JP2015044574A - Numerical analysis method of cord with rubber, and computer program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make easy creation of an analysis model used for numerical analysis of a cord with rubber for a rubber-made tire.SOLUTION: A numerical analysis method of numerically analyzing a cord with rubber 10 in which a cord bundle 20 formed by stranding plural cords 21 is covered with rubber 30, by a computer device 5 through modeling of the cord with rubber 10. The method comprises: a model creation step to create a three-dimensional analysis model M of the cord with rubber 10; and an analysis step to implement numerical analysis on the three-dimensional analysis model M. The model creation step includes: a cord model creation step St11 to create a cord model C in which the cord bundle 20 is divided into plural elements; a rubber model creation step St12 to create a three-dimensional rubber model G in which the rubber 30 is divided into plural elements, separately from the cord model C; and an embedding step St13 to embed the cord model C into the rubber model G.

Description

  The present invention allows a computer to perform a method of modeling and numerically analyzing a rubber cord for a rubber tire in which a cord bundle in which a plurality of cords are twisted and covered with rubber is coated, and a process for modeling the cord with rubber Relates to a computer program.

  Rubber tires used in automobiles are provided with carcass, belt, bead core and the like as reinforcing members, and rubber as a base material is reinforced by these reinforcing members. A carcass or belt has a plurality of cord bundles in which a plurality of metal cords are twisted together, and these cord bundles are arranged side by side in one direction (tread width direction). Is covered.

  In recent years, in order to shorten the development period of such rubber tires and reduce development costs, the performance of reinforcing members such as carcass and belts has been evaluated using numerical analysis by a computer (for example, non-patent) Reference 1).

Hideo Takahashi, 3 others, “Tensile rigidity of FRP columns with twisted cords”, [online], February 26, 2008, Japan Society of Mechanical Engineers, [Search September 21, 2012], Internet <URL: https: //www.jstage.jst.go.jp/article/kikaic1979/66/651/66_651_3690/_pdf>

In order to perform numerical analysis (FEM analysis) with a computer on a rubber-coated cord, which is a reinforcing member (carcass or belt) of a rubber tire as described above, in which a cord bundle in which a plurality of cords are twisted is covered with rubber. Needs to model this rubberized cord.
Various methods are conceivable for modeling the analysis target. In the case of a composite material including a metal cord and rubber having different physical property values, such as a cord with rubber for a rubber tire, for example, the following In this way, it can be modeled.

A plurality of cross-sectional images of actual rubberized cords are acquired at a predetermined pitch, and a two-dimensional analysis model is generated for each cross-sectional image. The generation of the two-dimensional analysis model is based on the acquired cross-sectional image. First, as shown in FIG. 19 (A), a plurality of codes 91 (code areas) constituting the code bundle 90 are each a plurality of codes. Split into elements.
Next, as shown in FIG. 19B, the rubber 92 (rubber region) existing around each cord 91 is divided into a plurality of elements. At this time, at the boundary between the rubber 92 and each cord 91, the node (91a) of the element of the cord 91 and the node (92a) of the element of the rubber 92 are matched to divide the region of the rubber 92 into a plurality of elements.
In this way, a two-dimensional analysis model of a cord with rubber is generated on the basis of each cross-sectional image, and elements of adjacent two-dimensional analysis models are associated with each other to generate a three-dimensional analysis model of a cord with rubber.

However, the cord with rubber includes a plurality of cords 91 (for example, 4 to 12 cords), the shape of the boundary between the cord 91 and the rubber 92 is complicated, and the plurality of cords 91 are twisted. Since it is spiral along the longitudinal direction, the position of the cord 91 is irregular for each cross section.
Therefore, as described above, the operation of generating the analysis model by matching the node (91a) of the element of the code 91 with the node (92a) of the element of the rubber 92 and dividing the region of the rubber 92 into a plurality of elements. Even using computer functions is very difficult.

  Therefore, the present invention provides a numerical analysis method including technical means that facilitates generation of an analysis model used for numerical analysis of a rubber-equipped cord for a rubber tire, and a computer for facilitating generation of the analysis model The purpose is to provide a program.

  The numerical analysis method for a rubber-attached cord according to an aspect of the present invention is a method of modeling a rubber-attached cord for a rubber tire in which a cord bundle in which a plurality of cords are twisted is covered with rubber, and performing a numerical analysis by a computer. A model generation step for generating a three-dimensional analysis model of the cord with rubber, a setting step for setting various conditions for the three-dimensional analysis model, and numerical values for the three-dimensional analysis model in which the various conditions are set An analysis step for performing analysis, wherein the model generation step includes: a code model generation step for generating a code model in which the code bundle is divided into a plurality of elements; and a three-dimensional model in which the rubber is divided into a plurality of elements. A rubber model generating step for generating a rubber model separately from the code model; and the code model for the rubber model. An embedding step, and in the embedding step, an element of the code model and the rubber model is allowed to overlap with each other, and the three-dimensional analysis model of the cord with rubber having the code model and the rubber model is provided. Generate.

  The computer program according to one aspect of the present invention is a computer program for causing a computer to generate a three-dimensional analysis model of rubber cords for rubber tires in which a cord bundle in which a plurality of cords are twisted is covered with rubber. The computer includes a code model generating means for generating a three-dimensional code model in which the code bundle is divided into a plurality of elements, a three-dimensional rubber model in which the rubber is divided into a plurality of elements, Separately from the code model, a rubber model generating means for generating, a program for causing the code model to function as an embedding means for embedding the code model in the rubber model, and the embedding means includes elements of the code model and the rubber model. Before having the cord model and the rubber model allowing overlapping To generate a three-dimensional analysis model of the rubber with a code.

  In addition, the computer program according to one aspect of the present invention is a method for generating a three-dimensional analysis model of a cord with rubber for a rubber tire in which a cord bundle in which a plurality of cords are twisted is covered with rubber, and the three-dimensional analysis model A computer program for causing a computer to perform numerical analysis on the computer, the computer comprising a code model generating means for generating a code model in which the code bundle is divided into a plurality of elements, and the rubber being a plurality of elements A rubber model generating means for generating a three-dimensional rubber model having a divided prismatic shape separately from the code model, an embedding means for embedding the code model in the rubber model and generating the three-dimensional analysis model, and A program for causing the three-dimensional analysis model to function as an analysis means for performing numerical analysis And the embedding means allows the longitudinal direction of the cord model to coincide with the longitudinal direction of the rubber model having a prismatic shape, and allows the elements of the cord model and the rubber model to overlap each other. A three-dimensional analysis model of the cord with rubber having the cord model and the rubber model is generated as a prismatic shape model, and the analysis means performs a shear numerical analysis with a direction parallel to one side of the prismatic shape model as a shear direction. A computer program that does.

According to the numerical analysis method of the present invention, it is easy to generate a three-dimensional analysis model of a cord with rubber, and the analysis time can be shortened.
In addition, according to the computer program of the present invention, it becomes easy to generate a three-dimensional analysis model of a cord with rubber.

It is explanatory drawing of the computer apparatus which performs the numerical analysis method of the cord with rubber | gum of this invention. It is explanatory drawing of a cord with rubber | gum. It is a flowchart explaining the numerical analysis method of the cord with rubber. It is a flowchart of a model production | generation step. It is explanatory drawing of a code model (in the case of a solid element). It is explanatory drawing of a rubber model. It is explanatory drawing of the three-dimensional analysis model (when a code model is a solid element) of a cord with rubber. It is explanatory drawing in the case of producing | generating a code model by simulating manufacture of a code bundle. It is explanatory drawing of a code model (in the case of a beam element). It is explanatory drawing of the three-dimensional analysis model (when a code model is a beam element) of a cord with rubber. It is explanatory drawing which simplified a part of three-dimensional analysis model. It is explanatory drawing which simplified a part of three-dimensional analysis model. It is explanatory drawing explaining the structural member of the rubber tire of an actual motor vehicle. It is an image figure of a shear numerical analysis. It is explanatory drawing explaining the conditions set in a setting step for a shear numerical analysis. It is an image figure of tensile numerical analysis. It is explanatory drawing explaining the conditions set in a setting step for tensile numerical analysis. It is explanatory drawing which shows an example of the data which the computer apparatus produced | generated. It is explanatory drawing explaining the production | generation method of the three-dimensional analysis model of the conventional cord with rubber | gum.

[Description of Embodiment of the Present Invention]
First, embodiments of the present invention will be listed and described.
(1) In the numerical analysis method for a cord with rubber according to an aspect of the present invention, a cord with rubber for a rubber tire in which a cord bundle in which a plurality of cords are twisted is covered with rubber is modeled and numerical analysis is performed by a computer. A method for generating a three-dimensional analysis model of the cord with rubber, a setting step for setting various conditions for the three-dimensional analysis model, and the three-dimensional analysis in which the various conditions are set An analysis step for performing numerical analysis on the model, wherein the model generation step includes a code model generation step for generating a code model in which the code bundle is divided into a plurality of elements, and the rubber is divided into a plurality of elements. A rubber model generating step for generating a three-dimensional rubber model separately from the code model; and An embedding step for embedding in a model, and in the embedding step, the code model and the rubber model are allowed to overlap with each other and the three-dimensional analysis model of the cord with rubber having the rubber model Is generated.

  According to this configuration, a code model is generated, a three-dimensional rubber model is generated separately from the code model, and a three-dimensional analysis model of a cord with rubber is generated by embedding the code model in the rubber model. Generation of a three-dimensional analysis model is facilitated. In other words, since the rubber element can be divided regardless of the code elements (nodes), it is particularly easy to generate a rubber model.

(2) In the embedding step, a weighting factor determined based on a geometric position of the code node in the rubber element is used for the code node of the code model overlapping the rubber element of the rubber model. Thus, it is preferable to restrain the rubber element at the rubber node.
As a result, it is possible to improve the accuracy of numerical analysis of a cord with rubber made of a composite material of cord and rubber.

(3) Further, in the code model generation step, it is preferable that the code model is generated based on a plurality of cross-sectional images of the rubberized cords obtained at a predetermined pitch.
In this case, it is possible to generate a code model based on the actual cord with rubber.
(4) Or, in the code model generation step, a code unit model obtained by dividing each code before forming a code bundle is generated, and an operation of twisting a plurality of the code unit models is simulated by a computer to generate the code model Is preferably produced.
In this case, by producing a cord bundle by twisting a plurality of cords, it is possible to obtain the residual stress applied to each cord by the simulation. In the analysis step, the residual stress is taken into consideration. Numerical analysis of the three-dimensional analysis model can be performed.

(5) In the setting step, an element having a physical property value of zero is preferably set in a part of the rubber model.
In actual production of a cord with rubber, for example, even if a small space in which the rubber is lost without being filled in the gap between the cords is generated, such rubber is lost according to the setting step. A small space can be modeled as an element having a physical property value of zero.

(6) In the numerical analysis method of (4), in the code model generation step, at least one of the plurality of code unit models is a waved code unit model, and the waved code unit model is It is preferable to simulate the operation of twisting with another single cord model by a computer.
In actual production of a cord with rubber, at least one cord may be a corrugated cord, and this can be modeled in the code model generation step.

(7) Preferably, in the code model generation step, a code model in which the code bundle is divided into a plurality of beam elements is generated. In this case, the generation of the code model is simplified, the number of nodes can be reduced, and the time for numerical analysis in the analysis step can be shortened.
(8) Alternatively, in the code model generation step, it is preferable to generate a three-dimensional code model in which the code bundle is divided into a plurality of solid elements. In this case, it is possible to perform analysis in consideration of the deformation of the cord due to the contact between the cords, which is particularly effective when performing a high strain tensile numerical analysis, for example.

(9) As described above, in the model generation step, the rubber model and the code model are generated separately. Therefore, the rubber model can be generated without being affected by the cord bundle (code model), so the rubber model can be generated in an arbitrary shape. For example, the rubber model is generated into a prismatic model. Is possible. Therefore, in the model generation step, the rubber model that has a prismatic shape is generated in the rubber model generation step, and in the embedding step, the longitudinal direction of the code model and the longitudinal direction of the rubber model that is a prismatic shape are matched. Then, a three-dimensional analysis model of the cord with rubber is generated as a prismatic shape model, and in the analysis step, a shear numerical analysis can be performed with a direction parallel to one side of the prismatic shape model as a shear direction.
In the case of a three-dimensional analysis model of a rubber cord with a circular cross section as in the past, it is impossible to perform a shear numerical analysis, but the three-dimensional analysis model of a rubber cord is a prism as in the above configuration. By generating as a shape model, it is possible to perform a shear numerical analysis. By performing this shear numerical analysis, it is possible to obtain, for example, the rigidity (interface rigidity) at the interface between the cord and the rubber as the analysis result.

(10) In the analysis step, further, a tensile numerical analysis is performed with the longitudinal direction of the cord bundle as a tensile direction, and data indicating the result of the shear numerical analysis and the result of the tensile numerical analysis is generated. Is preferred.
According to this configuration, for example, mapped data is generated based on the value of the analysis result when the tensile stiffness is the vertical axis and the shear stiffness (the interface stiffness) is the horizontal axis. Based on this data, It becomes possible to evaluate the performance of the rubber cord for rubber tires.

  (11) In addition, the computer program according to one aspect of the present invention causes a computer to generate a three-dimensional analysis model of a rubber tire cord with rubber covered with a cord bundle in which a plurality of cords are twisted. A computer model comprising: a code model generating means for generating a three-dimensional code model in which the code bundle is divided into a plurality of elements; and a three-dimensional rubber model in which the rubber is divided into a plurality of elements. Separately from the code model, a rubber model generating means for generating, and a program for causing the code model to function as an embedding means for embedding the code model in the rubber model, wherein the embedding means includes the code model and the rubber model. The cord model and the rubber model are allowed to overlap with each other. Wherein generating a three-dimensional analytical model of rubberized code.

  According to this configuration, a three-dimensional code model is generated, a three-dimensional rubber model is generated separately from the code model, and a three-dimensional analysis model of the cord with rubber is generated by embedding the code model in the rubber model. This makes it easy to generate this three-dimensional analysis model. In other words, since the rubber element can be divided regardless of the code elements (nodes), it is particularly easy to generate a rubber model.

Further, the embedding means uses the weighting coefficient determined based on the geometric position of the code node in the rubber element, the code node of the code model overlapping the rubber element of the rubber model, It is preferable to constrain to the rubber node of the rubber element.
This makes it possible to generate a three-dimensional analysis model that can improve the accuracy of numerical analysis of a cord with rubber made of a composite material of cord and rubber.

  (12) In addition, the computer program according to one aspect of the present invention generates a three-dimensional analysis model of a cord with rubber for a rubber tire in which a cord bundle in which a plurality of cords are twisted is covered with rubber, and the tertiary A computer program for causing a computer to perform numerical analysis on an original analysis model, the computer comprising a code model generating means for generating a code model in which the code bundle is divided into a plurality of elements, and a plurality of the rubbers A rubber model generating means for generating a three-dimensional rubber model having a prismatic shape divided into the elements in addition to the code model, and an embedding means for embedding the code model in the rubber model and generating the three-dimensional analysis model And for functioning as an analysis means for performing numerical analysis on the three-dimensional analysis model. The embedding means allows the longitudinal direction of the code model and the longitudinal direction of the rubber model having a prismatic shape to coincide with each other, and allows the elements of the code model and the rubber model to overlap each other. A three-dimensional analysis model of the cord with rubber having the cord model and the rubber model is generated as a prismatic shape model, and the analysis means performs a shear numerical analysis with a direction parallel to one side of the prismatic shape model as a shear direction. I do.

According to this configuration, since the rubber model is generated separately from the code model, the rubber element can be divided regardless of the elements (nodes) of the code, so that it is particularly easy to generate the rubber model.
In addition, since the rubber model and the code model are generated separately, the rubber model can be generated without being affected by the cord bundle (code model), and a rubber model having a prismatic shape can be generated. is there. For this reason, a three-dimensional analysis model of a cord with rubber can be generated as a prismatic shape model, and by using this prismatic shape model, a shear numerical analysis can be performed.

[Details of the embodiment of the present invention]
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
[1. overall structure〕
The numerical analysis method according to the present embodiment is a method of performing numerical analysis (FEM analysis) on a rubber-equipped cord for a rubber tire using a finite element method by a computer. This numerical analysis method includes a step of generating a three-dimensional analysis model of a cord with rubber by a computer.

  As shown in FIG. 2, the cord with rubber 10 to be analyzed is a part of a constituent member (carcass, breaker or belt) of a rubber tire of an automobile, and a plurality of cords (wires) 21 are twisted together. A cord bundle 20 is formed, and the cord bundle 20 is covered with a rubber 30. In the present embodiment, four cords 21 are twisted together. A plurality of the cords 10 with rubber shown in FIG. 2 are arranged in a direction orthogonal to the longitudinal direction of the cord bundle 20 to constitute a carcass or belt of a rubber tire. The rubberized cord 10 in the range shown in FIG. 2 is the object of numerical analysis.

  At least one of the four cords 21 is attached by a two-dimensional wave or a three-dimensional spiral, and the cord bundle 20 is manufactured by twisting the attached cords 21. Since the cord bundle 20 includes the cord 21 that is attached, the rubber 30 can be easily inserted between the cords 21 when the cord 10 with rubber is manufactured.

The cord 21 is made of steel, and the rubber 30 that is a base material of the tire is reinforced by the rubber-equipped cord 10 including the cord 21. In the numerical analysis method according to the present embodiment, the performance of the rubberized cord 10 serving as the reinforcing member of the rubber tire can be evaluated using numerical analysis by a computer.
The rubber 30 covering the cord bundle 20 is made of a material widely used for rubber tires.

  The numerical analysis method is performed using the computer apparatus 5 shown in FIG. The computer device 5 includes a main body 6, a keyboard 7 and a mouse 8 as input means for inputting information necessary for analysis, and a display device 9 as output means for outputting analysis result information. The main body 6 has an arithmetic processing unit (CPU) 6a, a storage device 6b composed of a hard disk, etc., and an information input interface 6c for capturing various information. The storage device 6b stores a computer program for executing the numerical analysis method. When this computer program is executed by the arithmetic processing unit 6a, the computer apparatus 5 is caused to function as a numerical analysis apparatus. That is, this computer program executes the generation of a three-dimensional analysis model of the rubber tire cord 10 with the rubber bundle 30 coated on the cord bundle 20 and the numerical analysis of the three-dimensional analysis model by the computer device 5. It is a computer program for making it happen.

[2. (Numerical analysis method)
Hereinafter, a method of modeling and numerically analyzing the rubberized cord 10 shown in FIG.
In the following description, one linear direction in the cross section of the cord with rubber, rubber, cord bundle, and model thereof is defined as the X direction, and the linear direction on the cross section orthogonal to the X direction is defined as the Y direction. The longitudinal direction of the cord with rubber is defined as the Z direction. The Z direction is orthogonal to the X direction and the Y direction. Then, a coordinate system including the X axis in the X direction, the Y axis in the Y direction, and the Z axis in the Z direction is defined.

  FIG. 3 is a flowchart for explaining a numerical analysis method for the cord 10 with rubber. In this numerical analysis method, a model generation step St10 for generating a three-dimensional analysis model M (see FIG. 7) of the cord with rubber 10 and various conditions such as a load condition and a boundary condition are set for the three-dimensional analysis model M. A setting step St20, and a three-dimensional analysis model M in which various conditions are set are analyzed numerically and an analysis step St30 for outputting an analysis result is provided.

[2.1 Model generation step St10]
FIG. 4 is a flowchart of the model generation step St10. The model generation step St10 includes a code model generation step St11 for generating a code model C (see FIG. 5 or FIG. 9) obtained by dividing the code bundle 20 of the cord with rubber 10 to be analyzed into a plurality of elements, and an analysis target. A rubber model generation step St12 for generating a three-dimensional rubber model G (see FIG. 6) obtained by dividing the rubber 30 in the rubber-equipped cord 10 into a plurality of elements.
As shown in FIGS. 5 and 6, the code model C and the rubber model G are generated separately and independently.

A code model C shown in FIG. 5 is a three-dimensional code model obtained by dividing the code 21 constituting the code bundle 20 into a plurality of solid elements (three-dimensional solid elements).
On the other hand, the code model C shown in FIG. 9 is a code model obtained by dividing each code 21 constituting the code bundle 20 into a plurality of beam elements (one-dimensional beam elements). In this case, the cords 21 are composed of beam elements, but the cord bundle 20 in which these cords 21 are bundled can be said to be a three-dimensional code model.

When the code model C is composed of a plurality of solid elements, the model generation step St10 further embeds the code model C composed of a plurality of solid elements in the rubber model G, and the three-dimensional analysis model M (see FIG. 7) is generated.
When the code model C is composed of a plurality of beam elements, the model generation step St10 embeds the code model C composed of a plurality of beam elements in the rubber model G, and a three-dimensional analysis model M of the cord 10 with rubber (see FIG. 10). ) To generate an embedding step St13. In FIG. 10, the mesh of the rubber model G is omitted in order to make the code model C easily visible.

[2.1.1 Rubber Model Generation Step St12]
The region occupied by the rubber 30 in the cord with rubber 10 shown in FIG. 2 is divided into a plurality of solid elements to generate a rubber model G (see FIG. 6). In this embodiment, it is divided into cubic rubber elements Eg having a predetermined length along each of the X direction, the Y direction, and the Z direction. The rubber element Eg is set smaller than the gap formed between the adjacent cords 21. This element division is performed with reference to a coordinate system composed of XYZ axes.

In this rubber model generation step St12, the rubber model G is generated ignoring the presence of the code 21. That is, the entire region occupied by the rubber cord 10 shown in FIG. 2 is divided into a plurality of rubber elements Eg.
The rubber model G is a mesh model used for numerical analysis by a finite element method, and is a rubber 30 that is a continuous body divided into a finite number of elements (rubber elements Eg).

  In the rubber model generation step St12, as shown in FIG. 6, the rubber model G is generated as a prismatic model. In particular, the rubber model G of the present embodiment is a quadrangular prism model whose cross section is a quadrangle. This square columnar rubber model G is a model longer in the Z direction (the same direction as the longitudinal direction of the cord bundle 20) than in the X direction and the Y direction.

[2.1.2 Code Model Generation Step St11]
[2.1.2.1 When obtaining code model C from multiple solid elements]
The area occupied by the cord 21 in the cord with rubber 10 shown in FIG. 2 is divided into a plurality of solid elements to generate a code model C (see FIG. 5).
In this step St11, the elements of the code 21 may not be divided along the X direction, the Y direction, and the Z direction, and the elements are divided on the basis of a coordinate system different from the coordinate system composed of the XYZ axes. May be. However, in this case, the coordinates of each node of the generated code model C are converted to the coordinates of the coordinate system composed of the XYZ axes.

  As a specific generation method of the code model C, a method of generating the cord bundle 20 by twisting a plurality of cords 21 (method 1) based on a cross-sectional image of the actual cord 10 with rubber 10 There is a method (method 2) of generating based on a result of simulation by a computer.

A method (method 1) based on the cross-sectional image of the cord with rubber 10 will be described.
A plurality of cross-sectional images of the cord with rubber 10 are acquired from an actual product with the cord with rubber 10 using an imaging device such as a CT scanning device. The CT scanning device captures a cross-sectional image of the rubberized cord 10 for each predetermined pitch in the Z direction (several millimeter pitch).
The data of each cross-sectional image is taken into the computer device 5 by the information input interface 6c of the computer device 5, and stored in the storage device 6b in association with the image numbers assigned in order from the start of imaging to the end of imaging.

The computer device 5 recognizes the area of the code 21 and the area of the rubber 30 by performing image analysis using the hue difference or brightness difference between the code 21 and the rubber 30 for each acquired cross-sectional image. . Then, only the area of the code 21 is divided into a plurality of elements, and a two-dimensional code section model is generated.
The elements included in the two-dimensional code section model are, for example, quadrilateral elements, and for the divided elements, the coordinates of the respective nodes, the element numbers, and the like are stored in the storage device 6b.
Further, the coordinates of the cross-sectional center (centroid) of each code 21 are obtained from each cross-sectional image by image processing, and the coordinates of the cross-sectional center of the code bundle 20 are obtained from the coordinates of the cross-sectional centers of these codes 21. In the present embodiment, since the four cords 21 are provided, a quadrilateral having apexes at the cross-sectional centers of the four cords 21 is obtained, and the center of gravity of the quadrilateral is regarded as the cross-sectional center of the cord bundle 20. Find the coordinates.

  Then, such processing is performed for each cross-sectional image, and each node of the two-dimensional code cross-sectional model generated from each cross-sectional image is adjacent to the cross-sectional center of the code bundle 20 in each cross-sectional image. The three-dimensional code model C (FIG. 5) using solid elements is generated by connecting to the nodes of the two-dimensional code section model.

  As described above, in the code model generation step St11, in the method (method 1) based on the cross-sectional image of the rubber-attached cord 10, cross-sectional images of the plurality of rubber-attached cords 10 are acquired at a predetermined pitch by the CT scanning device. A code model C is generated based on these cross-sectional images. In the case of this method, it is possible to generate the code model C based on the actual rubberized cord 10.

A method (method 2) based on the result of simulating the production of the cord bundle 20 will be described.
Each of the four linear cords 21 before the cord bundle 20 is modeled first. That is, each of the four linear codes 21 before forming the code bundle 20 is divided into solid elements to generate four code unit models T (see FIG. 8A).
Then, as shown in FIGS. 8 (A) to 8 (B), the operation of twisting these single cord models T in one place while feeding out each of these four cord simple models T in the longitudinal direction, Simulation is performed by the computer device 5. This simulation is a numerical analysis by the finite element method. In this analysis, a tension is applied to each cord single unit model T as a load condition. In addition, the manufacturing conditions for actually manufacturing the code bundle are set as simulation input conditions.

  As a result, a code bundle model composed of four code unit models T, that is, a three-dimensional code model C (see FIG. 5) using solid elements is generated. Then, from this simulation result, information such as the coordinates of the nodes of each code 21 included in the code model C, the element numbers, and the like are acquired, and these information are stored in the storage device 6b. Further, as a simulation result, information on stress and strain in each element can be acquired, and this information is also stored in the storage device 6b.

Further, as described above, in the actual production of the cord with rubber 10, at least one cord 21 may be used as a corrugated cord. A corrugated code is a code with a two-dimensional wave or a three-dimensional spiral.
Therefore, in the method (method 2), in the code model generation step St11, at least one of the four code unit models T is generated in advance as a waved code unit model. Then, the computer device 5 simulates the operation of twisting the corrugated cord single model T with another cord single model T.
As a result, at least one of the actual codes 21 is wavy, and therefore, the form of the actual code bundle 20 can be modeled by adopting the wavy code simple model in the simulation.

  As described above, in the code model generation step St11, in the simulation-based method (method 2), the code unit model T in which each code 21 before the code bundle 20 is divided into solid elements (three-dimensional elements) is generated. The operation of twisting the single cord model T is simulated by the computer device 5 to generate the code model C. In the case of this method, by manufacturing the cord bundle 20 by twisting the four cords 21, it is possible to obtain the residual stress applied to each cord 21 by simulation, and the subsequent analysis step (FIG. 3). In St30), it is possible to perform a numerical analysis on the three-dimensional analysis model M of the cord with rubber 10 in consideration of the residual stress.

  The code model C (see FIG. 5) generated by each of the method (method 1) and the method (method 2) is a mesh model used for performing numerical analysis by the finite element method, and is a continuum. The code 21 is divided into a finite number of elements (code elements Ec).

[2.1.2.2 When obtaining code model C from multiple beam elements]
2 is divided into a plurality of beam elements to generate a code model C (see FIG. 9) (code model generation step St11 in FIG. 4).
In this step St11, the code 21 is divided into a plurality of beam elements along its longitudinal direction, and the coordinates of each node are acquired as coordinates of a coordinate system composed of XYZ axes.

  As a specific method for generating the code model C, as in the case of the solid element, a method (part 3) for generating based on the cross-sectional image of the actual cord 10 with rubber, and a plurality of cords 21 are twisted together. Then, there is a method (part 4) of generating the code bundle 20 based on the result of simulation by a computer.

A method (method 3) based on the cross-sectional image of the cord with rubber 10 will be described.
A plurality of cross-sectional images of the cord with rubber 10 are acquired from an actual product with the cord with rubber 10 using an imaging device such as a CT scanning device. The CT scanning device captures a cross-sectional image of the rubberized cord 10 for each predetermined pitch in the Z direction (several millimeter pitch).
The data of each cross-sectional image is taken into the computer device 5 by the information input interface 6c of the computer device 5, and stored in the storage device 6b in association with the image numbers assigned in order from the start of imaging to the end of imaging.

The computer device 5 recognizes the area of the code 21 and the area of the rubber 30 by performing image analysis using the hue difference or brightness difference between the code 21 and the rubber 30 for each acquired cross-sectional image. .
Then, the coordinates of the cross-sectional center (centroid) of each code 21 are obtained from each cross-sectional image by image processing, and a curve connecting the cross-sectional centers of each code 21 acquired from each of the plurality of cross-sectional images is acquired. In the present embodiment, since there are four cords 21, four curves are obtained. Then, by dividing each curve into a plurality of beam elements, a code model C shown in FIG. 9 is generated.
The coordinates of each node of each cord 21 composed of a plurality of beam elements, the element numbers, and the like are stored in the storage device 6b.

  As described above, in the code model generation step St11, in the method (method 3) based on the cross-sectional image of the rubber-attached cord 10, cross-sectional images of the plurality of rubber-attached cords 10 are acquired at a predetermined pitch by the CT scanning device. A code model C is generated based on these cross-sectional images. In the case of this method, it is possible to generate the code model C based on the actual rubberized cord 10.

A method (method 4) based on the result of simulating the production of the cord bundle 20 will be described.
Each of the four linear cords 21 before the cord bundle 20 is modeled first. That is, each of the four linear codes 21 before forming the cord bundle 20 is divided into beam elements (one-dimensional beam elements) to generate four code unit models T (see FIG. 8A).
Then, as shown in FIGS. 8 (A) to 8 (B), the operation of twisting these single cord models T in one place while feeding out each of these four cord simple models T in the longitudinal direction, Simulation is performed by the computer device 5. This simulation is a numerical analysis by the finite element method. In this analysis, a tension is applied to each cord single unit model T as a load condition. In addition, the manufacturing conditions for actually manufacturing the code bundle are set as simulation input conditions.

  As a result, a cord bundle model composed of the four cord single models T, that is, a cord model C (see FIG. 9) using beam elements is generated. Then, from this simulation result, information such as the coordinates of the nodes of each code 21 included in the code model C, the element numbers, and the like are acquired, and these information are stored in the storage device 6b. Further, as a simulation result, information on stress and strain in each element can be acquired, and this information is also stored in the storage device 6b.

  Also in this (Method 4), as in the method (Method 2), in the code model generation step St11, at least one of the four code unit models T is generated in advance as a waved code unit model. doing. Then, the computer device 5 simulates the operation of twisting the corrugated cord single model T with another cord single model T.

  As described above, in the code model generation step St11, in the method based on the simulation (method 2), the code unit model T in which each code 21 before the code bundle 20 is divided into beam elements (one-dimensional elements) is generated. The operation of twisting the single cord model T is simulated by the computer device 5 to generate the code model C. In the case of this method, by manufacturing the cord bundle 20 by twisting the four cords 21, it is possible to obtain the residual stress applied to each cord 21 by simulation, and the subsequent analysis step (FIG. 3). In St30), it is possible to perform a numerical analysis on the three-dimensional analysis model M of the cord with rubber 10 in consideration of the residual stress.

  The code model C (see FIG. 9) generated by each of the method (method 3) and the method (method 4) is a mesh model used for performing numerical analysis by the finite element method, and is a continuum. The code 21 is divided into a finite number of elements (code elements Ec).

[2.1.3 Embedding Step St13]
As described above, the code model C (FIG. 5 or 9) and the rubber model G (FIG. 6) are generated separately and independently. Therefore, the code model C is overlapped with the rubber model G, the code model C is embedded in the rubber model G, and a three-dimensional analysis model M of the cord 10 with rubber is generated as shown in FIG. That is, the code model C and the rubber model G are superimposed on the three-dimensional coordinates of XYZ. At this time, elements (code elements, rubber elements) of the code model C and the rubber model G are allowed to overlap each other, and a three-dimensional analysis model M having the code model C and the rubber model G is generated.

In the embedding step St13, as will be described next, processing for constraining the degree of freedom of translation of each node is performed by the computer device 5 (the arithmetic processing device 6a).
Here, FIG. 11 is an explanatory diagram in which a part of the three-dimensional analysis model M is simplified, and this model M is a case where the code model C is composed of a plurality of solid elements.

As shown in FIG. 11, one rubber element Eg ₂ contained in the rubber model G are nodes i, j, k, l, m, n, o, and a p. The nodes of the code element Ec ₂ (part) of the solid elements included in the code model C are composed of S, T, U, V, W, X, Y, and Z.

As the restraining process, it is determined whether or not the node of the code element Ec ₂ exists in the region of the rubber element Eg ₂ because the code model C is embedded in the rubber model G. In the embodiment shown in FIG. 11, the code element Ec ₂ (part) of the solid element exists in the rubber element Eg ₂ , and such presence is determined based on the coordinate value of each node. Do it.
Then, in FIG. 11, for example, node Y code element Ec ₂ has detected that it is present on the side k-o of the rubber element Eg ₂ (near), the rubber element Eg ₂ sides k-o A weighting factor is determined based on the geometric position of the node Y above, and all the degrees of freedom (translational degrees of freedom) of the node Y are constrained to the nodes k and o using this weighting factor.

Such processing is also performed for other nodes and other solid elements.
There are multiple rubber element nodes around the code element node, but the distance from the rubber element node and the weighting factor are inversely proportional, and the closer to the rubber element node, the stronger the node. Be bound.

  FIG. 12 is an explanatory diagram in which a part of the three-dimensional analysis model M is simplified, and this model M is a case where the code model C is composed of a plurality of beam elements. Also in this case, in the embedding step St13, as will be described below, the computer device 5 (the arithmetic processing device 6a) performs processing for constraining the translational freedom of each node.

As shown in FIG. 12, one of the rubber elements Eg ₁ contained in the rubber model G are nodes a, b, c, d, e, f, g, and a h. The nodes of the code element Ec ₁ (part) of the beam elements included in the code model C are Q and R.

As the restraining process, it is determined whether or not the node of the code element Ec ₁ exists in the region of the rubber element Eg ₁ because the code model C is embedded in the rubber model G. In the embodiment shown in FIG. 12, the code element Ec ₁ (part) of the beam element is present in the rubber element Eg ₁ , and such presence is determined based on the coordinate value of each node. Do it.
Then, in FIG. 12, for example, node Q code element Ec ₁ has detected that they are present on the surface abfe rubber element Eg ₁ (near) geometry node Q of within the rubber element Eg ₁ A weighting factor is determined based on the geometric position, and all the degrees of freedom (translational freedom) of the node Q are constrained to the nodes a, b, f, and e using this weighting factor.
Further, the node R has detected that it is present in the gum element Eg _1, to determine the weighting factor based on the geometric positions of the node R in within the rubber element Eg _1, using the weighting factor All the degrees of freedom (translational degrees of freedom) of the node R are constrained to the nodes a, b, c, d, e, f, g, and h.

Such processing is also performed for other beam elements.
There are multiple rubber element nodes around the code element node, but the distance from the rubber element node and the weighting factor are inversely proportional, and the closer to the rubber element node, the stronger the node. Be bound.

As described above, each node (code node) of the code model C that overlaps the rubber element Eg of the rubber model G is used using the weighting coefficient determined based on the geometric position of the code node in the rubber element Eg. Then, a process of restraining to the rubber node of the rubber element Eg is performed.
Thereby, in the subsequent analysis step (St30 in FIG. 3), it is possible to increase the accuracy of numerical analysis of the cord with rubber 10 made of the composite material of the cord 21 and the rubber 30.

  The code model generation step St11, the rubber model generation step St12, and the embedding step St13 included in the model generation step St10 described above are executed by a computer program for model generation stored in the storage device 6b of the computer device 5 by the arithmetic processing unit 6a. It is advanced by being executed by.

That is, this computer program generates a code model C (see FIG. 5 or FIG. 9) in which the computer device 5 shown in FIG. 1 is divided into a plurality of elements from the cord bundle 20 of the rubberized cord 10 to be analyzed. A rubber model for generating a three-dimensional rubber model G (see FIG. 6) obtained by dividing the rubber 30 of the cord with rubber 10 to be analyzed into a plurality of elements separately from the code model C. This is a program for causing the model generation means 12 and the embedding means 13 to embed the code model C in the rubber model G.
Then, the model generation step St10 is executed by the code model generation means 11, the rubber model generation means 12, and the embedding means 13, which are functions of the computer device 5.
The embedding means 13 matches the longitudinal direction of the code model C with the longitudinal direction of the rubber model G having a quadrangular prism shape, and allows the elements of the code model C and the rubber model G to overlap with each other. A three-dimensional analysis model M (see FIG. 7) of the rubberized cord 10 having C and a rubber model G is generated as a prismatic shape model.

[2.2 Setting step St20]
In the setting step St20, the load conditions to be input to the three-dimensional analysis model M generated in the model generation step St10 are set, and the boundary conditions of the nodes at the ends of the model M are set. The setting of the load condition is based on a load (design load) acting on an actual rubber tire (a carcass or a belt including the rubber cord 10). The boundary condition is automatically set by the computer device 5 according to the initial setting.

In this setting step St20, the physical property values of the rubber element Eg and the cord element Ec are set. The physical property values are the density, elastic coefficient, Poisson's ratio, etc. of the material constituting the rubber 30 and the cord 21, and information necessary for the elastic deformation analysis using the finite element method in the later analysis step St30 is set. .
When the code model C is composed of beam elements, a cross-sectional area, a secondary moment of section, a torsional constant, a shape factor, and the like are further set as physical property values of the code element Ec.

In the rubber model G shown in FIG. 6, as described above, the entire cord with rubber 10 shown in FIG. 2 is divided into a plurality of rubber elements Eg. However, in this setting step St20, a part of the rubber model G is included. The element whose physical property values (density and elastic modulus) are zero is set.
This is because, in actual manufacture of the cord 10 with rubber, for example, a gap formed between the adjacent cords 21 and 21 may not be filled with the rubber 30 and a small space may be formed in which the rubber 30 is lost. It is. Therefore, in this setting step St20, such a small space in which the rubber 30 is missing is modeled as an element having a physical property value of zero.

  In addition, the element which makes a physical property value zero among the rubber elements Eg is determined as follows. When a cross-sectional image of the cord 10 with rubber is acquired by the CT scanning device as described above, a small space in which the rubber 30 is missing from the cross-sectional image is determined by image analysis using a hue difference or a brightness difference, The computer device 5 determines an element corresponding to the small space as an element having a physical property value of zero.

Further, as described in FIGS. 11 and 12, since the code element (part) is embedded in the region of the rubber element, the physical property value of the portion is not left as it is, It is preferable to correct according to the occupation ratio of the code.
Therefore, in this setting step St20, as a correction process, a process of obtaining a physical property value of a specific element that overlaps with the code element among the rubber elements based on the abundance ratio of the code and the rubber in the specific element is performed. The abundance ratio is, for example, a volume ratio, and a physical property value proportionally distributed by this ratio is adopted as the physical property value of the specific element.

  The above setting step St20 is advanced by executing the setting computer program stored in the storage device 6b of the computer device 5 by the arithmetic processing device 6a. That is, this computer program is a program for causing the computer device 5 shown in FIG. 1 to function as the setting means 14 that executes the processing of the setting step St20.

[2.3 Analysis step St30]
When the three-dimensional analysis model M (see FIGS. 7 and 10) of the cord with rubber 10 is generated in this way and the load conditions and the like are set, the computer device 5 performs the structural analysis using the finite element method. Do. For example, compression / tension analysis and shear analysis are performed, and characteristics such as stress, strain, and rigidity acting on each part of the model M are obtained.

When the code model C is generated by the method (method 2 and method 4), information on stress and strain in each element is acquired and stored in the storage device 6b as a simulation result of the method (method 2 and method 4). Has been. Therefore, when the structure analysis of the three-dimensional analysis model M including the code model C obtained by this method (method 2 and method 4) is performed, the method (method 2 and method 4) is applied to each element of the code model C as an initial value. The stress and strain obtained by this simulation are set as initial values. That is, the stress (strain) input as the initial value is used as the residual stress (residual strain) of the cord 10.
Thereby, in this analysis step, the numerical analysis of the three-dimensional analysis model M of the cord with rubber 10 can be performed in consideration of the residual stress of the cord 21 and the like.

  This analysis step St30 is advanced when the computer program for numerical analysis stored in the storage device 6b of the computer device 5 is executed by the arithmetic processing device 6a. That is, this computer program is a program for causing the computer device 5 shown in FIG. 1 to function as the analysis unit 15 that executes the analysis step St30 (shear numerical analysis and tensile numerical analysis described later) described below.

[2.3.1 Specific Example of Analysis Step St30 (Numerical Analysis)]
The target of numerical analysis will be described. FIG. 13 is an explanatory view illustrating components of a rubber tire for an automobile. The component to be numerically analyzed in this embodiment is a part b1 of the belt B shown in FIG. 13, and this part b1 corresponds to the cord with rubber 10 shown in FIG. In the case of an actual rubber tire, a circumferential load acts on the cord 10 with rubber. That is, a tensile load acts on the cord 10 with rubber, and since the belt B overlaps with a plurality of layers (two layers) in the radial direction, a shear load acts between the belts B and B in the lamination direction.

  Therefore, in order to obtain the tensile rigidity as the tensile strength of the cord 10 with rubber, a numerical numerical analysis using a three-dimensional analysis model M shown in FIG. 7 or 10 corresponding to one cord 10 with rubber is performed. Further, in order to obtain the shear stiffness (interface stiffness described later) as the shear strength of the cord with rubber 10 included in the belt B, the three-dimensional analysis model M shown in FIG. Shear numerical analysis using. Note that the three-dimensional analysis model M used in the tensile numerical analysis and the three-dimensional analysis model M used in the shear numerical analysis are the same.

The model generation step St10 for generating the three-dimensional analysis model M to be analyzed will be described again. As described above, in the model generation step St10, the rubber model G and the code model C are generated separately. For this reason, as in the present embodiment, a quadrangular prism-shaped rubber model G having a quadrangular cross section can be generated. Conventionally, only a rubber model G having a circular cross section can be generated as shown in FIG.
In the embedding step St13 of the present embodiment, the longitudinal direction of the code model C (cord bundle 20) and the longitudinal direction of the rubber model G having a quadrangular prism shape are matched, and the code model C and the rubber model G are combined. The three-dimensional analysis model M of the cord with rubber 10 is integrated as a quadrangular prism shape model (see FIGS. 7 and 10).

  Then, the analysis step ST30 is executed through the setting step St20. That is, boundary conditions and the like are set for the quadrangular prism shape model (three-dimensional analysis model M), and numerical analysis (structural analysis) by the finite element method using the quadrangular prism model is performed by the computer device 5. In this embodiment, as numerical analysis, the following shear numerical analysis and tensile numerical analysis are performed.

[2.3.2 Numerical shear analysis]
FIG. 14 is an image diagram of the shear numerical analysis. In FIG. 14, the description of the embedded code bundle 20 is omitted. As shown in FIG. 14, the shear numerical analysis of the present embodiment is the same for one side K1 of a three-dimensional analysis model (square prism shape model) M and another side K2 parallel to the one side K1. This is a numerical analysis (simulation) when a load in the opposite direction (+ f1, -f1) is applied.
FIG. 15 is an explanatory diagram for explaining the conditions set in the setting step St20 for the shear numerical analysis. The displacement of each node (all nodes) on one side K1 of the three-dimensional analysis model M, which is a quadrangular prism shape model, is constrained. As a load condition, the same amount of displacement is applied to each node (all nodes) on the other side face K2. The direction of this displacement is the direction along the surface of the side surface K2, and is the direction along the longitudinal direction of the quadrangular prism shape model (Z direction). In addition, as the load condition, for example, a displacement that generates a shear strain of about several tens of percent is set.

In this way, the three-dimensional analysis model M is generated as a prismatic shape model, and after the setting step St20, the computer device 5 performs numerical analysis by the finite element method, and the prismatic shape of the prismatic shape model (three-dimensional analysis model M) is obtained. Shear numerical analysis is performed with the direction parallel to one side K1 of the model as the shear direction.
By performing this shearing numerical analysis, it is possible to obtain the rigidity (that is, the interface rigidity) at the interface between the cord 21 (cord bundle 20) and the rubber 30 as the analysis result.
In the case of the conventional three-dimensional analysis model of the cord with rubber having a circular cross section shown in FIG. 19, two parallel planes (side surfaces) cannot be defined, and thus it is impossible to perform a shear numerical analysis. It is.

[2.3.3 Tensile numerical analysis]
FIG. 16 is an image diagram of tensile numerical analysis. In FIG. 16, the description of the embedded code bundle 20 is omitted. As shown in FIG. 16, the tensile numerical analysis of the present embodiment has the same size on the end surface M1 on the one side in the longitudinal direction of the three-dimensional analysis model (square prism shape model) M and the end surface M2 on the other side. Is a numerical analysis (simulation) when a load (+ f3, -f4) in the opposite direction is applied.
FIG. 17 is an explanatory diagram for explaining the conditions set in the setting step St20 for the tensile numerical analysis. The displacement of each node on one end face M1 of the three-dimensional analysis model M that is a quadrangular prism shape model is constrained. As a load condition, the same amount of displacement is applied to each node on the other end face M2. The direction of this displacement is a direction (Z direction) orthogonal to the end face M2. In addition, as the load condition, for example, a displacement at which a micro strain with a tensile strain of less than 1% is set is set.

In addition, although the restriction | limiting of the displacement of the node in the end surface M1 may be performed with respect to all the nodes in the end surface M1, it is preferable to make it only the node of the code model C in the end surface M1. That is, the displacement of all the nodes included in the code model C on one end face M1 of the three-dimensional analysis model M is constrained, and the displacement of the nodes included in the rubber model G is free (not constrained).
Similarly, the node displacement on the end face M2 may be applied to all the nodes on the end face M2, but it is preferable that only the nodes of the code model C on the end face M2 are provided. That is, displacement is given to all the nodes included in the code model C on the other end face M2 of the three-dimensional analysis model M, and no displacement is given to the nodes included in the rubber model G.
This is because a load in the circumferential direction of the tire acts on the cord 10 with rubber that the belt B (see FIG. 13), which is a constituent member of an actual rubber tire, has, for example. This is because the mode in which the rubber 30 loaded on the bundle 20 (the cord 21) and attached to the loaded cord bundle 20 is deformed along with the deformation of the cord bundle 20 becomes an actual mode. That is, as described above, the numerical analysis in which only the nodes included in the code model C are constrained and the displacement is given becomes an analysis close to an actual mode.

In this way, the three-dimensional analysis model M is generated as a prismatic shape model, and after the setting step St20, the computer apparatus 5 performs code analysis on the prismatic shape model (three-dimensional analysis model M) as a numerical analysis by the finite element method. Tensile numerical analysis is performed with the longitudinal direction of (code model C) as the tensile direction.
By performing this numerical tensile analysis, it is possible to obtain the tensile stiffness in the cord with rubber 10 as the analysis result.

[2.3.4 Evaluation process of cord 10 with rubber]
And the computer apparatus 5 performs a shear numerical analysis and a tensile numerical analysis, and when each value of the interface rigidity (shear rigidity) and the tensile rigidity of the cord 10 with rubber | gum is calculated | required, further, using these both values as an index, Data for performing performance evaluation of the cord with rubber 10 is generated. FIG. 18 is an explanatory diagram illustrating an example of the data generated by the computer apparatus 5.
As shown in FIG. 18, each value of the obtained interface stiffness and tensile stiffness is plotted in a two-dimensional map in which the tensile stiffness is the vertical axis and the interface stiffness is the horizontal axis. In addition, the plot of each shape in FIG. 18 is the result of having performed the numerical analysis regarding the cord 10 with rubber | gum of various characteristics.
As described above, the computer device 5 generates data indicating the relationship between the result of the shear numerical analysis and the result of the tensile numerical analysis. This data is output to, for example, the display device 9 shown in FIG. And based on this data, it becomes possible to perform performance evaluation of the cord 10 with rubber | gum for rubber tires.

[2.4. Others]
According to the above-described numerical analysis method for a cord with rubber according to the present embodiment, a code model C is generated, a three-dimensional rubber model G is generated independently from the code model C, and the code model C is converted into rubber. By embedding in the model G, the three-dimensional analysis model M of the cord with rubber can be generated, so that the generation of the three-dimensional analysis model M is facilitated. In particular, since the rubber element can be divided regardless of the element (node) of the cord, the rubber model can be easily generated. Moreover, the rubber model G can be made into an arbitrary three-dimensional shape, and as a result, the three-dimensional analysis model M combining the rubber model G and the code model C can be made into an arbitrary three-dimensional shape model.
As described above, since the rubber element Eg is set to be smaller than the gap formed between the cords 21, the number of the rubber elements Eg increases. Even in such a case, the rubber model G Is easy to generate, and the generation time of the model M is shortened.

Further, in the embedding step St13 of this embodiment, FIG. 12 as described with reference to (11), the code node Q code model C which overlaps the rubber element Eg ₁ rubber model G, code node in the rubber element Eg ₁ The rubber nodes a, b, f and e of the rubber element Eg ₁ are constrained using a weighting factor determined based on the geometric position of Q. This makes it possible to generate a three-dimensional analysis model M that can increase the accuracy of numerical analysis of the cord with rubber 10 made of a composite material of cord and rubber.

  In the code model generation step St11, when the code bundle 20 is generated as the code model C divided into a plurality of beam elements, a line (curve) passing through the center of the cross section of each cord 21 is divided into the plurality of beam elements. The code model C can be easily created, and the modeling time can be shortened. Further, the number of nodes is reduced as compared with the case of the solid element, and the time required for the numerical analysis in the analysis step St30 can be shortened.

  In the case where the load on the rubberized cord 10 (tensile load in the Z direction) is large and high strain analysis is performed, in the code model generation step St11, the code bundle 20 is divided into a plurality of solid elements as a three-dimensional code model C. It may be preferable to produce. This is because when the load applied to the rubber cord 10 (model M) is large, the cords 21 included in the cord bundle 20 may come into contact with each other, and the analysis considering the deformation of the cord 21 due to this contact is made possible. Because. That is, in order to consider the deformation of the cord 21 due to the contact between the cords 21, it is preferable to use a solid element.

  Further, in order to perform the shear numerical analysis, a three-dimensional model (rectangular shape model) having two parallel surfaces (K1, K2) as shown in FIG. The model M may be a hexagonal column other than the square column. In this case, the displacement of the nodes included in one surface (K1) of the three-dimensional model may be restricted, and the nodes included in the other surface (K2) parallel to the surface (K1) may be displaced. However, in the three-dimensional model, referring to FIG. 14, the width D2 of each of the two parallel surfaces (K1, K2) is made larger than the total width D1 of the cord bundle 20 (D2> D1).

The embodiments disclosed herein are illustrative and non-restrictive in every respect. The scope of rights of the present invention is not limited to the above-described embodiments, but includes all modifications within the scope equivalent to the configurations described in the claims.
For example, in the above-described embodiment, the number of the cords 21 is four, but the number may be other than this, for example, twelve. As the number of the cords 21 increases as described above, the structure of the rubber-equipped cord 10 becomes more complicated. However, according to the model generation method (model generation step) of the present embodiment, modeling can be easily performed.
The computer program can be stored in a recording medium such as a CD-ROM.

[Appendix]
The invention disclosed for reference (reference invention) will be described below.
Problems to be solved by this reference invention are as follows. That is, in order to perform numerical analysis (FEM analysis) with a computer, a rubber-attached cord in which a cord bundle in which a plurality of cords are twisted and constituting rubber reinforcing members (carcass and belt) is covered by a computer This rubberized cord needs to be modeled.
Various methods are conceivable for modeling the analysis target. In the case of a composite material including a metal cord and rubber having different physical property values, such as a cord with rubber for a rubber tire, for example, the following In this way, it can be modeled.

A cross-sectional image of the actual cord with rubber is acquired, and a two-dimensional analysis model is generated from the cross-sectional image. The generation of the two-dimensional analysis model is based on the acquired cross-sectional image. First, as shown in FIG. 19 (A), a plurality of codes 91 (code areas) constituting the code bundle 90 are each a plurality of codes. Split into elements.
Next, as shown in FIG. 19B, the rubber 92 (rubber region) existing around each cord 91 is divided into a plurality of elements. At this time, at the boundary between the rubber 92 and each cord 91, the node (91a) of the element of the cord 91 and the node (92a) of the element of the rubber 92 are matched to divide the region of the rubber 92 into a plurality of elements. In this way, a two-dimensional analysis model of the cord with rubber is generated based on each cross-sectional image.

Each cord included in the cord bundle of the actual cord with rubber has a spiral shape, so that each time the generated two-dimensional analysis model is moved along the longitudinal direction of the cord bundle with a predetermined dimension, a predetermined angle is obtained. The three-dimensional analysis model may be generated by rotating the nodes one by one and connecting the nodes of adjacent elements of the two-dimensional analysis model.
However, in the case of such a model generation method, the generated three-dimensional analysis model is a cylindrical model, but in the case of a cylindrical model, it is feasible to perform numerical numerical analysis with the longitudinal direction as the tensile direction. Although there is no shear numerical analysis.

Then, a reference invention aims at providing the numerical analysis method which becomes possible to perform a shear numerical analysis about the cord with rubber for rubber tires.
[Reference invention]
A method of modeling a rubber cord for a rubber tire in which a cord bundle in which a plurality of cords are twisted and covered with rubber is modeled and numerically analyzed by a computer,
A model generation step of generating a three-dimensional analysis model of the rubberized cord;
A setting step for setting various conditions for the three-dimensional analysis model;
An analysis step for performing numerical analysis on the three-dimensional analysis model in which the various conditions are set,
In the model generation step, a three-dimensional analysis model of the cord with rubber is generated as a prismatic shape model,
In the analyzing step, a numerical analysis method for a cord with rubber, which performs a shear numerical analysis with a direction parallel to one side of the prismatic model as a shear direction.
The items described with reference to FIGS. 1 to 18 can be applied to each step in the reference invention.
Moreover, you may combine arbitrarily at least one part of the matter (embodiment) demonstrated by FIGS.

DESCRIPTION OF SYMBOLS 5 Computer apparatus 6 Main body 6b Memory | storage device 6c Information input interface 6a Arithmetic processing apparatus 6a Processing apparatus 7 Keyboard 8 Mouse 9 Display apparatus 10 Code with rubber 11 Code model generation means 12 Rubber model generation means 13 Embedding means 14 Setting means 15 Analysis means 20 Cord bundle 21 Cord 30 Rubber B Belt b1 Partial C Code model D1 Full width of cord bundle D2 Face width Eg Rubber element Ec Cord element G Rubber model K1 Side face K2 Side face M: Three-dimensional analysis model of cord with rubber M1 End face M2 End face T: Code unit model

Claims (12)

A method of modeling a rubber cord for a rubber tire in which a cord bundle in which a plurality of cords are twisted and covered with rubber is modeled and numerically analyzed by a computer,
A model generation step of generating a three-dimensional analysis model of the rubberized cord;
A setting step for setting various conditions for the three-dimensional analysis model;
An analysis step for performing numerical analysis on the three-dimensional analysis model in which the various conditions are set,
The model generation step includes:
A code model generation step of generating a code model in which the code bundle is divided into a plurality of elements;
A rubber model generating step for generating a three-dimensional rubber model in which the rubber is divided into a plurality of elements, separately from the code model,
An embedding step of embedding the code model in the rubber model;
Including
In the embedding step, numerical analysis of the cord with rubber that generates a three-dimensional analysis model of the cord with rubber and the cord with rubber model by allowing the elements of the cord model and the rubber model to overlap each other Method.   In the embedding step, a code node of the code model that overlaps a rubber element of the rubber model is determined using a weight coefficient determined based on a geometric position of the code node in the rubber element. The numerical analysis method of the cord with rubber | gum of Claim 1 to which it restrains to the rubber node of this.   The numerical analysis method for a cord with rubber according to claim 1 or 2, wherein, in the code model generation step, the code model is generated based on a cross-sectional image of the cord with rubber acquired at a predetermined pitch.   The code model generation step generates a code single model obtained by dividing each code before the code bundle into elements, and generates the code model by simulating an operation of twisting a plurality of the single code models by a computer. The numerical analysis method of the cord with rubber | gum as described in 1 or 2.   The numerical analysis method for a cord with rubber according to any one of claims 1 to 4, wherein, in the setting step, an element having a physical property value of zero is set in a part of the rubber model. In the code model generation step,
5. The rubber-attached unit according to claim 4, wherein at least one of the plurality of cord unit models is a corrugated cord unit model, and the operation of twisting the corrugated cord unit model with another cord unit model is simulated by a computer. The numerical analysis method of the code.   The numerical analysis method for a cord with rubber according to any one of claims 1 to 6, wherein in the code model generation step, a code model in which the cord bundle is divided into a plurality of beam elements is generated.   The numerical analysis method for a cord with rubber according to any one of claims 1 to 6, wherein in the code model generation step, a three-dimensional code model in which the code bundle is divided into a plurality of solid elements is generated. In the model generation step,
In the rubber model generation step, the rubber model having a prismatic shape is generated, and in the embedding step, the longitudinal direction of the cord model is matched with the longitudinal direction of the rubber model in the shape of a prism, and the three-dimensional cord Generate an analysis model as a prismatic model,
In the analysis step,
The numerical analysis method for a cord with rubber according to any one of claims 1 to 8, wherein a shearing numerical analysis is performed with a direction parallel to one side of the prismatic model as a shearing direction. In the analysis step,
Furthermore, while performing the tensile numerical analysis with the longitudinal direction of the cord bundle as the tensile direction,
The numerical analysis method of the cord with rubber according to claim 9 which generates data which shows a result of said shear numerical analysis, and a result of said tensile numerical analysis. A computer program for causing a computer to generate a three-dimensional analysis model of a rubberized cord for a rubber tire in which a cord bundle in which a plurality of cords are twisted is covered with rubber,
The computer,
Code model generating means for generating a code model in which the code bundle is divided into a plurality of elements;
A rubber model generating means for generating a three-dimensional rubber model in which the rubber is divided into a plurality of elements, separately from the code model,
Embedding means for embedding the code model in the rubber model;
As a program to function as
The embedding means allows the elements of the code model and the rubber model to overlap each other and generates a three-dimensional analysis model of the code with rubber and the rubber-attached cord having the rubber model. A computer for generating a three-dimensional analysis model of a rubber-equipped cord for a rubber tire in which a cord bundle in which a plurality of cords are twisted is covered with rubber, and causing a computer to execute numerical analysis on the three-dimensional analysis model A program,
The computer,
Code model generating means for generating a code model in which the code bundle is divided into a plurality of elements;
A rubber model generating means for generating a three-dimensional rubber model having a prismatic shape in which the rubber is divided into a plurality of elements, separately from the code model,
Embedding means for embedding the code model in the rubber model and generating the three-dimensional analysis model;
And a program for causing the three-dimensional analysis model to function as an analysis means for performing numerical analysis,
The embedding means matches the longitudinal direction of the code model with the longitudinal direction of the rubber model having a prismatic shape, and allows the elements of the code model and the rubber model to overlap each other. And generating a three-dimensional analysis model of the rubberized cord having the rubber model as a prismatic shape model,
The computer program according to claim 1, wherein the analysis means performs a shear numerical analysis with a direction parallel to one side of the prismatic model as a shear direction.