Crosslinking reaction simulation device and internal bubble estimation device

Abstract

A cross-linking reaction simulation device (1) is provided with a storage unit (2), a thermal conductivity analysis unit (3) for performing thermal conductivity analysis during a cross-linking reaction of a polymer part (12) of a target workpiece model (WM), and a cross-linking reaction analysis unit (4) for analyzing the reaction rate of the cross-linking reaction of the polymer part (12), the storage unit (2) stores a target workpiece model (WM) having a polymer unit (12), an equivalent reaction amount calculation model (EM), and a slope coefficient (SC) set on the basis of the degree of progress of the crosslinking reaction of the polymer unit (12). The temperature acquisition unit acquires the temperature at each time as the result of thermal conductivity analysis for each unit of a polymer part (12) of a target workpiece model (WM) in a cross-linking reaction; and a reaction rate calculation processing unit (41) that calculates the equivalent reaction amount of the polymer part (12) at each time point, and calculates the reaction rate of the cross-linking reaction of the polymer part (12) on the basis of the calculated equivalent reaction amount.

Description

Technical Field

[0001] The present disclosure relates to a cross-linking reaction simulation device and an internal bubble estimation device. Background Art

[0002] In the past, the physical properties of chemical substances have been improved by subjecting polymers to crosslinking reactions. As such a polymer, rubber can be exemplified. In rubber, a three-dimensional grid-like crosslinking structure is formed between rubber molecular chains or in their molecular chains by adding sulfur, other crosslinking agents, vulcanization accelerators, etc. to the raw rubber and heating the rubber.

[0003] As a technique for estimating the vulcanization degree of rubber, that is, the reaction rate of the crosslinking reaction of rubber, there is a technique described in Non-Patent Document 1. The technique estimates the vulcanization degree from the temperature history of rubber based on the Arrhenius equation and estimates appropriate vulcanization conditions (mold temperature, vulcanization time).

[0004] Prior art literature

[0005] Non-patent literature

[0006] Non-patent document 1: Arimatsu Toshio, "The Reality of Vulcanization Process Design", Journal of the Rubber Association of Japan, Vol. 59, No. 3, (1986) Summary of the invention

[0007] Problems to be solved by the invention

[0008] However, the above-mentioned techniques are not sufficiently accurate and therefore cannot estimate the reaction rate of the cross-linking reaction of rubber with high accuracy.

[0009] In addition, when using the above-mentioned technology, it is preferred to estimate the temperature history of the polymer during the crosslinking reaction as accurately as possible. However, it is difficult to estimate the temperature history of the polymer during the crosslinking reaction. The following is an explanation.

[0010] For example, when a polymer is placed in a mold and a cross-linking reaction is carried out, the local temperature of the mold can be managed and measured. However, the heat conduction from the mold to the polymer, and then the heat conduction inside the polymer, is affected by the shape of the polymer, the composition of the filler contained in the polymer, and the like. Therefore, the temperature history of the rubber is different for each product when the shape of the product is different. Furthermore, even for products of the same shape, when the composition of the filler is different, each product with a different composition is also different. In particular, when the thermal diffusivity of the polymer is different from that of the filler, it is very difficult to estimate the temperature history of the polymer.

[0011] In addition, rubber products are made by molding and vulcanization, but the gas originally dissolved in the rubber or the gas generated by the vulcanization reaction dissolves in the rubber under the high temperature and high pressure conditions of vulcanization. When the mold is opened, the pressure applied to the rubber decreases, and the solubility of the gas in the rubber decreases, so bubbles are generated in the rubber when the vulcanization is not fully progressed. If the vulcanization time is extended and the vulcanization is allowed to proceed, bubbles will not be generated.

[0012] In the actual vulcanization of products, the total amount of heat received is different due to the different temperature rise history in the product interior at different distances from the mold as a heat source, and the vulcanization progress is different even with the same vulcanization time. Therefore, the latest vulcanized part needs to be vulcanized until no bubbles are seen. The vulcanization degree of the rubber of the latest vulcanized part at the time of opening the mold when the vulcanization time is formed until no bubbles are seen in the latest vulcanized part is called the foaming point vulcanization degree (hereinafter referred to as the foaming point). In order to determine the vulcanization time of the product, it is important to estimate the foaming point.

[0013] However, according to the above-mentioned technology, the foaming point cannot be estimated. Therefore, according to the prior art, there is a problem that the vulcanization time of the product cannot be predicted with high accuracy. This problem is not limited to rubber, and may also become a problem in the cross-linking reaction of polymers.

[0014] The present disclosure has been made in view of such a background, and an object of the present disclosure is to provide a cross-linking reaction simulation device and an internal bubble estimating device that can solve any of the above-mentioned problems.

[0015] Means used to solve problems

[0016] One embodiment of the present disclosure is a cross-linking reaction simulation device, comprising:

[0017] a storage unit that stores data used in the simulation;

[0018] a thermal conductivity analysis unit that performs thermal conductivity analysis during a cross-linking reaction of a polymer portion of a target workpiece model; and

[0019] A cross-linking reaction analysis unit is used to analyze the reaction rate of the cross-linking reaction of the polymer part using the result of the thermal conductivity analysis, wherein:

[0020] The storage unit stores:

[0021] The target workpiece model has the polymer portion configured to include a base polymer;

[0022] an equivalent reaction amount calculation model, which defines the equivalent reaction amount as a ratio of the reaction amount of the cross-linking reaction at the target reaction temperature for the target reaction time to the reaction amount of the cross-linking reaction at the reference reaction temperature for the reference reaction time, and is defined as including a slope coefficient representing the slope of the Arrhenius plot; and

[0023] The slope coefficient is set according to the progress of the cross-linking reaction of the polymer part,

[0024] The cross-linking reaction analysis unit comprises:

[0025] a temperature acquisition unit that acquires the temperature at each time point of each unit of the polymer portion of the target workpiece model in a cross-linking reaction as a result of the thermal conductivity analysis; and

[0026] A reaction rate calculation processing unit calculates the equivalent reaction amount of the polymer portion at each moment based on the acquired temperature at each moment of each unit of the polymer portion in the cross-linking reaction, the equivalent reaction amount calculation model, and the slope coefficient corresponding to the progress of the cross-linking reaction at the target moment, and calculates the reaction rate of the cross-linking reaction of the polymer portion based on the calculated equivalent reaction amount.

[0027] Another embodiment of the present disclosure is a cross-linking reaction simulation device, comprising:

[0028] A storage unit that stores data used in the simulation; and

[0029] A thermal conductivity analysis unit performs thermal conductivity analysis of a polymer portion of a target workpiece model during a crosslinking reaction, wherein:

[0030] The storage unit stores:

[0031] Forming die model;

[0032] a target workpiece model having the polymer portion configured to include a base polymer and carbon black; and

[0033] thermal diffusivity characteristics, which represent the relationship between the mass ratio of the carbon black to the base polymer and the thermal diffusivity of the polymer portion,

[0034] The thermal conductivity analysis unit comprises:

[0035] a condition input unit for inputting a mass ratio of the carbon black to the base polymer in the target workpiece model and a temperature condition of the molding die model;

[0036] a polymer thermal diffusivity determination unit that determines a polymer thermal diffusivity as a thermal diffusivity of the polymer portion of the target workpiece model based on the mass ratio input by the condition input unit and the thermal diffusivity characteristics stored in the storage unit; and

[0037] An analysis unit performs a thermal conductivity analysis using the polymer thermal diffusivity determined by the polymer thermal diffusivity determination unit and the temperature condition stored in the storage unit in a state where the target workpiece model is arranged in the molding die model.

[0038] Another aspect of the present invention is an internal bubble estimation device, which is applied to a cross-linking reaction process. In the cross-linking reaction process, after a polymer portion of a target workpiece model is subjected to a cross-linking reaction in a molding die model, the molding die model is demolded. The internal bubble estimation device estimates generation of bubbles inside the polymer portion of the target workpiece model accompanying demolding of the molding die model, wherein:

[0039] The internal bubble estimation device comprises:

[0040] a storage unit storing a cross-linking reaction curve defining a relationship between an elapsed time from the start of a cross-linking reaction and a torque, the torque being a value corresponding to a degree of progress of a cross-linking reaction in the polymer portion of the target workpiece model and being measurable by a cross-linking reaction characteristic tester using a test target polymer material corresponding to the polymer portion;

[0041] a reaction rate acquisition unit that acquires a reaction rate of a cross-linking reaction of the polymer portion of the target workpiece model;

[0042] a torque calculation unit that calculates the torque corresponding to the acquired reaction rate based on the reaction rate acquired by the reaction rate acquisition unit and the cross-linking reaction curve stored in the storage unit; and

[0043] An estimating unit estimates generation of bubbles inside the polymer portion of the target workpiece model based on the torque during mold release.

[0044] Effects of the Invention

[0045] According to one embodiment of the present disclosure, the equivalent reaction amount of the polymer part at each moment is calculated based on the slope coefficient corresponding to the progress of the cross-linking reaction at the target moment, and the reaction rate of the cross-linking reaction of the polymer part is calculated based on the calculated equivalent reaction amount. Thus, compared with the case where the reaction rate of the cross-linking reaction of the polymer part is calculated based on the equivalent reaction amount calculated without considering the progress of the cross-linking reaction, the reaction rate of the cross-linking reaction can be estimated with high accuracy.

[0046] According to another embodiment of the present disclosure, carbon black transfers heat more easily than the polymer part, so the mass ratio of carbon black has a greater influence on the thermal diffusivity of the polymer part. According to one embodiment of the present invention, the polymer thermal diffusivity, which is the thermal diffusivity of the polymer part of the target workpiece model, can be determined based on the mass ratio of carbon black to the base polymer. As a result, the temperature history of the polymer during the crosslinking reaction can be estimated with high accuracy.

[0047] According to another embodiment of the present disclosure, based on the torque that can be measured by a cross-linking reaction characteristic tester, the generation of bubbles inside the polymer part of the target workpiece model is estimated. When the pressure generated by the polymer part to suppress the bubbles is greater than the pressure that the bubbles want to expand, the generation of bubbles is suppressed. Therefore, by comparing the torque of the polymer part with the pressure that the bubbles of the polymer part want to expand, the foaming point can be predicted with high accuracy. Thus, the vulcanization time of the product can be estimated with high accuracy.

[0048] In addition, the reference numerals in parentheses described in the claims indicate the corresponding relationship with specific elements described in the embodiments described later, and do not limit the technical scope of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a block diagram showing the cross-linking reaction simulation device according to the first embodiment.

[0050] Figure 2 This is a diagram showing a state where a target workpiece model is arranged on a forming die model in the first embodiment.

[0051] Figure 3 It is a diagram showing a target workpiece model according to the first embodiment.

[0052] Figure 4 This is a flowchart showing the operation of the cross-linking reaction simulation device according to the first embodiment.

[0053] Figure 5 This is a diagram showing the change over time in temperature of each part in a state where the target workpiece model is arranged on the forming die model in the first embodiment.

[0054] Figure 6 This is a graph showing the measured values ​​and predicted values ​​of the temperature of the polymer portion in the prior art.

[0055] Figure 7 This is a graph showing the measured value and the predicted value of the temperature of the polymer portion in the first embodiment.

[0056] Figure 8 This is a graph showing the amount of change in thermal conductivity relative to the content of carbon black in the first embodiment.

[0057] Fig. 9 This is a diagram for explaining a state of an analysis mesh in a state where a target workpiece model is arranged in a forming die model in the first embodiment.

[0058] Fig.10 It is a schematic diagram which shows the structure of the vulcanization tester which concerns on 1st Embodiment.

[0059] Fig.11 FIG. 1 is a diagram for explaining a method of converting the torque measured by the vulcanization tester of the first embodiment into a reaction rate. Fig.11 (a) is a graph showing the change in torque relative to reaction time. Fig.11 (b) is a graph showing changes in reaction rate with respect to reaction time.

[0060] Fig.12 This is a diagram for explaining the calculation method of the slope coefficient in the cross-linking reaction analysis process according to the first embodiment.

[0061] Fig.13 This is a diagram for explaining the calculation method of the equivalent reaction amount in the cross-linking reaction analysis process according to the first embodiment.

[0062] Fig.14 This is a diagram for explaining a method of calculating the equivalent reaction amount from the equivalent reaction amount increase in the cross-linking reaction analysis process of the first embodiment.

[0063] Fig.15 This is a diagram for explaining the method of converting the equivalent reaction amount into the reaction rate in the cross-linking reaction analysis process according to the first embodiment.

[0064] Fig.16 This is a graph showing the measured values ​​and predicted values ​​of the reaction rate of the polymer part in the conventional technology.

[0065] Fig.17 This is a diagram for explaining a method of dividing a cross-linking reaction into different groups according to the degree of reaction progress and calculating activation energy for each group in the first embodiment.

[0066] Fig.18 This is a graph showing the measured values ​​and predicted values ​​of the reaction rate of the polymer part in the first embodiment.

[0067] Fig.19 This is a diagram for explaining a method of expressing the amount of change in reaction rate with respect to reaction time in the first embodiment.

[0068] Fig. 20 This is a diagram showing the amount of change in reaction rate with respect to reaction time in the first embodiment.

[0069] Fig.21 : is a graph showing the second function of the first embodiment.

[0070] Fig. 22 This is a diagram for explaining the state of the analysis mesh of the target workpiece model in the first embodiment.

[0071] Fig.23 This is a diagram showing a state where internal bubbles are generated in the polymer portion.

[0072] Fig.24 This is a graph showing the reaction rate at the foaming point in the cross-linking reaction, the reaction rate at the time of demolding, and the final reaction rate.

[0073] Fig.25 (a) is a graph showing the reaction rates at the bubble points of a plurality of samples. Fig.25 (b) is a graph showing the torque measured by a vulcanization tester at the foaming point of a plurality of samples.

[0074] Fig.26 This is a diagram for explaining the mechanism of suppressing internal bubbles.

[0075] Fig. 27 This is a heat map showing the reaction rate distribution of the polymer part in the first embodiment.

[0076] Fig.28 This is a diagram showing the amount of change in the elastic modulus of the target workpiece model in a direction perpendicular to the axis with respect to the response time when the mold temperature is low in the first embodiment.

[0077] Fig.29 This is a diagram showing the amount of change in the elastic modulus of the target workpiece model in a direction perpendicular to the axis relative to the response time when the mold temperature is medium in the first embodiment.

[0078] Fig.30 This is a diagram showing the amount of change in the elastic modulus of the target workpiece model in a direction perpendicular to the axis with respect to the response time when the mold temperature is high in the first embodiment.

[0079] Fig.31 This is a graph showing changes in the elastic modulus of the polymer portion and the state of generation of internal bubbles with respect to reaction time in the first embodiment.

[0080] Fig.32 This is a diagram visually showing the expected result of the generation of internal bubbles in the first embodiment. DETAILED DESCRIPTION

[0081] (First Embodiment)

[0082] 1. Configuration of the cross-linking reaction simulation device 1

[0083] 1-1. Overall structure of the cross-linking reaction simulation device 1

[0084] Reference Figure 1 The overall structure of the cross-linking reaction simulation device 1 of the first embodiment will be described. The cross-linking reaction simulation device 1 of this embodiment simulates a cross-linking reaction of cross-linking molecular chains of a base polymer.

[0085] The raw polymer is not particularly limited as long as the molecular chains can undergo cross-linking reaction with each other, and any polymer such as thermosetting resins such as phenolic resin, epoxy resin, melamine resin, urea resin, unsaturated polyester resin, alkyd resin, silicone resin, polyurethane, thermoplastic resins such as cross-linked polyethylene, cross-linked polypropylene, natural rubber, styrene-butadiene rubber, butadiene rubber, synthetic rubbers such as isoprene rubber, and elastomers can be appropriately selected. In this embodiment, a rubber containing natural rubber and synthetic rubber is used as a polymer. In addition, in the case of rubber, by heating in a state where a cross-linking agent such as sulfur is added, the molecular chains constituting the rubber are cross-linked, and a so-called vulcanization reaction occurs.

[0086] like Figure 1 As shown, the cross-linking reaction simulation device 1 includes a storage unit 2 , a thermal conductivity analysis unit 3 , a cross-linking reaction analysis unit 4 , a structure analysis unit 5 , an internal bubble estimation unit 6 (an example of an internal bubble estimation device), and a display unit 7 .

[0087] 1-2. Configuration of Storage Unit 2

[0088] The storage unit 2 stores data used in the simulation. The data includes a mold model MM, a target workpiece model WM, thermal conductivity analysis data TD used by the thermal conductivity analysis unit 3, crosslinking reaction analysis data RD used by the crosslinking reaction analysis unit 4, and internal bubble estimation data BD used by the internal bubble estimation unit 6.

[0089] Reference Figure 2 , the forming die model MM is described. Figure 2 As shown, the forming mold model MM is constructed to include a mold 10 and a hot plate 11 installed on the mold 10. The mold 10 includes a lower mold 10A located at the lower side and an upper mold 10B assembled from the upper side to the lower mold 10A. The hot plate 11 is constructed to include a lower hot plate 11A installed on the lower surface of the lower mold 10A and an upper hot plate 11B installed on the upper surface of the upper mold 10B. A lower cavity 100A opening upward is formed in the lower mold 10A. In addition, an upper cavity 100B opening downward is formed in the upper mold 10B. In a state where the lower mold 10A and the upper mold 10B are assembled, the target workpiece model WM is arranged in a space formed by the lower cavity 100A and the upper cavity 100B.

[0090] Reference Figure 3 , describe the object workpiece model WM. Figure 3 As shown, the object workpiece model WM has a polymer portion 12. The polymer portion 12 includes a raw polymer. Furthermore, the polymer portion 12 may also include additives such as antioxidants, carbon black, etc. The polymer portion 12 of this embodiment is configured to include a raw polymer and carbon black. The raw polymer is not particularly limited, and any material such as rubber, thermosetting resin, etc. can be appropriately selected. In this embodiment, the raw polymer is composed of rubber. The polymer portion 12 of this embodiment is a rubber portion configured to exert vibration-proof performance, and the object workpiece model WM is a model of a vibration-proof rubber device. However, the polymer portion 12 may also be a configuration including a thermosetting resin as a raw polymer, and may also be a configuration not including carbon black.

[0091] The polymer part 12 of this embodiment is formed into a cylindrical shape along the axis A extending in the up-down direction. An outer joining member 13 (an example of a joining member) formed into a cylindrical shape extending in the up-down direction is arranged on the outer periphery of the polymer part 12. The outer joining member 13 is made of metal, resin, or a composite of metal and resin. The outer joining member 13 of this embodiment is made of metal and is joined to the outer periphery of the polymer part 12. An inner joining member 14 (an example of a joining member) formed into a cylindrical shape extending in the up-down direction is arranged on the inner periphery of the polymer part 12. The inner joining member 14 is made of metal, resin, or a composite of metal and resin. The inner joining member 14 of this embodiment is made of metal and is joined to the inner periphery of the polymer part 12. The length dimension of the inner joining member 14 in the up-down direction is formed to be larger than the length dimension of the outer joining member 13 in the up-down direction. The upper surface and the lower surface of the polymer part 12 are formed into a concave shape. However, the shape of the polymer part 12 is not limited to the above shape. In addition, the target workpiece model WM may be configured not to include both or one of the outer joining member 13 and the inner joining member 14 .

[0092] Back to Figure 2 In a state where the target workpiece model WM is arranged in the forming die model MM, gaps 15 are formed between the forming die model MM and the outer joining member 13 and the inner joining member 14 .

[0093] Back to Figure 1The data TD for thermal conductivity analysis include: a thermal diffusivity characteristic TS, which represents the relationship between the mass ratio of carbon black to the raw polymer and the thermal diffusivity of the polymer portion 12; a contact heat transfer coefficient CH, which is the heat transfer coefficient between the forming mold model MM and the outer joining member 13 and the inner joining member 14 when the object workpiece model WM is configured in the forming mold model MM; an air heat transfer coefficient AC, which is the heat transfer coefficient of the air around the object workpiece model WM after the object workpiece model WM is demolded from the forming mold model MM; a temperature condition TC of the forming mold model MM, which is input from a condition input unit 30 described later; and an external air condition OC, which includes the air temperature around the object workpiece model WM after demolding.

[0094] The cross-linking reaction analysis data RD includes: an equivalent reaction amount calculation model EM, which defines the ratio of the reaction amount of the cross-linking reaction at the target reaction time at the target reaction temperature to the reaction amount of the cross-linking reaction at the reference reaction time at the reference reaction temperature as the equivalent reaction amount, and is defined as a slope coefficient representing the slope of the Arrhenius plot; and a slope coefficient SC, which is set according to the degree of progress of the cross-linking reaction of the polymer part 12. The cross-linking reaction analysis data RD also includes a first relationship data map DM1, a second relationship data map DM2, a first function F1, a second function F2, and a reference reaction curve RC described later.

[0095] The data BD for estimating internal bubbles includes a cross-linking reaction curve CC, which defines the relationship between the elapsed time from the start of the cross-linking reaction and the value corresponding to the degree of progress of the cross-linking reaction in the polymer part 12 of the target workpiece model WM, that is, the torque that can be measured using a test object polymer material equivalent to the polymer part 12 by a cross-linking reaction characteristic testing machine.

[0096] 1-3. Configuration of Thermal Conductivity Analysis Unit 3

[0097] The thermal conductivity analysis unit 3 performs thermal conductivity analysis of the polymer portion 12 of the target workpiece model WM during the crosslinking reaction. Figure 1 As shown, the thermal conductivity analysis unit 3 includes a condition input unit 30 , a polymer thermal diffusivity determination unit 31 , and an analysis unit 32 .

[0098] The condition input unit 30 inputs the mass ratio of carbon black to the raw material polymer in the target workpiece model WM and the temperature condition TC of the forming die model MM. The condition input unit 30 may be an input device such as a keyboard, a mouse, a trackball, a joystick, or an external storage medium such as a semiconductor memory or a hard disk memory.

[0099] The polymer thermal diffusivity determination unit 31 determines the polymer thermal diffusivity as the thermal diffusivity of the polymer portion 12 of the target workpiece model WM based on the mass ratio of carbon black input from the condition input unit 30 and the thermal diffusivity characteristics TS stored in the storage unit 2 .

[0100] The analysis unit 32 performs a thermal conductivity analysis of the polymer portion 12 of the target workpiece model WM during the crosslinking reaction using the polymer thermal diffusivity determined by the polymer thermal diffusivity determination unit 31 and the temperature condition TC stored in the storage unit 2 while the target workpiece model WM is arranged in the forming die model MM.

[0101] 1-4. Configuration of the cross-linking reaction analysis unit 4

[0102] The crosslinking reaction analysis unit 4 analyzes the reaction rate of the crosslinking reaction of the polymer portion 12 using the result of the thermal conductivity analysis by the thermal conductivity analysis unit 3. Figure 1 As shown, the cross-linking reaction analysis unit 4 includes a temperature acquisition unit 40 and a reaction rate calculation processing unit 41 .

[0103] The temperature acquisition unit 40 acquires the temperature of each cell of the polymer portion 12 of the target workpiece model WM in the cross-linking reaction at each time point as a result of the thermal conduction analysis by the thermal conduction analysis unit 3 .

[0104] The reaction rate calculation processing unit 41 calculates the equivalent reaction amount of the polymer part 12 at each moment based on the temperature of each unit of the polymer part 12 at each moment in the cross-linking reaction, the equivalent reaction amount calculation model EM, and the slope coefficient SC corresponding to the progress of the cross-linking reaction at the target moment, and calculates the reaction rate of the cross-linking reaction of the polymer part 12 based on the calculated equivalent reaction amount.

[0105] 1-5. Configuration of the structural analysis unit 5

[0106] The structural analysis unit 5 performs structural analysis using the reaction rate of the cross-linking reaction of the polymer part 12 analyzed by the cross-linking reaction analysis unit 4. Figure 1 As shown, the structure analysis unit 5 includes a temperature acquisition unit 50, a reaction rate acquisition unit 51, an elastic modulus allocation unit 52, and a characteristic acquisition unit 53. However, the temperature acquisition unit 50 may be omitted.

[0107] The temperature acquisition unit 50 acquires the temperature of each cell of the polymer portion 12 of the target workpiece model WM undergoing a cross-linking reaction at each time point as a result of the thermal conduction analysis by the thermal conduction analysis unit 3 .

[0108] The reaction rate acquisition unit 51 acquires the reaction rate of each unit of the polymer part 12 calculated by the reaction rate calculation processing unit 41 of the cross-linking reaction analysis unit 4 .

[0109] The elastic modulus allocating unit 52 allocates the elastic modulus according to the acquired reaction rate to the polymer portion 12 .

[0110] The characteristic acquisition unit 53 acquires the characteristics of the target workpiece model WM by performing structural analysis in a state where the elastic modulus is assigned to the polymer portion 12 .

[0111] 1-6. Configuration of Internal Bubble Estimation Unit 6

[0112] The internal bubble estimation unit 6 is used in a cross-linking reaction process in which the forming mold model MM is demolded after the polymer portion 12 of the target workpiece model WM undergoes a cross-linking reaction in the forming mold model MM. The internal bubble estimation unit 6 estimates the generation of internal bubbles in the polymer portion 12 of the target workpiece model WM accompanying the demolding of the forming mold model MM. Figure 1 As shown, the internal bubble estimating unit 6 includes a response rate acquiring unit 60 , a torque calculating unit 61 , and an estimating unit 62 .

[0113] The reaction rate acquisition unit 60 acquires the reaction rate of the cross-linking reaction of the polymer part 12 of the target workpiece model WM. The above reaction rate is the reaction rate at the time when the mold 10 is opened, that is, the time when the mold clamping pressure is released. In addition, when the polymer part 12 is rubber, the above reaction rate is also called the vulcanization degree at the time of demolding.

[0114] The torque calculation unit 61 calculates the torque (also referred to as the mold release torque) corresponding to the acquired reaction rate (reaction rate at mold release) based on the reaction rate acquired by the reaction rate acquisition unit 60 and the crosslinking reaction curve CC stored in the storage unit 2 .

[0115] The estimation unit 62 compares the torque (torque during demolding) calculated by the torque calculation unit 61 with the foaming point torque (described in detail below) calculated based on the foaming point vulcanization degree (described in detail below) of the polymer portion 12 to estimate whether bubbles are generated inside the polymer portion 12.

[0116] 1-7. Configuration of Display Unit 7

[0117] The display unit 7 displays a value obtained from the reaction rate according to the reaction time based on the analysis result of the crosslinking reaction analysis unit 4. In addition, the display unit 7 displays characteristics according to the temperature of the molding die model MM used in the crosslinking reaction of the polymer part 12 and the reaction time in the mold from the start of the crosslinking reaction to the demolding of the molding die model MM based on the result of the structural analysis of the structural analysis unit 5.

[0118] In addition, the display unit 7 displays the presence or absence of internal bubbles according to the temperature of the forming mold model MM and the reaction time in the mold from the start of the cross-linking reaction to the demolding of the forming mold model MM based on the estimation result of the internal bubble estimation unit 6. In addition, the display unit 7 displays the value obtained by the reaction rate corresponding to the temperature of the forming mold model MM and the reaction time in the mold from the start of the cross-linking reaction to the demolding of the forming mold model MM based on the analysis result of the cross-linking reaction analysis unit 4, together with the presence or absence of internal bubbles. In addition, the display unit 7 displays the characteristics corresponding to the temperature of the forming mold model MM and the reaction time in the mold from the start of the cross-linking reaction to the demolding of the forming mold model MM based on the result of the structural analysis of the structural analysis unit 5, together with the presence or absence of internal bubbles.

[0119] 2. Overall Operation of the Cross-linking Reaction Simulation Device 1

[0120] Reference Figure 4 The overall operation of the cross-linking reaction simulation device 1 according to the present embodiment will be described. However, the following description is an example of the operation of the cross-linking reaction simulation device 1, and the operation of the cross-linking reaction simulation device 1 is not limited to the following description.

[0121] When the crosslinking reaction simulation device 1 is activated, the thermal analysis process S1 is executed. The thermal analysis process S1 obtains the temperature at each time point for each unit of the polymer portion 12 of the target workpiece model WM in the crosslinking reaction. The details will be described later.

[0122] Next, a cross-linking reaction analysis process S2 is performed. In the cross-linking reaction analysis process S2, based on the temperature at each moment of each unit of the polymer portion 12 of the target workpiece model WM in the cross-linking reaction obtained as a result of the thermal conductivity analysis, the equivalent reaction amount calculation model EM, and the slope coefficient SC corresponding to the progress of the cross-linking reaction at the target moment, the equivalent reaction amount of the polymer portion 12 at each moment is calculated, and based on the calculated equivalent reaction amount, the reaction rate of the cross-linking reaction of the polymer portion 12 is calculated. The details will be described later.

[0123] Next, the structural analysis process S3 is executed. In the structural analysis process S3, the elastic modulus is allocated according to the reaction rate in each unit of the polymer part 12 calculated by the cross-linking reaction analysis unit 4, and the structural analysis is performed in a state where the elastic modulus is allocated to the polymer part 12, thereby acquiring the characteristics of the target workpiece model WM. The details will be described later.

[0124] Next, the internal bubble estimation process S4 is performed. In the internal bubble estimation process S4, based on the reaction rate of the polymer part 12 calculated by the cross-linking reaction analysis process and the cross-linking reaction curve CC stored in the storage unit 2, the torque corresponding to the reaction rate of the polymer part 12 is calculated, and based on the torque during demolding, the generation of internal bubbles inside the polymer part 12 of the target workpiece model WM is estimated. The details will be described later.

[0125] Next, display processing S5 is performed. In display processing S5, based on the estimation result of the internal bubble estimation unit 6, the presence or absence of internal bubble generation is displayed according to the temperature of the forming mold model MM and the reaction time in the mold from the start of the cross-linking reaction to the demolding of the forming mold model MM. In addition, based on the analysis result of the cross-linking reaction analysis unit 4, the value obtained by the reaction rate corresponding to the temperature of the forming mold model MM and the reaction time in the mold from the start of the cross-linking reaction to the demolding of the forming mold model MM is displayed together with the presence or absence of internal bubble generation. In addition, based on the result of the structural analysis of the structural analysis unit 5, the characteristics corresponding to the temperature of the forming mold model MM and the reaction time in the mold from the start of the cross-linking reaction to the demolding of the forming mold model MM are displayed together with the presence or absence of internal bubble generation.

[0126] When the display process S5 is completed, the operation of the cross-linking reaction simulation device 1 is completed.

[0127] 3. Thermal analysis processing S1

[0128] 3-1. Mass ratio of carbon black

[0129] Next, refer to Figure 2 as well as Figures 5 to 8 The details of the thermal conductivity analysis processing S1 are described below. Figure 2 As shown in the figure, in the state where the lower mold 10A and the upper mold 10B are combined, the outer bonding member 13 and the inner bonding member 14 are arranged in the space formed by the lower cavity 100A and the upper cavity 100B. Further, the raw polymer is injected into the space formed by the lower cavity 100A and the upper cavity 100B. After that, the molecular chain constituting the polymer part 12 is cross-linked in the mold 10.

[0130] like Figure 5As shown, the temperature of the hot plate 11 is set to be constant. The temperature of the mold 10 is set to the same temperature as that of the hot plate 11. The temperature of the polymer portion 12 during injection is lower than the set temperature of the mold 10. Therefore, the temperature of the mold 10 temporarily drops after the raw polymer is injected. Thereafter, the temperature of the mold 10 rises and becomes the same as the temperature of the hot plate 11. The temperature of the polymer portion 12 rises after being injected into the mold 10, and becomes the same as the temperature of the mold 10 after a sufficient period of time. The temperature of the inner joining member 14 and the outer joining member 13 can be the same as the outside air temperature in a state before being arranged in the mold 10, or can be preheated. When the temperature is the same as the outside air temperature, for example, it sometimes drops to around 0°C in winter. In addition, when preheated, the temperature can be raised to any temperature, for example, it can be raised to around 100°C. After the inner joining member 14 and the outer joining member 13 are arranged in the mold 10, the temperature of the inner joining member 14 and the outer joining member 13 rises due to heat conduction from the mold 10, and further rises after the raw polymer is injected, and becomes the same as the temperature of the mold 10 after sufficient time has passed.

[0131] like Figure 5 As shown, it takes a certain amount of time for the temperature of the polymer part 12 to reach the temperature of the hot plate 11 and the mold 10 and reach an equilibrium state. In order to calculate the unsteady process until reaching the equilibrium state, the following formula (1) is used. Formula (1) is a so-called unsteady heat conduction equation.

[0132] [Number 1]

[0133]

[0134] in,

[0135] t: time variable

[0136] x: position variable

[0137] T: Temperature

[0138] α: Thermal diffusivity

[0139] The above-mentioned thermal diffusivity α is represented by the following formula (2).

[0140] [Number 2]

[0141]

[0142] in,

[0143] λ: Thermal conductivity

[0144] ρ: density

[0145] C: Specific heat

[0146] The thermal diffusivity α and the thermal conductivity λ correspond to the thermal diffusivity characteristic TS. However, the thermal diffusivity characteristic TS is not limited to the thermal diffusivity α and the thermal conductivity λ.

[0147] When the thermal diffusivity α is known, the thermal diffusivity α can be directly used to calculate the temperature of the polymer portion 12 through the unsteady heat conduction equation (1). When the thermal diffusivity α is unknown, the thermal diffusivity α can be calculated using the thermal conductivity λ, the density ρ, and the specific heat C according to equation (2), and the calculated α can be used to calculate the temperature of the polymer portion 12 through equation (1).

[0148] However, when using the formula (1) to calculate the temperature of the polymer portion 12, the value described in the general JIS (Japanese Industrial Standards) or the like as the thermal diffusivity α of rubber is used, or when using the formula (2) to calculate the temperature of the polymer portion 12, the value described in the JIS or the like as the thermal conductivity λ is used. Figure 6 As shown in FIG. 1 , the value when the temperature of the polymer portion 12 of the target workpiece model WM disposed in the mold 10 is actually measured does not agree with the value when the temperature of the polymer portion 12 is predicted based on the formula (1) with sufficient accuracy. The inventors conducted intensive research and found that the reason is that the value of the thermal diffusivity α or thermal conductivity λ of the raw material polymer of the polymer portion 12 described in JIS or the like is different from the actual value of the thermal diffusivity α or thermal conductivity λ of the polymer portion 12.

[0149] Therefore, the temperature of the polymer portion 12 of the target workpiece model WM is measured to determine the thermal diffusivity α or thermal conductivity λ of the polymer portion 12, thereby obtaining the thermal diffusivity α or thermal conductivity λ of the polymer portion 12 of the target workpiece model WM.

[0150] Figure 7 The measured value of the temperature of the polymer portion 12 of the target workpiece model WM and the temperature calculated using the measured value of the thermal diffusivity α or the thermal conductivity λ obtained as described above are shown. It can be seen that the measured value and the predicted value of the temperature of the polymer portion 12 match with high accuracy.

[0151] However, the thermal diffusivity α or thermal conductivity λ of the polymer portion 12 constituting the target workpiece model WM varies depending on the type of the base polymer of the polymer portion 12, the amount or type of the additive added to the base polymer, etc. Therefore, it is complicated to actually measure the thermal diffusivity α or thermal conductivity λ for all polymer portions 12 having different formulations.

[0152] Therefore, the inventors focused on carbon black among the additive materials added to the polymer part 12. The rubber constituting the polymer part 12 is a material that is difficult to conduct heat. On the other hand, carbon black is a material that is easy to conduct heat. Therefore, it is believed that the thermal diffusivity α or thermal conductivity λ of the polymer part 12 is highly correlated with the mass ratio of carbon black to the raw material polymer constituting the polymer part 12. Examples of carbon black include furnace black, acetylene black, and Ketjen black.

[0153] Figure 8 The figure shows the relationship between the mass ratio of carbon black to the base polymer and the thermal conductivity λ of the polymer portion 12 when experiments were conducted using a plurality of base polymers and at different mass ratios of carbon black. Figure 8 In the figures, the mass ratio of carbon black to the base polymer is expressed in parts by mass. However, the mass ratio of carbon black to the base polymer may also be expressed in % by mass.

[0154] like Figure 8 As shown in FIG. 1 , the thermal conductivity λ of the polymer portion 12 has a linear relationship with the mass ratio of carbon black to the base polymer. In addition, it can be seen that the thermal conductivity λ of the polymer portion 12 is independent of the type of the base polymer. Thus, regardless of the type of the base polymer, the thermal conductivity λ of the polymer portion 12 can be predicted with high accuracy based on the amount of carbon black added. In addition, since the thermal diffusivity α can be calculated from the thermal conductivity λ using formula (2), the thermal diffusivity α can also be predicted with high accuracy.

[0155] 3-2. Contact heat transfer coefficient CH

[0156] like Figure 2 As shown, in a state where the outer joining member 13 is arranged in the mold 10, an outer gap 15A is sometimes formed between the inner surface of the mold 10 and the outer joining member 13. In this case, heat is transferred from the inner surface of the mold 10 to the outer joining member 13 via the air in the outer gap 15A. In the thermal conductivity analysis processing S1, it is assumed that the inner surface of the mold 10 and the outer joining member 13 are in contact, and the surface considering the outer gap 15A is selected in the mold 10 and the outer joining member 13, and the contact heat transfer coefficient CH is set according to the size of the outer gap 15A. The contact heat transfer coefficient CH is obtained by measuring the temperature behavior when the size of the outer gap 15A is changed in an experiment using a test piece, and analyzing and obtaining the value that can reproduce each temperature behavior.

[0157] In addition, when the inner bonding member 14 is arranged in the mold 10, an inner gap 15B is sometimes formed between the inner surface of the mold 10 and the inner bonding member 14. In this case, heat is transferred from the inner surface of the mold 10 to the inner bonding member 14 via the air in the inner gap 15B. In the thermal conductivity analysis process S1, it is assumed that the inner surface of the mold 10 and the inner bonding member 14 are in contact, and the surface considering the inner gap 15B is selected in the mold 10 and the inner bonding member 14, and the contact heat transfer coefficient CH is set according to the size of the inner gap 15B. The contact heat transfer coefficient CH is obtained by measuring the temperature behavior when the size of the inner gap 15B is changed in an experiment using a test piece, and analyzing and obtaining a value that can reproduce each temperature behavior.

[0158] As described above, the storage unit 2 stores the contact heat transfer coefficient CH at the gap 15A and the gap 15B between the forming die model MM and the die in a state where the target workpiece model WM is arranged in the forming die model MM.

[0159] In the thermal conductivity analysis process S1, the analysis unit 32 is configured to perform thermal conductivity analysis using the polymer thermal diffusivity determined by the polymer thermal diffusivity determination unit 31, the temperature condition TC stored in the storage unit 2, and the contact heat transfer coefficient CH, while the target workpiece model WM is arranged on the molding die model MM. Thus, the temperature of the polymer portion 12 can be predicted with high accuracy.

[0160] 3-3. Air heat transfer coefficient AC

[0161] After the target workpiece model WM is demolded from the molding die model MM, the temperature of the polymer portion 12 of the target workpiece model WM does not immediately decrease, and thus a cross-linking reaction proceeds in the polymer portion 12. Therefore, in the present embodiment, even after the target workpiece model WM is demolded from the molding die model MM, in order to predict the temperature of the polymer portion 12, the condition input unit 30 inputs the external air condition OC including the ambient temperature of the target workpiece model WM after demolding from the molding die model MM. Furthermore, the storage unit 2 stores the heat transfer coefficient of the air around the target workpiece model WM after demolding from the molding die model MM, that is, the air heat transfer coefficient AC.

[0162] The analysis unit 32 of this embodiment performs thermal conductivity analysis using the polymer thermal diffusivity determined by the polymer thermal diffusivity determination unit 31, the air heat transfer coefficient AC stored in the storage unit 2, and the external air condition OC in a state where the polymer portion 12 of the target workpiece model WM is released from the molding die model MM after the polymer portion 12 of the target workpiece model WM undergoes a cross-linking reaction in the molding die model MM. As a result, the temperature of the polymer portion 12 can be predicted with high accuracy in a state where the target workpiece model WM is released from the molding die model MM.

[0163] like Fig. 9 As shown, an analysis grid is produced for a state where the object workpiece model WM is arranged in the forming die model MM. The size of the analysis grid can be predetermined or input from the condition input unit 30. In producing the analysis grid, the characteristics (e.g., symmetry) of the shapes of the forming die model MM and the object workpiece model WM are taken into consideration. As a grid type, an eight-node solid element is used. However, any model can be used as the grid type, for example, a four-node solid element can also be used.

[0164] By using the analysis grid, the temperature of each node of the target workpiece model WM can be predicted. That is, the temperature distribution of the polymer portion 12 of the target workpiece model WM can be predicted. In particular, the temperature of each node of the polymer portion 12 at each time can be predicted.

[0165] 4. Cross-linking reaction analysis and processing S2

[0166] Next, the cross-linking reaction analysis process S2 will be described. Regarding the cross-linking reaction analysis process S2, the reaction rate will be described first. Next, the prior art will be described, and then the problems of the prior art will be described. After that, the cross-linking reaction analysis process of this embodiment will be described.

[0167] 4-1. About response rate

[0168] The reaction rate of the cross-linking reaction is determined as follows. Fig.10As shown, regarding the reaction rate of the rubber involved in this method, according to JIS K6300-2, a vulcanization tester 70 (an example of a cross-linking reaction characteristic tester) is used to calculate the reaction rate (vulcanization degree) based on the relationship between the torque and the reaction time obtained. As the vulcanization tester 70, for example, a vulcanizer (registered trademark) can be used. In addition, in the case of outputting vibration characteristics that take into account the reaction rate (vulcanization degree), for example, a rubber processability tester (RPA) can be used to measure the reaction behavior (vulcanization behavior) under the desired vibration conditions. RPA is configured to be able to set the vibration frequency and amplitude within a wide range. However, the raw polymer is not limited to the rubber described in JIS K6300-2. In addition, JIS K6300-2 is made based on ISO6502:1999, and a part of the prescribed items that are not in the corresponding international standard are added. Furthermore, part of the corresponding international standard is changed and deleted.

[0169] like Fig.10 As shown, the vulcanization tester 70 is provided with a disk 75 mounted on the front end of a rotor 74 between a lower die 72 and an upper die 73 having a cavity 71. The lower die 72 and the upper die 73 can be set to a predetermined temperature. The torsion angle of the rotor 74 can be selected to be +3° to -3° or +1° to -1°. A measurement sample 76 is arranged between the cavity 71 and the disk 75, and a cross-linking reaction is carried out while a rotational torque is applied from the disk 75 at a certain temperature, and the progress of the cross-linking reaction is detected based on the change in torque.

[0170] Fig.11 This shows an example of measurement results. Fig.11 (a) is a graph showing the change in torque relative to reaction time at a predetermined reaction temperature (crosslinking reaction curve CC). On the other hand, regarding the reaction rate, the minimum torque is defined as 0% reaction rate, and the maximum torque is defined as 100% reaction rate. Fig.11 (b) shows a graph (reference reaction curve RC) showing the change of reaction rate at a predetermined reaction temperature relative to reaction time. In the case of the rubber involved in this embodiment, the reaction rate is called the degree of vulcanization. The degree of vulcanization is defined as the degree of vulcanization when the physical properties of the vulcanized rubber (elastic modulus, elongation, tensile strength, hardness, etc.) are used as indicators. Fig.11 In (a), in the region from reaction time 0 to the reaction time showing the minimum torque, the crosslinking reaction of the polymer portion 12 is not reacted, and a plastic region is formed. Fig.11 In (b), in this region, the reaction rate is 0%.

[0171] 4-2. Calculation method of reaction rate

[0172] Next, the calculation method of reaction rate is described. In the above-mentioned non-patent literature 1, the equivalent reaction amount of cross-linking reaction is estimated by using the formula (4) involved in the equivalent reaction amount obtained by deforming the Arrhenius formula (3). In addition, the formula (4) involved in the equivalent reaction amount represents that the reaction amount under reaction temperature T and reaction time t is several times of the reaction amount under a certain reference temperature T0 and reference time t0. In addition, formula (4) is called equivalent vulcanization formula in the vulcanization reaction of rubber. By using this equivalent vulcanization formula, the reaction rate of the reaction return period described later can be predicted. In this mode, compared with the situation of using only the equivalent vulcanization formula, the prediction accuracy of the reaction return period can be further improved, which is described in detail later. In addition, in general analysis software, according to the formula (for example, Kamal's reaction rate formula) used when predicting the behavior of the thermosetting reaction of rubber, epoxy, etc., the reaction rate of the reaction return period cannot be predicted.

[0173] [Number 3]

[0174]

[0175] in,

[0176] k: reaction speed

[0177] A: Frequency factor

[0178] E: Activation energy

[0179] R: Gas constant

[0180] T: reaction temperature

[0181] [Number 4]

[0182]

[0183] in,

[0184] U: equivalent reaction volume

[0185] E: Activation energy

[0186] R: Gas constant

[0187] T: reaction temperature

[0188] T0: reference temperature

[0189] t: reaction time

[0190] Based on the Arrhenius formula (3), the formula is transformed as follows to derive the formula (4) of the equivalent reaction amount.

[0191] The reaction amount Z of the cross-linking reaction at the reaction time t is represented by the formula (5).

[0192] [Number 5]

[0193] Z=k×t…(5)

[0194] in,

[0195] Z: reaction volume

[0196] t: reaction time

[0197] According to the Arrhenius equation (3) and the above-mentioned equation (5), the reaction amount Z is expressed as the following equation (6).

[0198] [Number 6]

[0199]

[0200] Here, if the reaction amount Z0 at a reaction time t0 at a reaction temperature T0 serving as a certain reference is taken into consideration, Z0 is represented by the following formula (7).

[0201] [Number 7]

[0202]

[0203] If the ratio U of the reaction amount Z at reaction temperature T and reaction time t to the reaction amount Z0 at reaction temperature T0 and reaction time t0 is taken, the ratio U is expressed by the following formula (8).

[0204] [Number 8]

[0205]

[0206] If equations (6) and (7) are substituted into equation (8), equation (9) is obtained for the ratio U.

[0207] [Number 9]

[0208]

[0209] In the formula (9), when t0=1, the formula (9) is expressed as the above-mentioned formula (4).

[0210] When the reaction temperature T changes every moment, the increase in the equivalent reaction amount at a small time at the target moment is calculated based on the temperature at the target moment, the above-mentioned formula (4), and the slope coefficient SC, and the cumulative value of the equivalent reaction amount from the start of the cross-linking reaction to the target moment is calculated based on the increase in the equivalent reaction amount. The reaction rate at the target moment is calculated based on the cumulative value of the equivalent reaction amount from the start of the cross-linking reaction to the target moment.

[0211] Based on formula (4), the equivalent reaction amount increase ΔU at the target time of a small time Δt is i It is represented by the following formula (10).

[0212] [Number 10]

[0213]

[0214] in,

[0215] ΔU i : The increase in the equivalent reaction amount at a small time of the target moment

[0216] Δt: microsecond of the target moment

[0217] When the reaction temperature T changes moment by moment, the equivalent reaction amount U can be obtained by integrating it per unit time as shown in the following formula (11).

[0218] [Number 11]

[0219]

[0220] in,

[0221] U: equivalent reaction volume

[0222] E: Activation energy

[0223] R: Gas constant

[0224] T: reaction temperature

[0225] T0: reference temperature

[0226] Δt: microsecond of the target moment

[0227] The above-mentioned formula (4) is a formula inside Σ in the above-mentioned formula (11), and corresponds to each accumulated equivalent reaction amount.

[0228] In order to calculate the equation (4) or the equation (11), the value of (-E / R) is required. In the prior art, (-E / R) is obtained as follows.

[0229] By taking the natural logarithm of both sides of the Arrhenius formula (3), the following formula (12) is obtained.

[0230] [Number 12]

[0231]

[0232] in,

[0233] k: reaction speed

[0234] A: Frequency factor

[0235] E: Activation energy

[0236] R: Gas constant

[0237] T: reaction temperature

[0238] Regarding the above reaction amount, it is considered that the reaction time t at a predetermined reaction rate γ is γ The following equation (13) holds true between γ and the reaction rate k. The reaction rate γ can be any value between 0% and 100%, such as 5% and 90%, as appropriate.

[0239] [Number 13]

[0240]

[0241] in,

[0242] B: Any constant

[0243] t γ : Reaction time at a predetermined reaction rate γ

[0244] Take the natural logarithm of both sides of equation (13) and substitute it into equation (12) to transform the formula, thus obtaining equation (14).

[0245] [Number 14]

[0246]

[0247] From formula (14), we can know that ln(1 / t γ ) as the vertical axis and (1 / T) as the horizontal axis, when the time for the reaction rate to reach α% and each measurement temperature are plotted, a straight line can be approximated, and the slope of the straight line is (-E / R) (refer to Fig.12 ).

[0248] In actual reactions, Fig.13 As shown in FIG. 1 , the temperature changes with the passage of reaction time. In such a case, the equivalent reaction amount is calculated using equation (4) and equation (11) as follows.

[0249] First, if Fig.13 As shown, the reaction time is divided into predetermined intervals (eg, 1 minute). Next, the temperature is read at each predetermined interval.

[0250] Next, the equivalent reaction amount per predetermined interval is calculated using equation (4). In equation (4), the predetermined interval Δt is substituted for calculation. The calculation can be simplified by setting Δt=1 as the predetermined interval, for example.

[0251] Next, the ΔU calculated by equation (4) for each predetermined interval Δt is i Add. Fig.14 A specific calculation method will be described.

[0252] like Fig.14 As shown, the reaction time t is calculated by formula (4) i-1 , reaction temperature T i-1 The equivalent reaction quantity U i-1 Similarly, calculate the reaction time t i , reaction temperature T i The equivalent reaction quantity U i .

[0253] Next, U i-1 ×Δt and U i ×Δt. Thus, we get the reaction time t i-1 ~t i The cumulative value of the equivalent reaction amount at the time. In addition, in this method, Δt = 1 / 2t. Similarly, according to formula (11), the equivalent reaction amount ΔU is accumulated for each predetermined time from t = 1 to t = n. i , from which the equivalent reaction amount U can be obtained.

[0254] Next, the method for calculating the reaction rate based on the equivalent reaction amount U is described. First, the reaction amount Z at the reaction temperature T0 and the reaction time t is expressed by formula (5). Next, according to formula (5), the reaction amount Z0 at the reaction temperature T0 and the reaction time t0 is expressed by the following formula (15). Among them, the reaction temperature of formula (5) and formula (15) is the same value T0, so according to formula (3), each k is the same value.

[0255] [Number 15]

[0256] Z0=k×t0…(15)

[0257] When the above-mentioned equations (5) and (15) are substituted into the above-mentioned equation (8), the reaction rate k is reduced to obtain the following equation (16).

[0258] [Number 16]

[0259]

[0260] In the formula (16), if t0=1, the formula (16) is expressed as the following formula (17).

[0261] [Number 17]

[0262] U=t…(17)

[0263] According to formula (17), when t0=1, the reaction time t can be replaced by the equivalent reaction amount U. Fig.11 In the graph (b) showing the change in reaction rate at reaction temperature T0 relative to reaction time, the reaction time t can be replaced by the equivalent reaction amount U. Fig.15A graph with the vertical axis representing the reaction rate and the horizontal axis representing the equivalent reaction amount is shown in FIG. Based on this graph, the reaction rate can be calculated from the equivalent reaction amount U obtained by calculation.

[0264] 4-3. Problems with the reaction rate calculation method

[0265] However, when the reaction rate is estimated based on the above method, there is a problem that the difference from the actual measured value is large and sufficient accuracy cannot be obtained.

[0266] Fig.16 Indicates the change in reaction rate with respect to reaction time. When using equation (4), the reference temperature is set to 160°C, so when the reaction temperature is 160°C, the measured value and the predicted value agree with high accuracy.

[0267] However, the measured values ​​and the predicted values ​​do not fully agree with each other for the reaction temperature of 170° C. and the reaction temperature of 180° C. The predicted values ​​are generally larger than the measured values. In addition, the maximum values ​​of the reaction rate agree with each other because the maximum value of the reaction rate is defined as 100% as described above.

[0268] Reference Fig.17 , the reasons why the measured values ​​and predicted values ​​are not fully consistent in the prior art are explained. Fig.17 A graph showing changes in reaction rate with respect to reaction time is shown in . The cross-linking reaction according to the present embodiment proceeds through the following process.

[0269] In the initial stage of the reaction after the reaction starts, the reaction rate increases gradually. When the reaction is promoted after a certain period of time, the reaction rate increases sharply. Afterwards, when the reaction is carried out in the later stage, the increase in the reaction rate slows down and the reaction rate reaches a maximum value. After the reaction rate reaches a maximum value, it becomes a reaction return period in which the reaction is returned. In this reaction return period, the reaction rate decreases gradually.

[0270] In the above-mentioned technology, the period from the initial stage of the reaction to the reaction return stage is understood as a so-called crosslinking reaction. Therefore, the reaction rate is predicted using one activation energy E. As a result, it is believed that the measured value of the reaction rate is not sufficiently consistent with the predicted value.

[0271] 4-4. Cross-linking reaction analysis and processing of this embodiment

[0272] In this embodiment, a plurality of activation energies are calculated according to the progress state of the reaction, and the equivalent reaction amount is predicted based on the obtained activation energies. Based on this concept, equation (4) is transformed into the following equation (18).

[0273] [Number 18]

[0274]

[0275] Among them, E N : The activation energy of each reaction stage divided into N stages

[0276] exist Fig.17 In the example of dividing the progress of the reaction into four stages, namely, the initial stage of the reaction, the promotion stage of the reaction, the late stage of the reaction and the return stage of the reaction, are shown. However, the progress of the reaction can be divided into 2 to 3 or more than 5 arbitrary stages. In addition, the entire period including the reaction progress period and the return stage of the reaction can also be divided at equal intervals. As an index divided at equal intervals, the progress of the entire period of the cross-linking reaction can be used as a benchmark, for example, the progress of the cross-linking reaction can be divided by every 5%. However, the index divided is not limited to 5%, and can also be 1% to 4% or more than 6%.

[0277] In this method, the reaction rate of 0% to 5% is regarded as the initial stage of the reaction, the reaction rate of 5% to 50% is regarded as the promotion stage of the reaction, the reaction rate of 50% to 100% is regarded as the late stage of the reaction, and in the stage after the late stage of the reaction, the range of the reaction rate decreasing from 100% to 90% is regarded as the reaction return stage.

[0278] In each reaction stage, the activation energy E is calculated using the above formula (14). N The term (E N / R). Fig.17 As shown in the figure, (E1 / R) is about 12000 in the initial stage of the reaction (reaction rate 0% to 5%), (E2 / R) is about 9000 in the promotion stage of the reaction (reaction rate 5% to 50%), (E3 / R) is about 13000 in the late stage of the reaction (reaction rate 50% to 100%), and (E4 / R) is about 16000 in the return stage of the reaction (reaction rate 100% to 90%). N The numerical value of (E / R) is not limited to the above-mentioned value. In addition, when the period from the initial stage of the reaction to the reaction return period is considered as one reaction stage, (E / R) is 11,000.

[0279] exist Fig.18 In the figure, the results of predicting the reaction rate using the activation energies E1 to E4 obtained as described above are shown together with the measured values. Not only are the measured values ​​consistent with the predicted values ​​at the reference temperature of 160°C, but the measured values ​​are also consistent with the predicted values ​​at the reaction temperature of 170°C and the reaction temperature of 180°C. Thus, the reaction rate can be predicted with high accuracy.

[0280] In this embodiment, the slope coefficient SC is set to different values ​​in the reaction progress phase until the reaction rate of the crosslinking reaction reaches a peak and in the reaction return phase after the reaction rate exceeds the peak. In addition, in this embodiment, the slope coefficient SC is set to a value smaller in the reaction return phase than in the reaction progress phase.

[0281] In addition, in this embodiment, the slope coefficient SC is set to different values ​​in the initial reaction period, the reaction promotion period, the reaction late period and the reaction return period. In addition, in this embodiment, the slope coefficient SC in the reaction promotion period is set to a larger value than that in the initial reaction period and the reaction late period.

[0282] In addition, when the entire period of the cross-linking reaction is divided into equal intervals, the slope coefficient SC is set to a value corresponding to each division.

[0283] 4-5. Method for expressing the reaction rate of the cross-linking reaction

[0284] Reference Fig.19 , the method of expressing the reaction rate of the cross-linking reaction in this embodiment is described. Fig.19 This is a graph showing the change in the reaction rate of the cross-linking reaction with respect to the reaction time. The graph indicated by the solid line is the actual measured value of the reaction rate.

[0285] The reaction rate of the cross-linking reaction shown by the solid line gradually decreases by performing a return reaction after reaching a maximum value. Therefore, for example, there is a point where the reaction rate is 80% before the reaction rate reaches a maximum value and a point where the reaction rate is 80% after the reaction rate reaches a maximum value. In this case, if only the numerical value of the reaction rate is compared, it is impossible to distinguish between the numerical value of 80% before the reaction rate reaches a maximum value and the numerical value of 80% after the reaction rate reaches a maximum value.

[0286] Therefore, in the present embodiment, in the reaction progress period until the reaction rate of the cross-linking reaction reaches the peak, the start of the cross-linking reaction is set to 0%, and the increase in the reaction rate of the cross-linking reaction is defined within the range of 0% to 100%. In the reaction return period after the reaction rate exceeds the peak, the value obtained by adding the decrease in the reaction rate relative to the peak of the reaction rate to 100% is defined as the reaction rate of the cross-linking reaction.

[0287] If using Fig.19 As an example, the straight line extending from the point where the reaction rate is 100% parallel to the horizontal axis is used as the symmetry axis, and the graph of the reaction return period after the reaction rate exceeds the peak is reversed as shown by the arrow line B. Thus, the point where the reaction rate reaches a maximum value and the reaction rate reaches a maximum value can be expressed as a reaction rate of 120%. As a result, the reaction rate before the reaction rate reaches a maximum value and the reaction rate after the reaction rate reaches a maximum value can be clearly identified (refer to Fig. 20 ).

[0288] 4-6. Method for determining the value calculated by simulation

[0289] Next, the method for determining the value calculated by simulation is described. In this method, the slope coefficient SC and the reaction rate are determined using one or both of a database and a function. By using a database, the accuracy of the estimated value can be improved. On the other hand, by using a function, the calculation speed can be increased.

[0290] (1) Methods of using the database

[0291] like Figure 1 As shown, the storage unit 2 stores a first relationship data map DM1 defining the correspondence between the reaction rate of the crosslinking reaction of the polymer portion 12 and the slope coefficient SC. The reaction rate calculation processing unit 41 determines the slope coefficient SC using the reaction rate at the previous time and the first relationship data map DM1.

[0292] The storage unit 2 stores a second relationship data map DM2 defining the correspondence between the equivalent reaction amount integrated value and the reaction rate at the target time. The reaction rate calculation processing unit 41 determines the reaction rate at the target time using the equivalent reaction amount integrated value at the target time and the second relationship data map DM2.

[0293] The second relationship data map DM2 is set by a reference reaction curve RC based on the relationship between the crosslinking reaction time at a reference reaction temperature measured by a vulcanization tester 70 using a test object polymer material corresponding to the polymer portion 12 of the target workpiece model WM and the torque generated in the test object polymer material.

[0294] (2) How to use functions

[0295] like Figure 1 As shown, the storage unit 2 stores a first function F1 defining the correspondence between the reaction rate of the crosslinking reaction of the polymer portion 12 and the slope coefficient SC. The reaction rate calculation processing unit 41 determines the slope coefficient SC using the reaction rate at the previous time and the first function F1.

[0296] The first function F1 is set as different functions according to a plurality of reaction rate divisions set in accordance with the progress of the cross-linking reaction of the polymer portion 12. The number of divisions of the progress of the cross-linking reaction is arbitrary and can be divided into one or more than two. As for the function, any function including an n-order function of linear interpolation, a spline curve, etc. can be appropriately selected. In this embodiment, for example, a sixth-order function is preferably used. In addition, the number of divisions of the first function F1 can be related to the activation energy E of each progress stage of the reaction divided into N stages. N The divisions when the value is set are set independently.

[0297] The storage unit 2 stores a second function F2 defining the correspondence between the equivalent reaction amount integrated value and the reaction rate at the target time. The reaction rate calculation processing unit 41 determines the reaction rate at the target time using the equivalent reaction amount integrated value at the target time and the second function F2.

[0298] The second function F2 is set by a reference reaction curve RC based on the relationship between the crosslinking reaction time at a reference reaction temperature measured by a vulcanization tester 70 using a test object polymer material corresponding to the polymer portion 12 of the target workpiece model WM and the torque generated in the test object polymer material.

[0299] The second function F2 is set as different functions according to a plurality of reaction rate divisions set in accordance with the progress of the cross-linking reaction of the polymer portion 12. The number of divisions of the progress of the cross-linking reaction is arbitrary and can be divided into one or more than two. As for the function, any function such as an n-order function including linear interpolation, a spline curve, etc. can be appropriately selected. In this method, for example, a sixth-order function is preferably used. In addition, the number of divisions of the second function F2 can be related to the activation energy E of each progress stage of the reaction divided into N stages. N The divisions when the value is set are set independently.

[0300] exist Fig.21 In the embodiment, the second function F2 is an example of a function in which the degree of progress of the cross-linking reaction is divided into four stages. In this embodiment, the stages are divided into an initial stage of the reaction, a stage of promoting the reaction, a late stage of the reaction, and a stage of returning to the reaction. In each stage, the reaction rate and the reaction time are approximated by different functions.

[0301] Next, an analysis grid of the target workpiece model WM is prepared. The size of the analysis grid may be predetermined or may be input from the condition input unit 30. In preparing the analysis grid, the shape characteristics (e.g., symmetry) of the target workpiece model WM are considered. Fig. 22 The analysis mesh shown in the figure. As the mesh type, eight-node solid elements are used. However, any mesh type can be used, for example, four-node solid elements can also be used.

[0302] The reaction rate of each node can be calculated from the temperature of each node at each time of only the polymer portion 12 of the target workpiece model WM using the analysis grid.

[0303] 5. Structural analysis and processing S3

[0304] 5-1. Initial processing

[0305] Next, the structural analysis process S3 is described. The structural analysis unit 5 creates an analysis grid for the target workpiece model WM. The analysis grid for the target workpiece model WM may be the same as or different from the analysis grid created in the cross-linking reaction analysis process S2. In this embodiment, the analysis grid used in the structural analysis process S3 is the same as the analysis grid used in the cross-linking reaction analysis process S2.

[0306] 5-2. Temperature and reaction rate acquisition

[0307] Next, the structure analysis unit 5 obtains analysis results on the temperature distribution of the polymer portion 12 of the target workpiece model WM analyzed by the thermal conduction analysis unit 3 . The structure analysis unit 5 also obtains analysis results on the reaction rate of the polymer portion 12 of the target workpiece model WM analyzed by the crosslinking reaction analysis unit 4 .

[0308] 5-3. Elastic modulus prediction

[0309] Next, the structural analysis unit 5 calculates the elastic modulus of each node at each time of the polymer part 12 of the target workpiece model WM. First, a test piece with a reaction rate of 100% for the cross-linking reaction is prepared, and the elastic modulus of the test piece is measured. Next, the correction coefficient is calculated based on the quotient obtained by dividing the torque at the reaction rate of the target by the torque at the reaction rate of 100%. The above-mentioned torque is a torque that can be measured by the vulcanization tester 70. The structural analysis unit 5 calculates the elastic modulus of each node at each time by multiplying the measured elastic modulus by the calculated correction coefficient.

[0310] 5-4. Characteristic prediction

[0311] Next, the structural analysis unit 5 predicts the characteristics of the target workpiece model WM. Input conditions used in the finite element analysis are the temperature of each node at each time, the elastic modulus of each node at each time, and the boundary conditions of the outer joint member 13 and the inner joint member 14 .

[0312] After the input conditions are set, a force or strain is applied to the target workpiece model WM in a direction perpendicular to the axis line A of the target workpiece model WM.

[0313] The structural analysis unit 5 outputs the overall elastic modulus of the target workpiece model WM. In this method, the elastic modulus relative to the force statically applied in the direction at right angles to the axis A of the target workpiece model WM is predicted as a characteristic. However, the predicted characteristic is not limited to the elastic modulus relative to the force or strain in the direction at right angles to the axis A, and any physical property value such as the elastic modulus relative to the force vibrating in the direction at right angles to the axis A, the elastic modulus relative to the force statically applied in the direction along the axis A, and the elastic modulus relative to the force vibrating in the direction along the axis A can be predicted as a characteristic.

[0314] 6. Internal Bubble Estimation Process S4

[0315] Next, the internal bubble estimation process S4 is described. A rubber product as an example of this method is produced by molding and vulcanization. Therefore, the gas originally dissolved in the rubber or the gas generated by the vulcanization reaction is dissolved in the rubber under the high temperature and high pressure conditions of vulcanization. When the mold 10 is opened, the pressure applied to the rubber decreases, and the solubility of the gas in the rubber decreases. Therefore, when the vulcanization is not fully performed, internal bubbles 80 are sometimes generated in the polymer part 12 composed of rubber (see Fig.23 ).

[0316] If the vulcanization time is extended while the rubber is arranged in the mold 10 and the vulcanization is carried out, the internal bubbles 80 will not be generated. In the actual vulcanization of the product, the total amount of heat received is different at points inside the product at different distances from the mold 10 serving as the heat source due to the different temperature rise history, and the vulcanization progress is different even if the vulcanization time is the same. Therefore, the latest vulcanized portion needs to be heated in the mold 10 until the generation of internal bubbles 80 is no longer visible. The vulcanization degree of the rubber in the latest vulcanized portion at the time point when the mold 10 is opened when molding is performed with a vulcanization time until the generation of internal bubbles 80 is no longer visible in the latest vulcanized portion is referred to as the foaming point vulcanization degree (hereinafter referred to as the foaming point) (refer to Fig.24 ).

[0317] In order to suppress the internal bubbles 80, it is preferable to extend the heating time in the mold 10 as much as possible. However, if the heating time in the mold 10 is excessively extended, the manufacturing efficiency of the product decreases. Therefore, in order to determine the vulcanization time of the product, it is important to estimate the above-mentioned foaming point.

[0318] Fig.25 (a) in the figure shows the foaming point reaction rate when a plurality of fillers are added to a plurality of polymers in different blending amounts. The foaming point reaction rate is the reaction rate of the crosslinking reaction of the polymer part 12 at the foaming point.

[0319] Eight kinds of polymers A to H were used as raw material polymers. Samples A1 to A3 used raw material polymer A and varied the amount of filler blended. Similarly, samples B1 to B3 varied the amount of filler blended relative to raw material polymer B, and samples C1 to C3 varied the amount of filler blended relative to raw material polymer C. Since commercial products were used as samples, the type and amount of filler blended were not known accurately.

[0320] like Fig.25 As shown in (a) in FIG. 1 , the foaming point reaction rate greatly varies depending on the type of the base polymer and the amount of the filler added. Therefore, it is found that it is difficult to predict the foaming point of the polymer portion 12 using the foaming point reaction rate.

[0321] like Fig.26 As shown in FIG. 1 , it is considered that when the pressure P1 at which the internal bubbles 80 expand and the pressure P2 at which the polymer part presses the internal bubbles 80 are P1<P2, the internal bubbles 80 are pressed by the rubber and disappear. Therefore, the foaming point reaction rate is converted into the torque measured by the vulcanization tester 70 corresponding to the foaming point reaction rate, and compared among the samples.

[0322] Fig.25 (b) shows the foaming point torque when various fillers are added to various polymers in different blending amounts. As described above, the foaming point torque is a value obtained by converting the foaming point reaction rate into the torque measured by the vulcanization tester 70 corresponding to the foaming point reaction rate.

[0323] like Fig.25 As shown in (b), the torque (bubble point torque) at which the generation of the internal bubbles 80 is not observed is substantially the same regardless of the type of base polymer and the amount of filler added. That is, the bubble point can be easily predicted by using a torque that can be easily measured. Fig.25 The vertical axis of (b) in FIG. 8 shows the threshold value. When the torque during demolding of the target workpiece model WM does not exceed the threshold value, the estimating unit 62 of the internal bubble estimating unit 6 estimates that the internal bubbles 80 are generated in the polymer portion 12 of the target workpiece model WM.

[0324] The threshold value is set to a uniform value for a plurality of raw polymers. In addition, the threshold value is a torque corresponding to a reaction rate greater than the reaction rate of the cross-linking reaction at the foaming point of the polymer portion 12. However, the threshold value may also be set to a plurality of groups, and the threshold value may be set for each group. The plurality of groups may be divided according to any criterion.

[0325] The reaction rate acquisition unit 51 acquires the reaction rate of each portion of the polymer portion 12 , the torque calculation unit 61 calculates the torque of each portion of the polymer portion 12 , and the estimation unit 62 estimates the generation of the internal bubbles 80 at each portion of the polymer portion 12 .

[0326] 7. Display processing S5

[0327] Next, the display process S5 will be described. Figure 1 As shown, the display unit 7 displays a value obtained from the reaction rate according to the reaction time based on the analysis result of the cross-linking reaction analysis unit 4 .

[0328] Furthermore, the display unit 7 displays characteristics corresponding to the temperature of the mold model MM used in the crosslinking reaction of the polymer part 12 and the reaction time in the mold from the start of the crosslinking reaction to the demolding of the mold model MM based on the analysis result of the structure analysis unit 5 .

[0329] Furthermore, the display unit 7 displays the presence or absence of the generation of the internal bubbles 80 based on the estimation result of the internal bubble estimation unit 6 and the temperature of the mold model MM and the reaction time in the mold from the start of the crosslinking reaction to the demolding of the mold model MM.

[0330] Furthermore, the display unit 7 displays the value obtained from the reaction rate corresponding to the temperature of the mold model MM and the reaction time in the mold from the start of the cross-linking reaction to the demolding of the mold model MM based on the analysis result of the cross-linking reaction analysis unit 4, together with the presence or absence of the generation of the internal bubbles 80. However, the contents displayed by the display unit 7 are not limited to the above contents.

[0331] 7-1. Table-based display method

[0332] (1) Method of displaying response rate

[0333] With reference to Tables 1 to 4, a method of displaying the reaction rate of the cross-linking reaction using a table will be described.

[0334]

[0335] Table 1 summarizes the relationship between the mold temperature and the reaction time with respect to the reaction rate of the cross-linking reaction in the cell having the smallest reaction rate of the cross-linking reaction in the target workpiece model WM.

[0336] The reaction time recorded in Table 1 indicates the reaction time in a state where the target workpiece model WM is arranged inside the mold 10. In addition, the numerical value of the reaction rate recorded in Table 1 is a value calculated based on the temperature history of both the reaction time in a state where the target workpiece model WM is arranged inside the mold 10 and the time after the target workpiece model WM is demolded from the mold 10. The target workpiece model WM also undergoes a crosslinking reaction after being demolded from the mold 10, so the above considerations are necessary. In the following description, the same applies to the reaction time and reaction rate recorded in Tables 2 to 4.

[0337] In Table 1, the reaction rate of the region surrounded by the thick grid line in the upper right part is a value greater than 115%. In this region, the return reaction of the cross-linking reaction is excessively advanced, which is not preferable. However, the range of the reaction rate can be set arbitrarily, and a value different from 115% can also be used as the threshold value.

[0338] The reaction rate of the area surrounded by the bold grid lines in the lower left portion of Table 1 is less than 95%. In this area, the crosslinking reaction does not proceed sufficiently, so it is not preferred. However, the range of the reaction rate can be set arbitrarily, and a value different from 95% can also be used as the threshold value.

[0339] In Table 1, the regions other than the upper right region and the lower left region surrounded by thick grid lines are preferred regions from the viewpoint of the reaction rate of the crosslinking reaction. In addition, Table 1 does not describe information on the internal bubbles 80 described later.

[0340] Table 2 is a table summarizing the relationship between the mold temperature and the reaction time with respect to the average value of the cross-linking reaction of all the cells of the target workpiece model WM.

[0341]

[0342] In Table 2, the reaction rate of the region surrounded by the thick grid lines in the upper right part is a value greater than 115%. In this region, the return reaction of the cross-linking reaction is excessively advanced, which is not preferable. However, the range of the reaction rate can be set arbitrarily, and a value different from 115% can also be used as the threshold value.

[0343] The reaction rate of the area surrounded by the bold grid lines in the lower left portion of Table 2 is less than 95%. In this area, the crosslinking reaction does not proceed sufficiently, so it is not preferred. However, the range of the reaction rate can be set arbitrarily, and a value different from 95% can also be used as the threshold value.

[0344] In Table 2, regions other than the upper right region and the lower left region are preferred regions from the viewpoint of the reaction rate of the cross-linking reaction. In addition, in Table 2, information on the internal bubbles 80 described later is not described.

[0345] Table 3 summarizes the relationship between the mold temperature and the reaction time regarding the reaction rate of the cross-linking reaction in the cell having the highest reaction rate of the cross-linking reaction in the target workpiece model WM.

[0346]

[0347] In Table 3, the reaction rate of the region surrounded by the thick grid lines in the upper right part is a value greater than 115%. In this region, the return reaction of the cross-linking reaction is excessively advanced, which is not preferred. However, the range of the reaction rate can be set arbitrarily, and a value different from 115% can also be used as the threshold value.

[0348] The reaction rate of the area surrounded by the bold grid lines in the lower left portion of Table 3 is less than 95%. In this area, the crosslinking reaction does not proceed sufficiently, so it is not preferred. However, the range of the reaction rate can be set arbitrarily, and a value different from 95% can also be used as the threshold value.

[0349] In Table 3, regions other than the upper right region and the lower left region are preferred regions from the viewpoint of the reaction rate of the cross-linking reaction. In addition, in Table 3, information on the internal bubbles 80 described later is not described.

[0350] Table 4 is a table in which information on the internal air bubbles 80 is added to Table 2.

[0351]

[0352] In Table 4, the reaction rate of the region surrounded by the thick grid lines in the upper right part is a value greater than 115%. In this region, the return reaction of the cross-linking reaction is excessively advanced, which is not preferable. However, the range of the reaction rate can be set arbitrarily, and a value different from 115% can also be used as the threshold value.

[0353] In Table 4, the portion surrounded by double-line grid lines indicates that internal bubbles 80 are generated in the polymer portion 12 of the target workpiece model WM.

[0354] The reaction rate of the area below the dotted line in the portion surrounded by the double-line grid in the lower left portion of Table 4 is less than 95%. In this area, the cross-linking reaction does not proceed sufficiently, so it is not preferred. However, the range of the reaction rate can be set arbitrarily, and a value different from 95% can also be used as the threshold value.

[0355] In Table 4, the area above the dotted line in the area surrounded by the double-line grid indicates that the reaction rate of the cross-linking reaction is within the range of 95% to 115%, but internal bubbles 80 are generated in the polymer portion 12 of the target workpiece model WM. This area is not preferable as a product because the internal bubbles 80 are generated in the polymer portion 12.

[0356] In this embodiment, Table 4 is prepared by adding information on the internal bubbles 80 to the prediction results described in Table 2, but the present invention is not limited thereto, and information on the internal bubbles 80 can be added to the prediction results of the reaction rate at any temperature.

[0357] (2) Method of displaying elastic modulus

[0358] Table 5 summarizes the relationship between the mold temperature and the response time with respect to the elastic modulus of the target workpiece model WM.

[0359] The reaction time recorded in Table 5 indicates the reaction time in a state where the target workpiece model WM is arranged inside the mold 10. The values ​​of the elastic modulus recorded in Table 5 are values ​​calculated based on the temperature history of both the reaction time in a state where the target workpiece model WM is arranged inside the mold 10 and the time after the target workpiece model WM is released from the mold 10. The target workpiece model WM also undergoes a crosslinking reaction after being released from the mold 10, so the above considerations are necessary. In addition, in the following description, Figure 28 to Figure 31 The same is true for the reaction time and elastic modulus described above.

[0360]

[0361] The elastic modulus is the elastic modulus when a static force is applied in a direction perpendicular to the axis A of the target workpiece model WM. The values ​​in the table are ratios of the elastic modulus when the reaction rate of the cross-linking reaction is 100%. However, the direction of the force applied to the target workpiece model WM is not limited, and the elastic modulus can be used in the following cases: the case where a static force is applied in a direction parallel to the axis A of the target workpiece model WM, the case where a static force is applied in a direction rotating about the axis A of the target workpiece model WM, and the case where a static force is applied in a direction inclined relative to the axis A of the target workpiece model WM, etc., and the case where a force in any direction is applied. In addition, the force applied to the target workpiece model WM is not limited to a static force, and for example, it can also be the elastic modulus when vibration is applied to the target workpiece model WM.

[0362] Table 5 is a table obtained by assigning elastic modulus corresponding to the degree of vulcanization to each unit of the target workpiece model WM, performing structural analysis, and summarizing the relationship between the elastic modulus obtained by analysis, the mold temperature, and the reaction time. The meanings of the bold grid lines, double grid lines, and dashed grid lines recorded in Table 5 are the same as those recorded in Table 4, so repeated explanations are omitted. In addition, in Table 5, the cells entered with "-" are the locations where calculation errors occurred in the simulation of the elastic modulus.

[0363] Furthermore, in Table 5, arbitrary information such as information related to the internal air bubbles 80 can be added.

[0364] In this method, grid lines are used to distinguish the values ​​recorded in the table, but the method is not limited to this. The values ​​in the table can be distinguished by any method such as changing the color of the values ​​recorded in the table, changing the font, changing the font to italic or bold, changing the background color of the cells recording the values, changing the pattern of the background of the cells, etc.

[0365] 7-2. Display method based on heat map 90

[0366] Reference Fig. 27 , a method of displaying the reaction rate of the cross-linking reaction using the heat map 90 is described. Fig. 27 , a heat map 90 showing the distribution of the reaction rate of the cross-linking reaction in terms of depth for the target workpiece model WM is shown.

[0367] In the heat map 90, the outer joint member 13 and the inner joint member 14 in the target workpiece model WM are displayed as blank. In addition, in the target workpiece model WM, the polymer portion 12 is divided into regions 91 to 94 according to the magnitude of the crosslinking reaction rate and displayed, and each of the divided regions 91 to 94 is displayed in a darker or lighter manner according to the magnitude of the crosslinking reaction rate.

[0368] Region 91 has the highest reaction rate of the cross-linking reaction and is displayed in the darkest tone. Region 92 has the second highest reaction rate of the cross-linking reaction and is displayed in the second darkest tone. Region 93 has the third highest reaction rate of the cross-linking reaction and is displayed in the third darkest tone. Region 94 has the lowest reaction rate of the cross-linking reaction and is displayed in the lightest tone.

[0369] The display unit 7 displays the heat map 90 to the operator. The operator can intuitively understand the distribution of the crosslinking reaction rate of the polymer portion 12 by visually checking the regions 91 to 94 displayed in light and dark colors.

[0370] In the heat map 90 , all reaction conditions (eg, temperature, time, etc.) related to the target workpiece model WM can be created and outputted. In addition, the heat map 90 may be created and outputted only for predetermined reaction conditions.

[0371] The display method of the heat map 90 on the display unit 7 is not particularly limited, and for example, the display unit 7 may display the above-mentioned Table 5, and the operator may select each cell of the displayed Table 5, thereby displaying the heat map 90 under the reaction conditions corresponding to the cell. Alternatively, the operator may input the reaction conditions of the cross-linking reaction, and the heat map 90 corresponding to the input reaction conditions may be displayed.

[0372] In this embodiment, the heat map 90 is configured to display the polymer portion 12 divided into regions 91 to 94, but is not limited thereto, and may be configured to display the polymer portion 12 divided into 2 to 3, or 5 or more regions. In addition, in the heat map 90, a region with a high reaction rate may be displayed in a light tone, and a region with a low reaction rate may be displayed in a dark tone.

[0373] In addition, in the heat map 90, the area with a high reaction rate can be displayed with warm colors such as red, and the area with a low reaction rate can be displayed with cool colors such as blue, or the area with a high reaction rate can be displayed with cool colors such as blue, and the area with a low reaction rate can be displayed with warm colors such as red.

[0374] 7-3. Display method based on graph

[0375] (1) Method of displaying elastic modulus

[0376] Reference Figure 28 to Figure 30 , a method of displaying the elastic modulus of the target workpiece model WM using a graph is described. Figure 28 to Figure 30 This is a graph showing the elastic modulus of the target workpiece model WM relative to the reaction time of the cross-linking reaction. Fig.28 is a graph when the cross-linking reaction of the polymer portion 12 of the target workpiece model WM is carried out at the lowest temperature of the mold 10. Fig.29 This is a graph showing the case where the cross-linking reaction of the polymer portion 12 of the target workpiece model WM is carried out at a medium temperature of the mold 10. Fig.30 This is a graph showing the case where the cross-linking reaction of the polymer portion 12 of the target workpiece model WM is performed at the highest temperature of the mold 10. Figure 28 to Figure 30 In the figure, the solid line represents the measured value of the elastic modulus, and the dotted line represents the predicted value.

[0377] like Figure 28 to Figure 30 As shown, the elastic modulus increases after the cross-linking reaction starts and reaches a maximum value, and then decreases after reaching the maximum value.

[0378] The lowest temperature in the mold 10 Fig.28 The measured values ​​of elastic modulus agree with the predicted values ​​with high accuracy.

[0379] When the temperature of the mold 10 is moderate Fig.29 In the experiment, the measured value of the elastic modulus was inconsistent with the predicted value before 2 minutes after the reaction started, but after 2 minutes, the measured value and the predicted value were consistent with high accuracy. Before 2 minutes after the reaction started, the predicted elastic modulus was smaller than the measured value. However, for the area within 2 minutes after the reaction started, since it is not considered to be used as a product, the impact on the product is small.

[0380] The highest temperature in the mold 10 Fig.30 In the example, the measured value of the elastic modulus does not match the predicted value before 2 minutes after the reaction starts, but after 2 minutes, the measured value and the predicted value match with high accuracy. Before 2 minutes after the reaction starts, the predicted elastic modulus is smaller than the measured value. The difference between the measured value and the predicted value is larger than the case where the temperature of the mold 10 is moderate. However, as mentioned above, for the area within 2 minutes after the reaction starts, since it is not considered to be used as a product, the impact on the product is small.

[0381] (2) Method for displaying elastic modulus and internal bubbles 80 at the same time

[0382] Reference Fig.31 , a method of using a graph to display the prediction results of the elastic modulus of the polymer portion 12 of the target workpiece model WM and the generation of internal bubbles 80 is described. The temperature of the mold 10 is related to the above Fig.29 Also set the temperature to medium.

[0383] Fig.31 A graph showing the elastic modulus versus reaction time when a force is applied in a direction perpendicular to the axis A of the target workpiece model WM. The quadrilateral symbol represents the elastic modulus of the unit where the temperature of the polymer portion 12 of the target workpiece model WM is the highest value. The circular symbol represents the elastic modulus of the unit where the temperature of the polymer portion 12 of the target workpiece model WM is the middle value. The triangular symbol represents the elastic modulus of the unit where the temperature of the polymer portion 12 of the target workpiece model WM is the lowest value. Fig.31 In the figure, a blank symbol indicates a case where the internal bubble 80 is predicted to be generated, and a black symbol indicates a case where the internal bubble 80 is predicted not to be generated.

[0384] The graph of the unit in which the temperature of the polymer portion 12 is the highest value and the unit in which the temperature is the middle value passes through the reaction progress period and becomes a graph of the reaction return period.

[0385] In the unit where the temperature of the polymer part 12 is the highest value, the crosslinking reaction proceeds fastest. Therefore, it is predicted that when the reaction time exceeds 3 minutes and 3 minutes and 30 seconds have passed, the internal bubbles 80 will not be generated. In the unit where the temperature of the polymer part 12 is the highest, the return reaction of the crosslinking reaction also proceeds faster, so the elastic modulus is the lowest when the reaction time is 6 minutes.

[0386] In the unit where the temperature of the polymer portion 12 is a medium value, the crosslinking reaction also proceeds at a moderate level. Therefore, it is predicted that when the reaction time exceeds 3 minutes and 30 seconds and 4 minutes have passed, no internal bubbles 80 will be generated. The elastic modulus when the reaction time passes 6 minutes is greater than that of the unit where the temperature of the polymer portion 12 is the highest value.

[0387] In the unit where the temperature of the polymer portion 12 is the lowest value, the cross-linking reaction proceeds the slowest. Therefore, in the state before the reaction time is 4 minutes, it is predicted to be in the reaction progress period, and the elastic modulus increases with the passage of the reaction time. After the reaction time passes 4 minutes, it is predicted to be a return reaction of the cross-linking reaction, and the elastic modulus gradually decreases. In the unit where the temperature of the polymer portion 12 is the lowest value, when it is predicted that the reaction time exceeds 5 minutes and 5 minutes and 30 seconds have passed, no internal bubbles 80 are generated. At this time point, it is predicted that the internal bubbles 80 disappear in the entire area of ​​the polymer portion 12 of the object workpiece model WM. The elastic modulus predicted to be the maximum in the entire area of ​​the polymer portion 12 when the reaction time is 6 minutes.

[0388] As described above, it is predicted that the internal bubbles 80 will disappear in the entire region of the polymer portion 12 of the target workpiece model WM when the reaction time has passed for 5 minutes and 30 seconds, but in consideration of the risk rate, the reaction time of 6 minutes is adopted as the reaction time of the target workpiece model WM. It is predicted that the deviation of the elastic modulus of the polymer portion 12 will be 12% when the reaction time has passed for 6 minutes.

[0389] As described above, according to the present embodiment, for the target workpiece model WM, the reaction time at which the internal bubbles 80 are not generated can be predicted, and the variation in the elastic modulus of the polymer portion 12 at the reaction time can also be predicted.

[0390] (3) Method for visually displaying the internal air bubble 80

[0391] Reference Fig.32 , a method of visually displaying the prediction result of the generation of the internal bubbles 80 in the polymer portion 12 of the target workpiece model WM will be described.

[0392] Fig.32 The figure is a cross-sectional view of the target workpiece model WM, showing the possibility of the generation of the internal bubbles 80 in the polymer portion 12 in different depths. Fig.32 The darkest pattern is shown in the figure.

[0393] The polymer part 12 of the target workpiece model WM is Fig.32 The lightest pattern is shown in FIG. 1 . An elliptical region P and an elliptical region Q located inside the region P are shown inside the polymer portion 12. The region P is shown with a pattern slightly darker than the light pattern showing the polymer portion 12. The region Q is shown with a pattern slightly darker than the region P.

[0394] The following description will be made by taking as an example a case where, as a result of the inner bubble estimation process S4, the region P is determined to be a region where the inner bubble 80 is more likely to be generated, and the region Q is determined to be a region where the inner bubble 80 is more likely to be generated than the region P. The region P and the region Q correspond to regions where the inner bubble 80 is actually more likely to be generated (see Fig.23 ).

[0395] When the internal bubble estimation process S4 is completed, the display unit 7 displays Fig.32 The operator observes the target workpiece model WM displayed on the display unit 7. Fig.32 , visually confirm the outer bonding member 13 and the inner bonding member 14 represented by the darker pattern and the polymer portion 12 represented by the lighter pattern. The operator can intuitively understand that the outer bonding member 13 and the inner bonding member 14 represented by the darker pattern are different from the polymer portion 12. Thus, the operator can intuitively understand that in order to find the internal bubble 80, it is sufficient to confirm the polymer portion 12 represented by the lighter pattern. However, the outer bonding member 13 and the inner bonding member 14 may also be displayed as blank.

[0396] Next, the operator visually confirms that the region P and the region Q represented by the relatively dark pattern are displayed in the polymer portion 12 represented by the light pattern. Thus, the operator can intuitively understand that the internal bubbles 80 are likely to be generated in the region P and the region Q in the polymer portion 12. Furthermore, the region Q is displayed with a darker pattern than the region P, so it can be intuitively understood that the internal bubbles 80 are most likely to be generated in the region P. Thus, when studying the manufacturing conditions of the target workpiece model WM, it is sufficient to search for the internal bubbles 80 in the region where the possibility of generating the internal bubbles 80 is high, so the manufacturing conditions of the target workpiece model WM can be studied efficiently. However, the region where the possibility of generating the internal bubbles 80 is high may also be displayed with a relatively light pattern.

[0397] The present disclosure is not limited to the above-described embodiments, and can be applied to various embodiments without departing from the gist of the present disclosure.

[0398] In this embodiment, the internal bubble estimation unit 6 is configured to include a torque calculation unit 61, but is not limited thereto, and may also be configured to include: a reaction rate acquisition unit 60, which acquires the reaction rate (vulcanization degree) of the cross-linking reaction of the polymer part 12 of the target workpiece model WM; and an estimation unit 62, which estimates the generation of bubbles in the polymer part 12 of the target workpiece model WM based on the reaction rate during demolding. In this case, before performing a reaction analysis of the vulcanization reaction, the vulcanization degree under the torque that becomes a threshold value is obtained based on the reference reaction curve RC, and the vulcanization degree can be set as the vulcanization degree at the foaming point. In addition, the vulcanization degree at the foaming point can also be directly measured using a known measuring device such as a foaming point analyzer or a foaming point tester. Afterwards, a reaction analysis of the vulcanization reaction is performed, and the calculation result (vulcanization degree) of the reaction rate acquisition unit 60 is compared with the above-mentioned vulcanization degree at the foaming point, so that the generation of internal bubbles can be estimated. For example, when the vulcanization degree does not exceed the vulcanization degree at the foaming point, it is estimated that the internal bubbles 80 are generated in the polymer portion 12 of the target workpiece model WM.

Claims

1. A cross-linking reaction simulation device (1), comprising: a storage unit (2) for storing data used in the simulation; a thermal conductivity analysis unit (3) for performing thermal conductivity analysis of a polymer portion (12) of a target workpiece model (WM) during a crosslinking reaction; as well as A cross-linking reaction analysis unit (4) is used to analyze the reaction rate of the cross-linking reaction of the polymer part using the result of the thermal conductivity analysis, wherein: The storage unit stores: The target workpiece model has the polymer portion configured to include a base polymer; an equivalent reaction amount calculation model (EM) in which the ratio of the reaction amount of the cross-linking reaction at the target reaction temperature for the target reaction time to the reaction amount of the cross-linking reaction at the reference reaction temperature for the reference reaction time is defined as the equivalent reaction amount, and is defined as including a slope coefficient (SC) representing the slope of the Arrhenius plot; and The slope coefficient is set according to the progress of the cross-linking reaction of the polymer part, The cross-linking reaction analysis unit comprises: a temperature acquisition unit (40) for acquiring the temperature at each time point of each unit of the polymer part of the target workpiece model during the cross-linking reaction as a result of the thermal conductivity analysis; as well as A reaction rate calculation processing unit (41) calculates the equivalent reaction amount of the polymer part at each moment based on the acquired temperature at each moment of each unit of the polymer part in the cross-linking reaction, the equivalent reaction amount calculation model, and the slope coefficient corresponding to the progress of the cross-linking reaction at the target moment, and calculates the reaction rate of the cross-linking reaction of the polymer part based on the calculated equivalent reaction amount.

2. The cross-linking reaction simulation device according to claim 1, wherein: The polymer portion is a rubber portion configured to exhibit vibration-proof performance. The target workpiece model is a model of a vibration-proof rubber device.

3. The cross-linking reaction simulation device according to claim 1 or 2, wherein: The slope coefficient is set to different values ​​in the reaction progress period until the reaction rate of the cross-linking reaction reaches a peak and in the reaction return period after the reaction rate exceeds the peak.

4. The cross-linking reaction simulation device according to claim 3, wherein: The entire period including the reaction progress period and the reaction return period is divided into equal intervals, and the slope coefficient is set to a value corresponding to each division.

5. The cross-linking reaction simulation device according to claim 3, wherein: The slope coefficient is set to different values ​​in the initial reaction stage where the crosslinking reaction starts, the accelerated reaction stage where the reaction rate is faster than the initial reaction stage, and the late reaction stage where the reaction rate is slower than the accelerated reaction stage, in the crosslinking reaction until the reaction rate reaches the peak.

6. The cross-linking reaction simulation device according to claim 3, wherein: The slope coefficient is set to a smaller value in the reaction return period than in the reaction progress period.

7. The cross-linking reaction simulation device according to claim 3, wherein: The slope coefficient is set to a smaller value in the reaction return period than in the reaction progress period. The reaction progress period is divided into an initial reaction period in which the cross-linking reaction begins, a reaction promotion period in which the reaction speed is faster than the initial reaction period, and a late reaction period in which the reaction speed is slower than the reaction promotion period. The slope coefficient is set to a larger value in the reaction promotion period than those in the initial stage of the reaction and the late stage of the reaction.

8. The cross-linking reaction simulation device according to claim 1 or 2, wherein: The slope coefficient used at the target time is determined based on the reaction rate at the previous time. Based on the temperature at the target time, the equivalent reaction amount calculation model, and the slope coefficient, the equivalent reaction amount increase at the target time is calculated. Based on the equivalent reaction amount increase, the equivalent reaction amount cumulative value from the start of the cross-linking reaction to the target time is calculated, The reaction rate at the target time is calculated based on the accumulated value of the equivalent reaction amount from the start of the cross-linking reaction to the target time.

9. The cross-linking reaction simulation device according to claim 8, wherein: A first relationship data map (DM1) is stored, wherein the first relationship data map defines a corresponding relationship between a reaction rate of a cross-linking reaction of the polymer portion and the slope coefficient, The slope coefficient is determined using the response rate at the previous time and the first relationship data map.

10. The cross-linking reaction simulation device according to claim 8, wherein: A first function (F1) is stored, wherein the first function defines a corresponding relationship between a reaction rate of a cross-linking reaction of the polymer portion and the slope coefficient, The slope coefficient is determined using the reaction rate at the previous time and the first function.

11. The cross-linking reaction simulation device according to claim 10, wherein: The first function is set as different functions according to a plurality of reaction rate divisions set according to the degree of progress of the cross-linking reaction of the polymer portion.

12. The cross-linking reaction simulation device according to claim 8, wherein: A second relationship data map (DM2) is stored, wherein the second relationship data map defines a correspondence between the equivalent reaction amount cumulative value and the reaction rate at the target time. The reaction rate at the target time is determined using the equivalent reaction amount integrated value at the target time and the second relationship data map.

13. The cross-linking reaction simulation device according to claim 8, wherein: A second function (F2) is stored, wherein the second function defines a correspondence between the equivalent reaction amount cumulative value and the reaction amount at the target time. The reaction rate at the target time is determined using the equivalent reaction amount integrated value at the target time and the second function.

14. The cross-linking reaction simulation device according to claim 12, wherein: The second relationship data mapping is set by a reference reaction curve (RC), which is based on the relationship between the cross-linking reaction time at a reference reaction temperature measured by a cross-linking reaction characteristic testing machine (70) using a test object polymer material corresponding to the polymer part of the target workpiece model and the torque generated in the test object polymer material.

15. The cross-linking reaction simulation device according to claim 13, wherein: The second function is set by a reference reaction curve, which is based on the relationship between the cross-linking reaction time at a reference reaction temperature measured by a cross-linking reaction characteristic testing machine using a test object polymer material corresponding to the polymer part of the target workpiece model and the torque generated in the test object polymer material.

16. The cross-linking reaction simulation device according to claim 15, wherein: The second function is set as different functions according to a plurality of reaction rate divisions set according to the degree of progress of the cross-linking reaction of the polymer portion.

17. The cross-linking reaction simulation device according to claim 1 or 2, wherein: In the reaction progress period until the reaction rate of the cross-linking reaction reaches the peak, the start of the cross-linking reaction is defined as 0%, and the increase degree of the reaction rate of the cross-linking reaction is defined within the range of 0% to 100%. In the reaction return period after the reaction rate exceeds the peak, the value obtained by adding the degree of decrease in the reaction rate with respect to the reaction rate peak to 100% is defined as the reaction rate of the cross-linking reaction.

18. The cross-linking reaction simulation device according to claim 1 or 2, wherein: The cross-linking reaction simulation device further includes a display unit (7) for displaying a value obtained from the reaction rate corresponding to the target reaction time based on the analysis result of the cross-linking reaction analysis unit.

19. The cross-linking reaction simulation device according to claim 1 or 2, wherein: The cross-linking reaction simulation device further comprises a structure analysis unit (5) for performing structure analysis using the reaction rate of the cross-linking reaction of the polymer part analyzed by the cross-linking reaction analysis unit. The structural analysis unit comprises: a reaction rate acquisition unit (60) for acquiring the reaction rate of each unit of the polymer part calculated by the reaction rate calculation processing unit of the cross-linking reaction analysis unit; an elastic modulus allocating section (52) for allocating the elastic modulus corresponding to the acquired reaction rate in the polymer section; and A property acquisition unit (53) acquires the property of the target workpiece model by performing structural analysis in a state where the elastic modulus is assigned to the polymer portion.

20. The cross-linking reaction simulation device according to claim 19, wherein: The cross-linking reaction simulation device also includes a display unit, which displays the characteristics corresponding to the temperature of the molding die model (MM) used in the cross-linking reaction of the polymer part and the reaction time in the mold from the start of the cross-linking reaction to the demolding of the molding die model based on the result of the structural analysis.

21. The cross-linking reaction simulation device according to claim 19, wherein: The property of the target workpiece model is an elastic modulus of the target workpiece model.

22. The cross-linking reaction simulation device according to claim 1 or 2, wherein: The storage unit also stores: Forming die model; The target workpiece model includes the polymer portion further comprising carbon black; and Thermal diffusivity characteristics (TS), which represent the relationship between the mass ratio of the carbon black to the base polymer and the thermal diffusivity of the polymer portion, The thermal conductivity analysis unit comprises: a condition input unit (30) for inputting a mass ratio of the carbon black to the base polymer in the target workpiece model and a temperature condition of the molding die model; a polymer thermal diffusivity determination unit (31) that determines a polymer thermal diffusivity as a thermal diffusivity of the polymer portion of the target workpiece model based on the mass ratio input by the condition input unit and the thermal diffusivity characteristics stored in the storage unit; as well as An analysis unit (32) performs thermal conductivity analysis using the polymer thermal diffusivity determined by the polymer thermal diffusivity determination unit and the temperature condition stored in the storage unit, while the target workpiece model is arranged in the molding die model.

23. The cross-linking reaction simulation device according to claim 22, wherein: The thermal diffusivity characteristic is a relationship that does not depend on the type of the base polymer.

24. The cross-linking reaction simulation device according to claim 22, wherein: The thermal diffusivity characteristics are relationships set based on actually measured values ​​obtained when experiments were conducted with different mass ratios of carbon black in a plurality of base polymers.

25. The cross-linking reaction simulation device according to claim 22, wherein: The thermal diffusivity characteristic has a linear relationship with respect to the mass ratio of the carbon black.

26. The cross-linking reaction simulation device according to claim 22, wherein: The object workpiece model comprises: the polymer portion; and a joining member (13, 14) joined to the polymer portion, The storage unit further stores a contact heat transfer coefficient (CH), which is a heat transfer coefficient between the forming mold model and the joining member in a state where the target workpiece model is arranged on the forming mold model. The analyzing unit performs the thermal analysis using the polymer thermal diffusivity determined by the polymer thermal diffusivity determining unit, the temperature condition stored in the storage unit, and the contact heat transfer coefficient, while the target workpiece model is arranged on the molding die model.

27. The cross-linking reaction simulation device according to claim 22, wherein: The condition input unit inputs an external air condition (OC) including the temperature of the surroundings of the target workpiece model after being released from the molding die model. The storage unit further stores an air heat transfer coefficient (AC) as a heat transfer coefficient of air, The analysis unit performs the thermal conductivity analysis using the polymer thermal diffusivity determined by the polymer thermal diffusivity determination unit, the air heat transfer coefficient stored in the storage unit, and the external air conditions, in a state where the target workpiece model is demolded from the forming mold model after the polymer portion of the target workpiece model undergoes a cross-linking reaction within the forming mold model.

28. The cross-linking reaction simulation device according to claim 1 or 2, wherein: The storage unit also stores a forming die model. The cross-linking reaction simulation device further comprises an internal bubble estimating unit (6), which is used in a cross-linking reaction process. In the cross-linking reaction process, after the polymer part of the target workpiece model undergoes a cross-linking reaction in the molding die model, the molding die model is demolded. The internal bubble estimating unit estimates the generation of bubbles inside the polymer part of the target workpiece model accompanying the demolding of the molding die model. The internal air bubble estimating unit comprises: a reaction rate acquisition unit (60) for acquiring a reaction rate of a cross-linking reaction of the polymer portion of the target workpiece model; and An estimating unit (62) estimates the generation of bubbles inside the polymer portion of the target workpiece model based on the reaction rate during mold release.

29. The cross-linking reaction simulation device according to claim 28, wherein: The storage unit further stores a cross-linking reaction curve (CC) defining a relationship between an elapsed time from the start of a cross-linking reaction and a torque, the torque being a value corresponding to a degree of progress of a cross-linking reaction in the polymer portion of the target workpiece model and being measurable by a cross-linking reaction characteristic tester using a test target polymer material corresponding to the polymer portion, The internal bubble estimating unit further includes a torque calculating unit (61) for calculating the torque corresponding to the acquired reaction rate based on the reaction rate acquired by the reaction rate acquiring unit and the crosslinking reaction curve stored in the storage unit. The estimating unit estimates generation of bubbles inside the polymer portion of the target workpiece model based on the torque during mold release.

30. The cross-linking reaction simulation device according to claim 29, wherein: When the torque at the time of mold release does not exceed a preset threshold value, the estimating unit estimates that bubbles are generated inside the polymer portion of the target workpiece model.

31. The cross-linking reaction simulation device according to claim 30, wherein: The threshold value is set to a uniform value for a plurality of base polymers.

32. The cross-linking reaction simulation device according to claim 30, wherein: The threshold value is the torque corresponding to a reaction rate greater than a reaction rate of a cross-linking reaction at a foaming point of the polymer material.

33. The cross-linking reaction simulation device according to claim 29, wherein: The reaction rate acquisition unit acquires the reaction rate of each site of the polymer portion, The torque calculation section calculates the torque at each site of the polymer section, The estimating section estimates the generation of bubbles for each site of the polymer section.

34. The cross-linking reaction simulation device according to claim 29, wherein: The cross-linking reaction simulation device further includes a display unit that displays the presence or absence of generation of the bubbles based on the estimation result of the internal bubble estimation unit and the temperature of the mold model and the reaction time in the mold from the start of the cross-linking reaction to the demolding of the mold model.

35. The cross-linking reaction simulation device according to claim 34, wherein: The display unit displays the value obtained from the reaction rate corresponding to the temperature of the molding die model and the reaction time in the mold from the start of the crosslinking reaction to the demolding of the molding die model together with the presence or absence of the bubble generation based on the analysis result of the crosslinking reaction analysis unit.

36. The cross-linking reaction simulation device according to claim 34, wherein: The cross-linking reaction simulation device further includes a structure analysis unit configured to acquire characteristics of the target workpiece model by performing structure analysis using the reaction rate analyzed by the cross-linking reaction analysis unit. The display unit displays the characteristics corresponding to the temperature of the mold model and the reaction time in the mold from the start of the cross-linking reaction to the demolding of the mold model together with the presence or absence of the generation of the bubbles based on the result of the structural analysis.

37. A cross-linking reaction simulation device, comprising: A storage unit that stores data used in the simulation; and A thermal conductivity analysis unit performs thermal conductivity analysis of a polymer portion of a target workpiece model during a crosslinking reaction, wherein: The storage unit stores: Forming die model; a target workpiece model having the polymer portion configured to include a base polymer and carbon black; and thermal diffusivity characteristics, which represent the relationship between the mass ratio of the carbon black to the base polymer and the thermal diffusivity of the polymer portion, The thermal conductivity analysis unit comprises: a condition input unit for inputting a mass ratio of the carbon black to the base polymer in the target workpiece model and a temperature condition of the molding die model; a polymer thermal diffusivity determination unit that determines a polymer thermal diffusivity as a thermal diffusivity of the polymer portion of the target workpiece model based on the mass ratio input by the condition input unit and the thermal diffusivity characteristics stored in the storage unit; as well as An analysis unit performs a thermal conductivity analysis using the polymer thermal diffusivity determined by the polymer thermal diffusivity determination unit and the temperature condition stored in the storage unit in a state where the target workpiece model is arranged in the molding die model.

38. An internal bubble estimation device, the internal bubble estimation device being applied to a cross-linking reaction process, wherein in the cross-linking reaction process, after a polymer portion of a target workpiece model is subjected to a cross-linking reaction in a forming mold model, the forming mold model is demolded, and the internal bubble estimation device estimates generation of bubbles inside the polymer portion of the target workpiece model accompanying demolding of the forming mold model, wherein: The internal bubble estimation device comprises: a storage unit storing a cross-linking reaction curve defining a relationship between an elapsed time from the start of a cross-linking reaction and a torque, the torque being a value corresponding to a degree of progress of a cross-linking reaction in the polymer portion of the target workpiece model and being measurable by a cross-linking reaction characteristic tester using a test target polymer material corresponding to the polymer portion; a reaction rate acquisition unit that acquires a reaction rate of a cross-linking reaction of the polymer portion of the target workpiece model; a torque calculation unit that calculates the torque corresponding to the acquired reaction rate based on the reaction rate acquired by the reaction rate acquisition unit and the cross-linking reaction curve stored in the storage unit; as well as An estimating unit estimates generation of bubbles inside the polymer portion of the target workpiece model based on the torque during mold release.

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