Method for grasping dynamic friction characteristic of vulcanization rubber

Abstract

To provide a grasping method for accurately and easily calculating dynamic friction characteristics of vulcanization rubber.SOLUTION: In a two-dimensional model 10, vulcanization rubber 11 is defined as a rubber element continuum where multiple rubber elements 12 where one end is connected to a front surface 11a of the vulcanization rubber 11 and the other end is connected to a fixed surface 16 are juxtaposed in a slide direction of a projection 18. Each one of the rubber elements 12 has a structure where one unit 13a having elastic parts 14 and viscous parts 15 is arranged by allowing a displacement direction to be in parallel with a slide direction, the other unit 13b is arranged by allowing the displacement direction to be orthogonal to the slide direction, and the units 13a, 13b are orthogonally connected. When dynamic friction characteristics are grasped, a viscoelastic parameter of the vulcanization rubber 11, a profile parameter of a friction surface 17, and a friction condition parameter for identifying a slide speed of the projection 18 and a pressing amount of the projection 18 with respect to the vulcanization rubber 11 are input to an arithmetic device 2, so as to perform a simulation where the projection 18 slides along the front surface 11a in a pressed state of being pressed into the vulcanization rubber 11.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a method for determining the dynamic friction characteristics of vulcanized rubber, and more particularly to a method for determining the dynamic friction characteristics of vulcanized rubber, which can accurately and easily determine the dynamic friction characteristics of vulcanized rubber. [Background technology]

[0002] Friction performance is one of the evaluation indices for rubber products such as tires, conveyor belts, etc. For example, the friction performance of a tire greatly affects the fuel efficiency and driving performance of the vehicle on which the tire is mounted.

[0003] Various methods for evaluating the frictional performance of a rubber composition have been proposed (see Patent Document 1). In the method proposed in Patent Document 1, a model of the rubber composition is used by the finite element method to calculate the tensile strain and compressive strain that occur in the vicinity of the protrusions of the model when the model slides on a surface having protrusions. Then, the calculated tensile strain and compressive strain are simply compared as indicators to evaluate the frictional performance, so although this method is simple, there is room for improvement in terms of accurately grasping the dynamic frictional properties of the rubber composition. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2022-186101 A Summary of the Invention [Problem to be solved by the invention]

[0005] An object of the present invention is to provide a method for determining the dynamic friction characteristics of vulcanized rubber, which can accurately and easily calculate the dynamic friction characteristics of vulcanized rubber. [Means for solving the problem]

[0006] The method of grasping the dynamic frictional characteristics of vulcanized rubber of the present invention, which achieves the above-mentioned object, uses a two-dimensional model including vulcanized rubber and a friction surface having protrusions sliding on the surface of the vulcanized rubber to grasp the dynamic frictional characteristics of the vulcanized rubber when the protrusions are pressed into the vulcanized rubber and slide along the surface, and in the two-dimensional model, the vulcanized rubber is represented as a rubber element continuum in which a large number of rubber elements, one end of which is connected to the surface and the other end to a fixed surface, are arranged in parallel in the sliding direction of the protrusions, and each of the rubber elements is formed by connecting two units having an elastic portion and a viscous portion, one of the units is arranged with its displacement direction parallel to the sliding direction, and the other of the units is arranged with its displacement direction parallel to the sliding direction. In a structure in which the units are arranged with their displacement directions perpendicular to the sliding direction, and the units are connected to each other with their displacement directions perpendicular to each other, the two-dimensional model is stored in a computing device in advance, and when the dynamic friction characteristics are grasped, viscoelastic parameters indicating the viscoelastic characteristics of the vulcanized rubber, profile parameters indicating the surface shape of the friction surface, and friction condition parameters specifying the sliding speed of the protrusions and the amount of pressing of the protrusions into the vulcanized rubber are input to the computing device as parameters of the two-dimensional model, a simulation is performed in which the front protrusions slide along the surface in a state where they are pressed into the vulcanized rubber in the two-dimensional model, and the dynamic friction characteristics are grasped based on the results of this simulation. Effect of the Invention

[0007] According to the present invention, the two-dimensional model adopts a structure in which the units are connected with their displacement directions perpendicular to each other, thereby making it possible to more realistically approximate the deformation state of the vulcanized rubber when the protrusion slides on the surface. When grasping the dynamic friction characteristics, the viscoelastic parameters, the profile parameters, and the friction condition parameters are input to the arithmetic device as parameters of the two-dimensional model, thereby making it possible to more realistically reproduce the state when the protrusion of a desired specification slides on the surface of the vulcanized rubber of a desired specification under desired friction conditions. Therefore, by using the results of a simulation in which the protrusion slides along the surface in a state where it is pressed into the vulcanized rubber in the two-dimensional model, it becomes possible to accurately and easily calculate the dynamic friction characteristics of the vulcanized rubber against the friction surface. [Brief description of the drawings]

[0008] [Figure 1] FIG. 2 is an explanatory diagram illustrating a two-dimensional model used in the present invention. [Diagram 2] FIG. 2 is an explanatory diagram illustrating a model structure of the vulcanized rubber in FIG. [Diagram 3] 2 is an explanatory diagram illustrating a two-dimensional model in which a protrusion is pressed into and slides against the vulcanized rubber in FIG. 1. [Figure 4] FIG. 2 is an explanatory diagram illustrating a simulator. [Diagram 5] FIG. 2 is a flow diagram illustrating a procedure for understanding the dynamic friction characteristics of vulcanized rubber. [Figure 6] FIG. 2 is a graph illustrating the storage modulus and loss modulus of vulcanized rubber. [Figure 7] FIG. 7 is a graph illustrating the loss tangent of the vulcanized rubber of FIG. 6. [Figure 8] FIG. 11 is a graph illustrating profile data of the surface shape of the friction surface. [Figure 9] FIG. 1 is a graph illustrating measured values ​​and estimated values ​​(Examples and Reference Examples) of dynamic friction coefficients. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] Hereinafter, the method of grasping the dynamic friction characteristics of vulcanized rubber according to the present invention will be described based on the embodiment shown in the drawings.

[0010] The two-dimensional model 10 illustrated in FIG. 1 and FIG. 2 includes a vulcanized rubber 11 and a friction surface 17 having a protrusion 18 that slides on a surface 11a of the vulcanized rubber 11. In the present invention, the two-dimensional model 10 is used to perform a simulation in which the protrusion 18 slides along the surface 11a in a state where it is pressed into the vulcanized rubber 11 as illustrated in FIG. 3, and the dynamic friction characteristics of the vulcanized rubber 11 with respect to the friction surface 17 are grasped based on the simulation results. The X direction in the figure is the sliding direction in which the protrusion 18 moves relatively to the surface 11a. The Z direction perpendicular to the X direction is the thickness direction (height direction) of the vulcanized rubber 11 and the protrusion 18. In this embodiment, the vulcanized rubber 11 is fixed and the protrusion 18 (friction surface 17) is moved, but the vulcanized rubber 11 may be moved with the protrusion 18 (friction surface 17) fixed.

[0011] In this simulation, the vulcanized rubber 11 is assumed to be the tread rubber of the tire, and the friction surface 17 having the protrusions 18 is assumed to be the road surface on which the tire runs, thereby making it possible to grasp the dynamic friction characteristics of the tire when the tire runs on the road surface. The details of the two-dimensional model 10 will be described later.

[0012] This simulation is performed using a simulator 1 as shown in Fig. 4. The simulator 1 includes a calculation device 2 that performs data processing using various input and stored data. The calculation device 2 can be any of various known computers. The calculation device 2 includes a central processing unit (CPU) 3, a main storage unit (memory) 4, an auxiliary storage unit (e.g., HDD) 5, an input unit (keyboard, mouse) 6, and an output unit (display) 7. A constructed two-dimensional model 10 is stored in the auxiliary storage unit 5.

[0013] In this embodiment, the simulator 1 includes a viscoelasticity measuring device 8 and a surface shape measuring device 9. The viscoelasticity measuring device 8 acquires viscoelasticity property data of the vulcanized rubber 11. The viscoelasticity measuring device 8 may be any of various known viscoelasticity measuring devices such as a rheometer. Examples of the viscoelasticity property data include the storage modulus E' [Mpa], loss modulus E'' [Mpa], and loss tangent tan δ of the vulcanized rubber 11.

[0014] The surface shape measuring device 9 obtains profile data indicating the surface shape of the friction surface 17. That is, the surface shape measuring device 9 obtains profile data of the protrusions 18. As the surface shape measuring device 9, various known surface shape measuring devices (profile sensors) such as a combination of a microscope and a laser microscope, or a non-contact optical step gauge can be used.

[0015] To describe the two-dimensional model 10 in detail, as illustrated in FIG. 1, in the two-dimensional model 10, a surface 11a of the vulcanized rubber 11 faces a friction surface 17 having protrusions 18, and a back surface 11b of the vulcanized rubber 11 is fixed to a fixed surface 16. The vulcanized rubber 11 is modeled as a rubber element continuum in which a large number of rubber elements 12 are arranged in parallel in the X direction. The intervals between the rubber elements 12 adjacent to each other in the X direction are, for example, equal intervals. The intervals between the rubber elements 12 can be set arbitrarily, and are, for example, 1 μm to 100 μm. Each rubber element 12 extends in the Z direction, one end of which is connected and fixed to the surface 11a, and the other end of which is connected and fixed to the fixed surface 16.

[0016] As illustrated in Fig. 2, each rubber element 12 is formed by connecting two units 13a, 13b. Each unit 13a, 13b has an elastic portion (spring) 14a, 14b and a viscous portion (dashpot) 15a, 15b. One unit 13a is disposed with its displacement direction parallel to the Z direction, and the other unit 13b is disposed with its displacement direction parallel to the X direction perpendicular to the Z direction. The units 13a, 13b are connected to each other with their displacement directions perpendicular to each other.

[0017] For each of the units 13a and 13b, various known viscoelastic models having elastic parts 14a and 14b and viscous parts 15a and 15b, such as the Maxwell model, Voigt model, standard Maxwell model, standard Voigt model, generalized Maxwell model, and generalized Voigt model, can be used. In this embodiment, for each of the units 13a and 13b, a generalized Maxwell model is used in which a plurality of Maxwell models in which a pair of elastic parts 14a and viscous parts 15a or a pair of elastic parts 14b and viscous parts 15b are connected in series are arranged in parallel, and a single elastic part 14a or elastic part 14b is juxtaposed at one end of the parallel arrangement of these Maxwell models. In this embodiment, the elastic part 14a and the viscous part 15a constituting one unit 13a are displaced in the Z direction, and the elastic part 14b and the viscous part 15b constituting the other unit 13b are displaced in the X direction.

[0018] The elastic moduli of the elastic parts 14a, 14b arranged in parallel in each unit 13a, 13b are Eez, Eex, and the elastic moduli of the elastic parts 14a, 14b of each Maxwell model are Ekz, Ekx (k=1 to n). The relaxation times of the viscous parts 15a, 15b of each Maxwell model are τkz, τkx (k=1 to n). Viscosities ηkz, ηkx (k=1 to n) can be used instead of the relaxation times τkz, τkx (k=1 to n). The number n mentioned above is, for example, about 5 to 15.

[0019] The elastic moduli Eez, Eex, Ekz, Ekx and the relaxation times τkz, τkx are not uniform, but rather, for example, the elastic moduli Eez, Eex, Ekz, Ekx are distributed widely from a low elastic modulus (0.1 [Mpa]) to a high elastic modulus (100 [Mpa]), and the relaxation times τkz, τkx are distributed widely from a short time (1.E-06 [sec]) to a long time (10 [sec]). Each rubber element 12 is formed by connecting units 13a, 13b having elastic parts 14a, 14b and viscous parts 15a, 15b, and the units 13a, 13b are connected to each other with their displacement directions perpendicular to each other, thereby making it possible to reproduce the complex viscoelastic deformation of the actual vulcanized rubber 11.

[0020] Various parameters are input to this two-dimensional model 10, including a viscoelastic parameter P1 indicating the viscoelastic properties of the vulcanized rubber 11, a profile parameter P2 indicating the surface shape of the friction surface 17, and a friction condition parameter P3 specifying the sliding speed V of the protrusions 18 and the pushing amount d of the protrusions 18 against the vulcanized rubber 11. In this embodiment, a material constant P4 set based on the Poisson's ratio of the vulcanized rubber 11 is also input as a parameter of the two-dimensional model 10. The material constant P4 can be input arbitrarily.

[0021] The viscoelastic parameters P1 are the above-mentioned elastic modulus Eez [Mpa], elastic modulus Eex [MPa], elastic modulus Ekz (k=1 to n) [Mpa], elastic modulus Ekx (k=1 to n) [MPa], relaxation time τkz (k=1 to n) [s], and relaxation time τkx (k=1 to n). The viscoelastic parameters P1 are calculated based on the viscoelastic property data of the vulcanized rubber 11 acquired by the viscoelasticity measuring device 8.

[0022] The profile parameter P2 is the root mean square slope Δq, the root mean square height [μm], etc. of the friction surface 17 (protrusion 18). The profile parameter P2 is calculated based on the profile data of the friction surface 17 acquired by the surface shape measuring device 9. The shape of the protrusion 18 is identified based on the profile parameter P2.

[0023] The friction condition parameter P3 may include the sliding speed V and the indentation amount d, and may be the indentation load L instead of the indentation amount d, or another parameter may be added as necessary. Any desired value may be input for the friction condition parameter P3. The indentation amount d is the depth in the Z direction from the surface 11a of the vulcanized rubber 11 when the protrusion 18 is not pressed into the vulcanized rubber 11 to the deepest tip of the protrusion 18 pressed into the vulcanized rubber 11. Since there is a positive correlation between the indentation amount d and the indentation load L, the larger the indentation load L, the larger the indentation amount d, and the smaller the indentation load L, the smaller the indentation amount d.

[0024] The material constant P4 is set based on the inclination of the rubber element 12 with respect to the Z direction when the rubber element 12 is pressed in a direction perpendicular to the surface 11a (Z direction). More specifically, the material constant P4 is set as the amount of decrease in the force acting in the forward direction relative to the sliding direction (X direction) and the amount of increase in the force acting in the opposite direction to the sliding direction, caused by the inclination of the rubber element 12. The material constant P4 is, for example, determined by the Poisson's ratio v of the vulcanized rubber 11, the viscoelastic property (complex modulus) G in the X direction of the rubber element 12, x (ω), the viscoelastic property (complex modulus) G of the rubber element 12 in the Z direction z It is expressed by the following formula (1) using (ω). The maximum value of the amount of inclination ΔX in the X direction relative to the compressive strain in the Z direction of the rubber element 12 in FIG. 3 depends on the material constant P4, and the larger the material constant P4 is, the larger it becomes, and the smaller the material constant P4 is, the smaller it becomes. An appropriate value is adopted for the material constant P4 based on the results of experiments and simulations. When the Poisson's ratio v is 0.5 and the viscoelastic properties in the X direction and Z direction are equal, the material constant P4 is set to 3 / 4. The material constant P4 is set to a value of 0 to 2, for example.

[0025]

number

[0026] Next, an example of a procedure for grasping the dynamic friction characteristics of the vulcanized rubber 11 against the friction surface 17 by the simulator 1 using the two-dimensional model 10 will be described.

[0027] 5, a two-dimensional model 10 is constructed in advance and stored in the calculation device 2 (S110), and when the dynamic friction characteristics of the vulcanized rubber 11 are actually grasped, parameters P1 to P4 are input to the calculation device 2 (S120 to S150). Next, a simulation is performed using the two-dimensional model 10 to which the parameters P1 to P4 have been input, and the dynamic friction characteristics are grasped based on the simulation results (S160). The contents of each step (S110 to S160) will be described in detail below.

[0028] In step (S110), the above-mentioned two-dimensional model 10 is constructed and stored in the auxiliary storage unit 5. This step (S110) can be performed at any timing before the simulation is executed.

[0029] In step (S120), the viscoelastic parameter P1 of the vulcanized rubber 11 having the desired specifications is input to the calculation device 2. Specifically, the calculation device 2 executes data processing for outputting an input screen for the viscoelastic parameter P1 to the output unit 7, and the viscoelastic parameter P1 is input to the input screen by the input unit 6. The viscoelastic parameter P1 is calculated based on viscoelastic characteristic data in each of the X direction and Z direction of the vulcanized rubber 11 measured using the viscoelasticity measuring device 8. If each viscoelastic characteristic data has already been acquired for the vulcanized rubber, the already acquired viscoelastic characteristic data may be input to the calculation device 2 to calculate and use the viscoelastic parameter P1.

[0030] In acquiring viscoelastic property data using the viscoelasticity measuring device 8, the temperature and frequency may be arbitrarily set and measured, but it is preferable to use temperature-dependent measurement or / and frequency-dependent measurement, and it is more preferable to use the temperature-time conversion rule to expand the frequency range of the frequency-dependent measurement result. Specifically, the frequency-dependent measurement is performed at a plurality of temperatures. For example, the frequency-dependent measurement is performed by selecting about five frequencies from the range of frequencies that can be considered as the rubber region for a general rubber material, and measuring at each of the selected frequencies. The range of frequencies that can be considered as the rubber region is, for example, 1 Hz to 100 Hz. A composite curve is obtained by shifting each data obtained by the frequency-dependent measurement at a plurality of temperatures to a reference temperature. This composite curve becomes a master curve, and viscoelastic property data at a high frequency of 100 Hz or more (for example, about 10 kHz) can be obtained. The plurality of temperatures differs depending on the type of vulcanized rubber 11, but for example, about three temperatures are selected within the range of 0°C to 100°C.

[0031] 6 and 7 show viscoelastic property data in the X direction of vulcanized rubber 11 obtained by viscoelasticity measuring device 8. The solid line in FIG. 6 shows a master curve of the storage modulus E' [Mpa] of vulcanized rubber 11, and the dashed line shows a master curve of the loss modulus E'' [Mpa]. The solid line in FIG. 7 shows a master curve of the loss tangent tanδ of vulcanized rubber 11. The loss tangent tanδ is expressed as the ratio (E'' / E') of the loss modulus E'' to the storage modulus E'.

[0032] The viscoelastic property data obtained by the measurement is applied to the model (generalized Maxwell model) of vulcanized rubber 11 shown in FIG. 2 and analyzed. The storage modulus E' in the X direction is expressed as a function E' of frequency ω. x (ω), then the function E' x (ω) is expressed by the following formula (2). The loss modulus E'' in the X direction is expressed as a function E'' of frequency ω. x (ω), then the function E'' x (ω) is expressed by the following formula (3). In the following formulas (2) and (3), the relaxation time is τkx. The relaxation time τkx is expressed by the ratio (ηkx / Ekx) of the viscosity ηkx to the elastic modulus Ekx.

[0033]

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[0034]

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[0035] The elastic modulus Eex, the elastic modulus Ekx (k=1 to n), and the relaxation time τkx (k=1 to n) are calculated by fitting the above formulas (1) and (2) to the respective master curves in FIG. 6. Similarly, the elastic modulus Eez, the elastic modulus Ekz (k=1 to n), and the relaxation time τkz (k=1 to n) are calculated using the viscoelastic property data in the Z direction of the vulcanized rubber 11 acquired by the viscoelasticity measuring device 8. The calculated elastic modulus Eex, Eez, the elastic modulus Ekx, and the relaxation time τkx and τkz are the elastic part parameters, and the viscous part parameters (elastic modulus Eex, Eez, Ekx, Ekz) and the viscous part parameters (relaxation time τkx, τkz) are input to the calculation device 2 as the viscoelasticity parameters P1 and are used as parameters of the two-dimensional model 10. When the viscoelastic properties of the vulcanized rubber 11 in the X direction and the Z direction are equal, the viscoelastic property data of the vulcanized rubber 11 in either the X direction or the Z direction is obtained by the viscoelasticity measuring device 8, and the viscoelastic parameter P1 is calculated based on the obtained viscoelastic property data.

[0036] In step (S130), the profile parameters P2 of the friction surface 17 having the desired specifications are input to the calculation device 2. Specifically, the calculation device 2 executes data processing for outputting an input screen for the profile parameters P2 to the output unit 7, and the profile parameters P2 are input to the input screen by the input unit 6. The profile parameters P2 are calculated based on profile data measured using the surface shape measuring device 9. In the case of friction surface 17 for which profile data has already been acquired, the acquired profile data may be input to the calculation device 2 to calculate and use the profile parameters P2.

[0037] 8 illustrates an example of profile data of the friction surface 17 measured using the surface shape measuring device 9. Based on this profile data, the root-mean-square slope Δq and the root-mean-square height Pq are calculated. The calculated root-mean-square slope Δq and the root-mean-square height Pq are input to the calculation device 2 as profile parameters P2 and used as parameters of the two-dimensional model 10.

[0038] In step (S140), the friction condition parameter P3 is input to the calculation device 2. Specifically, the calculation device 2 executes data processing to output an input screen for the friction condition parameter P3 to the output unit 7, and the friction condition parameter P3 is input to the input screen by the input unit 6. Desired values ​​of the sliding speed V of the protrusion 18 and the push-in amount d or push-in load L are input to the calculation device 2 as the friction condition parameter P3, and are used as parameters of the two-dimensional model 10.

[0039] In step (S150), the material constant P4 of the vulcanized rubber 11 having the desired specifications is input to the calculation device 2. Specifically, the calculation device 2 executes data processing for outputting an input screen for the material constant P4 to the output unit 7, and the material constant P4 is input to the input screen by the input unit 6. If the material constant P4 is not used as a parameter of the two-dimensional model 10, step (S150) is omitted.

[0040] The above steps (S120 to S150) can be performed in any order. If the viscoelasticity data of the vulcanized rubber 11 and the profile data of the friction surface 17 used in the simulation have already been acquired, the simulator 1 does not need to include the viscoelasticity measuring device 8 and the surface shape measuring device 9, and these can be omitted.

[0041] In step (S160), as shown in Fig. 3, the calculation device 2 performs a simulation in which the protrusion 18 slides along the surface 11a in the two-dimensional model 10 to which parameters P1 to P4 have been input, while being pressed into the vulcanized rubber 11. The protrusion 18 moves in the X direction at a sliding speed V in a state where it is pressed into the vulcanized rubber 11 from the surface 11a by a pressing amount d. A center line P that passes through the center of the protrusion 18 in the X direction is depicted in Fig. 3.

[0042] In this way, the protrusion 18 slides along the surface 11a of the vulcanized rubber 11, and thus each rubber element 12 undergoes viscoelastic deformation. In each rubber element 12, the elastic parts 14a, 14b and the viscous parts 15a, 15b are displaced in the set displacement direction. In this embodiment, the material constant P4 is input as a parameter of the two-dimensional model 10, so that each rubber element 12 is inclined so as to fall in the X direction as the protrusion 18 slides. Therefore, in the two-dimensional model 10, the degree of inclination of the rubber element 12 in the vicinity of the protrusion 18 differs depending on the position in the X direction. The degree of deformation of the rubber element 12 differs between the front side 18a and the rear side 18b of the center line P of the protrusion 18 in the sliding direction, and the vulcanized rubber 11 is deformed into an asymmetric shape before and after the center line P in the X direction.

[0043] Such a deformation state of the vulcanized rubber 11 is similar to the deformation state of the actual vulcanized rubber 11, and the state in which the actual protrusion 18 slides along the surface 11a of the actual vulcanized rubber 11 is accurately reproduced. In the process in which the protrusion 18 slides along the surface 11a of the vulcanized rubber 11, the kinetic friction force F in the X direction that the protrusion 18 receives can be regarded as the force used to deform each rubber element 12 in the X direction during this process. In addition, the normal force N that the protrusion 18 receives during this process can be regarded as the force used to deform each rubber element 12 in the Z direction. The normal force N can be expressed by the following formula (4), and the kinetic friction force F can be expressed by the following formula (5). In the following formulas (4) and (5), the function g(x) represents the shape of the protrusion 18 and is based on the profile parameter P2. ~ x" indicates the position in the X direction of the center line P sliding at a speed V at time t, and is expressed by the following formula (6). "x" in the following formula (6) indicates the initial position of the center line P at the start of the simulation. a1 indicates the distance in the X direction from the center line P to the rightmost end of the rear side 18b in FIG. 3, and a2 indicates the distance in the X direction from the center line P to the leftmost end of the front side 18a. i indicates the k-th displacement of each model (generalized Maxwell model, etc.) in each unit 13a, 13b of the rubber element 12. The kinetic friction force F and normal force N in the simulation can be calculated to calculate the kinetic friction coefficient μd=F / N of the vulcanized rubber 11 against the friction surface 17. As the kinetic friction characteristic of the vulcanized rubber 11 against the friction surface 17, not only the kinetic friction coefficient μd but also an index that can be calculated using various data obtained from the simulation, such as the magnitude of the kinetic friction force F, can be used.

[0044]

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[0045]

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[0046]

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[0047] As described above, by adopting a structure in which units 13a, 13b having elastic portions 14 and viscous portions 15 are connected to each other with their displacement directions perpendicular to each other as the two-dimensional model 10, it is possible to more realistically approximate the deformation state of the vulcanized rubber 11 when the protrusions 18 slide on the surface 11a of the vulcanized rubber 11. Using a generalized Maxwell model for each of the units 13a, 13b as in this embodiment is advantageous in more realistically approximating the deformation state of the vulcanized rubber 11.

[0048] In order to reduce the burden of the calculation processing of the simulation, a simpler Maxwell model or the like may be adopted as each of the units 13a and 13b. Also, in order to reduce the burden of the calculation processing of the simulation, the material constant P4 as a parameter of the two-dimensional model 10 can be treated as 0. However, it is preferable to use a value other than 0 for the material constant P4.

[0049] In this two-dimensional model 10, at least the viscoelastic parameter P1, the profile parameter P2, and the friction condition parameter P3 are input to the calculation device 2 as parameters, so that the state when the protrusion 18 of the desired specification slides on the surface 11a of the vulcanized rubber 11 of the desired specification under the desired friction condition can be reproduced more realistically. That is, the specification of the vulcanized rubber 11 can be changed by changing the viscoelastic parameter P1, and the specification of the friction surface 17 can be changed by changing the profile parameter P2. And, the sliding speed V, the indentation amount d, and the indentation load L can be changed by changing the friction condition parameter P3. Therefore, by using this two-dimensional model 10, it becomes possible to accurately and easily calculate the dynamic friction characteristics when the protrusion 18 of the desired specification slides on the surface 11a of the vulcanized rubber 11 of the desired specification under the desired friction condition.

[0050] The viscoelastic properties of the vulcanized rubber 11 are highly temperature dependent. Therefore, in the simulation, the environmental temperature can be input as one of the friction condition parameters P3. The change in the viscoelastic properties of the vulcanized rubber due to temperature change can be obtained using a known temperature-frequency conversion formula such as the Arrhenius equation or the William-Landell-Ferry equation (WLF equation). By inputting the temperature, which has a large effect on the change in the viscoelastic properties, as the friction condition parameter P3, the dynamic friction properties under a wider variety of conditions can be understood.

[0051] The present invention is not limited to a specific embodiment, and various modifications and variations are possible within the scope of the gist of the present invention. EXAMPLES

[0052] [Measurement of dynamic friction coefficient] A vulcanized rubber sample was manufactured with the compounding shown in Table 1 below. A hemispherical sample with a diameter of 40 mm was pressed with a projection of a given friction surface and slid along the surface of the vulcanized rubber to measure the dynamic friction coefficient with a known friction tester to obtain an actual value. The sliding speed was adjusted to 0.001 mm / s to 10 mm / s, and the pressing load L of the projection against the sample was adjusted to 13 N.

[0053] [Table 1]

[0054] The profile data of the friction surface was measured using a known surface shape measuring device, and the measurement results were used to calculate the root mean square slope Δq and the root mean square height Pq. The calculated root mean square slope Δq was 0.944, and the root mean square height Pq was 33.64 [μm].

[0055] [Estimation of the dynamic friction coefficient] Using the two-dimensional model 10 illustrated in FIGS. 1 to 3, the dynamic friction coefficient of the above sample was calculated according to the procedure illustrated in FIG. 5 to obtain an estimated value (Example 1). The number of n in each of the units 13a and 13b of the vulcanized rubber 11 of the two-dimensional model 10 was set to 7. The storage modulus E' and loss modulus E'' of the sample were measured using a known rheometer. The values ​​are measured at temperatures of 0° C., 20° C., and 60° C., frequencies of 1 Hz, 3 Hz, 30 Hz, and 100 Hz, and dynamic strain of ±2%, and a master curve was created based on the measurement temperature of 20° C. The created master curve was fitted to the above-mentioned formulas (1) and (2) to obtain the elastic part parameters and viscous term parameters shown in Table 2 as the viscoelastic parameters P1 of the vulcanized rubber 11. Since the viscoelastic properties of the vulcanized rubber 11 in the X direction and the Z direction are substantially the same, the viscoelastic parameters P1 shown in Table 2 are common to the X direction and the Z direction of the vulcanized rubber 11.

[0056] [Table 2]

[0057] As the profile parameter P2 of the friction surface 17, the above-mentioned root mean square slope Δq of 0.944 and root mean square height Pq of 33.64 [μm] were used. As the friction condition parameter P3, a sliding speed of 0.001 mm / s to 10 mm / s and a pressing load of L13 [N] were used. The material constant P4 was 3 / 4. Using the above-mentioned formulas (4) to (6), the dynamic friction coefficient of the sample was calculated according to the procedure illustrated in FIG. 5 to obtain an estimated value (Example 1).

[0058] Furthermore, in the two-dimensional model 10 of FIGS. 1 to 3, the material constant P4 was set to 0, and the dynamic friction coefficient of the sample was calculated using the formulas (4) to (6) according to the procedure illustrated in FIG. 5 to obtain an estimated value (Example 2).

[0059] FIG. 9 shows the actual measured values, estimated values ​​(Example 1), and estimated values ​​(Example 2) of the dynamic friction coefficients of the above-mentioned samples. The white circles in FIG. 9 are the actual measured values, and the dashed line is an approximation curve of the actual measured values. The solid line in FIG. 9 shows the estimated values ​​(Example 1). The dashed-dotted line in FIG. 9 shows the estimated values ​​(Example 2). From the results shown in FIG. 9, Examples 1 and 2 show the same change in dynamic friction coefficient with respect to the sliding speed (convex shape) as the actual measured values. In particular, it can be seen that Example 1 is very close to the actual measured values. [Explanation of symbols]

[0060] 1. Simulator 2 Arithmetic unit 8 Viscoelasticity measuring device 9 Surface shape measuring device 10 2D Models 11 Vulcanized rubber 11a surface 11b Back side 12 Rubber elements Units 13a and 13b 14a, 14b Elastic part (spring) 15a, 15b Viscous part (dashpot) 16 Fixed surface 17 Friction surface 18 protrusions 18a Front side 18b Rear side

Claims

1. A method for grasping dynamic friction characteristics of vulcanized rubber, using a two-dimensional model including vulcanized rubber and a friction surface having protrusions sliding on a surface of the vulcanized rubber, grasping the dynamic friction characteristics of the vulcanized rubber when the protrusions slide along the surface in a state where the protrusions are pressed into the vulcanized rubber, comprising: In the two-dimensional model, the vulcanized rubber is treated as a rubber element continuum in which a large number of rubber elements, one end of which is connected to the surface and the other end of which is connected to a fixed surface, are arranged in parallel in the sliding direction of the protrusion, and each of the rubber elements is formed by connecting two units having an elastic portion and a viscous portion, one of the units is arranged with its displacement direction parallel to the sliding direction and the other unit is arranged with its displacement direction perpendicular to the sliding direction, and the units are connected to each other with their displacement directions perpendicular to each other, and the two-dimensional model is stored in advance in a calculation device, When grasping the dynamic friction characteristics, the following are input to the arithmetic device as parameters of the two-dimensional model: viscoelastic parameters indicating the viscoelastic characteristics of the vulcanized rubber, profile parameters indicating the surface shape of the friction surface, and friction condition parameters specifying the sliding speed of the protrusions and the amount of pressing of the protrusions into the vulcanized rubber; A method for grasping the dynamic friction characteristics of vulcanized rubber, comprising: simulating the front protrusion sliding along the surface of the two-dimensional model while being pressed into the vulcanized rubber; and grasping the dynamic friction characteristics based on the results of this simulation.

2. A method for grasping the dynamic friction characteristics of vulcanized rubber as described in claim 1, wherein a material constant that specifies the degree of inclination of the rubber element with respect to the perpendicular direction when the rubber element is pressed in a direction perpendicular to the surface is set based on the Poisson's ratio of the vulcanized rubber, and when grasping the dynamic friction characteristics, the material constant is input to the computing device as a parameter of the two-dimensional model.

3. 3. A method for grasping the dynamic friction characteristics of vulcanized rubber as described in claim 1 or 2, wherein a generalized Maxwell model is used in which, as each of the units, a plurality of Maxwell models, in which a pair of the elastic part and the viscous part are connected in series, are arranged in parallel, and a single elastic part is juxtaposed at one end of the parallel arrangement.

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