower molds 42 from above and below. The heating plate 46 is pressed while heating the upper and lower molds 42, and the heating control unit 48 is connected to the heating plate 46 and controls the temperature of the heating plate 46.

The heating control unit 48 is connected to the heating plate 46 and adjusts the temperature of the heating plate 46. When the heating controller 48 adjusts the temperature of the heating plate 46, the upper and lower molds 42 are adjusted to a predetermined temperature, and the upper and lower surfaces of the rubber support 30 are adjusted to a predetermined temperature.
The heating control unit 48 can input heating conditions for heating the rubber bearing 30 to vulcanize. As the heating condition, the temperature condition of the upper and lower molds 42 with respect to the heating elapsed time from the start of heating is input. The heating control unit 48 controls the temperature of the heating plate 46 based on this heating condition, and adjusts the temperature of the heating surface (upper and lower surfaces in FIG. 2) of the rubber support 30.

  The apparatus 10 calculates and predicts the temperature inside the object to be heated during the vulcanization process (during the heat treatment) for the object to be heated such as a rubber bearing for a bridge that is vulcanized by the vulcanization system 40. . Each part of the apparatus 10 will be described in detail.

  The equivalent area ratio calculation means 12 calculates the equivalent area ratio of the rubber bearing 30 based on the shape data of the rubber bearing 30 input from the input means 18. Here, the equivalent area ratio refers to the ratio of the area of the heating surface to the equivalent area of the side surface substantially perpendicular to the heating surface of the rubber support 30.

FIG. 3 is a schematic diagram for explaining the shape and structure of the rubber bearing 30. The rubber bearing 30 has a substantially rectangular parallelepiped shape, and a rubber layer 32 having a thickness of T _m (m = 1 to 5) and a metal layer 34 having a thickness of U _m (m = 1 to 6) are alternately stacked. It has a multilayered structure.

In the case of heating a rubber bearing having a multilayer laminated structure in this way, the equivalent area ratio calculating means 12 firstly determines the thickness of the metal layer 34 so that the heat conduction in the metal layer 34 can be assumed to be equivalent to the rubber layer in terms of heat conduction. Is converted. Then, using the converted thickness of the metal layer 34, an equivalent rubber thickness l _eq is calculated when the thermal diffusion coefficient α _RB of the rubber layer 32 is used as the thermal diffusion coefficient of the rubber bearing 30 as a whole.
Specifically, the thermal diffusion coefficient specific to the material of the rubber layer 32 is α _RB , the thermal diffusion coefficient specific to the material of the metal layer 34 is α _st , and the total thickness of the rubber layer 32 is L _RB (= T ₁ + T ₂ +... T ₅ ), and the total thickness of the metal layer 34 is L _st (= U ₁ + U ₂ +... U ₅ ), the equivalent rubber thickness l _eq is _expressed by the following formula (3 ).

The equivalent area ratio calculation means 12 calculates an equivalent area ratio A of the rubber bearing 30 based on the equivalent rubber thickness l _eq . Specifically, using the two sides a and b of the heating surface of the rubber bearing 30 and the above-described equivalent rubber thickness l _eq , the equivalent area ratio A of the rubber bearing 30 is calculated based on the following formula (4). To do.
A = [(a × b)] / [l _eq × (a + b)] (4)

The correction coefficient setting means 14 is in accordance with the equivalent area ratio A of the rubber bearing 30 based on a correction curve (correction function) representing the correspondence between the equivalent area ratio and the correction coefficient derived by the correction curve derivation system 50 described later. A correction coefficient k is set. In the thermal diffusion coefficient correction means 15, the correction coefficient k set by the correction coefficient setting means 14 is multiplied by the thermal diffusion coefficient α _RB specific to the material of the rubber layer and used as the thermal diffusion coefficient of the rubber support 30 as a whole. The thermal diffusion coefficient α _RB of the rubber layer 32 is corrected.

The temperature information calculation means 16 has the corrected thermal diffusion coefficient kc obtained by correcting the thermal diffusion coefficient α _RB by the thermal diffusion coefficient correction means 15 as a coefficient, and the height direction of the rubber bearing 30 ( A one-dimensional heat conduction analysis is performed using a one-dimensional heat diffusion equation centered on the vertical direction in FIG. The temperature information calculation means 16 calculates the temperature information of the central portion of the rubber bearing 30 (the middle between the upper surface and the lower surface, which is the heating surface) at the time when the desired heating time has elapsed, by this one-dimensional heat conduction analysis. The calculated temperature information of the central portion is output to a display device such as a monitor or a recording medium such as a paper surface, for example.

FIG. 4 is a schematic configuration diagram for explaining the correction curve deriving system 50 for deriving the above-described correction curve (correction function).
The correction curve derivation system 50 includes internal temperature measurement data of each of the plurality of reference rubber bearings 70 having different equivalent area ratios, and internal temperature analysis data that is a solution of a plurality of one-dimensional heat conduction equations having different thermal diffusion coefficients. Based on the above, a correction curve serving as a reference for setting the correction coefficient in the apparatus 10 is derived.
The correction curve deriving system 50 is provided at the center of the reference rubber bearing 70, and includes a temperature sensor 47 that detects temperature information of the center of the reference rubber bearing 70, and a reference rubber bearing 70 detected by the temperature sensor 47. It comprises a temperature information acquisition unit 49 that acquires temperature information and a correction coefficient deriving device 51. The correction coefficient derivation device includes an input unit 52, an internal temperature analysis unit 54, an approximate analysis information extraction unit 56, a reference correction coefficient calculation unit 58, a correction curve derivation unit 60, the operation of each unit, and the operation of the entire device. A control unit 62 that controls the sequence, a CPU 64, and a memory 66 are included.

The correction curve deriving system 50 derives a correction curve serving as a reference for setting a correction coefficient in the apparatus 10 prior to the calculation of the temperature inside (center portion) of the rubber bearing 30 by the apparatus 10. The correction curve deriving system 50 acquires information on the internal temperature change when each of the plurality of reference rubber supports 70 whose equivalent area ratio A is known in advance is heated using the heating system 40 under predetermined heating conditions. In addition, a one-dimensional heat conduction analysis is performed for a plurality of one-dimensional heat diffusion equations obtained by variously changing the heat diffusion coefficient. From the results of these one-dimensional heat conduction analyses, the above correction coefficient is derived and output.
The reference rubber bearing 70 has the same laminated structure as that of the rubber bearing 30 (that is, the laminated state of the metal layer and the rubber layer is substantially the same), and the equivalent area ratio is different (that is, the area of the heating surface or the equivalent of the side surface) It is an unvulcanized rubber bearing.

  During the vulcanization process by the heating system 40, the temperature near the center of the reference rubber bearing 70 is detected by the temperature sensor 47 and output as the internal temperature actual measurement data by the temperature information acquisition unit 49, and the correction curve deriving device 51. Is input. The correction curve deriving device 51 also receives an equivalent area ratio of each of a plurality of reference rubber bearings known in advance from the input unit 52, and the internal temperature actual measurement information input to the correction curve deriving device 51 is The internal temperature measurement information is stored in the memory 66 in association with the equivalent area ratio data of the reference rubber bearing. In addition, the heating condition in the vulcanization processing in the heating system 40 is also input from the input unit 52, and the memory 66 also stores this heating condition.

The control unit 62 of the correction function deriving device 51 controls the operation of each unit of the correction function deriving device 51. The control unit 62 also assigns the value of the thermal diffusion coefficient in the one-dimensional heat conduction equation. Here, the allocation refers to setting various values of the thermal diffusion coefficient in the one-dimensional heat conduction equation.
The internal temperature analysis unit 54 performs a one-dimensional heat conduction analysis on each of the one-dimensional heat conduction equations using each of the heat diffusion coefficients assigned by the control unit 62 as a coefficient with the above-described heating condition as a boundary condition. The internal temperature information of the rubber bearing at the time when the heating time has elapsed is calculated. Temperature information inside the reference rubber bearing 70, which is an analysis result of each one-dimensional heat conduction equation, is stored in the memory 66.

  The approximate analysis information extraction unit 56 calculates the internal temperature analysis information calculated by the internal temperature analysis unit 54 and stored in the memory 66, and is an analysis result of each one-dimensional heat conduction equation using various thermal diffusion coefficients, 66 is compared with the measured internal temperature data of each reference rubber support when the reference rubber support is vulcanized using the vulcanization system 40 under predetermined vulcanization conditions. The internal temperature analysis data closest to is extracted.

The reference correction coefficient calculation unit 58 is a reference correction coefficient k that is a ratio of the thermal diffusion coefficient of the one-dimensional heat conduction equation obtained from the extracted internal temperature analysis data to the thermal diffusion coefficient α _RB of the rubber layer of the rubber bearing 30 for bridges. 'Is calculated for each extracted internal temperature analysis information (that is, for each actually measured internal temperature data).

  The correction curve deriving unit 60 derives a correction curve by creating a scatter diagram representing the correlation between the equivalent area ratio of the reference rubber bearing 70 and the extracted thermal diffusion coefficient. The scatter diagram and the approximate function created by the correction curve deriving unit 60 will be described in detail later.

Hereinafter, a method for predicting the temperature of the rubber bearing 30 during the vulcanization process performed using the apparatus 10 will be described. FIG. 5 is a flowchart of an example of the method for predicting temperature information of an object to be heated according to the present invention, which is performed using the apparatus 10.
First, an equivalent area ratio is calculated and obtained for the rubber bearing 30 (step S100). The equivalent area ratio is calculated using (Equation 3) and (Equation 4) in the equivalent area ratio calculation means 12 based on the dimension data of the rubber bearing 30 input from the input means 18 of the apparatus 10 as described above. It is done.

The equivalent area ratio calculation unit 12 sends the calculated equivalent area ratio to the correction coefficient setting unit 14.
The correction coefficient setting means 14 derives a correction coefficient for correcting the thermal diffusion coefficient in the one-dimensional heat conduction equation according to the transmitted equivalent area ratio based on a correction curve derived in advance.

The correction curve used in calculating the correction coefficient is derived at least by the correction curve derivation system 50 shown in FIG. 2 prior to the derivation of the correction coefficient.
Here, the derivation of such a correction curve will be described in detail. FIG. 6 is a flowchart of correction curve derivation performed by the correction curve derivation system 50 shown in FIG.
In the correction curve derivation system 50, the vulcanization system 40 is used to perform the vulcanization process by actually heating a plurality of reference rubber supports 70 having different equivalent area ratios.

  First, a reference rubber bearing 70 having an equivalent area ratio different from that of the rubber bearing 30 is arranged at a predetermined position of the vulcanizing system 40. In the vulcanization system 40, the reference rubber support 70 is heated under the same vulcanization conditions (heating conditions) as the vulcanization conditions of the rubber support 30 to perform the vulcanization process. At this time, information on the internal temperature of the reference rubber bearing 70 during vulcanization acquired by the temperature information acquisition unit 49 is sequentially stored in the memory 66 (step S200). First, in this way, the memory 66 of the correction curve deriving device 50 stores measured data of changes in internal temperature when a plurality of reference rubber bearings having different equivalent area ratios are heated.

Next, the value of the thermal diffusion coefficient in the one-dimensional heat conduction equation is set (step S202). The thermal diffusion coefficient is set by assigning various thermal diffusion coefficient values by the control unit 62. Then, the one-dimensional heat conduction equations having various assigned thermal diffusion coefficients as coefficients are analyzed, the analysis result of the internal temperature of the reference rubber bearing is calculated, and the internal temperature analysis information is stored in the memory 66. (Step S204). When a one-dimensional heat conduction equation using this heat diffusion coefficient is analyzed and the analysis result is calculated for one heat diffusion coefficient, the heat conduction analysis by the one-dimensional heat conduction equation is performed for all assigned heat diffusion coefficients. It is determined whether it has been carried out (step S206), and if this determination is negative, the thermal diffusion coefficient is changed, and the internal temperature analysis information is calculated again and stored in the memory 66.
The correction function deriving device 50 performs a one-dimensional heat conduction analysis for each of a plurality of one-dimensional heat conduction equations having different heat diffusion coefficients. Then, the analysis result of the internal temperature change is acquired from each of the plurality of one-dimensional heat conduction equations, and the acquired internal temperature analysis information is stored in the memory 66.

Next, in the approximate analysis information extraction unit 56, the internal temperature analysis data stored in the memory 66 and the internal temperature actual measurement data stored in the memory 66 are compared and referenced, and each of the plurality of internal temperature actual measurement data is the most. Approximated internal temperature analysis information (approximate internal temperature analysis information) is extracted (step S208). Then, the reference correction coefficient calculation unit 58 calculates on the thermal diffusion coefficient alpha _RB, extracted reference approximating internal temperature analysis information is the ratio of the thermal diffusion coefficient of the one-dimensional heat conduction equation derived correction coefficient k ', respectively (step S210).

  Next, in the correction curve deriving unit 60, each of the reference rubber bearings 70 for obtaining the reference correction coefficient k ′ in each of the plurality of approximate internal temperature analysis information and the internal temperature actual measurement data approximated by each of the plurality of approximate internal temperature analysis information. A scatter diagram representing the correspondence with the equivalent area ratio is created. Based on this scatter diagram, a correction curve (correction function) for calculating a correction coefficient according to the equivalent area ratio is derived (step S210).

  FIG. 7 is a scatter diagram showing the correspondence between the equivalent area ratio and the reference correction coefficient k ′ created by the correction curve derivation system shown in FIG. 4 and a correction curve derived from this scatter diagram. Such a correction curve derived by the correction curve deriving system 50 is sent to the correction coefficient setting means 14. Such a correction curve is performed prior to step S102 (correction of thermal diffusion coefficient) in the flowchart of FIG. 5 and stored in the correction coefficient setting means 14.

After calculating the equivalent area ratio of the rubber bearing 30 in step S100, the thermal diffusion coefficient (the thermal diffusion coefficient α _RB of the rubber layer 32 as described above) in the one-dimensional heat conduction equation for calculating the internal temperature of the rubber bearing 30 is calculated. A correction coefficient for correction is set. This correction coefficient is set in the correction coefficient setting means 14 according to the value of the equivalent area ratio calculated by the equivalent area ratio calculation means 12 based on the correction curve shown in FIG.

Next, the thermal diffusion coefficient correction means 15 corrects the thermal diffusion coefficient α _RB of the rubber layer 32 representing the thermal diffusion coefficient of the rubber support 30 using the correction coefficient described above (step S104). Then, each one-dimensional heat conduction equation using the corrected thermal diffusion coefficient as a coefficient is analyzed, and the temperature of the central portion of the rubber bearing 30 is obtained as described above (step S104).

  In the apparatus 10, the internal temperature of the rubber bearing 30 during the vulcanization process (that is, during heating) is thus obtained by one-dimensional heat conduction analysis using the one-dimensional heat conduction equation. In the one-dimensional heat conduction equation used in the apparatus 10, the thermal diffusion coefficient is corrected based on the equivalent area ratio that is the ratio of the area of the heating surface to the side surface substantially perpendicular to the heating surface. In this way, by using the corrected thermal diffusion coefficient corrected according to the equivalent area ratio that also takes into account the influence of the side surface substantially perpendicular to the heating surface, the inflow of heat from the side surface substantially perpendicular to the heating surface, and the side surface Highly accurate one-dimensional heat conduction analysis that reflects the effect of heat outflow on

  Thus, based on the internal temperature analysis data about the rubber bearing 30 calculated by the highly accurate one-dimensional heat conduction analysis, the state of vulcanization inside the rubber bearing 30 when heated for a predetermined time is grasped. be able to. The rubber bearing 30 is a rubber bearing unvulcanized body for a bridge and is a relatively large structure. In the rubber support unvulcanized body for bridges, even when the two opposite heating surfaces are heated uniformly, the temperature at the center part is particularly difficult to increase due to the influence of heat flow from the side surfaces. When predicting the internal temperature for such a rubber bearing unvulcanized body for bridges, only using the thermal diffusion coefficient based on the material of the rubber bearing unvulcanized body does not reflect the effect of heat outflow from the side, The internal temperature cannot be predicted accurately. According to the method for predicting the internal temperature of an object to be heated according to the present invention, an accurate internal temperature reflecting the influence of heat outflow from the side surface can be easily predicted in a short time by using a one-dimensional heat conduction equation. . By setting the heating state based on the vulcanization state of the rubber bearing 30 thus predicted, it is possible to easily and accurately search for the optimum vulcanization condition (heating condition) desired in a short time. Is possible.

In the said embodiment, the temperature change of the center part of the rubber bearing 30 which is a multilayer laminated structure was calculated | required. In the method for predicting an internal temperature change of an object to be heated according to the present invention, the object to be heated for obtaining an internal temperature change is not limited to a multilayer laminated structure. For example, an unvulcanized body of a rubber product, such as a solid fender, all made of the same material, can be used as a heated body, and the temperature change inside the unvulcanized rubber product can be obtained. is there. At this time, the equivalent area ratio may be determined according to the actual length of the periphery of the unvulcanized rubber product heating surface and the height substantially perpendicular to the heating surface. For example, when the length of one side of the heating surface of the rubber product unvulcanized body is a, the length of the other side substantially perpendicular to the one side is b, and the height substantially perpendicular to the heating surface is l, in this case The equivalent area ratio A may be expressed by the following equation (4).
A = [m × (a × b)] / [l × (a + b)] (m is a constant) (4)
The to-be-heated body in this invention should just be columnar shape, and the shape of a heating surface and the layer structure of a height direction are not specifically limited.

In addition, it is very troublesome to obtain the temperature change inside the multilayer laminated structure using a one-dimensional heat conduction equation. In the above embodiment, the thermal diffusion coefficient α _RB of the rubber layer 32 is used as the thermal diffusion coefficient of the rubber support 30 as a whole. Then, the equivalent rubber thickness is calculated by converting the thickness of the metal layer 34 so that the heat conduction in the metal layer 34 can be assumed to be equivalent to the rubber layer in terms of heat conduction, and the equivalent aspect ratio is calculated according to the equivalent rubber thickness. Was calculated. As a result, the internal temperature change of the rubber bearing 30 can be simplified and simplified by a simple one-dimensional heat conduction equation with one thermal diffusion coefficient as a coefficient centering on the height direction of the rubber bearing 30 (vertical direction in FIG. 2). It is possible to obtain accurately. In the method for predicting the internal temperature of the heated body of the present invention, the internal temperature of the heated body can be predicted simply and accurately even if the heated body has a multilayer laminated structure.

  In the above-described embodiment, the temperature of the central portion when the rubber support for a bridge is heated from the two opposing heating surfaces is determined with the rubber support for a bridge as a heated body. The method for predicting the internal temperature of the heated body of the present invention is not limited to the heated body being a rubber bearing for a bridge. Moreover, it is not limited to heating a to-be-heated body from the two heating surfaces which oppose, Even when it heats from one surface, the internal temperature of a to-be-heated body can be estimated simply and correctly with a one-dimensional heat conduction equation.

  As mentioned above, although the internal temperature information prediction method of the to-be-heated body of this invention was demonstrated in detail, this invention is not limited to the said Example, In the range which does not deviate from the summary of this invention, various improvement and change are performed. Of course.

It is a schematic block diagram of the temperature prediction apparatus 10 which is an example of the internal temperature prediction apparatus of the to-be-heated body which implements the internal temperature prediction method of the to-be-heated body of this invention. It is a schematic block diagram explaining the vulcanization system which heats and vulcanizes the rubber bearing unvulcanized body which is an example of the to-be-heated body in this invention, and a rubber bearing unvulcanized body. It is the schematic explaining the shape and structure of the rubber bearing unvulcanized body which is an example of the to-be-heated body in this invention. It is a schematic block diagram explaining an example of the correction curve derivation system which derives the correction curve used in the internal temperature prediction method of the to-be-heated body by the temperature prediction apparatus. It is a flowchart figure of an example of the internal temperature prediction method of the to-be-heated body of this invention. FIG. 5 is a flowchart of correction curve derivation performed by the correction curve derivation system shown in FIG. 4. FIG. 5 is a scatter diagram showing a correspondence between an equivalent area ratio of a reference rubber-supported unvulcanized body and a reference correction coefficient k ′ created by the correction curve derivation system shown in FIG. 4.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Temperature prediction apparatus 12 Equivalent area ratio calculation means 14 Correction coefficient setting means 15 Thermal diffusion coefficient correction means 16 Temperature information calculation means 18 Input means 20 CPU
22 Memory 30 Rubber support unvulcanized body 32 Rubber layer 34 Metal layer 40 Vulcanization system 42 Upper and lower mold 44 Side mold 46 Heat plate 47 Temperature sensor 48 Heating control unit 49 Temperature information acquisition unit 50 Correction curve derivation system 52 Input unit 54 Inside Temperature analysis unit 56 Approximation analysis information extraction unit 58 Reference correction coefficient calculation unit 60 Approximate function derivation unit 62 Control unit 64 CPU
66 Memory 70 Rubber bearing for reference

Claims (6)

A method of predicting a temperature-time change of the heated object when a columnar heated object having two opposed surfaces is heated from at least one of the two opposed surfaces,
A correction step of correcting a thermal diffusion coefficient characterizing the heated object according to an area ratio representing a ratio of the area of the heated surface to an equivalent area of a side surface substantially perpendicular to the heated surface of the heated object;
Using the corrected thermal diffusion coefficient as a coefficient, the one-dimensional heat conduction equation with the height direction of the heated object as an axis, and the boundary condition according to a predetermined heating condition, the temperature of the heated object A prediction step for predicting a time change,
The equivalent area of the side surface is determined according to the length of the periphery of the heating surface of the heated body and the height of the heated body in a direction substantially perpendicular to the heating surface. Prediction method. The heated object is a substantially rectangular parallelepiped or a substantially cube.
When the length of one side of the heating surface is a, the length of the other side of the heating surface substantially perpendicular to the one side is b, and the height in the direction substantially perpendicular to the heating surface of the heated object is l,
The method of predicting the internal temperature of the heated object according to claim 1, wherein the equivalent area S of the side surface is expressed by the following formula (1).
S = 1 × (a + b) (1) The correction step is to correct the thermal diffusion coefficient by multiplying the thermal diffusion coefficient by a correction coefficient set according to the area ratio of the heated object,
3. The method for predicting the internal temperature of a heated object according to claim 1, wherein the correction coefficient is set based on a correspondence relationship between an equivalent area ratio and a correction coefficient that are obtained in advance. When the heated body is a laminated member in which a plurality of different plate-like members are laminated in the height direction,
A thermal diffusion coefficient that characterizes the material of one plate-like member among the plurality of plate-like members is used as a thermal diffusion coefficient that characterizes the heated object,
And according to the ratio of the thermal diffusion coefficient of each plate-like member to the thermal diffusion coefficient of said one plate-like member, the thickness in the height direction of each plate-like member is corrected, respectively, and the corrected total value Is used as the height of the object to be heated, The internal temperature prediction method for the object to be heated according to any one of claims 1 to 3. The heated body is a laminated member in which n types of plate-like members B _m (m = 1, 2,... N) made of different materials are laminated in the height direction,
When the thermal diffusion coefficient α ₁ characterizing the material of _one plate-like member B ₁ among the n types of plate-like members B _m is used as the thermal diffusion coefficient characterizing the object to be heated,
The total thickness in the height direction of each of the n types of plate-like members is 1 _m (m = 1, 2,... n), and the thermal diffusion coefficient characterizing the material of each plate-like member is α _m (M = 1, 2,..., N), and assuming that the total value after the correction is l _eq ,
5. The method for predicting the internal temperature of a heated object according to claim 4, wherein the l _eq is expressed by the following formula (2).

A program for causing a computer to predict a temperature-time change of the heated object when a columnar heated object having two opposed surfaces is heated from at least one of the two opposed surfaces. There,
A procedure for correcting a thermal diffusion coefficient characterizing the heated object according to an area ratio representing a ratio of the area of the heated surface to an equivalent area of a side surface substantially perpendicular to the heated surface of the heated object;
Using the corrected thermal diffusion coefficient as a coefficient, the one-dimensional heat conduction equation with the height direction of the heated object as an axis, and the boundary condition according to a predetermined heating condition, the temperature of the heated object Has a procedure to predict time changes;
The equivalent area of the side surface is determined according to the length of the periphery of the heating surface of the heated body and the height of the heated body in a direction substantially perpendicular to the heating surface. Prediction program.

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