Method for predicting the viscoelastic properties of rubber materials

Abstract

This method allows for the prediction of viscoelastic properties of rubber materials in the high-frequency range in a shorter time and with fewer steps than conventional methods. [Solution] The method includes: a measurement step in which a rubber material is deformed while changing the frequency at a single temperature and the viscoelastic properties of the rubber material are measured at each frequency; a first prediction step in which the viscoelastic properties of the rubber material at a first frequency exceeding the frequency measured in the measurement step are predicted based on an exponential approximation line obtained by exponentially approximating the correlation data between the frequency and the viscoelastic properties obtained in the measurement step; and a second prediction step in which the viscoelastic properties of the rubber material at a second frequency exceeding the first frequency are predicted to be constant with the viscoelastic properties of the rubber material at the first frequency, wherein the first frequency is 500 Hz or more and 1500 Hz or less, and the second frequency is 3000 Hz or less.

Description

Technical Field

[0001] The present invention relates to a method for predicting the viscoelastic properties of rubber materials.

Background Art

[0002] Conventionally, as a method for measuring the viscoelastic properties of rubber materials, dynamic viscoelasticity measurement is known. Dynamic viscoelasticity measurement is a method for measuring the viscoelastic properties of a rubber material by applying a strain or stress that changes with time to a test piece made of the rubber material and measuring the stress or strain generated thereby.

[0003] On the other hand, in dynamic viscoelasticity measurement, it is difficult to measure the viscoelastic properties of rubber materials in a wide frequency range with a single viscoelasticity tester. Therefore, Patent Document 1 discloses a method of creating a master curve using a temperature-frequency conversion rule and calculating the viscoelastic properties of a rubber material in a wide frequency range. More specifically, after measuring the frequency dispersion of the viscoelastic property values of the rubber material at a plurality of temperatures with a viscoelasticity tester, a shift factor is obtained using the WLF equation (experimental equation (13) described in JIS K 6394), and the frequency dependence curve at each measurement temperature is shifted according to this shift factor to create a master curve.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] Conventional methods, including those described in Patent Document 1, require measuring the viscoelastic properties of rubber materials at multiple temperatures, which presents the challenge of being time-consuming. Furthermore, creating a master curve based on the measurement data requires complex data processing such as data conversion and interpolation, making it inefficient. [Means for solving the problem]

[0006] A method for predicting the viscoelastic properties of a rubber material according to one aspect of the present invention is a method for predicting the viscoelastic properties of a rubber material, comprising: a measurement step of deforming the rubber material while changing the frequency at one temperature and measuring the viscoelastic property value of the rubber material at each frequency; a first prediction step of predicting the viscoelastic property value of the rubber material at a first frequency exceeding the frequency measured in the measurement step, based on an exponential approximation line obtained by exponentially approximating the correlation data between the frequency and the viscoelastic property value obtained in the measurement step; and a second prediction step of predicting the viscoelastic property value of the rubber material at a second frequency exceeding the first frequency as being constant with the viscoelastic property value of the rubber material at the first frequency, wherein the first frequency is 500 Hz or more and 1500 Hz or less, and the second frequency is 3000 Hz or less. [Effects of the Invention]

[0007] According to the method for predicting the viscoelastic properties of rubber materials according to the present invention, the viscoelastic property values ​​of rubber materials in the high-frequency range can be predicted in a shorter time and with fewer steps than conventional methods. [Brief explanation of the drawing]

[0008] [Figure 1] This figure shows a flowchart illustrating a method for predicting the viscoelastic properties of a rubber material according to the present invention. [Figure 2] This figure shows an example of correlation data between the frequency measured in the measurement step and the viscoelastic property value in the method for predicting the viscoelastic properties of rubber materials according to the present invention. [Figure 3] This figure shows an example of an exponential approximation line calculated in the prediction step of the method for predicting the viscoelastic properties of rubber materials according to the present invention. [Figure 4] This figure shows an example of an exponential approximation line calculated in the prediction step of the method for predicting the viscoelastic properties of rubber materials according to the present invention. [Figure 5] This figure shows an example of correlation data between the frequency measured in the measurement step and the viscoelastic property value in the method for predicting the viscoelastic properties of rubber materials according to the present invention. [Figure 6] This figure shows an example of an exponential approximation line calculated in the prediction step of the method for predicting the viscoelastic properties of rubber materials according to the present invention. [Figure 7] This figure shows an example of an exponential approximation line calculated in the prediction step of the method for predicting the viscoelastic properties of rubber materials according to the present invention. [Figure 8] This figure shows the finite element models used in the simulations of the examples and comparative examples. [Figure 9] This figure shows the analysis results obtained in Example 1 and Comparative Example 1, specifically the results in the direction perpendicular to the axis. [Figure 10] This figure shows the analysis results obtained in Example 2 and Comparative Example 2, specifically the results in the direction perpendicular to the axis. [Modes for carrying out the invention]

[0009] As mentioned above, conventionally, for example, 1.0 × 10 -2 Hz~1.0×10 6 When calculating the viscoelastic properties of rubber materials over a wide frequency range, such as Hz, a master curve is created using the temperature-frequency conversion rule. More specifically, the frequency dispersion of the viscoelastic properties of the rubber material is measured at multiple temperatures using a viscoelasticity tester. In the above method, the frequency dispersion of the viscoelastic properties of the rubber material is generally measured in the range of 1 Hz to several hundred Hz using a viscoelasticity tester. Then, the frequency-dependent curves at each measurement temperature are shifted using the temperature-frequency conversion rule to create a master curve that shows the viscoelastic properties of the rubber material over a wide frequency range.

[0010] On the other hand, when designing devices that incorporate rubber materials, such as vibration isolation devices including engine mounts and motor mounts, it is not always necessary to have viscoelastic properties of the rubber material over a wide frequency range. For example, when designing a vibration isolation device using simulations with the finite element method, it may be necessary to have viscoelastic properties of the rubber material only at frequencies of approximately 100 Hz to 3000 Hz.

[0011] However, directly measuring the viscoelastic properties of rubber materials at frequencies of approximately 1000Hz to 3000Hz using existing viscoelasticity testing machines is difficult due to the specifications of these machines. Therefore, when calculating the viscoelastic properties of rubber materials at frequencies of approximately 1000Hz to 3000Hz, it was necessary to measure the viscoelastic properties of the rubber material at multiple temperatures and create a master curve, as described above. As a result, there was a problem that measuring the viscoelastic properties of rubber materials was time-consuming. Furthermore, when creating a master curve based on measurement data at multiple temperatures, complex data processing such as conversion and interpolation of measurement data was required, which also presented a challenge in terms of manpower.

[0012] As a result of our investigations, we have found a method for calculating the viscoelastic properties of a rubber material at frequencies of approximately 1000 Hz to 3000 Hz by measuring the frequency dispersion of the viscoelastic properties of a rubber material at a single temperature using a viscoelasticity tester, and then using an exponential approximation line obtained by exponentially approximating the correlation data between the measured frequency and the viscoelastic properties. Specifically, up to a first frequency of approximately 1000 Hz, a predicted value of the viscoelastic properties is obtained using an exponential approximation line obtained by exponentially approximating the correlation data between the measured frequency and the viscoelastic properties, and the viscoelastic properties in the range higher than the first frequency are considered to be the same value as the viscoelastic properties at the first frequency.

[0013] According to this method, since the viscoelastic property values of the rubber material are measured only at one temperature, it is not necessary to measure the viscoelastic property values of the rubber material at a plurality of temperatures, and the measurement time can be shortened. Further, when predicting the viscoelastic property values of the rubber material from the measurement data, it can be predicted only by calculating an exponential approximation line, so it is not necessary to perform complicated data processing, leading to a reduction in man-hours. Further, according to this method, as described above, since it is not necessary to measure the viscoelastic property values of the rubber material at a plurality of temperatures, the viscoelastic property values of the rubber material can be predicted using a viscoelasticity tester having a simple configuration without a temperature adjustment function. In particular, this method is particularly effective when the loss tangent (tanδ) of the rubber material is 0.1 or more.

[0014] Hereinafter, an example of an embodiment of a method for predicting the viscoelastic properties of a rubber material according to the present invention will be described in detail with reference to the drawings. The embodiment described below is merely an example, and the present invention is not limited to the following embodiments. Further, in this specification, the description "numerical value A to numerical value B" includes the numerical values A and B and can be read as "numerical value A or more and numerical value B or less".

[0015] Hereinafter, a method for predicting the viscoelastic properties of a rubber material according to the present embodiment will be described with reference to FIGS. 1 to 3. FIG. 1 is a diagram showing a flowchart of a method for predicting the viscoelastic properties of a rubber material according to the present embodiment.

[0016] As shown in FIG. 1, the method for predicting the viscoelastic properties of the rubber material of the present embodiment includes a preparation step S1 of preparing a test piece made of a rubber material, a measurement step S2 of measuring the viscoelastic property values of the rubber material using a viscoelasticity tester, and a prediction step S3 of predicting the viscoelastic property values of the rubber material.

[0017] The preparation step S1 is a step of preparing a test piece made of a rubber material as described above. Note that the shape, size, etc. of the test piece made of the rubber material produced in the preparation step S1 are not particularly limited as long as they can be adapted to the viscoelasticity tester used in the measurement step S2. The shape of the test piece is, for example, a sheet shape, a columnar shape, or a block shape.

[0018] A rubber material is a substance having rubber-like elasticity, inclusive of plastics elastomers such as vulcanized rubber and thermoplastic elastomers. In this embodiment, vulcanized rubber is used as the rubber material.

[0019] Vulcanized rubber is a rubber material obtained by vulcanizing a rubber composition prepared by blending various compounding agents including a vulcanizing agent such as sulfur with a rubber polymer. Vulcanized rubber can be obtained, for example, by preparing a rubber composition by kneading each component according to a conventional method using a mixer such as a Banbury mixer, and then heating and vulcanizing the rubber composition according to a conventional method.

[0020] Examples of the rubber polymer contained in the vulcanized rubber include natural rubber (NR), isoprene rubber (IR), butadiene rubber (BR), styrene butadiene rubber (SBR), butyl rubber (IIR), acrylonitrile butadiene rubber (NBR), acrylonitrile butadiene styrene rubber (ABS), brominated butyl rubber (BR-IIR), fluororubber, silicone rubber, etc. These rubber polymers may be used alone or in combination of two or more.

[0021] In addition, as compounding agents contained in the vulcanized rubber, various compounding agents commonly used in the rubber industry, such as fillers such as carbon black and silica, softening agents, anti-aging agents, zinc white, stearic acid, wax, vulcanization accelerators, etc., can be used.

[0022] The glass transition temperature of the rubber material is, for example, -60°C to -20°C, preferably -55°C to -25°C. When the glass transition temperature is within the range of -60°C to -20°C or -55°C to -25°C, the error of the predicted value calculated in the prediction step S3 described later becomes small, and the prediction accuracy of the viscoelastic characteristic value of the rubber material is improved.

[0023] Measurement step S2 is a step in which the viscoelastic properties of a test specimen made of the rubber material prepared in the above preparation step S1 are measured at, for example, one temperature. More specifically, in measurement step S2, the test specimen is deformed using a viscoelasticity tester while changing the frequency, and the viscoelastic properties of the test specimen are measured at each frequency. Examples of viscoelastic properties include the storage modulus, loss modulus, complex modulus, and loss tangent (tanδ).

[0024] Figure 2 shows an example of correlation data between the frequency measured in measurement step S2 of Example 1 described later and the viscoelastic properties (storage modulus, loss modulus) of the rubber material. Here, in measurement step S2, it is preferable to measure the viscoelastic properties of the rubber material in at least a portion of the range of 50 Hz to 400 Hz using a viscoelasticity tester. If the measurement frequency is lower than 50 Hz, the error due to the exponential approximation line described later may become large. Also, the wider the frequency measurement range, the smaller the error due to the exponential approximation line becomes, and the accuracy of predicting the viscoelastic properties of the rubber material improves. An example of a measurement range is 60 Hz to 300 Hz. The frequency measurement interval is, for example, 10 Hz, preferably 8 Hz or less, and more preferably 5 Hz or less.

[0025] The measurement temperature can be appropriately set according to the temperature conditions of the viscoelastic properties of the rubber material to be predicted. In other words, when predicting the viscoelastic properties of a rubber material at a standard temperature (23°C), the viscoelastic properties of the rubber material are measured at room temperature. Furthermore, as a result of the inventors' studies, it has become clear that when the viscoelastic properties of a rubber material are measured at a standard temperature, the error due to the exponential approximation line is reduced, and the accuracy of predicting the viscoelastic properties of the rubber material is improved. Therefore, the effects of the present invention are more pronounced when the measurement temperature is the standard temperature.

[0026] The viscoelasticity tester used in measurement step S2 is not particularly limited as long as it is capable of deforming the test specimen at the above-mentioned frequency. A specific example of a viscoelasticity tester is the viscoelasticity tester manufactured by TA Instruments (product name "RSA-G2"). Furthermore, as described above, the method for predicting the viscoelastic properties of rubber materials of the present invention can predict the viscoelastic property values ​​of rubber materials using only measurement results at standard temperatures. Therefore, the viscoelasticity tester used in the method for predicting the viscoelastic properties of rubber materials of the present invention does not need to have a temperature control function.

[0027] Prediction step S3 includes a first prediction step and a second prediction step. In the first prediction step, the viscoelastic properties of the rubber material at a first frequency in the range of 500 Hz to 1500 Hz are predicted based on an exponential approximation line obtained by exponentially approximating the correlation data between frequency and viscoelastic properties obtained in measurement step S2. In the second prediction step, the viscoelastic properties of the rubber material at a second frequency higher than the first frequency are predicted to be the same as the viscoelastic properties of the rubber material at the first frequency. Note that known methods can be used to derive the exponential approximation line.

[0028] Here, the first frequency can be appropriately set within the range of 500Hz to 1500Hz depending on the loss tangent (tanδ) of the rubber material, etc. The first frequency tends to increase as the loss tangent (tanδ) of the rubber material increases. For example, if the loss tangent (tanδ) of the rubber material is 0.1 or greater, the first frequency may be set within the range of 1000Hz to 1500Hz, and if the loss tangent (tanδ) of the rubber material is less than 0.1, the first frequency may be set within the range of 500Hz to 1000Hz.

[0029] Furthermore, the second frequency is greater than the first frequency and is below 3000 Hz. In other words, when predicting the viscoelastic properties of rubber materials using this method when the second frequency is higher than 3000 Hz, i.e., when predicting the viscoelastic properties of rubber materials at frequencies higher than 3000 Hz, the discrepancy between the predicted value and the measured value becomes large.

[0030] Figures 3 and 4 show examples of predicted values ​​including the exponential approximation line calculated in prediction step S3 of Example 1 described later. Figures 3 and 4 show the case where the first frequency is 1500 Hz. In Figure 3, the storage modulus of the rubber material is shown as the viscoelastic property value of the rubber material, and in Figure 4, the loss modulus of the rubber material is shown as the viscoelastic property value of the rubber material. [Examples]

[0031] The following are examples, but the present invention is not limited to these examples.

[0032] <Example 1> [Manufacturing Steps] Using a Banbury mixer, 100 parts by mass of styrene-butadiene rubber ("Toughden 2000" manufactured by Asahi Kasei Corporation) was mixed with 50 parts by mass of carbon black ("Seasto 3" manufactured by Tokai Carbon Co., Ltd.), 2 parts by mass of zinc oxide ("Zinc Oxide No. 1" manufactured by Mitsui Mining & Smelting Co., Ltd.), 1 part by mass of stearic acid ("Lunaq S-20" manufactured by Kao Corporation), 2 parts by mass of sulfur ("Rubber Powder Sulfur 150 Mesh" manufactured by Hosoi Chemical Industry Co., Ltd.), and 1 part by mass of vulcanization accelerator ("Noxellar CZ" manufactured by Ouchi Shinko Chemical Industry Co., Ltd.). This prepared an unvulcanized rubber composition.

[0033] [Measurement Steps] The frequency dependence of the storage modulus and loss modulus of the test specimens prepared in the above steps was measured using a viscoelasticity tester (product name "KCH701-30") manufactured by Sagimiya Seisakusho Co., Ltd. The detailed measurement conditions are as follows. The measurement results for the storage modulus and loss modulus are shown in Figure 2. As a result, the loss tangent (tanδ) at 100 Hz of the rubber material in Example 1 was 0.12.

[0034] <Measurement conditions> • Measurement direction: Axial (see Figure 2) ·Measurement temperature: 23℃ (standard temperature) ·Load condition: 0±0.05mm vibration • Measurement range: 60Hz to 300Hz (in 5Hz increments)

[0035] [Prediction Step] Based on the correlation data between the frequency obtained in the measurement steps described above and the storage modulus and loss modulus, an exponential approximation line was calculated (see Figures 3 and 4). 1500 Hz was adopted as the first frequency, and the storage modulus and loss modulus at frequencies higher than 1500 Hz were assumed to be the same as those at 1500 Hz. The storage modulus at 1500 Hz calculated from the exponential approximation line was 32.5 MPa, and the loss modulus was 6.3 MPa.

[0036] <Example 2> As the rubber material, a rubber material with a loss tangent (tanδ) of 0.08 at 100 Hz was used. Figure 5 shows the measurement results of the storage modulus and loss modulus in the measurement step of the rubber material in Example 2. Furthermore, an exponential approximation line was calculated based on the correlation data between the frequency obtained in the measurement step and the storage modulus and loss modulus (see Figures 6 and 7). Then, 500 Hz was adopted as the first frequency, and the storage modulus and loss modulus at frequencies higher than 500 Hz were set to be the same as the storage modulus and loss modulus at 500 Hz. The storage modulus at 500 Hz calculated from the exponential approximation line was 4.3 MPa, and the loss modulus was 0.5 MPa.

[0037] <Comparative Example 1> Based on the correlation data between the storage modulus and loss modulus of the rubber material in Example 1, a linear approximation line was calculated using the least squares method (see Figures 3 and 4). As in Example 1, 1500 Hz was adopted as the first frequency, and the storage modulus and loss modulus at frequencies higher than 1500 Hz were assumed to be the same as those at 1500 Hz. The storage modulus at 1500 Hz calculated from the linear approximation line was 24.5 MPa, and the loss modulus was 3.5 MPa.

[0038] <Comparative Example 2> Based on the correlation data between the storage modulus and loss modulus of the rubber material in Example 2, a linear approximation line was calculated using the least squares method (see Figures 6 and 7). As in Example 2, 500 Hz was adopted as the first frequency, and the storage modulus and loss modulus at frequencies higher than 500 Hz were assumed to be the same as those at 500 Hz. The storage modulus at 500 Hz calculated from the linear approximation line was 4.25 MPa, and the loss modulus was 0.47 MPa.

[0039] [Simulation Evaluation] Next, to evaluate the accuracy of the storage modulus and loss modulus of the rubber material calculated in the prediction step described above, an analytical simulation was performed using the predicted values ​​of storage modulus and loss modulus in Examples 1 and 2 and Comparative Examples 1 and 2, and compared with the measured values. This simulation uses the finite element method to determine the change in the absolute spring constant with respect to the input vibration frequency of the rubber material contained in the motor mount. In the simulation, the measured values ​​of storage modulus and loss modulus at 100 Hz, the predicted values ​​of storage modulus and loss modulus at the first frequency, and the predicted values ​​of storage modulus and loss modulus at 2000 Hz were input and the analysis was performed. The simulation was performed using the software "Abaqus" manufactured by SIMULIA.

[0040] Figure 8 shows the finite element model of the motor mount used in the simulation. As shown in Figure 8, the motor mount comprises an inner cylinder, an outer cylinder surrounding the outer circumference of the inner cylinder, and a rubber material connecting the outer cylinder and the inner cylinder.

[0041] Figure 9 shows the frequency characteristics of the absolute spring constant of the rubber material obtained by the above simulation using the storage modulus and loss modulus predicted by the methods of Example 1 and Comparative Example 1, respectively. Figure 10 also shows the frequency characteristics of the absolute spring constant of the rubber material obtained by the above simulation using the storage modulus and loss modulus predicted by the methods of Example 2 and Comparative Example 2, respectively. Figures 9 and 10 show the frequency characteristics of the absolute spring constant of the rubber material when the inner cylinder is vibrated in the direction perpendicular to the axis. In addition, measured values ​​of the frequency characteristics of the absolute spring constant of each rubber material are also shown in Figures 9 and 10.

[0042] As shown in Figure 9, when using a rubber material with a loss tangent (tanδ) of 0.12, the measured values ​​show a peak in the absolute spring constant due to surging around 1300 Hz. Similarly, in the simulation using the predicted values ​​from Example 1, a peak in the absolute spring constant due to surging appears around 1300 Hz, just like the measured values. In other words, when using a rubber material with a loss tangent (tanδ) of 0.12, predicting the storage modulus and loss modulus using an exponential approximation line shows a small deviation from the measured values. On the other hand, in the simulation using the predicted values ​​from Comparative Example 1, a peak in the absolute spring constant due to surging appears around 1200 Hz. In other words, when using a rubber material with a loss tangent (tanδ) of 0.12, predicting the storage modulus and loss modulus using a linear approximation line shows a large deviation from the measured values.

[0043] Furthermore, as shown in Figure 10, when using a rubber material with a loss tangent (tanδ) of 0.0.08, the measured values ​​show that the rubber material exhibits a peak in the absolute spring constant due to surging around 700 Hz. In simulations using the predicted values ​​of Example 2 and Comparative Example 2, the rubber material exhibits a peak in the absolute spring constant due to surging around 700 Hz, similar to the measured values. Therefore, this method can be adopted even when the loss tangent (tanδ) is small, and it can be said to be particularly effective when the loss tangent (tanδ) is large.

[0044] Figures 9 and 10 show the results of evaluating the frequency characteristics of the absolute spring constant of the rubber material when the inner cylinder is excited in the direction perpendicular to the axis during simulation. Similar results were obtained when evaluating the frequency characteristics of the absolute spring constant of the rubber material when the inner cylinder is excited in the axial direction (see Figure 8).

[0045] Although embodiments of the present invention have been described above, these embodiments are presented as examples and are not intended to limit the scope of the invention. The embodiments can be implemented in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. Embodiments and their omissions, substitutions, and modifications are included in the scope and spirit of the invention, as well as in the claims and their equivalents. [Explanation of Symbols]

[0046] S1 Fabrication step, S2 Measurement step, S3 Prediction step

Claims

1. A method for predicting the viscoelastic properties of rubber materials, A measurement step in which a rubber material is deformed at a single temperature while changing the frequency, and the viscoelastic properties of the rubber material are measured at each frequency, A first prediction step in which, based on an exponential approximation line obtained by exponentially approximating the correlation data between the frequency and the viscoelastic property value obtained in the measurement step, predicts the viscoelastic property value of the rubber material at a first frequency exceeding the frequency measured in the measurement step, A second prediction step in which the viscoelastic properties of the rubber material at a second frequency exceeding the first frequency are predicted to be constant with the viscoelastic properties of the rubber material at the first frequency, Includes, The first frequency is 500 Hz or higher and 1500 Hz or lower. A method for predicting the viscoelastic properties of a rubber material, wherein the second frequency is 3000 Hz or less.

2. The method for predicting the viscoelastic properties of a rubber material according to claim 1, wherein the aforementioned temperature is 23°C.

3. The method for predicting the viscoelastic properties of a rubber material according to claim 1, wherein the loss tangent (tanδ) of the rubber material at 100 Hz is 0.1 or greater.

4. The method for predicting the viscoelastic properties of a rubber material according to claim 1, wherein the first frequency is a frequency exceeding the settable upper limit frequency of the measuring device used in the measurement step.

5. The method for predicting the viscoelastic properties of a rubber material according to claim 1, wherein in the measurement step, the viscoelastic properties of the rubber material are measured in at least a portion of the range of 50 Hz or more and 400 Hz or less.

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