Analysis and design methods for vulcanized rubber products

Abstract

To provide a method enabling vulcanized state to be confirmed for each of a plurality of rubber members constituting a vulcanized rubber product.SOLUTION: A method for analyzing a vulcanized rubber product including a plurality of rubber members having different formulations includes: a step S1 in which a computer calculates, for each of the plurality of rubber members, an equivalent vulcanization amount ECU received during vulcanization of the vulcanized rubber product or a first index which is an indicator using the ECU; and a step S2 in which the computer outputs the first index for each of the plurality of rubber members.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present disclosure relates to methods for analyzing and designing vulcanized rubber products. [Background technology]

[0002] A method for designing a pneumatic tire is described in Patent Document 1. In this method, an objective function representing physical quantities for evaluating tire performance, vulcanization condition variables that determine the physical properties of each rubber member, and design variables that determine the physical properties of the rubber member and reinforcing material are defined, and the vulcanization condition variables and design variables that provide the optimal value of the objective function are found. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent No. 5128853 Summary of the Invention [Problem to be solved by the invention]

[0004] It is generally known that in vulcanized rubber products, including tires, if multiple rubber components are vulcanized more than necessary, the physical properties of the multiple rubber components are adversely affected due to changes in the crosslinked structure. Therefore, in order to produce vulcanized rubber products with desired performance, it is important not to vulcanize the multiple rubber components more than necessary.

[0005] However, the vulcanization state of multiple rubber components tends to differ depending on the compounding, so there has been a demand for a method that can check the vulcanization state of each of multiple rubber components.

[0006] The present disclosure has been devised in consideration of the above-described circumstances, and its main purpose is to provide a method that makes it possible to check the vulcanization state of each of the multiple rubber components that make up a vulcanized rubber product. [Means for solving the problem]

[0007] The present disclosure provides a method for analyzing a vulcanized rubber product that includes multiple rubber components with different formulations, the method including the steps of: calculating, for each of the multiple rubber components, an equivalent vulcanization amount ECU that the vulcanized rubber product receives during vulcanization; or a first index that is an index using the same; and outputting, for each of the multiple rubber components, the first index. [Effects of the Invention]

[0008] By employing the above steps, the analysis method for a vulcanized rubber product of the present disclosure makes it possible to check the vulcanization state for each of the multiple rubber components that make up the vulcanized rubber product. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a perspective view showing a computer for executing the method for analyzing and designing a vulcanized rubber product of the present embodiment. [Figure 2] FIG. 2 is a cross-sectional view of the vulcanized rubber product of the present embodiment. [Figure 3] FIG. 2 is a partial cross-sectional view of a mold, a bladder, and an unvulcanized rubber product (tire) during the vulcanization process. [Figure 4] 3 is a flowchart showing the processing steps of the method for analyzing a vulcanized rubber product according to the present embodiment. [Figure 5] 10 is a flowchart showing the processing procedure of a first index calculation step of the present embodiment. [Figure 6] 10 is a flowchart showing an example of a processing procedure of a temperature data acquisition step according to the present embodiment. [Figure 7] 1A and 1B are diagrams illustrating an example of a mold model, an unvulcanized tire model, and a bladder model. [Figure 8] 1 is a graph showing time-series temperature data (relationship between temperature and vulcanization time) of a rubber member. [Figure 9] FIG. 10 is a distribution diagram of the first index of the present embodiment. [Figure 10] 1 is a graph showing the relationship between the physical properties of a rubber member and the equivalent vulcanization amount. [Figure 11]10 is a flowchart showing a processing procedure of a first index calculation step according to another embodiment of the present disclosure. [Figure 12] 10 is a flowchart showing the procedure of a coefficient input step. [Figure 13] 3 is a graph showing a first relationship which is the relationship between the physical properties of a rubber member and vulcanization time. [Figure 14] FIG. 10 is a distribution diagram of a first index according to another embodiment of the present disclosure. [Figure 15] 10 is a flowchart showing an example of a processing procedure of a method for analyzing a vulcanized rubber product according to another embodiment of the present disclosure. [Figure 16] 3 is a flowchart showing the processing steps of the method for designing a vulcanized rubber product according to the present embodiment. [Figure 17] 10 is a flowchart showing the processing steps of a method for designing a vulcanized rubber product according to another embodiment of the present disclosure. [Figure 18] 1 is a graph showing the relationship between the amount of change in the first index and the amount of change in the measured performance for a plurality of types of vulcanized rubber products. [Figure 19] 1 is a graph showing the relationship between predicted changes in performance and actually measured changes in performance for a plurality of types of vulcanized rubber products. DETAILED DESCRIPTION OF THE INVENTION

[0010] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. It should be understood that the drawings include exaggerated representations and representations that differ from the dimensional ratios of actual structures in order to facilitate understanding of the contents of the disclosure. Furthermore, identical or common elements are designated by the same reference numerals throughout the embodiments, and redundant explanations will be omitted. Furthermore, the specific configurations shown in the embodiments and drawings are intended to facilitate understanding of the contents of the present disclosure, and the present disclosure is not limited to the specific configurations shown in the drawings.

[0011] In the method for analyzing a vulcanized rubber product of this embodiment (hereinafter, sometimes simply referred to as the "analysis method"), a vulcanized rubber product including a plurality of rubber components with different formulations is analyzed. The analysis method of this embodiment uses a computer.

[0012] [computer] 1 is a perspective view showing a computer for executing the analysis method and design method for vulcanized rubber products of this embodiment. The computer 1 of this embodiment includes, for example, a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with, for example, a central processing unit (CPU), a read-only memory (ROM), a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. The storage device also stores software and the like for executing the analysis method of this embodiment.

[0013] [Vulcanized rubber products] The vulcanized rubber product is not particularly limited as long as it is made up of a plurality of rubber components with different formulations. The vulcanized rubber product of this embodiment is exemplified by a tire. Fig. 2 is a cross-sectional view of a vulcanized rubber product 2G (tire 2) of this embodiment.

[0014] The tire 2 of this embodiment is configured as, for example, a pneumatic tire for a passenger car. However, the tire 2 is not limited to this form and may be configured as, for example, a pneumatic tire for heavy loads or a tire for a motorcycle. The tire 2 of this embodiment is configured to include a plurality of rubber members 3 and a fibrous member 4.

[0015] The fibrous member 4 of this embodiment includes, for example, a carcass 4a, an inner belt 4b, and an outer belt 4c. The carcass 4a extends from the tread portion 2a through the sidewall portion 2b to the bead cores 5 of the bead portions 2c. The inner belt 4b and the outer belt 4c are disposed outside the carcass 4a in the tire radial direction and inside the tread rubber 3a.

[0016] The rubber members 3 of this embodiment include, for example, a tread rubber 3a, a sidewall rubber 3b, a clinch rubber 3c, a bead apex rubber 3d, and an inner liner rubber 3e. The tread rubber 3a is disposed on the outer side of the outer belt 4c in the tread portion 2a. The sidewall rubber 3b is disposed on the outer side of the carcass 4a in the sidewall portion 2b. The clinch rubber 3c is fixed to the inner side of the sidewall rubber 3b in the tire radial direction. The bead apex rubber 3d extends from the bead core 5 outward in the tire radial direction. The inner liner rubber 3e is disposed on the inner surface of the carcass 4a. In this embodiment, the rubber members 3a to 3e of this embodiment have different formulations (for example, at least some of the rubber material, filler, additives, etc.).

[0017] [Vulcanization molding] The vulcanized rubber product 2G of this embodiment (in this example, a tire 2) is produced, according to convention, by vulcanizing and molding an unvulcanized rubber product 8G (tire 8) including a plurality of rubber members 3 shown in FIG. 2. Here, "unvulcanized" includes all states that have not yet reached complete vulcanization, and the so-called semi-vulcanized state is included in this "unvulcanized" state. FIG. 3 is a partial cross-sectional view of a mold 11, a bladder 12, and the unvulcanized rubber product 8G (tire 8) during the vulcanization process.

[0018] In the vulcanization process of this embodiment, for example, a mold 11 is used to shape the outer surface of a vulcanized rubber product 2G (in this example, a tire 2), and a bladder 12 is used to expand within the cavity of an unvulcanized rubber product 8G (tire 8) set in the mold 11.

[0019] The mold 11 of this embodiment is configured to include, for example, a pair of sidewall molding dies 13, 13 having sidewall molding surfaces 13s, and a tread molding die 14 having a tread molding surface 14s. The tread molding die 14 is divided in the tire circumferential direction. The sidewall molding die 13 and the tread molding die 14 are fitted together to form a molding surface 11s that can mold the outer surface 2o of the tire 2. A heating means (not shown), such as an electric heater, is arranged in the mold 11.

[0020] The bladder 12 of this embodiment is made of, for example, an expandable rubber-like elastic body. A high-pressure fluid (not shown) is supplied to the internal space 12s of the bladder 12 from, for example, a supply means (not shown). The high-pressure fluid may be, for example, a mixture of water vapor and at least one inert gas, such as nitrogen, or a plurality of inert gases. The temperature of the high-pressure fluid is set to, for example, approximately 140 to 220°C.

[0021] In the vulcanization step, the unvulcanized rubber product (tire 8) is heated and pressurized between the mold 11 and the bladder 12 to produce the vulcanized rubber product 2G (tire 2) shown in FIG.

[0022] [Method for analyzing vulcanized rubber products (first embodiment)] Incidentally, in a vulcanized rubber product 2G including a tire 2, if the multiple rubber members 3 are vulcanized more than necessary, the crosslinked structure will change, adversely affecting the physical properties of the multiple rubber members 3 after vulcanization. For this reason, in order to manufacture a vulcanized rubber product 2G (tire 2) with desired performance, it is important not to vulcanize the multiple rubber members 3 more than necessary. On the other hand, the vulcanization state of the multiple rubber members 3 (for example, the speed of the vulcanization reaction, the equivalent vulcanization amount ECU, etc.) tends to vary depending on their compounding.

[0023] The analysis method of this embodiment makes it possible to confirm the vulcanization state for each rubber member 3 constituting the vulcanized rubber product 2G to be evaluated (in this example, the tire 2). Fig. 4 is a flowchart showing the processing steps of the analysis method of the vulcanized rubber product 2G of this embodiment.

[0024] [First index calculation step (first embodiment)] In the analysis method of this embodiment, first, a computer 1 (shown in FIG. 1) calculates a first index, which is an equivalent vulcanization amount ECU received during vulcanization of a vulcanized rubber product 2G to be evaluated or an index using the equivalent vulcanization amount ECU, for each of the plurality of rubber members 3 shown in FIG. 3 (first index calculation step S1). In the first index calculation step S1 of this embodiment, the equivalent vulcanization amounts ECU of the plurality of rubber members 3 are calculated as the first index. FIG. 5 is a flowchart showing the processing procedure of the first index calculation step S1 of this embodiment.

[0025] In the calculation of the equivalent vulcanization amount ECU in this embodiment, for example, temperature data (time-series temperature data) showing the relationship between temperature and time during vulcanization molding is used for each of the multiple rubber members 3 shown in Fig. 3. Therefore, in the first index calculation step S1 in this embodiment, first, time-series temperature data is acquired for each of the multiple rubber members 3 (temperature data acquisition step S11).

[0026] [Temperature data acquisition process] The time-series temperature data of the plurality of rubber members 3 may be obtained, for example, by installing a temperature sensor (not shown) in the mold 11 and measuring the temperature during vulcanization of the vulcanized rubber product 2G to be evaluated. Alternatively, the time-series temperature data may be obtained by performing a vulcanization simulation using a computer 1 (shown in FIG. 1). In the temperature data obtaining step S11 of this embodiment, time-series temperature data of the plurality of rubber members 3 is obtained by performing a vulcanization simulation. FIG. 6 is a flowchart showing an example of the processing procedure of the temperature data obtaining step S11 of this embodiment. FIG. 7 is a diagram showing an example of the mold model 21, the unvulcanized tire model 32, and the bladder model 22.

[0027] [Input mold model] In the temperature data acquisition step S11 of this embodiment, first, a mold model 21 (shown in FIG. 7) is input to a computer 1 (shown in FIG. 1) (step S21). In this embodiment, for example, based on design data (e.g., CAD data) of the mold 11 (shown in FIG. 3), the mold 11 is discretized (modeled) into a plurality (a finite number) of elements F(i) (i = 1, 2, ...) that can be handled by a numerical analysis method. This sets up the mold model 21 having an internal space 21i for arranging an unvulcanized rubber product model 31 (unvulcanized tire model 32).

[0028] As the numerical analysis method, for example, the finite element method, the finite volume method, the difference method, or the boundary element method can be appropriately adopted. In this embodiment, the finite element method is adopted. For each element F(i), for example, a tetrahedral solid element or the like is adopted. In the case of a two-dimensional model, a quadrilateral element or the like can be adopted.

[0029] Each element F(i) has a plurality of nodes 34. Numerical data such as an element number, a node number, a node coordinate value, and material properties (rigidity, Young's modulus, thermal conductivity, density, specific heat, thermal expansion coefficient, etc.) of the mold 11 (shown in FIG. 3) are defined for each element F(i). Such a mold model 21 can be easily set (modeled) by using, for example, commercially available meshing software.

[0030] The mold model 21 includes a pair of first mold models 23, 23 that model a pair of sidewall molds 13, 13 (shown in FIG. 3), and a second mold model 24 that model a tread mold 14 (shown in FIG. 3). The first mold model 23 and the pair of second mold models 24, 24 are combined together to form a molding surface 21s for molding the outer surface 32o of the unvulcanized tire model 32. The mold model 21 is input into a computer 1 (shown in FIG. 1).

[0031] [Enter unvulcanized rubber product model] Next, in the temperature data acquisition step S11 of this embodiment, an unvulcanized rubber product model 31 is input to the computer 1 (shown in FIG. 1) (step S22). In this embodiment, based on design data (e.g., CAD data) of the mold 11 (shown in FIG. 3), the unvulcanized rubber product 8G (unvulcanized tire 8) shown in FIG. 3 is discretized (modeled) into a finite number of elements G(i) (i = 1, 2, ...) that can be handled by a numerical analysis method. In this way, the unvulcanized rubber product model 31 (in this example, an unvulcanized tire model 32) is set.

[0032] In the unvulcanized rubber product model 31 (unvulcanized tire model 32) of this embodiment, for example, a plurality of rubber member models 35 are defined, each modeling a plurality of rubber members 3 (shown in FIG. 3). Furthermore, in the unvulcanized rubber product model 31 (unvulcanized tire model 32), for example, a fiber member model 36 is defined, each modeling a fiber member 4 (shown in FIG. 3) of an unvulcanized tire 8.

[0033] The multiple rubber member models 35 include a tread rubber model 35a that models the tread rubber 3a (shown in FIG. 3) and a sidewall rubber model 35b that models the sidewall rubber 3b (shown in FIG. 3). The multiple rubber member models 35 further include a clinch rubber model 35c that models the clinch rubber 3c (shown in FIG. 3) and a bead apex rubber model 35d that models the bead apex rubber 3d (shown in FIG. 3). The multiple rubber member models 35 further include an inner liner rubber model 35e that models the inner liner rubber 3e (shown in FIG. 3).

[0034] The elements G(i) are the same as the elements F(i) of the mold model 21. Each element G(i) is configured to include a plurality of nodes 37. Numerical data such as an element number, a node number, node coordinate values, and material properties (rigidity, Young's modulus, thermal conductivity, density, specific heat, thermal expansion coefficient, etc.) of the unvulcanized rubber member 3 and the fiber member 4 shown in FIG. 3 are defined for each element G(i). The unvulcanized rubber product model 31 (unvulcanized tire model 32) is stored in the computer 1 (shown in FIG. 1).

[0035] [Enter bladder model] Next, in the temperature data acquisition step S11 of this embodiment, a bladder model 22 is input to the computer 1 (shown in FIG. 1) (step S23). In this embodiment, for example, based on design data (e.g., CAD data) of the mold 11 and bladder 12 shown in FIG. 3, the bladder 12 is modeled (discretized) using a plurality (a finite number) of elements H(i) (i = 1, 2, ...) that can be handled by a numerical analysis method. In this way, the bladder model 22 is set.

[0036] The elements H(i) are similar to the elements F(i) of the mold model 21 and the elements G(i) of the unvulcanized tire model 32. Each element H(i) is configured to include a plurality of nodes 38. Numerical data such as an element number, node numbers, node coordinate values, and material properties (rigidity, Young's modulus, thermal conductivity, density, specific heat, thermal expansion coefficient, etc.) of the bladder 12 (shown in FIG. 3) are defined for each element H(i). The bladder model 22 is stored in the computer 1.

[0037] [Layout of unvulcanized rubber product model (tire model) and bladder model] Next, in the temperature data acquisition step S11 of this embodiment, the unvulcanized rubber product model 31 (in this example, the tire model 32) and the bladder model 22 are placed in the internal space 21i of the mold model 21 (step S24). In step S24 of this embodiment, the unvulcanized rubber product model 31 (the unvulcanized tire model 32) and the bladder model 22 can be placed in the internal space 21i of the mold model 21 based on a procedure similar to the placement step of a patent document (Japanese Patent No. 6871528), for example.

[0038] Boundary Condition Definition Next, in the temperature data acquisition step S11 of this embodiment, boundary conditions for calculating heat transfer of the unvulcanized rubber product model 31 (unvulcanized tire model 32), mold model 21, and bladder model 22 are defined in the computer 1 (shown in FIG. 1) (step S25). The boundary conditions of this embodiment include, for example, the initial temperatures of the mold model 21, unvulcanized rubber product model 31 (unvulcanized tire model 32), and bladder model 22, as well as the temperature conditions of the mold model 21 and bladder model 22 during the vulcanization process. The temperature conditions of this embodiment include the time-series temperatures of the mold 11 and bladder 12 shown in FIG. 3 during the heating and cooling processes. These boundary conditions can be defined, for example, based on a procedure similar to the boundary condition definition step in a patent document (Japanese Patent No. 6871528). These boundary conditions are input into the computer 1 (shown in FIG. 1).

[0039] Calculate heat transfer Next, in the temperature data acquisition step S11 of this embodiment, the computer 1 (shown in FIG. 1) calculates the heat transfer of the unvulcanized rubber product model 31 (unvulcanized tire model 32), the mold model 21, and the bladder model 22 (step S26). In step S26 of this embodiment, the mold model 21 with an increased temperature is calculated based on the initial temperature and temperature conditions of the mold model 21. As a result, in step S26, the heat transfer at the contact surface 40 between the unvulcanized rubber product model 31 (unvulcanized tire model 32) and the mold model 21 is calculated.

[0040] Furthermore, in step S26 of this embodiment, the bladder model 22 with an increased temperature is calculated based on the initial temperature and temperature conditions of the bladder model 22. As a result, in step S26, heat transfer at the contact surface 42 between the unvulcanized rubber product model 31 (unvulcanized tire model 32) and the bladder model 22 is calculated.

[0041] In this way, in step S26 of the present embodiment, it is possible to calculate the unvulcanized rubber product model 31 (unvulcanized tire model 32) whose temperature has increased, based on the temperatures of the mold model 21 and the bladder model 22. As a result, in step S26 of the present embodiment, it is possible to calculate the temperatures of the multiple rubber members 3 (multiple rubber member models 35) that change from moment to moment during vulcanization molding (in this example, the heating process and the cooling process), similar to the actual vulcanization process shown in Fig. 3 .

[0042] In step S26 of this embodiment, thermal analysis (heat transfer calculation) is performed for each unit step of the simulation until a predetermined heat transfer calculation time has elapsed. The thermal analysis can be performed using commercially available finite element analysis application software such as Abaqus manufactured by Dassault Systèmes, LS-DYNA manufactured by LSTC, or NASTRAN manufactured by MSC.

[0043] In this embodiment, the temperatures of the multiple rubber member models 35 are calculated for each unit step of the simulation at the nodes 37 of the elements G(i) that make up each rubber member model 35. In step S26 of this embodiment, time-series temperature data is acquired for each of the multiple rubber member models 35 (in this example, the tread rubber model 35a to the inner liner rubber model 35e). This time-series temperature data is acquired, for example, at a predetermined node (representative point) among the multiple nodes 37 that make up each rubber member model 35, but this is not particularly limited and may be acquired, for example, by averaging the temperatures of the multiple nodes 37. FIG. 8 is a graph showing time-series temperature data (the relationship between temperature and vulcanization time) of the rubber member 3. In FIG. 8, for example, the temperature data of the tread rubber model 35a is shown as a representative. The time-series temperature data of the multiple rubber members 3 is stored in the computer 1 (shown in FIG. 1).

[0044] [Calculate equivalent vulcanization amount] Next, in the first index calculation step S1 of this embodiment, an equivalent vulcanization amount ECU that is received during vulcanization of the vulcanized rubber product 2G to be evaluated is calculated for each of the multiple rubber members 3 shown in FIG. 3 (step S12). The equivalent vulcanization amount ECU is used to identify the speed of the vulcanization reaction, which changes depending on the temperature of the rubber member 3 during vulcanization molding. A larger value of the equivalent vulcanization amount ECU indicates that the vulcanization reaction is progressing more. Therefore, the first index is correlated with the vulcanization state.

[0045] To obtain the equivalent vulcanization amount (ECU), for example, the following formula (1) is used. The following formula (1) is based on the Arrhenius equation. Note that the equivalent vulcanization amount is not limited to the form obtained by the following formula (1).

[0046]

number

[0047] In the above formula (1), the activation energy E, gas energy R, and reference temperature T0 can be set appropriately depending on, for example, the rubber compounding and vulcanization conditions. The activation energy E is set to, for example, 83.72 kJ / mol. The gas energy R is set to, for example, 8.318 J / mol·deg. The reference temperature is set to, for example, 414.86 K.

[0048] In step S12 of this embodiment, each temperature T identified from the time-series temperature data (shown in FIG. 8) for the multiple rubber members 3 and the elapsed time t at that temperature T are respectively substituted into the above formula (1). As a result, in step S12 of this embodiment, an equivalent vulcanization amount ECU is obtained for each of the multiple rubber members 3. The equivalent vulcanization amount ECU for the multiple rubber members 3 is stored in the computer 1 (shown in FIG. 1) as a first index.

[0049] [Output first index] Next, in the analysis method of this embodiment, the computer 1 (shown in FIG. 1) outputs a first index for each of the multiple rubber members 3 shown in FIG. 3 (step S2). The first index of this embodiment is output to, for example, the display device 1d of the computer 1 or an output device such as a printer. The output format of the first index is not limited as long as it is output for each of the multiple rubber members 3. In step S2 of this embodiment, a distribution diagram of the first indexes of the multiple rubber members 3 is output. FIG. 9 is a distribution diagram of the first index of this embodiment.

[0050] As shown in Fig. 9, the distribution diagram of this embodiment is configured as a contour diagram in which the magnitude of the first index (in this example, the equivalent vulcanization amount) is displayed as a shade of color for each of the multiple rubber members 3 that make up the vulcanized rubber product 2G (in this example, a tire 2) to be evaluated. In Fig. 9, the larger the first index, the lighter it is displayed. To create the distribution diagram (contour diagram), for example, a general-purpose postprocessor (such as HyperView manufactured by Altair) is used.

[0051] As described above, the equivalent vulcanization amount ECU is used to identify the speed of the vulcanization reaction, which changes depending on the temperature of the rubber members 3 during vulcanization molding, and the larger the value of the equivalent vulcanization amount ECU, the more progressed the vulcanization reaction is. Therefore, in such a distribution diagram, it is possible to check at a glance the vulcanization state (for example, the progress of the vulcanization reaction) for each of the multiple rubber members 3 based on the first index (equivalent vulcanization amount) output for each of the multiple rubber members 3.

[0052] [Evaluate the first indicator] Next, in the analysis method of this embodiment, it is evaluated whether the vulcanization state of the plurality of rubber members 3 is good or not based on the first index (step S3). The evaluation may be performed by the computer 1 (shown in FIG. 1) or by an operator.

[0053] The evaluation of the vulcanization state is appropriately performed based on the first index. In step S3 of this embodiment, the equivalent vulcanization amount ECU and the optimum equivalent vulcanization amount ECU are calculated for each of the plurality of rubber members 3. optimum The absolute values ​​of the differences between the values ​​are calculated, and if the absolute values ​​are equal to or less than a predetermined threshold, it is determined that the vulcanization state of the plurality of rubber members 3 is good.

[0054] Optimal equivalent vulcanization amount ECU optimum is the most preferable vulcanization amount for each rubber member 3. optimum is specified as the equivalent vulcanization amount ECU at the time when the rubber member 3 reaches the desired physical properties.

[0055] Optimal equivalent vulcanization amount ECU of this embodimentoptimum is determined based on the relationship between the physical properties of the rubber member 3 and the equivalent vulcanization amount ECU. Such a relationship can be easily determined, for example, by preparing a test piece with the same composition as the rubber member 3 and conducting a test using the test piece and a vibration vulcanization tester (curelastometer) or a rubber processing tester (RPA) specified in JIS K6300. Fig. 10 is a graph showing the relationship between the physical properties of the rubber member 3 and the equivalent vulcanization amount ECU. Fig. 10 shows the relationship for one rubber member 3 as a representative example.

[0056] 10, the loss tangent tanδ and the torque TQ are shown as the physical properties of the rubber member 3. In this embodiment, the equivalent vulcanization amount A when the loss tangent tanδ is the smallest (most preferable) or the equivalent vulcanization amount B when the torque TQ reaches the required torque (most preferable) is determined as the optimum equivalent vulcanization amount ECU optimum The optimum equivalent vulcanization amount ECU optimum can be appropriately obtained depending on the physical properties required for the rubber member 3.

[0057] The threshold value used for evaluating the vulcanization state can be set appropriately for each of the multiple rubber members 3. The threshold value is specified based on, for example, the degree of adverse effect on the physical properties of each rubber member 3 due to over-vulcanization.

[0058] In step S3, if it is determined that the vulcanization state of the plurality of rubber members 3 is good ("Yes" in step S3), a vulcanized rubber product 2G is manufactured (step S4) based on, for example, the compounding of the plurality of rubber members 3, the vulcanization conditions, and the design factors of the vulcanized rubber product 2G. The vulcanization conditions include, for example, the temperature conditions and the vulcanization time.

[0059] On the other hand, if it is determined in step S3 that the vulcanization state of multiple rubber members 3 is not good ("No" in step S3), the composition, vulcanization conditions, design factors, etc. of the rubber members 3 whose vulcanization state is not good are changed (step S5), and the first index calculation steps S1 to S3 are performed again.

[0060] In this way, the analysis method of this embodiment makes it possible to check the vulcanization state based on the first index output for each of the multiple rubber members 3 shown in Fig. 9, and further makes it possible to change the compounding of the rubber members 3 and the vulcanization conditions based on the vulcanization state results. As a result, the analysis method of this embodiment makes it possible to design and manufacture a vulcanized rubber product 2G in which the multiple rubber members 3 are vulcanized in a good state.

[0061] [Method for analyzing vulcanized rubber products (second embodiment)] [First index calculation step (second embodiment)] In the first index calculation step S1 in the above-described embodiments, the equivalent vulcanization amounts of the multiple rubber members 3 are calculated as the first index, but the present invention is not limited to this. For example, the first index may be an over vulcanization index OV calculated by the following formula (2). OV=(ECU-ECU necessary ) / ECU necessary ×P …(2) however, ECU: Equivalent vulcanization amount of rubber material ECU necessary : Required equivalent vulcanization amount of rubber material P: Coefficient indicating the degree of adverse effect on physical properties due to over-vulcanization

[0062] In the above formula (2), the required equivalent vulcanization amount ECU necessary is the equivalent vulcanization amount required for each of the plurality of rubber members 3 to exhibit the desired physical properties. necessary is calculated appropriately based on the relationship between the physical properties of the rubber member 3 and the equivalent vulcanization amount ECU shown in FIG. 10. The equivalent vulcanization amount ECU is calculated based on the relationship between the physical properties of the rubber member 3 and the equivalent vulcanization amount ECU shown in FIG. 10. optimum It may be the same as or different from (in this example, the equivalent vulcanization amount A or B shown in FIG. 10).

[0063] In the above formula (2), the coefficient P is a parameter that specifies the degree of adverse effect on the physical properties due to over-vulcanization for each of the plurality of rubber members 3 shown in Fig. 3. The coefficient P in this embodiment is determined by the optimal equivalent vulcanization amount ECU optimumThis coefficient P indicates the magnitude of adverse effects (reversion) on physical properties after the temperature has passed (in an over-vulcanized state). Such adverse effects tend to differ depending on the compounding of the multiple rubber members 3. These coefficients P are specified for each of the multiple rubber members 3 in the coefficient input step S13 described below.

[0064] In the above formula (2), the required equivalent vulcanization amount ECU is calculated from the equivalent vulcanization amount ECU necessary By reducing the required equivalent vulcanization amount, ECU necessary The amount of equivalent vulcanization that exceeds the amount of equivalent vulcanization (ECU-ECU necessary ) is obtained. This over-equivalent vulcanization amount (ECU-ECU necessary ) to the ECU necessary The over-vulcanization index OV is calculated by multiplying the value obtained by dividing by 1 by a coefficient P that indicates the degree of adverse effect on physical properties due to over-vulcanization.

[0065] For example, over-equivalent vulcanization amount (ECU-ECU necessary Even if the coefficient P is large, the deterioration of physical properties due to over-vulcanization is small in the rubber member 3 where the coefficient P is small (the adverse effect on physical properties due to over-vulcanization is small). necessary Even if the coefficient P is small, the deterioration of physical properties due to over-vulcanization is significant for rubber members 3 with a large coefficient P. In this way, compared to the equivalent vulcanization amount ECUs of the previous embodiments, the over-vulcanization index OV makes it possible to appropriately grasp the deterioration of physical properties due to over-vulcanization by taking into account the magnitude of the adverse effect on physical properties due to over-vulcanization, which tends to differ for each of multiple rubber members 3. Figure 11 is a flowchart showing the processing procedure of the first index calculation step S1 of another embodiment of the present disclosure.

[0066] [Coefficient input process] In the first index calculation step S1 of this embodiment, first, a coefficient P indicating the degree of adverse effect on physical properties due to over-vulcanization is input to the computer 1 (shown in FIG. 1) for each of the plurality of rubber members 3 shown in FIG. 3 (coefficient input step S13). FIG. 12 is a flowchart showing the processing procedure of the coefficient input step S13.

[0067] [Get the first relationship] In the coefficient input step S13 of this embodiment, a first relationship, which is the relationship between the physical properties during vulcanization molding and the vulcanization time, is acquired for each of the multiple rubber members 3 (step S31). The first relationship can be acquired as appropriate. In this embodiment, for example, test pieces having the same composition as the multiple rubber members 3 are prepared, and tests are conducted using these test pieces and a vibration vulcanization tester (curelastometer) or a rubber processing tester (RPA) specified in JIS K6300. In this way, the first relationship can be acquired for each of the multiple rubber members 3.

[0068] FIG. 13 is a graph showing a first relationship, which is the relationship between the physical properties of the rubber member 3 and the vulcanization time. In FIG. 13, the first relationship of one rubber member 3 is shown as a representative. The physical properties of the rubber member 3 in this embodiment include loss tangent tanδ and torque TQ. Such a first relationship is useful for understanding the changes in the physical properties of the rubber member 3 over the course of vulcanization time. The first relationships of multiple rubber members 3 are stored in the computer 1.

[0069] [Specify the first point in time] Next, in the coefficient input step S13 of this embodiment, the computer 1 (shown in FIG. 1) determines a first time point J1 for each of the plurality of rubber members 3 shown in FIG. 3 based on the first relationship (step S32). The first time point J1 can be determined as appropriate. In this embodiment, the first time point J1 is determined by the required equivalent vulcanization amount ECU necessary , or optimal equivalent vulcanization amount ECU optimum The first time point J1 is determined as the time required for the required equivalent vulcanization amount ECU necessary Physical properties and optimal equivalent vulcanization amount ECU optimum The first time point J1 identified for each of the rubber members 3 is stored in the computer 1.

[0070] [Obtain the amount and rate of change of physical properties] Next, in the coefficient input step S13 of this embodiment, the computer 1 acquires the amount of change or the rate of change in the physical property from the first point in time J1 for each of the multiple rubber members 3 based on the first relationship (step S33). The amount of change and the rate of change in the physical property can be acquired as appropriate. In this embodiment, the amount of change and the rate of change in the physical property between the first point in time J1 and a predetermined second point in time J2 are acquired. The second point in time J2 can be set as appropriate as long as it is later than the first point in time J1, and can be set, for example, at the end of vulcanization of the vulcanized rubber product 2G.

[0071] The change in physical property includes, for example, an increase Δtanδ in loss tangent tanδ from the first time point J1a and a decrease ΔTQ in torque TQ from the first time point J1b. The larger the absolute values ​​of these increase Δtanδ and decrease ΔTQ, the greater the deterioration in physical property due to overvulcanization after the first time point J1 (J1a or J1b in this example).

[0072] The rate of change of a physical property includes, for example, the ratio (Δtanδ / tanδ) of the increment Δtanδ to the loss tangent tanδ at the first point in time J1a. That is, the ratio (Δtanδ / tanδ) indicates the rate of increase from the loss tangent tanδ at the first point in time J1a. The rate of change of a physical property also includes the increment Δtanδ divided by the vulcanization time between the first point in time J1a and the second point in time J2. Such a rate of change indicates the rate of increase from the loss tangent tanδ at the first point in time J1a (the slope of the loss tangent tanδ).

[0073] The rate of change of a physical property may include, for example, the ratio (ΔTQ / TQ) of the aforementioned decrease ΔTQ to the torque TQ at the first point in time J1b. That is, the ratio (ΔTQ / TQ) indicates the rate of decrease from the torque TQ at the first point in time J1a. The rate of change of a physical property may also include the decrease ΔTQ divided by the vulcanization time between the first point in time J1b and the second point in time J2. Such a rate of change indicates the rate of decrease from the torque TQ at the first point in time J1b (the slope of the torque TQ).

[0074] The larger the absolute values ​​of the change rates of these physical properties, the greater the deterioration of the physical properties due to overvulcanization after the first time point J1 (J1a or J1b in this example).

[0075] In step S33 of this embodiment, at least one of the above-mentioned change amount and change rate of the physical property may be calculated. The change amount or change rate of the physical property is obtained for each of the multiple rubber members 3 and stored in the computer 1 (shown in FIG. 1).

[0076] [Specify coefficient P] Next, in a coefficient input step S13 of this embodiment, the computer 1 (shown in FIG. 1) specifies the amount of change or rate of change in the physical property as a coefficient P for each of the multiple rubber members 3 shown in FIG. 3 (step S34). The amount of change or rate of change in the physical property specified as the coefficient P is selected as appropriate. In step S34 of this embodiment, the increase Δtanδ in the loss tangent tanδ from the first point in time J1a, which is calculated as the amount of change in the physical property, is specified as the coefficient P.

[0077] In order to clarify the difference in the over vulcanization index OV of each rubber member 3 (described later), the coefficient P may be calculated by multiplying the change amount or the change rate of the physical property by a predetermined factor (for example, 100 times). The coefficient P is specified for each of the multiple rubber members 3 and stored in the computer 1 (shown in FIG. 1).

[0078] [Calculate the over-vulcanization index] Next, in the first index calculation step S1 of this embodiment, the computer 1 (shown in FIG. 1) calculates the over vulcanization index OV using the equivalent vulcanization amount ECU (step S14). In step S14, for each of the plurality of rubber members 3 shown in FIG. 3, the equivalent vulcanization index ECU obtained in step S14 and the required equivalent vulcanization amount ECU are used to calculate the over vulcanization index OV. necessary and a coefficient P indicating the degree of adverse effect on physical properties due to over-vulcanization are substituted into the above formula (2). In this way, the over-vulcanization index OV is calculated for each of the multiple rubber members 3. The over-vulcanization index OV is input to the computer 1 as a first index.

[0079] [Output of first index (second embodiment)] Next, in step S2 of outputting the first index of this embodiment, an over vulcanization index OV is output as the first index for each of the plurality of rubber members 3. In this embodiment, as in the previous embodiments, a distribution diagram of the first indexes of the plurality of rubber members 3 is output. Fig. 14 is a distribution diagram of the first index of another embodiment of the present disclosure.

[0080] 14, the distribution map of this embodiment is configured as a contour map in which the magnitude of the first index (in this example, the over vulcanization index OV) is displayed by a shade of color for each of the multiple rubber members 3 that make up the vulcanized rubber product 2G. In FIG. 14, the larger the first index, the lighter it is displayed.

[0081] As described above, the over-vulcanization index OV is used to identify the deterioration of physical properties due to over-vulcanization, taking into account the magnitude of the adverse effects on physical properties due to over-vulcanization. The larger the value of this over-vulcanization index OV, the more severe the deterioration of physical properties due to over-vulcanization. Therefore, this distribution chart makes it possible to quickly check the deterioration of physical properties (vulcanization state) of each rubber member 3 due to over-vulcanization, compared to the distribution chart (shown in FIG. 9) in which the equivalent vulcanization amount ECU is displayed as the first index.

[0082] [Evaluating the first index (second embodiment)] Next, in the step S3 of evaluating the vulcanization state in this embodiment, the over vulcanization index OV is compared with a predetermined threshold value for each of the rubber members 3 shown in Fig. 14. If the over vulcanization index OV is equal to or less than the threshold value, it is determined that the vulcanization states of the rubber members 3 are good. The threshold value can be set appropriately and is specified based on, for example, the degree of adverse effect on the physical properties of each rubber member 3 caused by over vulcanization.

[0083] As described above, in the analysis method of this embodiment, as in the previous embodiments, the vulcanization state can be confirmed based on the first index output for each of the plurality of rubber members 3 shown in Fig. 14. Furthermore, in this embodiment, the compounding of the rubber members 3 and the vulcanization conditions can be changed in consideration of deterioration of the physical properties of each rubber member 3 due to over-vulcanization. As a result, the analysis method of this embodiment makes it possible to design and manufacture a vulcanized rubber product 2G in which the plurality of rubber members 3 are vulcanized in a good state.

[0084] [Method for analyzing vulcanized rubber products (third embodiment)] In the above-described embodiments, the vulcanized state of the vulcanized rubber product 2G is evaluated based on the first index (shown in FIGS. 9 and 14) output for each of the rubber members 3, but the present invention is not limited to such an embodiment. For example, the performance of the vulcanized rubber product 2G (shown in FIG. 2) may be predicted based on the first index.

[0085] The predicted performance can be set appropriately depending on the vulcanized rubber product 2G. Since the vulcanized rubber product 2G in this embodiment is a tire 2, the performance of the tire 2 (for example, at least one of the longitudinal spring constant, lateral spring constant, rolling resistance performance, and contact shape of the tire 2) is predicted. In this embodiment, the rolling resistance performance is predicted.

[0086] The performance of the vulcanized rubber product 2G can be predicted based on the first index as needed. As described above, the first index indicates the vulcanization state of each rubber member 3 shown in FIG. 3. This vulcanization state (first index) correlates with the physical properties of each rubber member 3. Furthermore, the first index of the vulcanized rubber product 2G (shown in FIG. 3) as a whole, determined from the first indexes of the multiple rubber members 3, correlates with the performance of the vulcanized rubber product 2G (shown in FIG. 2). Therefore, the performance of the vulcanized rubber product 2G can be predicted based on the first index.

[0087] As a result of extensive research, the present inventors have found that there is a correlation between the amount of change in the first index between a reference vulcanized rubber product 2G (not shown) and the vulcanized rubber product 2G to be evaluated, and the amount of change in performance between the reference vulcanized rubber product 2G and the vulcanized rubber product 2G to be evaluated. Note that the reference vulcanized rubber product 2G can be selected as appropriate as long as it is different from the vulcanized rubber product 2G to be evaluated (for example, the compounding or structure of the multiple rubber members 3 is different).

[0088] Furthermore, they found that the change in the first index is the difference in performance between the vulcanized rubber product 2G to be evaluated and the reference vulcanized rubber product 2G. Furthermore, they found that the performance of the vulcanized rubber product 2G to be evaluated can be determined by adding this difference in performance (the change in the first index) to the performance of the reference vulcanized rubber product 2G.

[0089] In this embodiment, the amount of change between the performance of the reference vulcanized rubber product 2G and the performance of the vulcanized rubber product 2G to be evaluated is determined based on the amount of change between the first index of the reference vulcanized rubber product 2G and the first index of the vulcanized rubber product 2G to be evaluated. Fig. 15 is a flowchart showing an example of the processing procedure of a method for analyzing vulcanized rubber products according to another embodiment of the present disclosure.

[0090] [Acquired the first index for standard vulcanized rubber products] In the analysis method of this embodiment, first, a computer 1 (shown in FIG. 1) acquires a first index of a predetermined reference vulcanized rubber product 2G (not shown) (step S6). In step S6 of this embodiment, first, a first index is calculated for each of the plurality of rubber members 3 constituting the reference vulcanized rubber product 2G. The calculation of the first indexes of the plurality of rubber members 3 is performed based on the same procedure as the first index calculation step S1 (shown in FIGS. 5 and 11) of the previous embodiments.

[0091] Next, in step S6 of this embodiment, the first index of the reference vulcanized rubber product 2G is calculated based on the first index determined for each of the plurality of rubber members 3. In step S6 of this embodiment, the first index of the reference vulcanized rubber product 2G is determined by averaging the first indexes of the plurality of rubber members 3.

[0092] The average calculation of the first indexes of the multiple rubber members 3 may be a weighted average that takes into account the degree of influence of each rubber member 3 on the performance of the vulcanized rubber product 2G. The first index of the reference vulcanized rubber product 2G is stored in a computer 1 (shown in FIG. 1).

[0093] [Acquire the performance of standard vulcanized rubber products] Next, in the analysis method of this embodiment, the computer 1 (shown in FIG. 1) acquires the performance of a reference vulcanized rubber product 2G (not shown) (step S7). The performance can be acquired appropriately, for example, based on a known procedure. For example, the performance (in this example, rolling resistance performance) may be acquired by conducting a test using an actual reference vulcanized rubber product 2G (in this example, a tire), or the performance may be acquired by conducting a simulation using the computer 1.

[0094] In step S7 of this embodiment, a simulation is performed using a tire model (not shown) that models a reference tire 2 and a road surface model (not shown) that models a road surface, to obtain rolling resistance performance. Such a simulation can be performed, for example, based on the procedure described in Patent Document (JP 2016-051391 A). Note that it is desirable that the physical properties of the multiple rubber members 3 that make up the reference vulcanized rubber product (tire) are defined in the multiple rubber member models that make up the tire model. This allows the rolling resistance performance of the reference tire to be obtained with high accuracy. The performance of the reference vulcanized rubber product 2G is stored in a computer 1 (shown in FIG. 1).

[0095] [Obtain the first indicator of the vulcanized rubber product being evaluated] Next, in the analysis method of this embodiment, the computer 1 (shown in FIG. 1) acquires a first index of the vulcanized rubber product 2G (shown in FIG. 3) to be evaluated (step S8). In step S8 of this embodiment, the first index (shown in FIGS. 9 and 14) acquired for each of the multiple rubber members 3 constituting the vulcanized rubber product 2G to be evaluated in the first index calculation step S1 (shown in FIGS. 5 and 11) is used.

[0096] In step S8 of this embodiment, the first index of the vulcanized rubber product 2G to be evaluated is obtained by averaging the first indexes of the multiple rubber members 3 shown in Fig. 3. Note that the average calculation of the first indexes of the multiple rubber members 3 may be a weighted average that takes into account the degree of influence of each rubber member 3 on the performance of the vulcanized rubber product 2G. The first index of the vulcanized rubber product 2G to be evaluated is stored in the computer 1 (shown in Fig. 1).

[0097] [Get the change in the first index] Next, in the analysis method of this embodiment, the computer 1 (shown in FIG. 1) obtains the amount of change between the first index of the reference vulcanized rubber product 2G (not shown) and the first index of the vulcanized rubber product 2G to be evaluated (shown in FIG. 3) (step S9). In this embodiment, in step S9, the first index of the reference vulcanized rubber product 2G (in this example, the average value of the first indexes of the multiple rubber members 3) is subtracted from the first index of the vulcanized rubber product 2G to be evaluated (in this example, the average value of the first indexes of the multiple rubber members 3). This determines the amount of change in the first index of the vulcanized rubber product 2G to be evaluated relative to the reference vulcanized rubber product 2G. The amount of change in the first index is stored in the computer 1.

[0098] [Obtain the performance of the vulcanized rubber product to be evaluated] Next, in the analysis method of this embodiment, the computer 1 (shown in FIG. 1) acquires the performance of the vulcanized rubber product 2G (shown in FIG. 2) to be evaluated (step S10). As described above, the change in the first index indicates the difference in performance of the vulcanized rubber product 2G to be evaluated relative to the reference vulcanized rubber product 2G (not shown). Therefore, in step S10 of this embodiment, the change in the first index acquired in step S9 is added to the performance of the reference vulcanized rubber product 2G acquired in step S7 to determine the performance of the vulcanized rubber product 2G to be evaluated (in this example, rolling resistance performance).

[0099] In this way, in the analysis method of this embodiment, in order to determine the performance of the vulcanized rubber product 2G (shown in FIG. 2) to be evaluated, it is not necessary to perform tests or simulations such as those in step S7 for obtaining the performance of the reference vulcanized rubber product 2G. Therefore, in the analysis method of this embodiment, the performance of the vulcanized rubber product 2G to be evaluated can be calculated in a short time. The performance of the vulcanized rubber product 2G to be evaluated is stored in computer 1 (shown in FIG. 1).

[0100] [Evaluating the performance of vulcanized rubber products] Next, in the analysis method of this embodiment, the performance of the vulcanized rubber product 2G to be evaluated is evaluated as to whether it is good or not (step S31). The evaluation may be performed by a computer 1 (shown in FIG. 1) or an operator.

[0101] In this embodiment, when the performance (in this example, rolling resistance performance) of the vulcanized rubber product 2G to be evaluated is equal to or less than a predetermined threshold, the performance of the vulcanized rubber product 2G to be evaluated is determined to be good. The threshold is set appropriately depending on the performance required of the vulcanized rubber product 2G (in this example, the tire 2).

[0102] If it is determined in step S31 that the performance of the vulcanized rubber product 2G to be evaluated is good ("Yes" in step S31), the vulcanized rubber product 2G is manufactured (step S4). For example, the blend of the multiple rubber members 3 that constitute the vulcanized rubber product 2G to be evaluated, vulcanization conditions, and design factors of the vulcanized rubber product 2G are used in the manufacture of this vulcanized rubber product 2G. The vulcanization conditions include, for example, temperature conditions and vulcanization time.

[0103] On the other hand, if it is determined in step S31 that the performance of the vulcanized rubber product 2G to be evaluated is not good ("No" in step S31), the compounding, vulcanization conditions, design factors, etc. of the rubber member 3 constituting the vulcanized rubber product 2G to be evaluated are changed (step S5). Then, the first index calculation steps S1 to S31 are performed again.

[0104] In this way, the analysis method of this embodiment makes it possible to predict and evaluate the performance of the vulcanized rubber product 2G to be evaluated based on the first indexes of the multiple rubber members 3. Therefore, the analysis method of this embodiment makes it possible to design and manufacture a vulcanized rubber product 2G having desired performance.

[0105] Furthermore, in the analysis method of this embodiment, the performance of the vulcanized rubber product 2G is evaluated for the vulcanized rubber product 2G that is determined to be in a good vulcanized state in step S3, which makes it possible to design and manufacture the vulcanized rubber product 2G with desired performance in a short time and reliably.

[0106] [Method for designing vulcanized rubber products (first embodiment)] The first index obtained by the analysis method of the above-described embodiments may be used in a design method for a vulcanized rubber product (hereinafter, sometimes simply referred to as a "design method"). In the design method of this embodiment, a vulcanized rubber product 2G (shown in FIG. 2) including a plurality of rubber members 3 with different compositions is designed. A computer 1 (shown in FIG. 1) is used to design the vulcanized rubber product 2G.

[0107] In the design method of this embodiment, the first index obtained by the analysis method of the previous embodiment is used as an objective function, and the required equivalent vulcanization amount ECU necessary An optimal solution of the design factors that optimizes the objective function is found using the coefficient P as design factors. Then, based on the optimal solution, the compounding of each of the plurality of rubber members 3 (shown in FIG. 3) is determined.

[0108] The optimal solution for the design factors is found based on an optimization algorithm using a computer 1. The optimization algorithm is used to determine optimal design factors (e.g., the above-mentioned parameters) that satisfy an arbitrary objective function under certain constraints. Examples of the optimization algorithm include a genetic algorithm (GA) and particle swarm optimization (PSO). Such optimization algorithms are suitable for searching for a global optimal solution while preventing the system from falling into a local solution. The calculation method of this embodiment employs particle swarm optimization (PSO), which has a relatively short calculation time, but a genetic algorithm (GA) or the like may also be employed.

[0109] In particle swarm optimization (PSO), optimization is performed by creating multiple initial conditions (first generation), finding the objective function for each condition, and updating each condition (generational change) so that it approaches the most desirable objective function. Random numbers are used to update each condition, allowing a wide search for optimal conditions. Details of particle swarm optimization (PSO) can be found in various documents, such as "Particle Swarm Optimization and Nonlinear Systems," IEICE Fundamentals Review (Institute of Electronics, Information and Communication Engineers), Vol. 5, No. 2, August 2011.

[0110] Enter Constraints Fig. 16 is a flowchart showing the processing steps of the design method for a vulcanized rubber product of this embodiment. In the design method of this embodiment, first, predetermined constraint conditions are input to the computer 1 (shown in Fig. 1) (step S41). The constraint conditions are conditions (design criteria) that must be met when manufacturing a vulcanized rubber product 2G (shown in Fig. 2). The constraint conditions of this embodiment include the required equivalent vulcanization amount ECU for each of the multiple rubber members 3 shown in Fig. 3. necessary and the range of coefficient P, which indicates the degree of adverse effect on physical properties due to over-vulcanization. Such constraints are set appropriately according to, for example, the compounding specifications of the plurality of rubber members 3. The constraints are stored in the computer 1.

[0111] [Enter initial values ​​for design factors] Next, in the design method of this embodiment, initial values ​​of design factors (first-generation design factors) are input to the computer 1 (shown in FIG. 1) for each of the multiple rubber members 3 shown in FIG. 3 (step S42). The initial values ​​of the design factors are used to calculate the first index.

[0112] The initial values ​​of the design factors in this embodiment are the required equivalent vulcanization amount ECU for each of the plurality of rubber members 3 shown in FIG. necessary , and a coefficient P indicating the degree of adverse effect on physical properties due to over-vulcanization are input. necessary and the coefficient P are determined within the range of the respective constraints.

[0113] In this embodiment, multiple sets of design factors are set for each of the multiple rubber members 3. One set constitutes the design factors of one vulcanized rubber product 2G. These sets differ from each other in at least one of the design factors. This makes it possible to obtain design factors for multiple types of vulcanized rubber products 2G. The initial values ​​of the design factors are stored in the computer 1 (shown in FIG. 1).

[0114] [Get the first index] Next, in the design method of this embodiment, the computer 1 (shown in FIG. 1) acquires (step S43) a first index for each of the plurality of rubber members 3. The first index can be acquired based on the processing procedure of the analysis method of the previous embodiments (first index calculation step S1 shown in FIGS. 5 and 11).

[0115] In step S43 of this embodiment, first, based on the processing procedure of the temperature data acquisition step S11 (shown in FIG. 6), time-series temperature data is acquired for each of the rubber members 3 shown in FIG. 3. In this embodiment, one piece of time-series temperature data is acquired for each of the rubber members 3 based on one predetermined vulcanization condition.

[0116] Next, in step S43 of this embodiment, an equivalent vulcanization amount ECU is calculated for each of the plurality of rubber members 3 shown in FIG. 3 based on the time-series temperature data and the above formula (1). Then, in step S43, the equivalent vulcanization amount ECU and the initial values ​​of the design factors in step S42 (required equivalent vulcanization amount ECU for each of the plurality of rubber members 3) are added to the above formula (2). necessary and coefficient P) are substituted, an over vulcanization index OV is acquired for each of the plurality of rubber members 3.

[0117] As described above, in step S42 of this embodiment, the design factors of the plurality of types of vulcanized rubber products 2G (in this example, the required equivalent vulcanization amount ECU for each of the plurality of rubber members 3) are calculated. necessary and coefficient P) are obtained. Therefore, by substituting these design factors into the above formula (2), the over vulcanization index OV for each of the multiple rubber members 3 in the multiple types of vulcanized rubber products 2G is obtained.

[0118] In this embodiment, the over vulcanization index OV is acquired as the first index for each of the plurality of rubber members 3. The first index is stored in the computer 1.

[0119] [Determine the objective function] Next, in the design method of this embodiment, the computer 1 determines whether or not the objective function is satisfied (step S44). A first index is set for the objective function of this embodiment.

[0120] In step S44 of this embodiment, first, from among the multiple types of vulcanized rubber products 2G, a vulcanized rubber product 2G having the best average value of the first indexes of all the rubber members 3 (i.e., the first indexes of each vulcanized rubber product 2G) is selected. Then, for the selected vulcanized rubber product 2G, if the first indexes of the multiple rubber members 3 are equal to or less than a predetermined threshold, it is determined that the objective function is satisfied. The threshold is specified based on, for example, the degree of adverse effect on the physical properties of each rubber member 3 due to over-vulcanization.

[0121] If it is determined that the objective function is satisfied ("Yes" in step S44), the design factors (required equivalent vulcanization amount ECU) of the plurality of rubber members 3 constituting the selected vulcanized rubber product 2G are necessary and coefficient P) is determined as the optimal solution of the design variables (step S45). On the other hand, if it is determined that the objective function is not satisfied ("No" in step S44), the design variables are updated based on the optimization algorithm (step S46), and steps S41 to S44 are performed again.

[0122] Update Design Factors Next, in the design method of this embodiment, the computer 1 (shown in FIG. 1) updates the design factors for each of the multiple rubber members 3 shown in FIG. 3 based on an optimization algorithm (step S46). In step S46 of this embodiment, for example, among the multiple types of vulcanized rubber products 2G, excluding the vulcanized rubber product 2G selected in step S44 (i.e., the vulcanized rubber product 2G with the best objective function), the design factors of the multiple rubber members 3 constituting the other vulcanized rubber products 2G are updated (generational change). Such design factor updating (generational change) can be performed appropriately based on particle swarm optimization (PSO) with reference to the above-mentioned paper, etc. The updated design factors are stored in the computer 1 (shown in FIG. 1).

[0123] After the design factors are updated, steps S43 to S44 are performed again based on the design factors of the vulcanized rubber product 2G with the best objective function and the updated design factors of the other vulcanized rubber products 2G. Therefore, in the design method of this embodiment, an optimal solution of the design factors of the vulcanized rubber product 2G that satisfies the objective function (in this example, the required equivalent vulcanization amount ECU necessary and coefficient P) can be reliably determined.

[0124] [Decide on the composition] Next, in the design method of this embodiment, the computer 1 (shown in FIG. 1) determines the compounding of each of the plurality of rubber members 3 shown in FIG. 3 based on the optimal solution of the design factors (step S47). In step S47 of this embodiment, the required equivalent vulcanization amount ECU necessaryand coefficient P, the compounding of the plurality of rubber members 3 is adjusted so as to achieve an ideal vulcanization state. The compounding to be adjusted includes, for example, polymers, fillers, oils, vulcanizing agents, vulcanization accelerators, and vulcanization retarders that constitute the rubber members 3. The compounding adjustment is performed, for example, by changing a rubber member 3 having a large over vulcanization index OV among the plurality of rubber members 3 to a compounding that reduces coefficient P, which indicates the degree of adverse effect on physical properties due to over vulcanization, or a compounding that slows down the vulcanization reaction. Meanwhile, the equivalent vulcanization amount ECU calculates the required equivalent vulcanization amount ECU necessary For the rubber members 3 that are slow to reach the vulcanization state, the formulation is changed to one that accelerates the vulcanization reaction rate. As a result, the design method of this embodiment makes it possible to reliably design and manufacture a vulcanized rubber product 2G in which all of the rubber members 3 are in a good vulcanized state.

[0125] [Method for designing vulcanized rubber products (second embodiment)] In the design method of the above embodiment, the required equivalent vulcanization amount ECU necessary In the above example, the compounding of the plurality of rubber members 3 is determined by finding an optimal solution for the design factors of the coefficients P and P, but the present invention is not limited to this. For example, the dimensions and vulcanization conditions of the plurality of rubber members 3 may be used as design factors, and a vulcanized rubber product 2G may be designed from an optimal solution for these design factors. Fig. 17 is a flowchart showing the processing steps of a method for designing a vulcanized rubber product according to another embodiment of the present disclosure.

[0126] [Enter constraints (second embodiment)] In step S41 of inputting constraints in this embodiment, the constraints are set, for example, as the ranges of dimensions of the plurality of rubber members 3 and the ranges of vulcanization conditions (for example, temperature conditions and vulcanization time). Such constraints are set as appropriate according to, for example, the standards of the vulcanized rubber product 2G and the specifications of the vulcanization equipment including the mold 11. The constraints are stored in the computer 1 (shown in FIG. 1).

[0127] [Enter initial values ​​for design factors] In step S42 of inputting the initial values ​​of the design factors in this embodiment, the dimensions of the multiple rubber members 3 shown in Fig. 3 and the vulcanization conditions (for example, temperature conditions and vulcanization time) are input as the initial values ​​of the design factors (first-generation design factors). These dimensions and vulcanization conditions are determined within the range of constraint conditions.

[0128] In this embodiment, multiple sets of dimensions and vulcanization conditions for multiple rubber members 3 are set. One set constitutes the design factor of one vulcanized rubber product 2G. These sets differ from each other in at least one of the design factors. This makes it possible to obtain design factors for multiple types of vulcanized rubber products 2G. Initial values ​​of the design factors are stored in the computer 1.

[0129] [Get the first index] Next, in step S43 of acquiring the first index in this embodiment, the first index can be acquired for each of the multiple rubber members 3 based on the analysis method of the previous embodiments (first index calculation step S1 shown in Figures 5 and 11).

[0130] In step S43 of this embodiment, first, based on the processing procedure of the temperature data acquisition step S11 (shown in FIG. 6), time-series temperature data is acquired for each of the plurality of rubber members 3 shown in FIG. 3. In this embodiment, based on the dimensions and vulcanization conditions of the plurality of rubber members 3 determined as design factors, time-series temperature data of each of the plurality of rubber members 3 is acquired for each of the plurality of types of vulcanized rubber products 2G (each collection of design factors).

[0131] Next, in step S43 of this embodiment, the equivalent vulcanization amount ECU is calculated for the plurality of rubber members 3 shown in Fig. 3 based on the time-series temperature data and the above formula (1). Then, in step S43, the equivalent vulcanization amount ECU and the required equivalent vulcanization amount ECU are added to the above formula (2). necessary and the coefficient P are substituted, whereby the over vulcanization index OV is acquired for each of the plurality of rubber members 3.

[0132] Required equivalent vulcanization amount ECU of this embodiment necessaryThe coefficients P and P are determined for each of the plurality of rubber members 3, and a common coefficient is used for the plurality of types of vulcanized rubber products 2G. Meanwhile, in this embodiment, time-series temperature data of the plurality of rubber members 3 is acquired for each of the plurality of types of vulcanized rubber products 2G (each set of design factors). Based on this temperature data, an equivalent vulcanization amount ECU and an over vulcanization index OV (first index) are acquired for each of the plurality of vulcanized rubber products 2G.

[0133] In this embodiment, the over vulcanization index OV is acquired as the first index for each of the plurality of rubber members 3. The first index is stored in the computer 1.

[0134] [Determining the objective function (second embodiment)] In the determining step S44 of this embodiment, similarly to the previous embodiments, first, from among the multiple types of vulcanized rubber products 2G, a vulcanized rubber product 2G having the best average value of the first indexes of all the rubber members 3 (i.e., the first indexes of each vulcanized rubber product 2G) is selected. Then, for the selected vulcanized rubber product 2G, if the first indexes of the multiple rubber members 3 are equal to or less than a predetermined threshold, it is determined that the objective function is satisfied.

[0135] If it is determined in step S44 that the objective function is satisfied ("Yes" in step S44), the design parameters (in this example, dimensions and vulcanization conditions) of the multiple rubber members 3 that make up the selected vulcanized rubber product 2G are determined as the optimal solution of the design parameters (step S45). On the other hand, if it is determined that the objective function is not satisfied ("No" in step S44), the design parameters are updated based on the optimization algorithm (step S46), and steps S41 to S44 are performed again. The design parameter update procedure is performed based on the same procedure as in the previous embodiments.

[0136] [Designing vulcanized rubber products] Next, in the design method of this embodiment, a computer 1 (shown in FIG. 1) designs a vulcanized rubber product based on the optimal solutions of the design factors (step S48). In this embodiment, the dimensions of the mold 11 and a heating means (not shown) for the mold 11 are designed based on the dimensions and vulcanization conditions of the multiple rubber members 3 determined as the optimal solutions. As a result, the design method of this embodiment makes it possible to reliably design and manufacture a vulcanized rubber product 2G in which all of the rubber members 3 are in a good vulcanized state.

[0137] Although particularly preferred embodiments of the present disclosure have been described in detail above, the present disclosure is not limited to the illustrated embodiments and can be modified and implemented in various forms. [Example]

[0138] [Example A] Based on the processing procedure shown in Fig. 4, vulcanized rubber products including multiple rubber components with different formulations were analyzed (Examples 1 and 2). The tire shown in Fig. 2 was used for the vulcanized rubber product. The multiple rubber components included tread rubber, sidewall rubber, clinch rubber, bead apex rubber, and inner liner rubber.

[0139] In Examples 1 and 2, a first index calculation process was first carried out to calculate the equivalent vulcanization amount ECU received during vulcanization of a vulcanized rubber product or a first index which is an index using the same for each of multiple rubber components.

[0140] In Example 1, the equivalent vulcanization amounts of the multiple rubber members were calculated as the first index based on the procedure shown in Fig. 5. On the other hand, in Example 2, the over vulcanization indexes of the multiple rubber members were calculated as the first index based on the procedure shown in Fig. 11.

[0141] Then, distribution maps of the first index (equivalent vulcanization amount) of the plurality of rubber members were output for each of Examples 1 and 2. Fig. 9 shows the distribution map of the first index (over-vulcanization index) for Example 1. Fig. 14 shows the distribution map of the first index for Example 2.

[0142] As a result of the test, it was possible to confirm the vulcanization state of each of the rubber members 3 based on the first index output for each of the rubber members in Examples 1 and 2. Furthermore, in Example 2, since the over-vulcanization index was output as the first index, it was possible to confirm at a glance the deterioration in the physical properties of each rubber member 3 due to over-vulcanization, compared to Example 1, in which the equivalent vulcanization amount was output as the first index.

[0143] [Example B] Based on the processing procedure shown in Fig. 15, the performance of multiple types of vulcanized rubber products was predicted (Example 3). The multiple types of vulcanized rubber products have different formulations for at least one rubber component among multiple rubber components that make them up. The vulcanized rubber products are tires, and the performance to be predicted is rolling resistance performance.

[0144] In Example 3, a predetermined standard vulcanized rubber product different from the multiple types of vulcanized rubber products was first produced. Next, in Example 3, the first index and performance of the standard vulcanized rubber product were obtained (actually measured). The first index was calculated as the average value of the first index (over-vulcanization index) of the multiple rubber members constituting the standard vulcanized rubber product.

[0145] Next, in Example 3, the first index was obtained for each of a plurality of types of vulcanized rubber products. The first index was calculated as the average value of the first index (over-vulcanization index) of a plurality of rubber members constituting each vulcanized rubber product.

[0146] Next, the amount of change (absolute value of difference) between the first index of the multiple types of vulcanized rubber products and the first index of the reference vulcanized rubber product was obtained. Furthermore, the amount of change in the first index of the multiple types of vulcanized rubber products was added to the performance of the reference vulcanized rubber product, thereby predicting the performance of the multiple types of vulcanized rubber products.

[0147] For comparison, the performance of several types of vulcanized rubber products was measured using the same procedure as for the standard vulcanized rubber product (experimental example).Then, the amount of change (absolute value of the difference) between the measured performance of the several types of vulcanized rubber products and the performance of the standard vulcanized rubber product was calculated.

[0148] 18 is a graph showing the relationship between the change in the first index (absolute value of the difference) and the change in the measured performance (absolute value of the difference) for multiple types of vulcanized rubber products. As shown in FIG. 18, in Example 3, it was confirmed that there is a correlation between the change in the first index between the reference vulcanized rubber product and multiple types of vulcanized rubber products and the change in the measured performance.

[0149] In Example 3, the amount of change (absolute value of difference) between the performance of a standard vulcanized rubber product and the predicted performance of multiple types of vulcanized rubber products was determined. Fig. 19 is a graph showing the relationship between the amount of change in predicted performance and the amount of change in actually measured performance for multiple types of vulcanized rubber products.

[0150] 19, it was confirmed that there was a correlation between the predicted performance and the actually measured performance in Example 3. Therefore, it was confirmed that the performance of the vulcanized rubber product could be predicted based on the first index in Example 5.

[0151] [Note] The present disclosure includes the following aspects.

[0152] [Disclosure 1] 1. A method for analyzing a vulcanized rubber product comprising a plurality of rubber components with different formulations, comprising: A step in which a computer calculates, for each of the plurality of rubber members, an equivalent vulcanization amount ECU received during vulcanization of the vulcanized rubber product or a first index which is an index using the equivalent vulcanization amount ECU; and outputting the first indicator for each of the plurality of rubber members by the computer. Analysis methods for vulcanized rubber products. [Disclosure 2] The method for analyzing a vulcanized rubber product according to Disclosure 1, wherein the outputting step outputs a distribution map of the first index of the plurality of rubber members. [Disclosure 3] The method for analyzing a vulcanized rubber product according to Disclosure 1 or 2, wherein the first index is the equivalent vulcanization amount ECU of the plurality of rubber members. [Disclosure 4] the step of calculating the first index includes a step of inputting a coefficient P, which indicates the degree of adverse effect on physical properties due to overvulcanization, for each of the plurality of rubber members into the computer; The method for analyzing a vulcanized rubber product according to Disclosure 1 or 2, wherein the first index is an over vulcanization index OV calculated by the following formula: OV=(ECU-ECU necessary ) / ECU necessary ×P however, ECU: Equivalent vulcanization amount of rubber material ECU necessary : Required equivalent vulcanization amount of rubber material P: Coefficient [Disclosure 5] The step of inputting the coefficient P includes a step of acquiring a first relationship, which is a relationship between a physical property during vulcanization molding and a vulcanization time, for each of the plurality of rubber members, and inputting the first relationship into the computer; The computer calculates the required equivalent vulcanization amount ECU for each of the plurality of rubber members based on the first relationship. necessary or a first time point when the rubber component reaches an optimum equivalent vulcanization amount, and obtains the change amount or rate of change in the physical property from the first time point; The method for analyzing a vulcanized rubber product described in Disclosure 4 includes a step in which the computer specifies the amount of change or the rate of change as the coefficient P for each of the plurality of rubber components. [Disclosure 6] The method for analyzing a vulcanized rubber product according to any one of Disclosures 1 to 5, further comprising a step in which the computer predicts the performance of the vulcanized rubber product based on the first index. [Disclosure 7] The vulcanized rubber product is a tire, The method for analyzing a vulcanized rubber product according to any one of Disclosures 1 to 6, wherein the performance is rolling resistance performance. [Disclosure 8] 1. A method for designing a vulcanized rubber product comprising a plurality of rubber components with different formulations, comprising: The computer A step of acquiring the first index based on the analysis method for the vulcanized rubber product according to any one of the present disclosures 1 to 7; a required equivalent vulcanization amount ECU (Equation Control Unit) that uses the first index of the plurality of rubber members as an objective function and is an equivalent vulcanization amount required for vulcanizing the plurality of rubber members; necessary and a coefficient P indicating the degree of adverse effect on physical properties due to over-vulcanization of the rubber member as design factors, and obtaining an optimal solution of at least one of the design factors that satisfies the objective function based on an optimization algorithm under predetermined constraint conditions; and determining the blending ratios of the plurality of rubber members based on the optimal solution. How to design vulcanized rubber products. [Disclosure 9] 1. A method for designing a vulcanized rubber product comprising a plurality of rubber components with different formulations, comprising: The computer A step of acquiring the first index based on the analysis method for the vulcanized rubber product according to any one of the present disclosures 1 to 7; a step of determining an optimal solution of at least one of the design factors that satisfies the objective function based on an optimization algorithm under predetermined constraint conditions, using the first index of the plurality of rubber members as an objective function and dimensions and vulcanization conditions of the plurality of rubber members as design factors; and designing the vulcanized rubber product based on the optimal solution. How to design vulcanized rubber products. [Explanation of symbols]

[0153] S1: Calculating the first index S2: Step of outputting the first index

Claims

1. 1. A method for analyzing a vulcanized rubber product comprising a plurality of rubber components with different formulations, comprising: a step of calculating, by a computer, a first index which is an index using an equivalent vulcanization amount ECU received during vulcanization of the vulcanized rubber product for each of the plurality of rubber members; and a step of outputting the first indicator for each of the plurality of rubber members by the computer, the step of calculating the first index includes a step of inputting a coefficient P, which indicates a degree of adverse effect on physical properties due to overvulcanization, for each of the plurality of rubber members into the computer; The method for analyzing a vulcanized rubber product, wherein the first index is an over vulcanization index OV calculated by the following formula: OV=(ECU-ECU necessary) / ECU necessary ×P however, ECU: Equivalent vulcanization amount of rubber material ECU necessary: ​​Required equivalent vulcanization amount of rubber material P: Coefficient

2. The method for analyzing a vulcanized rubber product according to claim 1 , wherein the outputting step outputs a distribution map of the first index of the plurality of rubber members.

3. The step of inputting the coefficient P comprises the steps of: obtaining a first relationship, which is the relationship between the physical properties during vulcanization molding and the vulcanization time, for each of the plurality of rubber members; and inputting the first relationship into the computer; a step in which the computer specifies, for each of the plurality of rubber components, a first time point that is a time point at which the required equivalent vulcanization amount ECU necessary is reached or a time point at which an optimal equivalent vulcanization amount for the rubber component is reached based on the first relationship, and obtains the amount of change in the physical property or the rate of change in the physical property from the first time point; The method for analyzing a vulcanized rubber product according to claim 1 or 2, further comprising the step of: specifying, by the computer, the amount of change or the rate of change as the coefficient P for each of the plurality of rubber members.

4. A method for analyzing vulcanized rubber products described in any one of claims 1 to 3, further comprising a step in which the computer predicts the performance of the vulcanized rubber product based on the first index.

5. The vulcanized rubber product is a tire, The method for analyzing a vulcanized rubber product according to claim 4 , wherein the performance is rolling resistance performance.

6. A method for designing a vulcanized rubber product comprising a plurality of rubber components with different formulations, comprising: The computer A step of acquiring the first index based on the method for analyzing the vulcanized rubber product according to any one of claims 1 to 5; a step of determining an optimal solution for at least one of the design factors that satisfies the objective function based on an optimization algorithm under predetermined constraints, using the first index of the plurality of rubber members as an objective function, and a required equivalent vulcanization amount ECU necessary, which is an equivalent vulcanization amount required to vulcanize the plurality of rubber members, and a coefficient P, which indicates the degree of adverse effect on physical properties due to over-vulcanization of the rubber members, as design factors; and determining the blending ratios of the plurality of rubber members based on the optimal solution. How to design vulcanized rubber products.

7. A method for designing a vulcanized rubber product comprising a plurality of rubber components with different formulations, comprising: The computer A step of acquiring the first index based on the method for analyzing the vulcanized rubber product according to any one of claims 1 to 5; a step of determining an optimal solution of at least one of the design factors that satisfies the objective function based on an optimization algorithm under predetermined constraint conditions, using the first index of the plurality of rubber members as an objective function and dimensions and vulcanization conditions of the plurality of rubber members as design factors; and designing the vulcanized rubber product based on the optimal solution. How to design vulcanized rubber products.

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