JP5650445B2 - Simulation method - Google Patents

Description

  The present invention relates to a simulation method for calculating an evaluation value indicating the performance of a rubber product using foamed rubber, and a simulation apparatus for executing the simulation method.

  In the development of tires, due to the development of simulation methods such as the finite element method and the computer environment, the physical quantities of newly designed tires can be measured without actually manufacturing tires and attaching them to automobiles for load tests and running tests. It is possible to calculate and visualize the state of deformation of the tire and to calculate the evaluation value of the tire performance (see, for example, Patent Document 1).

  The performance of tires using foamed rubber with a plurality of voids formed in the tread portion (see, for example, Patent Document 2) is also evaluated using a simulation method.

JP 2006-76404 A JP 2009-173840 A

  In the simulation method by dividing a tire using foamed rubber into a finite number of elements, an evaluation value close to that of an actual tire can be calculated by defining an element size that also considers bubbles. Specifically, in order to input physical property values representing the characteristics of the bubbles into the elements, the tire is divided into a finite number of elements so as to include the elements constituting the bubbles. However, if bubbles are taken into account, the element size has to be extremely reduced, which greatly increases the amount of calculation. For this reason, the simulation is performed by dividing into the same number of elements as those of a normal tire in which foam rubber is not used.

  However, since bubbles are not taken into consideration, tires using foamed rubber have an evaluation value obtained from a test using an actual tire and an evaluation value obtained by simulation compared to a normal tire. There was a big gap. This is not limited to tires, and the same problem occurs in other rubber products using foamed rubber.

  Therefore, the present invention has been made in view of such a situation, and for a rubber product in which foamed rubber is used, a simulation method capable of obtaining a highly accurate evaluation value without significantly increasing the amount of calculation, And it aims at providing a simulation apparatus.

  In order to solve the above-described problems, the present invention has the following features. A feature of the present invention is a simulation method for calculating an evaluation value indicating the performance of a rubber product using foamed rubber in which a plurality of voids are formed, and a rubber product model in which the rubber product is divided into a finite number of elements And a physical property value setting step for setting a physical property value of a rubber product for the rubber product model. In the physical property value setting step, the physical property value has a Poisson's ratio ν. For the element corresponding to the foam rubber, the Poisson's ratio ν is corrected by the foaming rate P, and the corrected Poisson's ratio is set for the rubber product model. The gist is that the void volume ratio per unit volume.

  Another feature of the present invention is that when the corrected Poisson's ratio ν is a corrected Poisson's ratio ν ′, the Poisson's ratio ν is corrected using ν ′ = ν (1-P) in the physical property value setting step. The gist is to do.

  Another feature of the present invention is a simulation method for calculating an evaluation value indicating the performance of a rubber product using a foamed rubber having a plurality of voids, wherein the rubber product is divided into a finite number of elements. A model setting step for setting a product model; and a physical property value setting step for setting a physical property value of the rubber product for the rubber product model. In the physical property value setting step, the physical property value includes a volume V The volume V of the element corresponding to the foamed rubber is corrected by the foaming rate P, the corrected volume V is set for the rubber product model, and the foaming rate P The gist is that the void volume ratio per unit volume.

  Another feature of the present invention is that when the corrected volume V is a corrected volume V ′, the physical property value setting step corrects the volume V using V ′ = V (1−P). The gist.

  Another feature of the present invention is a simulation method for calculating an evaluation value indicating the performance of a rubber product using a foamed rubber having a plurality of voids, wherein the rubber product is divided into a finite number of elements. A model setting step for setting a product model; and a physical property value setting step for setting a physical property value of the rubber product for the rubber product model. In the physical property value setting step, the physical property value includes a tangent loss. Tan δ is included, and for the element corresponding to the foamed rubber, the tan δ is corrected by the foaming rate P, and the corrected tan δ is set for the rubber product model. The gist is the void volume ratio per unit volume of rubber.

  Another feature of the present invention is that when the corrected tan δ is corrected tan δ ′, the physical property value setting step corrects the tan δ using tan δ ′ = tan δ (1-P). .

  Another feature of the present invention is that the rubber product is a tire.

  Another feature of the present invention is summarized in that the performance is rolling resistance.

  Another feature of the present invention is that it is a simulation apparatus for executing the simulation method according to any one of claims 1 to 8.

  According to the simulation method and the simulation apparatus according to the present invention, an accurate evaluation value can be obtained for a rubber product using foamed rubber without significantly increasing the amount of calculation.

FIG. 1 is a cross-sectional view along the tread width direction and the tire radial direction of a tire 10 according to the present embodiment. FIG. 2 is a diagram illustrating a configuration of the simulation apparatus 500 according to the present embodiment. FIG. 3 is a flowchart for explaining the simulation method according to the present embodiment. FIG. 4 is a perspective view showing the tire model 100 according to the present embodiment. FIG. 5 is a perspective view illustrating the tire model 100, the wheel model 200, and the road surface model 300 according to the present embodiment.

  An example of the simulation method and the simulation apparatus 500 according to the present invention will be described with reference to the drawings. Specifically, (1) schematic configuration of tire 10, (2) configuration of simulation device 500, (3) simulation method, (4) comparative evaluation, (5) action and effect, (6) other embodiments. explain.

  In the following description of the drawings, the same or similar parts are denoted by the same or similar reference numerals. It should be noted that the drawings are schematic and ratios of dimensions and the like are different from actual ones. Accordingly, specific dimensions and the like should be determined in consideration of the following description. It goes without saying that the drawings include parts having different dimensional relationships and ratios.

(1) Schematic Configuration of Tire 10 A schematic configuration of the tire 10 according to the present embodiment will be described with reference to FIG. FIG. 1 is a cross-sectional view along the tread width direction and the tire radial direction of a tire 10 according to the present embodiment.

  As shown in FIG. 1, the tire 10 includes a tread portion 20, a bead portion 30, a carcass 40, and a belt 50. The tread portion 20 has a land portion partitioned by grooves. In the tread portion 20, a portion in contact with the road surface is formed by the foamed rubber layer 25. The foam rubber layer 25 is formed of foam rubber in which a plurality of voids are formed. The plurality of voids are formed in the foamed rubber layer 25 without extreme bias. The bead unit 30 includes a bead core 32 and a bead filler 35. The bead core 32 is configured by a bead wire (not shown). The bead filler 35 is provided to increase the rigidity of the bead portion 30. The carcass 40 is disposed so as to straddle between the pair of bead portions 30. The carcass 40 encloses a pair of bead portions 30. The belt 50 is formed by covering a plurality of parallel cords with rubber. The belt 50 is located between the tread portion 20 and the carcass 40.

(2) Configuration of Simulation Device 500 The configuration of the simulation device 500 according to the present embodiment will be described with reference to FIG. FIG. 2 is a diagram illustrating a configuration of the simulation apparatus 500 according to the present embodiment.

  As illustrated in FIG. 2, the simulation apparatus 500 includes an input unit 510, a storage unit 520, a processing unit 530, and a display unit 540. The input unit 510 prompts the input of a value necessary for simulating the behavior of the tire model 100 described later. If necessary, input of values such as a wheel model 200 and a road surface model 300 described later may be prompted. Storage unit 520 stores a program or the like for executing processing by processing unit 530. Based on the value input by the input unit 510 and the value stored in the storage unit 520, the processing unit 530 analyzes the behavior of the tire model 100 by dividing the analysis into a finite number of elements such as a finite element method. To analyze. The display unit 540 displays the behavior result analyzed by the processing unit 530. The simulation apparatus 500 executes the simulation method according to the present embodiment.

(3) Simulation Method The simulation method according to the present embodiment will be described with reference to FIGS. FIG. 3 is a flowchart for explaining the simulation method according to the present embodiment. FIG. 4 is a perspective view showing the tire model 100 according to the present embodiment. FIG. 5 is a perspective view illustrating the tire model 100, the wheel model 200, and the road surface model 300 according to the present embodiment.

(3.1) Step S1
Step S1 is a model setting step. In step S1, a tire model 100 obtained by dividing the tire 10 into a finite number of elements is set. Specifically, as shown in FIG. 4, nodal coordinate values and shapes are defined for each of the elements constituting the tire model 100. For example, in the tire model 100, the foamed rubber layer 25, the bead portion 30, and other internal rubber that form the tread portion 20 may be modeled as solid elements. The carcass 40 and the belt 50 may be modeled as shell elements, membrane elements, or river elements. The nodal coordinate values and the definition of the shape are input through the input unit 510.

  The tire model 100 is digitized into a format that can be handled by a computer device by dividing the tire into a plurality of elements by element division corresponding to the finite element method (FEM), that is, mesh division. It is a thing.

  In addition to the tire model 100, as shown in FIG. 5, a wheel model 200 in which a wheel is divided into a finite number of elements, a road surface model 300 in which a road surface is divided into a finite number of elements, or the like may be set.

(3.2) Step S2
Step S2 is a physical property value setting step. In step S <b> 2, the physical property value of the tire 10 is set for the tire model 100. A physical property value is defined for each of the elements constituting the tire model 100. Physical properties include elastic constants, Poisson's ratio, density, volume, tan δ, and the like. In the present embodiment, step S2 includes step S22, step S24, and step S26.

  The physical property value is input to each element by the input unit 510 (step S22). When the Poisson ratio ν is input to the element corresponding to the foamed rubber layer 25, the input Poisson ratio ν is corrected by the foaming rate P (step S24). The expansion ratio P is a void volume ratio per unit volume of the foam rubber. That is, the expansion ratio P is expressed using the following formula 1.

P = _Vpoorus / _Vbulk ... Formula 1
V _porous represents the volume of voids contained in the unit volume of the foamed rubber. V _bulk represents a unit volume of the foamed rubber.

  When the Poisson's ratio ν is input to the element corresponding to the foamed rubber layer 25, for example, correction is performed using the following Equation 2.

ν ′ = ν (1−P) Equation 2
ν ′ is a corrected Poisson's ratio (hereinafter abbreviated as a corrected Poisson's ratio).

  The corrected Poisson's ratio ν 'is set to an element corresponding to the foamed rubber layer 25 (step 26).

  Since foamed rubber has voids, it behaves differently than normal rubber (that is, rubber that has no voids and is tightly filled with rubber). For this reason, an evaluation value close to an actual tire can be calculated by correcting the Poisson's ratio ν with the foaming rate P. The method of correcting the Poisson's ratio ν by the foaming rate P creates a tire model that divides the tire into a finite number of elements so as to include the elements that make up the bubbles, and the amount of computation is extremely large compared to the method of simulation. Few.

  Similarly, when the volume V is input to the element corresponding to the foamed rubber layer 25, the input volume V is corrected by the foaming rate P (step S24).

  When the volume V is input to the element corresponding to the foamed rubber layer 25, for example, correction is performed using the following Expression 2.

V ′ = V (1-P) Equation 3
V ′ is a volume after correction (hereinafter abbreviated as correction volume).

  The correction volume V ′ is set to an element corresponding to the foamed rubber layer 25 (step 26).

  Similarly, when tan δ (that is, tangent loss) is input to the element corresponding to the foamed rubber layer 25, the input tan δ is corrected by the foaming rate P (step S24).

  When tan δ is input to the element corresponding to the foamed rubber layer 25, for example, correction is performed using the following Expression 2.

tan δ ′ = tan δ (1-P) Equation 4
tan δ ′ is a corrected tan δ (hereinafter abbreviated as corrected tan δ ′).

  The correction tan δ 'is set to an element corresponding to the foamed rubber layer 25 (step 26).

  When the evaluation value includes rolling resistance, it is preferable to use the corrected volume V ′ or / and the corrected tan δ ′. Rolling resistance is one of the causes of strain energy loss caused by tire deformation. In the tire 10 in which the foam rubber is used, the strain energy loss is reduced by the amount of the gap as compared with the tire 10 in which the foam rubber is not used. Therefore, by correcting the volume V and / or tan δ using the foaming rate P, an evaluation value close to an actual tire can be calculated.

  Note that the correction volume V ′ and the correction tan δ ′ may be used not only when the evaluation value is rolling resistance but also when calculating other evaluation values.

  Physical property values input to elements that do not correspond to the foamed rubber layer 25 (for example, elements corresponding to the bead portion 30, the carcass 40, the belt 50, and other internal rubber) are set to the respective elements as they are. Further, even if the physical property value input to the element corresponding to the foamed rubber layer 25 is not the Poisson's ratio ν, volume V, and tan δ, the input physical property value is set to each element as it is.

  If the Poisson's ratio ν, the volume V, and tan δ are stored in the storage unit 520 in advance, and the corresponding physical property value is input, the processing unit 530 can be set to correct the input physical property value.

(3.3) Step S3
In step S3, boundary conditions are set. The boundary conditions include conditions for using the tire 10 such as air pressure, load, slip angle, speed, or rim width. Note that step S3 is not necessarily performed after step S2, and step 2 may be performed after step 3.

(3.4) Step S4
In step 4, an analysis is performed based on the settings in steps S1 to S3. Specifically, the processing unit 530 performs distortion of each element by finite element method analysis based on the coordinate data of each element stored in the storage unit 520 and the values input in Step 2 and Step 3. Analyze stress. Since numerical analysis by finite element method analysis or the like is common, detailed description is omitted. Thereby, an evaluation value indicating the performance of the tire 10 is calculated.

(3.5) Step S5
In step 5, the result analyzed by the processing unit 530 in step 4 is displayed. Specifically, the analyzed result is displayed on the display unit 540.

(4) Comparative evaluation In order to confirm the effect of the present invention, a simulation method (Example) based on physical property values (Poisson's ratio ν, volume V, tan δ) corrected by the foaming rate P and based on uncorrected physical property values. The simulation method (comparative example) was compared and evaluated. Specifically, it is as follows.

  An evaluation value indicating tire performance (contact length, rolling resistance) was measured by actually using a tire using foamed rubber. For a tire using foamed rubber, an evaluation value indicating the performance of the tire was calculated by a simulation method based on the finite element method. In the example, the Poisson's ratio ν, the volume V, and the tangent loss (tan δ) were corrected using the foaming rate P. Specifically, when calculating the evaluation value indicating the contact length, the Poisson's ratio ν is corrected using Equation 2. When calculating the evaluation value indicating the rolling resistance, the volume V and the tangent loss were corrected using Equation 2, Equation 3, and Equation 4. In the comparative example, no correction was performed.

  Further, an evaluation value indicating tire performance (contact length, rolling resistance) was measured by actually using a tire that did not use foam rubber. Table 1 shows the results of relatively expressing other evaluation values with this evaluation value being 100. The prediction is an evaluation value obtained using a simulation method, and the actual measurement is an evaluation value measured using an actual tire.

For reference, an evaluation value indicating the performance of the tire was also calculated for a tire not using foamed rubber by a simulation method based on the finite element method.

  As shown in Table 1, in the tire that does not use foam rubber, the contact length and the rolling resistance match the actual measurement and the prediction.

  In the tire using foamed rubber, the actual measurement and the prediction do not match in both the example and the comparative example, but the value of the example is closer to the actual measurement than the comparative example. Therefore, it has been clarified that by performing the correction with the foaming rate P, an evaluation value with higher accuracy than the comparative example can be obtained.

(5) Action / Effect According to the simulation method according to the present embodiment, the Poisson's ratio ν is corrected by the expansion ratio P for the element corresponding to the foamed rubber, and the corrected Poisson's ratio is set for the rubber product model . Further, according to the simulation method according to the present embodiment, the volume V of the element corresponding to the foamed rubber is corrected by the foaming rate P, and the corrected volume V is set for the rubber product model. Further, according to the simulation method according to the present embodiment, tan δ is corrected by the foaming rate P for the element corresponding to the foam rubber, and the corrected tan δ is set for the rubber product model.

  Since foamed rubber has voids, it behaves differently than normal rubber (that is, rubber that has no voids and is tightly filled with rubber). By correcting the Poisson's ratio ν, volume V, and tan δ that cause the different behaviors so as to match the actual behavior, an evaluation value close to the actual tire can be calculated. The method of correcting the Poisson's ratio ν by the foaming rate P creates a tire model that divides the tire into a finite number of elements so as to include the elements that make up the bubbles, and the amount of computation is extremely large compared to the method of simulation. Since there are few, calculation time does not take much.

  According to the simulation method according to the present embodiment, the Poisson's ratio is corrected using Equation 2. Further, according to the simulation method according to the present embodiment, the volume V is corrected using Equation 3. Further, according to the simulation method according to the present embodiment, tan δ is corrected using Equation 4. According to this, since correction is performed using a simple expression, the amount of calculation required for correction can be extremely reduced.

(6) Other Embodiments Although the contents of the present invention have been disclosed through the embodiments of the present invention, it should not be understood that the descriptions and drawings constituting a part of this disclosure limit the present invention.

  For example, the pseudo rolling analysis may be performed in the simulation method according to the present embodiment. In the pseudo-rolling analysis, the balance of forces in the steady state of the tire model 100 is directly obtained without rotating the tire model 100. Thereby, analysis time can be shortened.

  In the present embodiment, the simulation method related to the tire 10 has been described. However, the simulation method is not limited to this, and a simulation related to another rubber product using foamed rubber may be used.

  As described above, the present invention includes various embodiments not described herein. Therefore, the technical scope of the present invention is defined only by the invention specifying matters according to the scope of claims reasonable from the above description.

  DESCRIPTION OF SYMBOLS 10 ... Tire, 20 ... Tread part, 25 ... Foam rubber layer, 30 ... Bead part, 32 ... Bead core, 35 ... Bead filler, 40 ... Carcass, 50 ... Belt, 100 ... Tire model, 200 ... Wheel model, 300 ... Road surface Model 500 ... Simulation device 510 ... Input unit 520 ... Storage unit 530 ... Processing unit 540 ... Display unit

Claims (1)

A simulation method for calculating an evaluation value indicating the performance of a tire using foamed rubber in which a plurality of voids are formed,
A model setting step in which a computer divides a tire using foamed rubber in which a plurality of voids are formed into a finite number of elements and sets a tread pattern model having a groove ;
A physical property value setting step in which the computer sets a physical property value of a tire for a tread pattern model having the groove ;
Have
In the physical property value setting step,
The physical property values include the Poisson's ratio ν of rubber,
The computer, for the element corresponding to the foam rubber, correct the Poisson ratio ν by the foaming rate P, set the corrected Poisson ratio for the tread pattern model having the groove ,
The foaming ratio P is defined as a void volume ratio per unit volume of the foam rubber ,
When the corrected Poisson's ratio ν is the corrected Poisson's ratio ν ′,
A simulation method for correcting the Poisson's ratio ν using ν ′ = ν (1-P) in the physical property value setting step .

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