Method for predicting physical property value of vulcanized rubber

Abstract

To provide a method capable of accurately predicting physical property values of vulcanized rubbers.SOLUTION: The present invention relates to a method for predicting physical property values of vulcanized rubbers. This method comprises: a first step of acquiring a plurality of temperature histories showing the relation between a rubber temperature and a vulcanization time when a plurality of rubber materials are vulcanized under different vulcanization conditions; a second step of acquiring a first physical property value from each of the vulcanized rubbers vulcanized under the multiple temperature histories; and a third step of determining a temperature dependency coefficient E in an equation (1) that minimizes the error of an approximation equation, in order to obtain the approximation equation for estimating the first physical property value after vulcanization of a rubber material vulcanized under an arbitrary temperature history from a feature quantity F based on a conversion equation calculated by the equation (1), where F is a feature quantity, t is a vulcanization time (min), E is a temperature dependency coefficient, R is a gas constant, T(s) is a measured temperature during vulcanization (K).SELECTED DRAWING: Figure 7

Description

[Technical Field]

[0001] The present invention relates to a method for predicting physical property values ​​of vulcanized rubber. [Background technology]

[0002] Patent Document 1 listed below describes a method for predicting tire performance. This method includes a first step of inputting time-series temperature data of the rubber members when an unvulcanized tire including the unvulcanized rubber members is vulcanized and molded, a second step of predicting the physical properties of the rubber members after vulcanization based on the temperature data of the rubber members, and a third step of predicting the performance of the tire after vulcanization based on the physical properties of the rubber members. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2023-073083 Summary of the Invention [Problem to be solved by the invention]

[0004] In the technology of Patent Document 1, an equivalent vulcanization amount (ECU) is used to predict the physical property values ​​of a rubber member. Such an equivalent vulcanization amount is useful for predicting the physical property values ​​because it reflects the temperature during vulcanization, but there is room for further improvement in the prediction accuracy.

[0005] The present invention has been devised in view of the above circumstances, and its main object is to provide a method capable of predicting the physical properties of vulcanized rubber with high accuracy. [Means for solving the problem]

[0006] The present invention provides a method for predicting the physical properties of vulcanized rubber, comprising: a first step of acquiring a plurality of temperature histories showing the relationship between rubber temperature and vulcanization time when a plurality of rubber materials are vulcanized under different vulcanization conditions; a second step of acquiring a first physical property value from each of the vulcanized rubbers vulcanized under the plurality of temperature histories; and a third step of determining a temperature dependency coefficient E of the following equation (1) that reduces an error in the approximation equation to obtain an approximation equation for estimating the first physical property value after vulcanization of the rubber material vulcanized under an arbitrary temperature history from a feature quantity F based on a conversion equation calculated by the following equation (1).

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[0007] The method of predicting the physical properties of vulcanized rubber of the present invention employs the above steps, making it possible to predict the physical properties of vulcanized rubber with high accuracy. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 1 is a perspective view showing an example of a computer for executing a method for predicting physical property values ​​of vulcanized rubber. [Figure 2] FIG. 1 is a cross-sectional view showing an example of a rubber product. [Figure 3] 1 is a flowchart showing an example of a processing procedure of a method for predicting physical property values ​​of vulcanized rubber. [Figure 4] 10 is a graph showing an example of a plurality of temperature histories. [Figure 5] 10 is a graph showing an example of the relationship between a feature amount and a first physical property value of a rubber material after vulcanization. [Figure 6] 1A and 1B are diagrams illustrating an example of a rubber product model and a mold model. [Figure 7]10 is a graph showing an example of the relationship between a feature amount and a first physical property value. [Figure 8] 10 is a flowchart illustrating an example of a processing procedure of a prediction method according to another embodiment of the present invention. [Figure 9] 10 is a graph showing an example of the relationship between a feature amount and a second physical property value. [Figure 10] 1(a) is a graph showing the relationship between the characteristic amount and the loss tangent of Example 1, and FIG. 1(b) is a graph showing the relationship between the equivalent vulcanization amount and the loss tangent of Comparative Example. [Figure 11] 1 is a graph showing the relationship between the estimated value of the loss tangent estimated by the approximation formula of the first embodiment and the measured value of the loss tangent. [Figure 12] Graph (a) shows the relationship between the feature value and the swelling degree, graph (b) shows the relationship between the feature value and the absolute value of the complex modulus, and graph (c) shows the relationship between the feature value and the loss tangent. DETAILED DESCRIPTION OF THE INVENTION

[0009] Hereinafter, embodiments of the present invention 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 invention. 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 for the purpose of understanding the contents of the present invention, and the present invention is not limited to the specific configurations shown in the drawings.

[0010] In the method for predicting the physical properties of vulcanized rubber (hereinafter sometimes referred to as the "prediction method") of this embodiment, the physical properties of a rubber material vulcanized with an arbitrary temperature history (i.e., vulcanized rubber) are predicted. The prediction method of this embodiment uses a computer.

[0011] [computer] FIG. 1 is a perspective view showing an example of a computer 1 for executing a method for predicting physical property values ​​of vulcanized rubber. 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 prediction method of this embodiment. Therefore, the computer 1 is configured as a prediction device 1A for predicting physical property values ​​of vulcanized rubber.

[0012] The vulcanized rubber is not particularly limited as long as it is vulcanized rubber. An example of vulcanized rubber is a rubber material (vulcanized rubber) that constitutes a vulcanized rubber product. The rubber product of this embodiment is exemplified by a tire. Note that the rubber product is not limited to a tire, and may be, for example, a laminated rubber bearing for seismic isolation. FIG. 2 is a cross-sectional view showing an example of a rubber product 2.

[0013] The rubber product 2 is configured as a tire 2A. The tire 2A of this embodiment is configured as, for example, a pneumatic tire for a passenger car. However, the tire 2A 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 2A of this embodiment is configured to include a fibrous member 3 and vulcanized rubber 4.

[0014] The fibrous member 3 includes, for example, a carcass 3a, an inner belt 3b, and an outer belt 3c. The carcass 3a extends from the tread portion 2a through the sidewall portion 2b to the bead cores 5 of the bead portions 2c. The inner belt 3b and the outer belt 3c are disposed outside the carcass 3a in the tire radial direction and inside the tread rubber 4a.

[0015] The vulcanized rubber 4 includes a tread rubber 4a, a sidewall rubber 4b, a clinch rubber 4c, a bead apex rubber 4d, and an inner liner rubber 4e. The tread rubber 4a is disposed on the outer side of the outer belt 3c in the tread portion 2a. The sidewall rubber 4b is disposed on the outer side of the carcass 3a in the sidewall portion 2b. The clinch rubber 4c is fixed to the inner side of the sidewall rubber 4b in the tire radial direction. The bead apex rubber 4d extends from the bead core 5 outward in the tire radial direction. The inner liner rubber 4e is disposed on the inner surface of the carcass 3a.

[0016] The vulcanized rubber (rubber material) of this embodiment contains, for example, a filler, a cross-linking agent, etc. Examples of the filler include silica and carbon black.

[0017] Incidentally, in order to predict the performance of a rubber product 2, it is important to accurately estimate the physical property values ​​of the vulcanized rubber 4 that constitutes the rubber product 2. To estimate such physical property values, for example, the equivalent cure amount (ECU) is used. The equivalent cure amount is useful for estimating physical property values ​​because it reflects the temperature during vulcanization (temperature-vulcanization time conversion rule). However, there is still room for further improvement in the accuracy of predicting physical property values.

[0018] As a result of extensive research, the inventors have found that the physical property values ​​of vulcanized rubber 4 fluctuate due to the influence of reversion. The inventors have also found that it is effective to predict the physical property values ​​of vulcanized rubber 4 based on a newly devised feature quantity F that takes into account the temperature dependency of reversion. The feature quantity F is calculated using the following formula (1). In the following formula (1), the measured temperature T(s) is the absolute temperature.

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[0019] The feature quantity F is based on a conversion formula (in this example, an Arrhenius-type empirical formula) similar to the equivalent vulcanization amount (ECU). Therefore, the feature quantity F is related to the physical property values ​​of vulcanized rubber as a parameter for specifying the vulcanization state.

[0020] In the above formula (1), the activation energy, which was substituted as a fixed value in the known formula used to calculate the equivalent cure amount (ECU), is replaced with a temperature dependency coefficient E as a variable. Therefore, the feature value F is treated as a corrected ECU obtained by correcting the equivalent cure amount (ECU). Note that 8.318 J / (mol K) is substituted for the gas constant R in the above formula (1), just like in the formula for calculating the equivalent cure amount.

[0021] An arbitrary value is substituted for the temperature dependency coefficient E, taking into account the temperature dependency of reversion. Here, the activation energy (83720 J / mol) used to calculate the equivalent vulcanization amount does not take reversion into account. Therefore, by substituting a value greater than the activation energy for the temperature dependency coefficient E, it becomes possible to calculate the feature quantity F taking into account the temperature dependency of reversion.

[0022] The temperature dependency of reversion may differ depending on the type (e.g., differences in formulation, etc.) of the vulcanized rubber 4. Therefore, in order to more accurately predict the physical property values ​​of the vulcanized rubber 4, it is preferable to appropriately determine the temperature dependency coefficient E depending on the vulcanized rubber 4 to be predicted.

[0023] [Method for predicting physical properties of vulcanized rubber (first embodiment)] Based on the above findings, the prediction method of this embodiment can accurately predict the physical property values ​​of the vulcanized rubber 4. In this embodiment, the vulcanized rubber 4 whose physical property values ​​are predicted is exemplified as the sidewall rubber 4b constituting the tire 2A, but is not particularly limited thereto and may be, for example, the tread rubber 4a. Fig. 3 is a flowchart showing an example of the processing procedure of the method for predicting the physical property values ​​of the vulcanized rubber.

[0024] [Acquire multiple temperature histories (first step)] In the prediction method of this embodiment, first, a plurality of temperature histories showing the relationship between rubber temperature and vulcanization time are acquired (first step S1).

[0025] In the first step S1, a plurality of temperature histories are obtained when a plurality of rubber materials are vulcanized under different vulcanization conditions. Fig. 4 is a graph showing an example of the plurality of temperature histories. Fig. 4 shows representative temperature histories (first to fifth temperature histories) obtained from five rubber materials.

[0026] The temperature histories (first temperature history to fifth temperature history) indicate the change in temperature of the rubber material over time during vulcanization. These temperature histories can be obtained by vulcanizing an unvulcanized rubber material under different vulcanization conditions. 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.

[0027] In Figure 4, "0" on the time axis indicates the start time of vulcanization for each temperature history. "t1" on the time axis indicates the end time of vulcanization for the first temperature history. "t2" on the time axis indicates the end time of vulcanization for the second temperature history. "t3" on the time axis indicates the end time of vulcanization for the third temperature history. "t4" on the time axis indicates the end time of vulcanization for the fourth temperature history. "t5" on the time axis indicates the end time of vulcanization for the fifth temperature history.

[0028] The multiple temperature histories are used in the third step S3 described below to determine the temperature dependency coefficient E to obtain an approximate formula for estimating the first physical property value of the vulcanized rubber 4 from the feature value F calculated by the above formula (1).

[0029] Fig. 5 is a graph showing an example of the relationship between the feature amount F and the first physical property value of a rubber material after vulcanization. Fig. 5 plots the feature amount F calculated by the above formula (1) and the physical property value (first physical property value) of the rubber material after vulcanization through the temperature history for each of the 10 temperature histories including the temperature history (first temperature history to fifth temperature history) shown in Fig. 4.

[0030] In this embodiment, the feature value F shown in FIG. 5 is obtained by substituting the measured temperature during vulcanization and the temperature dependency coefficient E into the above formula (1) for each of the multiple temperature histories shown in FIG. 4. The measured temperature during vulcanization is the temperature measured from the vulcanization start time (0 minute) to the vulcanization end time (any of t1 to t5 minutes) for each of the multiple temperature histories. Also, in FIG. 5, for reference, the feature value F is calculated by substituting the activation energy (83720 J / mol) for the temperature dependency coefficient E.

[0031] The approximate formula is used to estimate the post-vulcanization physical property value (first physical property value) of a rubber material vulcanized under an arbitrary temperature history from the feature amount F calculated using the arbitrary temperature history and the above formula (1). In this embodiment, the approximate formula is obtained based on an approximate curve 6 drawn to fit data showing the relationship between the feature amount and the first physical property value (data plotted in FIG. 5). To obtain such an approximate formula, for example, commercially available spreadsheet software or the like is used.

[0032] In this way, multiple temperature histories are used to obtain the above-mentioned approximation formula. Therefore, for example, if the multiple rubber materials used to obtain the temperature histories (for example, the first to fifth temperature histories shown in FIG. 4) have different formulations, the correlation between the temperature histories (feature amount F) and the physical property values ​​will be weak, and the prediction accuracy of the approximation formula may decrease. Therefore, it is preferable that the multiple rubber materials have the same formulation. Note that if there is a strong correlation between the temperature histories (feature amount F) and the physical property values, rubber materials with different formulations may be included.

[0033] The vulcanization conditions can be set as appropriate as long as different temperature histories are acquired. The vulcanization conditions in this embodiment include, for example, the vulcanization temperature (temperature conditions set in the heat source (not shown) of the vulcanization mold) and the vulcanization time. By varying such vulcanization conditions and heating (vulcanizing), for example, the rubber product 2 shown in FIG. 2, multiple temperature histories of the rubber material (e.g., tread rubber 4a) contained in the rubber product 2 can be acquired. Note that the acquisition of the temperature histories is not limited to a mode in which the rubber product 2 is heated; for example, the rubber material alone may be heated (vulcanized).

[0034] The number of multiple temperature histories is set in consideration of, for example, the calculation accuracy required for the approximation formula, the cost required to obtain the approximation formula, etc. In this embodiment, the number is set to 5 to 50 (10 in this example).

[0035] The temperature history can be acquired as appropriate. The first step S1 of this embodiment includes a vulcanization simulation step for calculating the temperature history shown in FIG.

[0036] In the vulcanization simulation of this embodiment, the temperature history of a rubber material (e.g., tread rubber 4a) when the rubber product 2 is vulcanized using a vulcanization mold (not shown) for vulcanizing the rubber product 2 shown in Fig. 2 is calculated by the computer 1 shown in Fig. 1. This makes it possible to accurately calculate the temperature history of the rubber material that constitutes the rubber product 2 when the rubber product 2 is vulcanized. Note that in the vulcanization simulation, for example, the temperature history when the rubber material alone is vulcanized may also be calculated.

[0037] The vulcanization simulation can be carried out as needed as long as the temperature history of the rubber material can be obtained. Fig. 6 is a diagram showing an example of a rubber product model 7 and a mold model 8.

[0038] In the vulcanization simulation of this embodiment, a rubber product model 7 modeled on the rubber product 2 shown in FIG. 2 and a mold model 8 modeled on a vulcanization mold (not shown) are created. The rubber product model 7 and mold model 8 are discretized into a finite number of elements F(i) (i = 1, 2, ...). Next, heat transfer between the rubber product model 7 and the mold model 8 is calculated. In this heat transfer calculation, the temperature of each element F(i) is calculated for each unit step of the simulation. Then, from the elements F(i) constituting the rubber product model 7, one element F(i) constituting the rubber material to be predicted (in this example, the tread rubber model 10a) is selected. Then, based on the temperature calculated for the selected element F(i), the temperature history of the rubber material constituting the rubber product is acquired. This heat transfer calculation can be performed in a similar procedure to the first step of Patent Document 1.

[0039] In the first step S1 of this embodiment, the vulcanization simulation described above makes it possible to calculate multiple temperature histories based on different vulcanization conditions without actually vulcanizing the rubber product 2 or rubber material shown in Fig. 2. This makes it possible to suppress increases in costs required for obtaining multiple temperature histories and for obtaining approximate formulas.

[0040] Furthermore, in order to improve the prediction accuracy of the approximation formula, it is important to acquire multiple temperature histories in a distributed manner. In this embodiment, the vulcanization simulation process can be repeatedly performed with different vulcanization conditions until a desired temperature history is acquired. Therefore, multiple distributed temperature histories can be easily and reliably acquired. The temperature histories of multiple rubber materials (for example, the first to fifth temperature histories shown in FIG. 4) are stored in a computer 1 (shown in FIG. 1).

[0041] [Obtain the first physical property value of vulcanized rubber] Next, in the prediction method of this embodiment, a first physical property value is acquired from each of vulcanized rubbers 4 (shown in FIG. 2) vulcanized under a plurality of temperature histories (second step S2).

[0042] In this embodiment, a plurality of temperature histories (for example, the first to fifth temperature histories shown in FIG. 4) are calculated by a vulcanization simulation step included in the first step S1. In this case, the vulcanized rubber 4 (shown in FIG. 2) required to obtain the first physical property value is not produced in the first step S1. Therefore, in the second step S2 of this embodiment, prior to obtaining the first physical property value, the vulcanized rubber 4 vulcanized with a plurality of temperature histories is produced.

[0043] In the second step S2 of this embodiment, first, a plurality of unvulcanized rubber materials (not shown) are prepared. From the above viewpoint, it is preferable that these plurality of rubber materials have the same composition. Furthermore, the dimensions of the rubber materials may be determined in consideration of the measurement of the first physical property value, and the like, and the rubber materials may be formed as test specimens having a predetermined size. An example of the size of the test specimen is a thickness of 0.5 mm, a length of 10 mm, and a width of 5 mm.

[0044] Next, in the second step S2 of this embodiment, the unvulcanized rubber material (test piece) is vulcanized based on each of the multiple temperature histories (for example, the first to fifth temperature histories shown in FIG. 4) acquired in the first step S1. This produces vulcanized rubber (not shown). The rubber material is vulcanized as appropriate. For example, a known dynamic rubber process analyzer (for example, the "D-RPA3000" manufactured by Montec) is used to vulcanize the rubber material of this embodiment. Such an analyzer makes it possible to easily vulcanize the rubber material while reproducing multiple temperature histories. The rubber material may also be vulcanized using a press (hereinafter sometimes referred to as "press vulcanization").

[0045] Next, in the second step S2 of this embodiment, a first physical property value of the vulcanized rubber 4 is measured. The first physical property value can be appropriately acquired as long as it is a physical property value that can be acquired from the vulcanized rubber 4. Generally, the physical property values ​​that can be acquired from the vulcanized rubber 4 include a physical property value that changes depending on the amount of vulcanization. This amount of vulcanization differs for each of the multiple temperature histories acquired in the first step S1 (for example, the first to fifth temperature histories shown in FIG. 4), and therefore correlates with the above-mentioned feature amount F based on the conversion formula. Therefore, by acquiring such a physical property value as the first physical property value, it becomes possible to acquire an approximation formula that can estimate the first physical property value that changes depending on the feature amount F (amount of vulcanization) from the feature amount F in the third step S3 described below.

[0046] The first physical property value can be appropriately acquired as long as it is a physical property value that changes depending on the amount of vulcanization. The first physical property value preferably includes at least one of the swelling degree, loss tangent, and absolute value of the complex modulus of elasticity of the vulcanized rubber 4. The absolute values ​​of the swelling degree, loss tangent, and complex modulus of elasticity affect the performance of the rubber product 2 made of the vulcanized rubber 4. Therefore, by acquiring an estimated value of the first physical property value, it is possible to evaluate the performance of the rubber product 2.

[0047] The swelling degree (toluene swelling degree) is the mass change rate of a vulcanized rubber (test piece, not shown) before and after immersion in toluene at room temperature for 24 hours (mass after immersion / mass before immersion).

[0048] The absolute values ​​of the loss tangent and complex modulus are values ​​measured using a viscoelasticity spectrometer under the conditions shown below in accordance with the provisions of JIS K6394 "Vulcanized rubber and thermoplastic rubber - Determination of dynamic properties - General guidelines." Initial strain: 10% Amplitude: ±2% Frequency: 10Hz Deformation mode: tension Temperature: 70℃ Viscoelasticity spectrometer: GABO "Iplexar (registered trademark)"

[0049] In this embodiment, the swelling degree is acquired as the first physical property value. The first physical property value (the swelling degree in this example) acquired for each of a plurality of temperature histories (for example, including the first to fifth temperature histories shown in FIG. 4) is stored in the computer 1 (shown in FIG. 1).

[0050] [Determine the temperature dependence coefficient of the approximate formula (Step 3)] Next, in the prediction method of this embodiment, a temperature dependency coefficient E of the above formula (1) is determined (third step S3). The temperature dependency coefficient E is used to reduce an error in the approximation formula (for example, the approximation curve 6 shown in FIG. 5). As described above, the approximation formula is used to estimate the first physical property value after vulcanization of a rubber material vulcanized with an arbitrary temperature history (not shown) from the feature amount F calculated by the above formula (1). The error in the approximation formula refers to the error between the first physical property value estimated using the approximation formula from the feature amount F (i.e., the first physical property value on the approximation curve 6) and the actual first physical property value.

[0051] As described above, taking into consideration the temperature dependency of reversion, an arbitrary value is substituted for the temperature dependency coefficient E. The feature quantity F corresponding to the first physical property value shown in FIG. 5 varies depending on the magnitude of the value substituted for the temperature dependency coefficient E.

[0052] Fig. 7 is a graph showing an example of the relationship between the feature amount F and the first physical property value. Fig. 7 shows a graph showing the relationship between the feature amount F and the first physical property value for each different temperature dependency coefficient E. Fig. 7 shows graphs based on three temperature dependency coefficients E as representatives.

[0053] 7, in the graph on the left, the feature quantity F is calculated by substituting the same value as the activation energy (83720 x 1.0) for the temperature dependency coefficient E. Therefore, the feature quantity F in the graph on the left is the same value as the equivalent vulcanization amount (ECU).

[0054] Of the three graphs shown in Figure 7, the center graph and the right graph have a value greater than the activation energy substituted for the temperature dependency coefficient E. Therefore, the feature quantity F in the center graph and the right graph is greater than the equivalent vulcanization amount (ECU), and the temperature dependency of reversion can be taken into account. In the center graph, the value obtained by multiplying the activation energy by 1.46 (i.e., 83720 x 1.46) is substituted for the temperature dependency coefficient E. In the right graph, the value obtained by multiplying the activation energy by 3.0 (i.e., 83720 x 3.0) is substituted for the temperature dependency coefficient E.

[0055] 7, the feature quantity F corresponding to the first physical property value varies depending on the different temperature dependency coefficients E. By adjusting the temperature dependency coefficient E in this way, it becomes possible to specify an approximation formula with a small error between the first physical property value estimated from the feature quantity F using the approximation formula (i.e., the first physical property value on the approximation curve 6) and the actual first physical property value plotted based on the feature quantity F.

[0056] In the third step S3 of this embodiment, first, a feature amount F is calculated based on multiple temperature histories and the above formula (1) for each of multiple different temperature dependence coefficients E. Next, an approximate formula (approximate curve 6) is obtained based on the relationship between the feature amount F and the first physical property value for each of multiple different temperature dependence coefficients E.

[0057] Next, in a third step S3 of this embodiment, an estimate of the first physical property value calculated by the approximation formula is obtained for each of the plurality of temperature-dependence coefficients E. Next, in the third step S3 of this embodiment, an error between the first physical property value and the estimate of the first physical property value is obtained for each of the plurality of temperature-dependence coefficients E. Then, of the plurality of temperature-dependence coefficients E, the temperature-dependence coefficient E with the smallest error is determined. The error can be obtained, for example, as a root-mean-square error (RMSE).

[0058] Among the graphs shown in Fig. 7, the error between the first physical property value and the estimated value of the first physical property value calculated by the approximation formula (i.e., the first physical property value on approximation curve 6) is the smallest in the central graph. The temperature dependency coefficient E of this central graph (83720 x 1.46 in this example) is determined as the temperature dependency coefficient E that minimizes the error of the approximation formula. The determined temperature dependency coefficient E is stored in a computer (shown in Fig. 1).

[0059] As described above, in the prediction method of this embodiment, unlike the equivalent vulcanization amount in which the activation energy is used as a fixed value, the first physical property value is specified based on the feature value F which uses the temperature dependency coefficient E as a variable. By determining this temperature dependency coefficient E so as to reduce the error of the approximation formula (approximation curve 6), it becomes possible to specify an approximation formula that better represents the relationship between the feature value F and the first physical property value.

[0060] As described above, by substituting a value greater than the activation energy for the temperature dependency coefficient E, it becomes possible to accurately predict the first physical property value from the feature value F that takes into account the temperature dependency of reversion. From this perspective, when the temperature dependency coefficient E is defined as 83720×A, the variable A is preferably set to be greater than 1.0, more preferably 1.5 or greater. On the other hand, if the variable A is too large, the temperature dependency of reversion may be taken into account more than necessary, which may make it difficult to accurately predict the first physical property value. From this perspective, the variable A, in combination with the above-mentioned lower limit value, is preferably set to be 3.0 or less, more preferably 2.5 or less. As an example, the variable A is preferably 1.5 to 3.0 or 1.5 to 2.5.

[0061] Furthermore, in order to determine a temperature dependence coefficient E that reduces the error in the approximation formula, the variable A that specifies candidates for the temperature dependence coefficient E shown in FIG. 7 may be set in increments of, for example, 0.01 to 0.10 within the above range.

[0062] [Determine the approximate formula (4th step)] Next, in the prediction method of this embodiment, an approximate formula is determined based on the determined temperature dependency coefficient E (fourth step S4). In the third step S3 of this embodiment, as shown in FIG. 7, an approximate formula (approximate curve 6) is obtained for each of a plurality of temperature dependency coefficients E. Of these approximate formulas, an approximate formula into which the determined temperature dependency coefficient E is substituted is identified. This identified approximate formula can be determined as the approximate formula for estimating the first physical property value from the feature quantity F calculated using the above formula (1) and the temperature dependency coefficient E.

[0063] The procedure for determining the approximation formula is not limited to the above. For example, the feature amount F may be calculated for each of a plurality of temperature histories using the above formula (1) into which the determined temperature dependency coefficient E is substituted, and the approximation formula may be newly acquired based on the feature amount F and the first physical property value corresponding to the feature amount F. The determined approximation formula is stored in the computer 1 shown in FIG. 1.

[0064] [Calculate the performance values ​​of rubber products] Next, in the prediction method of this embodiment, the performance value of the rubber product 2 shown in Fig. 2 is calculated (step S8). In step S8 of this embodiment, the approximation formula determined in the fourth step S4 is used to estimate the first physical property value of the vulcanized rubber 4 contained in the rubber product 2. Then, a structural analysis is performed based on the estimated first physical property value, so that the performance value of the rubber product 2 can be calculated.

[0065] To estimate the first physical property value of the vulcanized rubber 4, first, heat transfer between the rubber product model 7 and the mold model 8 shown in FIG. 6 is calculated based on predetermined vulcanization conditions. In step S8 of this embodiment, first, the temperature history is calculated for all elements F(i) constituting the rubber material to be predicted in the rubber product model 7. Next, the feature values ​​F of all elements F(i) are calculated using the temperature histories of all these elements F(i) and the above formula (1) into which the determined temperature dependency coefficient E is substituted. Next, the feature values ​​of all elements F(i) are substituted into the determined approximation formula, thereby allowing the first physical property value of each element F(i) to be estimated.

[0066] Next, in step S8 of this embodiment, the first physical property value estimated for each element F(i) is defined for each element F(i) constituting the vulcanized rubber to be predicted. Then, a structural analysis of the rubber product model 7 is performed to predict the performance value of the rubber product model 7 (rubber product 2). When the rubber product 2 is a tire 2A as in this embodiment, the rolling resistance of the tire 2A may be calculated, for example, based on the procedure of step 3 of Patent Document 1. The performance values ​​of the rubber product 2 are stored in a computer 1 (shown in FIG. 1).

[0067] [Judge whether the performance values ​​meet the standards] Next, in the prediction method of this embodiment, it is determined whether or not the performance values ​​of the rubber product 2 satisfy predetermined criteria (step S9). In this embodiment, whether or not the performance values ​​satisfy the criteria is determined by a computer 1 (shown in FIG. 1), but this is not particularly limited. For example, an operator may make the determination based on the performance values ​​output from the computer 1. The criteria are set appropriately depending on the performance required of the rubber product 2.

[0068] If the performance values ​​of the rubber product 2 satisfy the criteria ("Yes" in step S9), the rubber product 2 is vulcanized (manufactured) based on the vulcanization conditions set in the heat transfer analysis (step S10). On the other hand, if the performance values ​​do not satisfy the criteria ("No" in step S9), step S11 is performed to change the vulcanization conditions, and steps S8 and S9 are performed again. The vulcanization conditions can be changed as appropriate, for example, so that the performance values ​​satisfy the criteria. This makes it possible to manufacture a rubber product 2 with the desired performance.

[0069] The prediction method of this embodiment makes it possible to identify the vulcanization conditions for the rubber product 2 to exhibit the desired performance, without actually vulcanizing and molding the rubber product 2 and conducting experiments using the rubber product 2. Therefore, the prediction method of this embodiment makes it possible to design and manufacture the rubber product 2 in a short time and at low cost.

[0070] [Method for predicting physical properties of vulcanized rubber (second embodiment)] In the above embodiments, an approximate formula for estimating a first physical property value is obtained from the feature amount F, but the present invention is not limited to this. For example, an approximate formula for estimating a second physical property value different from the first physical property value may be further determined.

[0071] The second physical property value can be appropriately acquired as long as it is a physical property value that can be acquired from the vulcanized rubber 4 shown in Fig. 2. In this embodiment, the second physical property value is acquired as a physical property value that changes depending on the vulcanization amount, similar to the first physical property value. This makes it possible to acquire an approximate expression that can estimate the second physical property value that changes depending on the feature amount F (vulcanization amount).

[0072] The second physical property value can be appropriately acquired as long as it is a physical property value different from the first physical property value and changes depending on the amount of vulcanization. Like the first physical property value, the second physical property value preferably includes at least one of the absolute values ​​of the swelling degree, loss tangent, and complex modulus of the vulcanized rubber 4. The absolute values ​​of the swelling degree, loss tangent, and complex modulus of the vulcanized rubber 4 affect the performance of the rubber product 2 made of the vulcanized rubber 4, so acquiring an estimated value of the second physical property value enables performance evaluation of the rubber product 2. In this embodiment, the loss tangent is acquired as the second physical property value. FIG. 8 is a flowchart showing an example of the processing procedure of a prediction method according to another embodiment of the present invention.

[0073] [1st process ~ 3rd process] In the prediction method of this embodiment, the first step S1 to the third step S3 shown in Fig. 3 are performed. As a result, in this embodiment, as in the previous embodiments, a temperature dependency coefficient E that reduces an error in an approximation formula for estimating a first physical property value from a feature quantity F can be determined.

[0074] [4th step] Next, in the prediction method of this embodiment, a fourth step S4 is performed, as in the previous embodiments. As a result, in this embodiment, an approximate formula for estimating the first physical property value from the feature quantity F can be determined based on the determined temperature dependence coefficient E. Note that in this embodiment, if there is no need to estimate the first physical property value, the fourth step S4 may be omitted.

[0075] [Obtain fewer types of temperature history than in the first process (5th process)] Next, in the prediction method of this embodiment, a plurality of temperature histories, the number of which is smaller than that in the first step S1, are acquired (fifth step S5). The plurality of temperature histories are used to determine an approximation formula for estimating the second physical property value from the feature quantity F in a seventh step S7 described below.

[0076] The feature quantity F used to estimate the second physical property value is calculated based on the above formula (1), similar to the feature quantity F used to estimate the first physical property value. The temperature dependency coefficient E in the above formula (1) is set appropriately. In this embodiment, the temperature dependency coefficient E determined in the third step S3 can be used (reused) as the temperature dependency coefficient E. In this way, the temperature dependency coefficient E common to the first physical property value is used to calculate the feature quantity F for estimating the second physical property value because the first physical property value and the second physical property value have in common the fact that they change depending on the amount of vulcanization and are correlated with the feature quantity F based on the conversion formula.

[0077] As described above, in this embodiment, the above formula (1) into which the temperature dependency coefficient E determined in the third step S3 is substituted is used to calculate the feature quantity F for estimating the second physical property value. Therefore, in the seventh step S7 described below, unlike the third step S3, a large number of temperature histories required for determining the temperature dependency coefficient E are not required. Therefore, the cost required for determining an approximation formula for estimating the second physical property value can be reduced.

[0078] The number of the plurality of temperature histories acquired in the fifth step S5 can be set appropriately as long as it is less than that in the first step S1. In this embodiment, the number is set to 2 to 10 (3 in this example) taking into consideration the calculation accuracy required for the approximation formula, the cost required to acquire the approximation formula, etc.

[0079] In the fifth step S5 of this embodiment, similar to the first step S1, multiple temperature histories are acquired when multiple rubber materials are vulcanized under different vulcanization conditions. These multiple temperature histories can be acquired by vulcanizing unvulcanized rubber materials under different vulcanization conditions. The vulcanization conditions are as described above. Furthermore, it is preferable that the multiple rubber materials used to acquire the multiple temperature histories have the same composition. Note that if there is a strong correlation between the temperature history (feature amount F) and the physical property values, rubber materials with different compositions may be included.

[0080] Multiple temperature histories can be acquired as appropriate. The fifth step S5 of this embodiment includes a vulcanization simulation step for calculating multiple temperature histories, similar to the first step S1. Details of the vulcanization simulation are as described above. Such vulcanization simulation can suppress increases in costs required for acquiring multiple temperature histories and for acquiring approximate expressions. Furthermore, since the vulcanization simulation step can be repeatedly performed with different vulcanization conditions until a desired temperature history is acquired, multiple dispersed temperature histories can be easily and reliably acquired.

[0081] In the fifth step S5, some of the temperature histories may be selected from the multiple temperature histories acquired in the first step S1 (for example, the first to fifth temperature histories shown in FIG. 4). In this case, for example, from the multiple temperature histories acquired in the first step S1, it is preferable to select the temperature history in which the feature amount F calculated by the above formula (1) is maximum, the temperature history in which the feature amount F is minimum, and the temperature history in which the feature amount F is close to the average value. This allows multiple dispersed temperature histories (feature amount F) to be acquired, making it possible to determine an approximation formula with high prediction accuracy. Furthermore, since there is no need to newly acquire temperature histories, the cost required to acquire multiple temperature histories can be reduced. The multiple temperature histories are stored in computer 1 (shown in FIG. 1).

[0082] [Obtaining the second physical property value of vulcanized rubber] Next, in the prediction method of this embodiment, a second physical property value different from the first physical property value is obtained from each of the vulcanized rubbers vulcanized under the multiple temperature histories obtained in the fifth step S5 (sixth step S6). Details of the second physical property value are as described above.

[0083] In this embodiment, a plurality of temperature histories are calculated by the vulcanization simulation step included in the fifth step S5. In this case, the vulcanized rubber 4 (shown in FIG. 2) required to obtain the second physical property value is not produced in the sixth step S6. Therefore, in the sixth step S6 of this embodiment, the vulcanized rubber 4 vulcanized with a plurality of temperature histories is produced prior to obtaining the second physical property value.

[0084] In the sixth step S6 of this embodiment, first, a plurality of unvulcanized rubber materials (not shown) are prepared. From the above-mentioned viewpoint, it is preferable that these plurality of rubber materials have the same composition. The dimensions of the rubber materials are as described above.

[0085] Next, in the sixth step S6 of this embodiment, the unvulcanized rubber material (test piece) is vulcanized based on each of the multiple temperature histories acquired in the fifth step S5, for example, using a known dynamic rubber process analyzer. This produces vulcanized rubber (not shown). The rubber material may also be press-vulcanized.

[0086] Next, in the sixth step S6 of this embodiment, the second physical property value of the vulcanized rubber 4 is measured. Details of the second physical property value are as described above. The second physical property values ​​acquired for each of the plurality of temperature histories (in this example, the loss tangents acquired for each of the three temperature histories) are stored in the computer 1 (shown in FIG. 1).

[0087] [Determine an approximate formula for estimating the second physical property value (7th step)] Next, in the prediction method of this embodiment, an approximation formula for estimating the second physical property value is determined (seventh step S7). The approximation formula is used to estimate the second physical property value after vulcanization of a rubber material vulcanized with an arbitrary temperature history from the feature quantity F calculated by the above formula (1) into which the determined temperature dependency coefficient E is substituted.

[0088] 9 is a graph showing an example of the relationship between the feature amount F and the second physical property value. In the seventh step S7 of this embodiment, for each of the plurality of temperature histories acquired in the fifth step S5 (three temperature histories in this example), the feature amount F calculated by the above formula (1) into which the temperature dependency coefficient E determined in the third step S3 is substituted, and the second physical property value corresponding to the feature amount F are identified. Based on data showing the relationship between the feature amount F and the second physical property value (data plotted in FIG. 9), an approximation formula (approximation curve 11) capable of estimating the second physical property value from the feature amount F is determined.

[0089] As described above, in the prediction method of this embodiment, the temperature dependency coefficient E, which is common to the first physical property value, is used to calculate the feature quantity F used to estimate the second physical property value. Therefore, an approximation formula (approximation curve 11) for estimating the second physical property value from the feature quantity F can be determined quickly and at low cost. Furthermore, the second physical property value is common to the first physical property value in that it changes depending on the vulcanization amount, and is correlated with the feature quantity F based on the conversion formula. Therefore, even if the temperature dependency coefficient E, which is common to the first physical property value, is used, the prediction accuracy of the second physical property value can be maintained. The determined approximation formula is stored in computer 1 shown in FIG. 1.

[0090] [Calculate the performance values ​​of rubber products] Next, in the prediction method of this embodiment, the performance values ​​of the rubber product 2 shown in Fig. 2 are calculated (step S8). In step S8 of this embodiment, the approximation formula determined in the fourth step S4 is used to estimate a first physical property value of the vulcanized rubber 4 contained in the rubber product 2. Furthermore, the approximation formula determined in the seventh step S7 is used to estimate a second physical property value of the vulcanized rubber 4 contained in the rubber product 2. Then, a structural analysis is performed based on the estimated first and second physical property values, so that the performance values ​​of the rubber product 2 can be calculated.

[0091] To estimate the first and second physical property values ​​of the vulcanized rubber 4, first, heat transfer between the rubber product model 7 and the mold model 8 shown in FIG. 6 is calculated based on predetermined vulcanization conditions. In step S8 of this embodiment, first, the temperature history is calculated for all elements F(i) constituting the rubber material to be predicted in the rubber product model 7. Next, the feature values ​​F of all elements F(i) are calculated using the temperature history of all elements F(i) and the above formula (1) into which the determined temperature dependency coefficient E is substituted. Next, the feature values ​​of all elements F(i) are substituted into the approximate formula determined in the fourth step S4 and the approximate formula determined in the seventh step S7, thereby estimating the first and second physical property values ​​of each element F(i).

[0092] Next, in step S8 of this embodiment, the first and second physical property values ​​estimated for each element F(i) are defined for each element F(i) constituting the vulcanized rubber to be predicted. Then, a structural analysis of the rubber product model 7 is performed to predict the performance values ​​of the rubber product model 7 (rubber product 2). The performance values ​​of the rubber product 2 are stored in the computer 1 (shown in FIG. 1).

[0093] [Judge whether the performance values ​​meet the standards] Next, in the prediction method of this embodiment, it is determined whether or not the performance values ​​of the rubber product 2 satisfy predetermined criteria (step S9). If the performance values ​​of the rubber product 2 satisfy the criteria ("Yes" in step S9), the rubber product 2 is vulcanized (manufactured) based on the vulcanization conditions set in the heat transfer analysis (step S10). On the other hand, if the performance values ​​do not satisfy the criteria ("No" in step S9), step S11 is performed to change the vulcanization conditions, and steps S8 and S9 are performed again. The vulcanization conditions can be changed as appropriate, for example, so that the performance values ​​satisfy the criteria. This makes it possible to manufacture a rubber product 2 with desired performance.

[0094] As with the previous embodiments, the prediction method of this embodiment makes it possible to identify the vulcanization conditions for the rubber product 2 to exhibit the desired performance, without actually vulcanizing and molding the rubber product 2 and conducting experiments using the rubber product 2. Therefore, the prediction method of this embodiment makes it possible to design and manufacture the rubber product 2 in a short time and at low cost.

[0095] [Method for predicting physical properties of vulcanized rubber (third embodiment)] In the above embodiments, an approximation formula for estimating the first physical property value and / or the second physical property value is determined, but the present invention is not limited to this. For example, an approximation formula for estimating a physical property value (such as a third physical property value) different from the first physical property value and the second physical property value may be determined.

[0096] The third physical property value can be appropriately acquired as long as it is a physical property value that can be acquired from the vulcanized rubber 4. In this embodiment, the third physical property value is acquired as a physical property value that changes depending on the amount of vulcanization, similar to the first and second physical property values. In this case, similar to the first and second physical property values, the third physical property value preferably includes at least one of the swelling degree, loss tangent, and absolute value of the complex modulus of elasticity of the vulcanized rubber 4 (in this example, the absolute value of the complex modulus of elasticity).

[0097] In this embodiment, an approximation formula for the third physical property value is determined based on a processing procedure similar to that of the fifth step S5 to the seventh step S7 shown in FIG. 8. As a result, the temperature-dependence coefficient E common to the first and second physical property values ​​is used to calculate the feature value F used to estimate the third physical property value, so that the approximation formula for estimating the third physical property value from this feature value F can be determined quickly and at low cost. Furthermore, the third physical property value is common to the first and second physical property values ​​in that it changes depending on the vulcanization amount, and is correlated with the feature value F based on the conversion formula. Therefore, even if the temperature-dependence coefficient E common to the first and second physical property values ​​is used, the prediction accuracy of the third physical property value can be maintained. The determined approximation formula is stored in the computer 1 shown in FIG. 1.

[0098] [Method for predicting physical properties of vulcanized rubber (fourth embodiment)] In the first step S1 of the embodiments described above, the temperature history is calculated by a vulcanization simulation step, but the present invention is not limited to this. The first step S1 may also include a vulcanization step in which the temperature history is determined by actual measurement. In the vulcanization step of this embodiment, the temperature history of the rubber material when the rubber product 2 is vulcanized is obtained using a vulcanization mold (not shown) for vulcanizing the rubber product 2 shown in FIG. 2. As a result, in this embodiment, the temperature history can be obtained with higher accuracy than in the vulcanization simulation step of the embodiments described above. In the vulcanization step, the rubber material alone may be press-vulcanized.

[0099] In this embodiment, the vulcanized rubber 4 required to obtain the first physical property value is prepared in the first step S1. Therefore, in the second step S2 of this embodiment, the first physical property value can be obtained without newly preparing the vulcanized rubber 4.

[0100] Although a particularly preferred embodiment of the present invention has been described in detail above, the present invention is not limited to the illustrated embodiment and can be modified and implemented in various ways. [Example]

[0101] [Example A] A first physical property value (loss tangent) of vulcanized rubber was predicted (Example 1) based on the first to third steps of the processing procedure shown in Fig. 3. In Example 1, the loss tangent was predicted as the first physical property value.

[0102] In Example 1, multiple temperature histories were obtained, each showing the relationship between rubber temperature and vulcanization time when multiple rubber materials were vulcanized under different vulcanization conditions (first step). Next, in Example 1, the loss tangent was obtained from each of the vulcanized rubbers vulcanized under the multiple temperature histories (second step). Then, in order to obtain an approximation formula for estimating the loss tangent from the feature quantity F, a temperature dependency coefficient E was determined that reduces the error of the approximation formula (third step).

[0103] In the third step, an approximate expression based on the relationship between the feature quantity F and the loss tangent was obtained for each of the different temperature dependency coefficients E. Then, among these temperature dependency coefficients E, the temperature dependency coefficient E that had the smallest error between the loss tangent and the estimated value of the loss tangent calculated by the approximate expression was determined. Furthermore, in Example 1, a fourth step of determining an approximate expression was performed based on the determined temperature dependency coefficients E.

[0104] For comparison, the equivalent cure amount (ECU) was calculated based on multiple temperature histories (Comparative Example). Then, in the Comparative Example, the relationship between the equivalent cure amount and the loss tangent was obtained. Furthermore, in the Comparative Example, an approximation formula for estimating the loss tangent from the equivalent cure amount was determined. Common specifications are as follows: Temperature history of the first process: 50 pieces Determined temperature dependence coefficient E: 83720 x 2.2 Activation energy: 83720 J / mol

[0105] Fig. 10(a) is a graph showing the relationship between the feature quantity F and the loss tangent in Example 1. In Fig. 10(a), the feature quantity F is calculated based on the determined temperature dependency coefficient E. Fig. 10(b) is a graph showing the relationship between the equivalent vulcanization amount (ECU) and the loss tangent in the comparative example.

[0106] The feature amount F of Example 1 shown in Fig. 10(a) has a higher correlation with the loss tangent than the equivalent vulcanization amount (ECU) of the comparative example shown in Fig. 10(b). It was confirmed that Example 1, in which an approximation formula for estimating the loss tangent is obtained from such feature amount F, can predict the physical property values ​​of the vulcanized rubber with higher accuracy than the comparative example, in which an approximation formula for estimating the loss tangent is obtained from the equivalent vulcanization amount (ECU).

[0107] 11 is a graph showing the relationship between the estimated value of the loss tangent estimated by the approximation formula of Example 1 and the measured value of the loss tangent. In Example 1, the root mean square error (RMSE) was 0.0029, and the maximum error was 0.0069. Therefore, in Example 1, the physical properties of the vulcanized rubber could be predicted with high accuracy.

[0108] [Example B] The physical property values ​​of vulcanized rubber were predicted (Example 2) based on the processing procedure shown in Fig. 8. In Example 2, the degree of swelling was predicted as the first physical property value.

[0109] In Example 2, a plurality of temperature histories were obtained showing the relationship between rubber temperature and vulcanization time when a plurality of rubber materials with the same compound were press-vulcanized under different vulcanization conditions (first step). Next, in Example 2, the swelling degree was obtained from each of the vulcanized rubbers vulcanized under the plurality of temperature histories (second step). Then, in order to obtain an approximate equation for estimating the swelling degree from the feature quantity F, a temperature dependency coefficient E was determined that reduces the error of the approximate equation (third step).

[0110] In the third step, an approximate formula based on the relationship between the feature amount F and the swelling degree was obtained for each different temperature-dependence coefficient E. Then, among these temperature-dependence coefficients E, the temperature-dependence coefficient E that had the smallest error between the swelling degree and the estimated value of the swelling degree calculated by the approximate formula was determined. Furthermore, in Example 2, a fourth step of determining an approximate formula was carried out based on the determined temperature-dependence coefficient E.

[0111] Next, in Example 2, a plurality of temperature histories, the number of which was smaller than that in the first step, were acquired (fifth step). Next, in Example 2, a second physical property value different from the first physical property value was acquired from each of the vulcanized rubbers vulcanized using a dynamic rubber process analyzer (RPA) based on the plurality of temperature histories acquired in the fifth step (sixth step). In Example 2, the absolute value of the complex modulus was predicted as the second physical property value.

[0112] Next, in Example 2, an approximation formula was determined to estimate the absolute value of the complex modulus after vulcanization of a rubber material vulcanized with an arbitrary temperature history from the feature value F calculated using the determined temperature dependence coefficient E (seventh step).

[0113] Furthermore, in Example 2, an approximation formula for estimating the third physical property value from the feature amount was determined based on the procedures of Steps 5 to 7. In Example 2, the loss tangent was acquired as the third physical property value.

[0114] In Example 2, the first, second, and third physical property values ​​were obtained for two types of vulcanized rubber: a press-vulcanized rubber and a dynamic rubber process analyzer (RPA).The first, second, and third physical property values ​​of these vulcanized rubbers were then estimated using approximate formulas determined based on the procedures of steps 1 to 7.The common specifications are as follows: Temperature history of the first process: 8 pieces Temperature history of the 5th process: 3 pieces Determined temperature dependence coefficient E: 83720 x 2.0

[0115] Fig. 12(a) is a graph showing the relationship between the feature value F and the degree of swelling. Fig. 12(b) is a graph showing the relationship between the feature value F and the absolute value of the complex modulus. Fig. 12(c) is a graph showing the relationship between the feature value F and the loss tangent. In these graphs, "●" indicates the physical property values ​​(8 pieces) of vulcanized rubber that was press-vulcanized, and "○" indicates the physical property values ​​(50 pieces) of vulcanized rubber that was vulcanized by a dynamic rubber process analyzer (RPA).

[0116] 12(a) to 12(c), in both the press-vulcanized vulcanized rubber and the vulcanized rubber vulcanized by a dynamic rubber process analyzer (RPA), the correlation between the feature quantity F and the swelling degree, the correlation between the feature quantity F and the absolute value of the complex modulus, and the correlation between the feature quantity F and the loss tangent are high. Therefore, it was confirmed that in Example 2, the physical property values ​​of the vulcanized rubber can be predicted with high accuracy.

[0117] Furthermore, in Example 2, unlike Example 1 (loss tangent), the degree of swelling was acquired as the first physical property value, but the absolute value of the complex modulus as the second physical property value and the loss tangent as the third physical property value could be accurately predicted using the temperature dependence coefficient E based on the degree of swelling. Even when the absolute value of the complex modulus was acquired as the first physical property value, the degree of swelling as the second physical property value and the loss tangent as the third physical property value could also be accurately predicted using the temperature dependence coefficient E determined based on the absolute value of the complex modulus. Therefore, it was confirmed that the first physical property value, the second physical property value, and the third physical property value could be accurately predicted regardless of the type of first physical property value used to determine the temperature dependence coefficient E.

[0118] [Note] The present invention includes the following aspects.

[0119] [Invention 1] A method for predicting physical properties of vulcanized rubber, comprising: A first step of acquiring a plurality of temperature histories showing the relationship between rubber temperature and vulcanization time when a plurality of rubber materials are vulcanized under different vulcanization conditions; a second step of acquiring a first physical property value from each of the vulcanized rubbers vulcanized under the plurality of temperature histories; and a third step of determining a temperature dependency coefficient E of the following formula (1) that reduces an error in the approximation formula in order to obtain an approximation formula for estimating the first physical property value after vulcanization of the rubber material vulcanized with an arbitrary temperature history from a feature quantity F based on a conversion formula calculated by the following formula (1), A method for predicting the physical properties of vulcanized rubber.

number

[0120] E temperature dependence coefficient

Claims

1. A method for predicting physical properties of vulcanized rubber, comprising: a first step of acquiring a plurality of temperature histories showing the relationship between rubber temperature and vulcanization time when a plurality of rubber materials are vulcanized under different vulcanization conditions; a second step of acquiring a first physical property value from each of the vulcanized rubbers vulcanized under the plurality of temperature histories; and a third step of determining a temperature dependency coefficient E of the following formula (1) that reduces an error in the approximation formula to obtain an approximation formula for estimating the first physical property value after vulcanization of the rubber material vulcanized with an arbitrary temperature history from a feature quantity F based on a conversion formula calculated by the following formula (1): A method for predicting the physical properties of vulcanized rubber. [Equation 1] where: F: Feature t: vulcanization time (minutes) E: Temperature dependency coefficient R: gas constant T(s): Measured temperature during vulcanization (K)

2. 2. The method for predicting physical property values ​​of vulcanized rubber according to claim 1, further comprising a fourth step of determining the approximate formula based on the determined temperature dependency coefficient E.

3. a fifth step of acquiring a plurality of temperature histories, the number of which is smaller than that of the first step; a sixth step of acquiring a second physical property value different from the first physical property value from each of the vulcanized rubbers vulcanized at the plurality of temperature histories acquired in the fifth step; 2. The method for predicting the physical property values ​​of vulcanized rubber according to claim 1, further comprising: a seventh step of determining an approximation formula for estimating the second physical property value after vulcanization of the rubber material vulcanized with an arbitrary temperature history from the feature quantity F calculated by the above formula (1) into which the determined temperature dependence coefficient E is substituted.

4. 2. The method for predicting the physical property values ​​of vulcanized rubber according to claim 1, wherein the first physical property value is a physical property value of the vulcanized rubber that changes depending on the amount of vulcanization.

5. The method for predicting physical property values ​​of vulcanized rubber according to claim 4 , wherein the first physical property value includes at least one of the swelling degree, loss tangent, and absolute value of complex modulus of the vulcanized rubber.

6. 2. The method for predicting physical property values ​​of vulcanized rubber according to claim 1, wherein the first step includes a vulcanization simulation step of calculating the temperature history.

7. 2. The method for predicting physical property values ​​of vulcanized rubber according to claim 1, wherein the first step includes a vulcanization step of determining the temperature history by actual measurement.

8. 2. The method for predicting physical property values ​​of vulcanized rubber according to claim 1, wherein the temperature dependency coefficient E is 83720×A (A is 1.0 to 3.0).

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