JP2011122279A - Method for preparing twist structure model and computer program for preparing twist structure model - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an analytical model of a twist structure suitable for multiscale simulation. <P>SOLUTION: A method for preparing a twist structure model includes: preparing a solid model of monofilament wires and a solid model of a matrix composing the twist structure (step S101); next assembling the solid model of the wires in the interior of the solid model of the matrix (step S102); then dividing the surface of the solid model of the wires and the surface of the solid model of the matrix with a plurality of meshes composed of a plurality of nodal points (step S103), wherein the nodal points of the meshes on one surface are superimposed on the nodal points of the meshes on the other surface when the plurality of meshes present on the one surface are projected onto the other surface in the opposite surfaces of the solid model of the matrix; and subsequently dividing the interior of the solid model of the wires and the solid model of the matrix with a plurality of tetrahedral elements using the meshes on the surface of the solid model of the wires and the surface of the solid model of the matrix (step S104). <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to modeling a twisted structure such as a reinforcing cord, which is a reinforcing material for a tire, into an analysis model that can be analyzed by a computer.

  Conventional tires have been developed through repeated trials and tests, which has the problem of poor development efficiency. In order to solve this problem, a method that can predict the physical properties of a tire, that is, the performance of the tire without producing a prototype by numerical analysis using a computer has been proposed and put into practical use in recent years. ing. When the performance of a tire is predicted by numerical analysis using a computer, it is necessary to make an analysis model that can be analyzed by the computer. The tire is a structure in which rubber is reinforced by a reinforcing cord such as a carcass or a belt. Regarding the analysis modeling of the reinforcement cord, for example, in Patent Document 1, a tire cord that creates a two-dimensional model of a tire cord and develops the created two-dimensional model in the longitudinal direction of the tire cord to create a three-dimensional shape An analysis model creation method is disclosed.

JP, 2008-230375, A [0028], [0045], FIG. 5, FIG. JP, 2007-265382, A [0004], [0022]

  Incidentally, in recent years, an analysis technique called multi-scale simulation has been used. This analysis method is used to analyze a problem in which two events with greatly different scales are related to each other. When analyzing the performance and characteristics of a tire reinforcement cord using multiscale simulation, it is necessary to model the reinforcement cord in a form suitable for multiscale simulation. However, the patent document 2 does not mention the multi-scale simulation, and even if the tire reinforcement code is modeled by the method disclosed in the patent document 2, the multi-scale simulation cannot be applied. . The present invention has been made in view of the above, and an object of the present invention is to create an analysis model of a twisted structure such as a reinforcing cord suitable for multiscale simulation.

  In order to solve the above-described problems and achieve the object, a method for creating a twisted structure model according to the present invention is a combination of a base material and a twisted wire obtained by twisting a plurality of monofilament strands. When creating an analysis model of the twisted structure that can be analyzed by a computer with respect to the twisted structure that is embedded and reinforces the structure, the computer is a solid solid that is a solid model of the plurality of monofilament strands. A base material solid model which is a solid model of the base material and the base material solid model, and the computer forms a stranded solid model composed of a plurality of the solid wire solid models inside the base material solid model. And the computer includes a plurality of meshes composed of a plurality of nodes on the surface of the solid wire model. When a plurality of meshes existing on one surface are projected onto the other surface on the opposite surfaces of the base material solid model, the nodes of the mesh on one surface become the meshes of the mesh on the other surface. Dividing the surface of the base material solid model with a plurality of meshes composed of a plurality of nodes so as to overlap the nodes, and the computer using the mesh of the surface of the element solid solid model, Create a wire model by dividing the interior of the model with a plurality of tetrahedron elements composed of a plurality of nodes, and use the mesh of the surface of the matrix solid model to create multiple interiors of the matrix solid model. A base material model is created by dividing a plurality of tetrahedron elements composed of nodal points, and a twisted structure model composed of the wire model and the base material model is created. Characterized in that it comprises a forward, a.

  In order to solve the above-described problems and achieve the object, a method for creating a twisted structure model according to the present invention is a combination of a base material and a twisted wire obtained by twisting a plurality of monofilament strands. When creating an analysis model of the twisted structure that can be analyzed by a computer with respect to the twisted structure that is embedded and reinforces the structure, the computer is a solid solid that is a solid model of the plurality of monofilament strands. A procedure for creating a model and a base material solid model that is a solid model of the base material, and the computer divides the surface of the wire solid model with a plurality of meshes composed of a plurality of nodes, When a plurality of meshes existing on one surface are projected onto the other surface of the opposite surfaces of the base material solid model, Dividing the surface of the base material solid model with a plurality of meshes composed of a plurality of nodes so that the nodes of the mesh on the surface overlap the nodes of the mesh on the other surface; Using the mesh of the surface of the solid model, the interior of the solid wire model is divided into a plurality of tetrahedral elements composed of a plurality of nodes to create a wire model, and the surface of the base material solid model A step of creating a base material model by dividing the interior of the base material solid model using a mesh into a plurality of tetrahedral elements composed of a plurality of nodes; and And a procedure for creating a twisted structure model composed of the wire model and the base material model by being incorporated in a material model.

  As a desirable aspect of the present invention, the solid wire model has the same shape between a plurality of cross sections orthogonal to the central axis in the twisted state of the monofilament wire constituting the stranded wire. Is preferred.

  As a desirable mode of the present invention, in the twisted structure model, at least one condition among fixing, peeling, and contact is given between the wire model and the base material model constituting the twisted structure model. It is preferred that

  As a desirable mode of the present invention, the mesh created on the surface of the solid wire model is perpendicular to the central axis in the twisted state of the monofilament wire constituting one of the sides of the mesh. It is preferable that it exists on a cross section.

  As a desirable mode of the present invention, in a cross section orthogonal to the longitudinal direction of the twisted structure model, the tetrahedral element on the surface of the base material model has a larger dimension than the tetrahedral element on the surface of the strand model. Is preferred.

  As a desirable mode of the present invention, the base material is preferably rubber.

  As a desirable mode of the present invention, it is preferable that a periodic boundary condition is given to the opposing surfaces of the twisted structure model.

  In order to solve the above-described problems and achieve the object, a computer program for creating a twisted structure model according to the present invention causes a computer to execute the method for creating a twisted structure model.

  INDUSTRIAL APPLICABILITY The present invention can create an analysis model of a twisted structure such as a reinforcement cord suitable for multiscale simulation.

FIG. 1 is a cross-sectional view showing a meridional section passing through a rotation axis of a tire. FIG. 2 is an explanatory diagram showing a configuration of a twisted structure model creation device according to the present embodiment. FIG. 3-1 is a cross-sectional view showing a tire reinforcing cord and rubber as a base material. FIG. 3-2 is a cross-sectional view illustrating an example in which a tire reinforcement cord and a base rubber material are modeled by a computer. FIG. 4 is a flowchart showing a procedure of a method for creating a twisted structure model according to the present embodiment. FIG. 5 is a perspective view showing a solid model of a base material constituting the twisted structure. FIG. 6 is a perspective view showing a solid model of a stranded wire constituting the stranded structure. FIG. 7 is a front view showing the arrangement of monofilament strands constituting the stranded wire. FIG. 8 is a perspective view showing a solid model of a monofilament wire. FIG. 9 is a plan view showing a cross-sectional shape of a solid model of a monofilament wire. FIG. 10 is a perspective view showing a unit cell. FIG. 11A is a perspective view of a stranded wire solid model obtained by dividing the surface of the solid wire model with a mesh. FIG. 11B is a perspective view of a base material solid model whose surface is divided by a mesh. FIG. 12 is a perspective view showing a state in which the surface of the solid wire model is divided by a mesh. FIG. 13 is an explanatory diagram of a mesh. FIG. 14 is an enlarged view of the surface of the solid wire model divided by the mesh. FIG. 15 is a perspective view showing another example in which the surface of the solid wire model is divided by a mesh. FIG. 16 is a perspective view for explaining the base material solid model. FIG. 17 is an enlarged view of the surface of a base material solid model in which the surface is divided by a mesh. FIG. 18 is a schematic diagram showing a mesh relationship between opposing surfaces of a base material solid model whose surface is divided by a mesh. FIG. 19 is a side view of a twisted structure model. 20 is a cross-sectional view taken along line AA in FIG. FIG. 21 is a cross-sectional view of the wire model constituting the twisted structure model. FIG. 22-1 is a perspective view of a tetrahedral element. FIG. 22-2 is a perspective view of a tetrahedral element. FIG. 23 is an explanatory diagram of the boundary between the wire model and the base material model. FIG. 24 is a schematic diagram illustrating an example of a twisted structure model. FIG. 25 is a schematic diagram showing a relationship between a twisted structure model and a coordinate system. FIG. 26 is a schematic diagram illustrating an example in which a tensile test simulation is performed by applying strain to a twisted structure model. FIG. 27 is a flowchart showing a procedure of a method for creating a twisted structure model according to a modification of the present embodiment.

  Hereinafter, the present invention will be described in detail with reference to the drawings. The present invention is not limited by the following contents. The following constituent elements include those that can be easily assumed by those skilled in the art and those that are substantially the same. The application target of the present invention is applicable to any tire having a reinforcing cord, and is not limited to a pneumatic tire. In the following, for convenience of explanation, a pneumatic tire is referred to as a tire unless otherwise specified.

  FIG. 1 is a cross-sectional view showing a meridional section passing through a rotation axis of a tire. As shown in FIG. 1, a carcass 2, a belt 3, a belt cover 4, and a bead core 5 appear on the meridional section of the tire 1. The tire 1 is a composite material structure in which rubber as a base material is reinforced by a reinforcing cord such as a carcass 2, a belt 3, or a belt cover 4 as a reinforcing material. Here, a layer of a reinforcing cord made of a cord material such as a metal fiber or an organic fiber, such as the carcass 2, the belt 3, and the belt cover 4, is referred to as a cord layer.

  The carcass 2 is a strength member that serves as a pressure vessel when the tire 1 is filled with air. The carcass 2 supports a load by its internal pressure and withstands a dynamic load during traveling. The belt 3 is a layer of reinforcing cords in which rubberized cords arranged between the cap tread 6 and the carcass 2 are bundled. In the case of a bias tire, it is called a breaker. In the radial tire, the belt 3 plays an important role as a shape retention and strength member.

  A belt cover 4 is disposed on the ground surface G side of the belt 3. The belt cover 4 is formed by arranging, for example, organic fiber materials in layers, and has a role as a protective layer for the belt 3 and a role as a reinforcing layer for the belt 3. The bead core 5 is a bundle of steel wires that supports the cord tension generated in the carcass 2 by internal pressure. The bead core 5 becomes a strength member of the tire 1 together with the carcass 2, the belt 3, the belt cover 4, and the tread. A groove 7 is formed on the ground surface G side of the cap tread 6. This improves drainage during rainy weather. The side portion of the tire 1 is called a sidewall 8 and connects between the bead core 5 and the cap tread 6. Further, a shoulder portion Sh is provided between the cap tread 6 and the sidewall 8. Next, the apparatus which performs the preparation method of the twist structure model which concerns on this embodiment is demonstrated.

  FIG. 2 is an explanatory diagram showing a configuration of a twisted structure model creation device according to the present embodiment. The twisted structure model creation device (hereinafter referred to as model creation device) 50 shown in FIG. 2 is a combination of a base material and a twisted wire obtained by twisting a plurality of monofilament strands, and is embedded in a structure. An analysis model of the twisted structure that can be analyzed by a computer is created for the twisted structure that reinforces the structure. And the model creation apparatus 50 performs the creation method of the twist structure model which concerns on this embodiment, and produces the analysis model of a twist structure.

  The model creation device 50 includes a processing unit 50p and a storage unit 50m. The processing unit 50p and the storage unit 50m are connected via an input / output unit (I / O) 59. The processing unit 50p includes a solid model creation unit 51, a model synthesis unit 52, a mesh division unit 53, and an element division unit 54. These execute the creation method of the twisted structure model according to the present embodiment. The solid model creation unit 51, the model synthesis unit 52, the mesh division unit 53, and the element division unit 54 are connected to the input / output unit 59 and configured to exchange data with each other. An input / output device 60 is connected to the model creation device 50, and an input device 61 and a display device 62 are connected to the input / output device 60. The input / output device 60 inputs information necessary for creating the twisted structure model to the processing unit 50p and the storage unit 50m via the input / output unit (I / O) 59.

  The solid model creation unit 51 creates a solid wire model that is a solid model of a plurality of monofilament wires and a base material solid model that is a solid model of the base material. The model synthesis unit 52 incorporates the solid wire model created by the solid model creation unit 51 inside the base material solid model created by the solid model creation unit 51. The mesh division unit 53 divides the surface of the solid wire model and the surface of the base material solid model with a plurality of meshes formed of a plurality of nodes. At this time, when a plurality of meshes existing on one surface are projected onto the other surface of the opposing surface of the base material solid model, the nodes of the mesh on one surface overlap the nodes of the mesh on the other surface. The surface of the base material solid model is divided. The element dividing unit 54 uses a mesh of the surface of the solid wire model to create a wire model in which the inside of the wire solid model is divided by a plurality of tetrahedral elements composed of a plurality of nodes. In addition, the element dividing unit 54 creates a base material model obtained by dividing the inside of the base material solid model by a plurality of tetrahedral elements formed of a plurality of nodes, using a mesh on the surface of the base material solid model. Thereby, the element dividing unit 54 creates a twisted structure model composed of the wire model and the base material model.

  The storage unit 50m stores a computer program including processing procedures of a method for creating a twisted structure model according to the present embodiment, which will be described later, various data, and the like. Here, the storage unit 50m can be configured by a volatile memory such as a RAM (Random Access Memory), a nonvolatile memory, a hard disk device, or a combination thereof. The processing unit 50p can be configured by a memory and a CPU (Central Processing Unit).

  The computer program is a combination of the computer program already recorded in the solid model creation unit 51, the model synthesis unit 52, etc. included in the processing unit 50p, and the processing procedure of the method for creating the twisted structure model according to the present embodiment. It may be realized. Further, the model creation apparatus 50 uses a dedicated hardware instead of the computer program, and uses a solid model creation unit 51, a model synthesis unit 52, a mesh division unit 53, an element division unit provided in the processing unit 50p. 54 may be realized.

  FIG. 3-1 is a cross-sectional view showing a tire reinforcing cord and rubber as a base material. FIG. 3-2 is a cross-sectional view illustrating an example in which a tire reinforcement cord and a base rubber material are modeled by a computer. As shown in FIG. 3A, in the tire, a reinforcing cord C such as a belt or a carcass is embedded in a rubber LB that is a base material. In tire rolling analysis, vibration analysis, and the like, a computer-analyzed model (analysis model) is used to perform analysis by a computer. For this reason, in the rolling analysis and vibration analysis of the tire, it is necessary to convert the analysis target into an analysis model prior to the analysis.

  For example, when analyzing the structure of a tire or the reinforcement cord C with attention paid to the reinforcement cord C, it is preferable to make the shape of the reinforcement cord C an analysis model as faithfully as possible. However, when analyzing the structure and behavior of a tire by FEM (Finite Element Method) analysis, as shown in Fig. 3-2, a simple plate element CP that normally exhibits similar behavior to the reinforcement cord C is used. The reinforcement cord C is often modeled. In the example shown in FIG. 3-2, rubber is modeled by a solid element LS. Such a plate element CP may not be sufficient to study the structure of the reinforcing cord C.

  Further, the reinforcing cord C has a complicated twisted structure of wires and fibers, and the twisting direction and pitch length differ depending on the structure. In the analysis using the finite element method, it is necessary to faithfully reproduce such a shape and perform element division based on the finite element method to create an analysis model. In addition, when analyzing by focusing on the reinforcing cord C, such as examining a new reinforcing structure of the reinforcing cord C, a simulation as disclosed in Patent Document 2 is considered in consideration of the difference in scale between the tire and the reinforcing cord C. Is preferably applied. However, simply dividing the reinforcing cord C into elements based on the finite element method may hinder the execution of multiscale simulation (or multiscale analysis) as disclosed in Patent Document 2. Here, the multi-scale simulation makes it possible to analyze the micro structure and the macro structure in cooperation with each other. In the multi-scale simulation, for example, a problem in which two phenomena having different orders of magnitude in scale are related to each other, for example, an analysis is performed by associating a phenomenon of a material at a microscope level with a phenomenon of the entire structure.

  For the multi-scale simulation, a known general-purpose finite element analysis solver, for example, a general-purpose finite element analysis program manufactured by ABAQUS, Inc. can be used. As an example of multi-scale simulation in a tire, for example, simulation using a micro model for determining the mechanical properties of a heterogeneous material, for example, uniaxial tension of a heterogeneous material, simulation of a tensile test, compression test, etc. In addition, a simulation of dynamic behavior using a tire macro model having a tire made of a rubber material as a structure is executed.

  When a tire is a structure to be analyzed, a tire model is created as a macro model by using a reinforcing cord that is a twisted structure or a rubber material such as tread rubber or bead rubber as a heterogeneous material. Then, an internal pressure filling simulation that reproduces the dynamic behavior of the internal pressure filling of the tire and a grounding simulation that reproduces the mechanical behavior when the tire filled with the internal pressure is pressed against the ground and a load is applied are executed.

  Furthermore, in order to reproduce the behavior of the micro region of the heterogeneous material during the mechanical behavior of the structure, a simulation of the mechanical behavior using a micro model is executed. For example, a simulation result using a macro model is given to the micro model, and stress, strain, and the like in the micro model are calculated.

  In the simulation using the micro model, the material constant of each material phase in the micro model is changed according to the internal variable value. Initially, the material constants of the micro model are set so as to have substantially the same material property values even though the material properties unique to each material phase are inherently different. Then, any one of force, displacement, stress, and strain is given as an input to a predetermined position, and the simulation is executed. After that, with respect to the micro model deformed by this simulation, the internal variable value is changed while maintaining the given input, and the material constant of the micro model is set so as to have the value of the material characteristic unique to each material phase. Once set, the simulation continues until the simulation results converge.

  The method for creating a twisted structure model according to the present embodiment creates an analysis model suitable for multi-scale simulation when creating an analysis model of a twisted structure like the reinforcement cord C. Next, a procedure for realizing a method for creating a twisted structure model according to the present embodiment will be described. The creation method of the twisted structure model according to the present embodiment can be realized by the model creation device 50 described above.

  FIG. 4 is a flowchart showing a procedure of a method for creating a twisted structure model according to the present embodiment. FIG. 5 is a perspective view showing a solid model of a base material constituting the twisted structure, and FIG. 6 is a perspective view showing a solid model of a twisted line constituting the twisted structure. FIG. 7 is a front view showing the arrangement of monofilament strands constituting the stranded wire. FIG. 8 is a perspective view showing a solid model of a monofilament strand, and FIG. 9 is a plan view showing a cross-sectional shape of the solid model of the monofilament strand.

  A reinforcing cord (for example, a reinforcing belt or a carcass) that is a twisted structure is configured by combining a base material (for example, rubber) and a twisted wire obtained by twisting a plurality of monofilament strands. And it is embedded in a structure (for example, a tire etc.), and this structure is reinforced. The reinforcing cord includes an organic fiber cord, a steel cord, and a glass cord. The monofilament is one element constituting the twisted structure. For example, when the reinforcing cord is a steel cord, the monofilament is each strand.

  In executing the method for creating a twisted structure model according to the present embodiment, in step S101, the solid model creating unit 51 of the model creating apparatus 50 shown in FIG. A base material solid model 10 (see FIG. 5) is created, and a solid wire model 21 (FIG. 6), which is a solid model of a plurality of monofilament strands constituting the stranded wire of the reinforcing cord, is created. In addition, the strand solid model 20 which is a solid model of a strand is comprised by the some strand solid model 21. FIG. The solid model creation unit 51 temporarily stores information (coordinate information, material constants, etc.) of the created base material solid model 10 and the wire solid model 21 in the storage unit 50m of the model creation device 50.

  Here, the solid model is a model created by one technique of three-dimensional modeling. A solid means a solid and can express a solid internal structure that cannot be expressed by a wire frame model or a surface model. The solid model includes not only a solid surface but also information on the contents surrounded by the surface.

  In the present embodiment, the base material solid model 10 has a rectangular parallelepiped shape, and holes 11 in which both end faces of the plurality of solid wire models 21 shown in FIG. 6 appear are provided on both end faces 10Ta and 10Tb. The base material solid model 10 is preferably a rectangular parallelepiped shape from the viewpoint of creating a twisted structure model suitable for multi-scale simulation, but when a plurality of base material solid models 10 are combined, they can be combined without gaps. Any shape can be used. As such a shape, for example, there is a regular hexagonal column shape, and the base material solid model 10 may be a regular hexagonal column shape. As shown in FIG. 6, the stranded wire solid model 20 is configured by spirally twisting a plurality of (three in the present embodiment) strand solid models 21. And as shown in FIG. 7, as for the strand solid model 20, the space | interval L of each strand solid model 21 is equal.

  The strand solid model 21 has the same shape between a plurality of cross sections orthogonal to the central axis Zc (same as the central axis of the strand solid model 21) in a twisted state of the monofilament strand constituting the strand. It is preferable that That is, in the solid wire model 21, it is preferable that the cross section perpendicular to the central axis Zc has the same shape throughout the entire length of the solid wire model 21. The shape in the cross section is, for example, a circle as shown in FIG. Thus, by making the cross section orthogonal to the central axis Zc of the solid wire model 21 all the same shape over the entire length of the solid wire model 21, a twisted structure model having a different cross-sectional shape for each place is created. You can avoid that. As a result, a twisted structure model suitable for multiscale simulation can be created.

  FIG. 10 is a perspective view showing a unit cell. When step S101 is completed, the process proceeds to step S102, and the model synthesis unit 52 of the model creation device 50 shown in FIG. 2 installs the stranded solid model 20 composed of a plurality of strand solid models 21 inside the base material solid model 10. The built-in unit cell 30 is created. In the unit cell 30, end faces of a plurality of solid wire solid models 21 appear from holes 11 provided in the end face of the base material solid model 10. The model synthesis unit 52 temporarily stores information (coordinate information, material constants, etc.) of the created unit cell 30 in the storage unit 50m. Next, the process proceeds to step S103.

  FIG. 11A is a perspective view of a stranded wire solid model obtained by dividing the surface of the solid wire model with a mesh. FIG. 11B is a perspective view of a base material solid model whose surface is divided by a mesh. FIG. 12 is a perspective view showing a state in which the surface of the solid wire model is divided by a mesh. FIG. 13 is an explanatory diagram of a mesh. FIG. 14 is an enlarged view of the surface of the solid wire model divided by the mesh. FIG. 15 is a perspective view showing another example in which the surface of the solid wire model is divided by a mesh. FIG. 16 is a perspective view for explaining the base material solid model. FIG. 17 is an enlarged view of the surface of a base material solid model in which the surface is divided by a mesh. FIG. 18 is a schematic diagram showing a mesh relationship between opposing surfaces of a base material solid model whose surface is divided by a mesh.

  In step S103, the mesh dividing unit 53 of the model creating device 50 shown in FIG. 2 performs the surface and mother of the solid wire model 21 constituting the stranded solid model 20 as shown in FIGS. 11-1 and 11-2. The surface of the material solid model 10 is divided (mesh division) with a mesh composed of a plurality of nodes. In this case, the mesh division unit 53 reads information on the solid wire model 21 and the base material solid model 10 stored in the storage unit 50m, generates a mesh on each surface, and divides the mesh.

  As shown in FIG. 12, the surface of the solid wire model 21 is divided by a plurality of meshes 22. The mesh 22 has a right triangle shape composed of three nodes 24 as shown in FIG. As shown in FIG. 14, the mesh dividing portion 53 is such that one of the sides of the mesh 22 exists on the cross-section 21CS orthogonal to the central axis Zc in the twisted state of the monofilament strand constituting the stranded wire. A mesh 22 is generated on the surface of the solid wire model 21. In this way, the mesh 22 is regularly generated on the surface of the solid wire model 21. In addition, although the space | interval between adjacent cross sections 21CS and 21CS may be non-uniform intervals, it is preferable that they are equal intervals. In this way, the mesh 22 is more regularly generated on the surface of the solid wire model 21.

  FIG. 15 shows the solid wire model 121 in which the mesh 122 is not regularly generated on the surface. However, when this is done, the stress distribution, strain distribution, etc. on the monofilament wire constituting the twisted structure cannot be accurately evaluated. There is a fear. However, when the mesh 22 is regularly generated on the surface of the solid wire model 21 as in the present embodiment, the stress distribution and strain distribution on the monofilament wire can be accurately evaluated.

  As shown in FIG. 16, the base material solid model 10 has a total of six surfaces. That is, the side surfaces 13A, 13B, 13C, 13D and the end surfaces 13E, 13F. The mesh 12 illustrated in FIG. 17 is generated on the side surfaces 13A, 13B, 13C, and 13D and the end surfaces 13E and 13F of the base material solid model 10. Similar to the mesh 22 formed on the surface of the solid wire solid model 21, the mesh 12 has a right triangle shape including three nodes 14.

  In this embodiment, the mesh 12 generated on the surface of the base material solid model 10 is obtained by projecting a plurality of meshes 12 existing on one surface onto the other surface, and the nodes 14 of the mesh 12 generated on the one surface. Is generated so as to overlap the node 14 of the mesh 12 generated on the other surface. For example, although the side surface 13B and the side surface 13D of the base material solid model 10 are opposed to each other, a mesh formed on the side surface 13B is represented by reference numeral 12B, and a mesh formed on the side surface 13D is represented by reference numeral 12D. The mesh 12B is composed of three nodes 14B, and the mesh 12D is composed of three nodes 14D.

  In this case, when the respective nodes 14B constituting the mesh 12B are projected onto the respective nodes 14D constituting the mesh 12D, the two overlap. That is, when each node 14B of the mesh 12B is moved in a direction perpendicular to the side surface 13B on which the mesh 12B is generated, the node 14D of the mesh 12D generated on the surface of the side surface 13D that faces the side surface 13B and is parallel to the side surface 13B. Matches. All the meshes 12B generated on the surface of the side surface 13B and all the meshes 12D generated on the surface of the side surface 13D have such a relationship. The same applies to all meshes 12 generated on the surfaces of the opposite side surfaces 13A and 13C and all meshes 12 generated on the surfaces of the opposite end surfaces 13E and 13F. By doing in this way, the twist structure model suitable for multiscale simulation can be created. In step S103, when the meshes 12 and 22 are formed on the surface of the base material solid model 10 and the surface of the solid wire model 21, respectively, the mesh dividing unit 53 stores the information in the storage unit 50m. Then, the process proceeds to step S104.

  FIG. 19 is a side view of a twisted structure model. 20 is a cross-sectional view taken along line AA in FIG. FIG. 21 is a cross-sectional view of the wire model constituting the twisted structure model. 22-1 and 22-2 are perspective views of the tetrahedral element. FIG. 23 is an explanatory diagram of the boundary between the wire model and the base material model. In step S104, the element dividing unit 54 of the model creating device 50 shown in FIG. 2 uses a mesh 22 on the surface of the solid wire model 21 to form a plurality of nodes that include a plurality of nodes inside the solid wire model 21. A wire model is created by dividing the structure into tetrahedral elements, and a plurality of tetrahedral elements are formed by using a mesh 12 on the surface of the base material solid model 10 and a plurality of nodes inside the base material solid model 10. Divide and create a base material model. Thereby, as shown in FIG. 20, a twisted structure model 30M composed of the wire model 21M and the base material model 10M is created.

  As shown in FIG. 19, the outer side of the twisted structure model 30M is a base material model 10M, and a plurality of meshes 12 are formed on the surface. As shown in FIG. 20, the twisted structure model 30M is configured by arranging a wire model 21M inside a base material model 10M. The base material model 10M is composed of tetrahedral elements 15 (FIG. 22-1) composed of a plurality of nodes 14, and the strand model 21M is tetrahedral elements 25 (FIG. 22— composed of a plurality of nodes 24). 1). The tetrahedral elements 15 and 25 shown in FIG. 22A are four-node tetrahedral elements each composed of four nodes 14 and 24. The tetrahedron elements 15 and 25 may be 10-node tetrahedron elements composed of 10 nodes 14 and 24 as shown in FIG. 22-2.

  In creating the strand model 21M, the element division unit 54 divides the interior of the strand solid model 21 into tetrahedral elements 25 using the mesh 22 formed on the surface of the strand solid model 21. Therefore, one surface of the tetrahedral element 25 appears on the surface of the strand model 21M. At this time, the element dividing unit 54 reads information on the solid wire model 21 stored in the storage unit 50m, and divides the element from the mesh 22 toward the inside of the solid wire model 21. Information (coordinate information, material constants, etc.) of each tetrahedral element 25 generated by element division is stored in the storage unit 50m by the element division unit 54.

  Similarly, when creating the base material model 10M, the element division unit 54 divides the interior of the base material solid model 10 into tetrahedral elements 15 using the mesh 12 formed on the surface of the base material solid model 10. To do. Therefore, one surface of the tetrahedral element 15 appears on the surface of the base material model 10M. At this time, the element division unit 54 reads information on the base material solid model 10 stored in the storage unit 50m, and divides the element from the mesh 12 toward the inside of the base material solid model 10. Information (coordinate information, material constants, etc.) of each tetrahedral element 15 generated by element division is stored in the storage unit 50m by the element division unit 54.

  In the cross section orthogonal to the longitudinal direction of the twisted structure model 30M, that is, the cross section shown in FIG. 20, the tetrahedral element 15 on the surface of the base material model 10M has a dimension larger than that of the tetrahedral element 25 on the surface of the strand model 21M. Larger is preferred. By doing in this way, in the twisted structure model 30M, the vicinity of the wire model 21M having a large deformation is divided more finely by a small tetrahedral element, and the outside of the base material model 10M having a relatively small deformation is a tetrahedron having a relatively large deformation. Can be divided by element. As a result, it is possible to improve the calculation accuracy in the vicinity of the wire model 21M while suppressing an increase in calculation time.

  The dimensions of the tetrahedral elements 15, 25 are compared on the longest side. Moreover, it is preferable that the dimension of the tetrahedral element 15 on the surface of the base material model 10M is at least twice the dimension of the tetrahedral element 25 on the surface of the strand model 21M. In this way, calculation accuracy can be improved more reliably while suppressing an increase in calculation time. Further, the dimensions of the tetrahedral element 15 constituting the base material model 10M may be reduced from the surface of the base material model 10M toward the surface of the wire model 21M. In this way, since a rapid dimensional change of the tetrahedral element 15 can be suppressed, a decrease in calculation accuracy can be suppressed.

  In the twisted structure model 30M, at least one of fixing, peeling, and contact may be given to the boundary 31 (see FIG. 23) between the base material model 10M and the wire model 21M. Thereby, adhesion, peeling, and contact between the base material of the twisted structure and the monofilament strand can be evaluated. This condition is given by the processing unit 50p of the model creation device 50. The twisted structure model 30M is completed by the above procedure (step S105).

  The completed twisted structure model 30M is embedded in, for example, a reinforcing layer of a tire analysis model. Then, a multi-scale simulation is executed using the tire analysis model in which the twisted structure model 30M is embedded. In executing the multiscale simulation, a cyclic symmetry condition is set in the twisted structure model 30M. Next, the cyclic symmetry condition will be briefly described.

  FIG. 24 is a schematic diagram illustrating an example of a twisted structure model. FIG. 25 is a schematic diagram showing a relationship between a twisted structure model and a coordinate system. FIG. 26 is a schematic diagram illustrating an example in which a tensile test simulation is performed by applying strain to a twisted structure model. The twisted structure model 30M shown in FIG. 24 is created by the procedure described above. The twisted structure model 30M is an analytical model of a twisted structure composed of a monofilament wire and a base material having different mechanical characteristics. The strand model 21M and the base material model 10M each have mechanical characteristics. Is different.

  In such a twisted structure model 30M, when a coordinate system as shown in FIG. 26 is set, periodic symmetry conditions for the boundary surface F1 and the boundary surface F2 will be described. As shown in FIG. 26, the boundary surfaces F1 and F2 Nodes A and B facing each other are associated as corresponding nodes. This association is performed for each node on the boundary surfaces F1 and F2.

  For example, in the case of performing a tensile test simulation by applying the strain set in the y1 direction in FIG. 26 to the twisted structure model 30M, that is, in the case of simulation by strain control, for the associated nodes A and B, A relational expression using a displacement gradient tensor is created. That is, a displacement gradient tensor created by strain is calculated, and this displacement gradient tensor can be used together with the displacement vectors of the nodes A and B to relate to the difference of the displacement vectors between the nodes A and B.

That is, in the twisted structure model 30M, the relational expression is determined so that the average value of strain becomes a set value (so as to be the average strain). In the relational expression, the displacement vector of the node A and the displacement vector of the node B are Wa and Wb, respectively, and a virtual node D that is independent from the nodes in the twisted structure model 30M is introduced, and the displacement vector of the node D is defined as Let Wd be the position vectors of nodes A and B, respectively, Ya and Yb, and let H be the displacement gradient tensor. At this time, the following equation (1) is determined by using the value on the right side of the following equation (2) (the value obtained by applying the displacement gradient tensor to the difference between the displacement vectors of the nodes A and B) as the displacement vector at the node D. .
Wb−Wa = Wd (1)
Wd = H · (Yb−Ya) (2)
As described above, in the simulation, a virtual node D is introduced, and the relational expression of the expression (1) is given as a constraint condition between the nodes A, B, and D, so that the value shown in the expression (2) is the displacement of the node D. Simply giving it as a vector sets the cyclic symmetry condition in the micro model.

(Modification)
FIG. 27 is a flowchart showing a procedure of a method for creating a twisted structure model according to a modification of the present embodiment. The creation method of the twisted structure model according to this modification can be realized by the model creation device 50 shown in FIG. The method for creating the twisted structure model according to the present modification is substantially the same as the method for creating the twisted structure model described above, but the strand model 21M is separately provided from the strand solid model 21 and the base material solid model 10, respectively. And the base material model 10M are different from each other after combining them.

  For this reason, when the model creation device 50 executes the creation method of the twisted structure model according to the present modification, the element dividing unit 54 includes the element solid model 21 having the mesh formed on the surface, the base material solid model 10, Are divided by the tetrahedral elements 25 and 15 separately. In addition, the model synthesis unit 52 incorporates a stranded wire model composed of a plurality of strand models 21M created by the element dividing unit 54 into the base material model 10M to create a stranded structure model 30M.

  In executing the method for creating a twisted structure model according to this modification, Step S201 is the same as Step S101 in the method for creating a twisted structure model described above. In step S202, the mesh dividing unit 53 of the model creating apparatus 50 divides the surface of the created solid wire model 21 and the surface of the base material solid model 10 into meshes 22 and 12 composed of a plurality of nodes (mesh). To divide. The mesh division is as described above.

  Next, in step S <b> 203, the element dividing unit 54 of the model creation device 50 uses the mesh 22 on the surface of the strand solid model 21 to form a plurality of four surfaces including a plurality of nodes inside the strand solid model 21. A wire model is created by dividing by a body element, and the inside of the matrix solid model 10 is divided by a plurality of tetrahedral elements composed of a plurality of nodes using the mesh 12 on the surface of the matrix solid model 10. To do. This technique is as described above.

  Next, in step S204, the model synthesis unit 52 of the model creation device 50 incorporates a stranded wire model composed of the plurality of strand models 21M created by the element division unit 54 into the base material model 10M, and performs twisting. A structure model 30M is created. Thereby, the twisted structure model 30M is completed (step S205).

  As described above, in the present embodiment and its modification, in creating an analysis model of a twisted structure composed of a base material and a plurality of monofilament strands, the solid model of the monofilament strand and the base material Create a solid wire model inside. Then, the surface of the solid wire model and the surface of the base material solid model are divided by a plurality of meshes composed of a plurality of nodes. At this time, when a plurality of meshes existing on one surface are projected onto the other surface on the opposing surfaces of the base material solid model, the mesh nodes formed on one surface are meshes formed on the other surface. It overlaps with the node of. Then, using the mesh of the surface of the solid wire model and the surface of the base metal solid model, the inside of the solid wire model and the inside of the solid material model are composed of multiple tetrahedron elements composed of multiple nodes. To divide. Thereby, in this embodiment and its modification, the analysis model of a twist structure like a reinforcement cord suitable for multiscale simulation can be created.

  As described above, the method for creating a twisted structure model and the computer program for creating a twisted structure model according to the present invention can analyze a twisted structure such as a reinforcement cord, which is a reinforcing material for a tire, with a computer. It is useful for modeling, and is particularly suitable for creating an analysis model suitable for multiscale simulation.

DESCRIPTION OF SYMBOLS 1 Tire 2 Carcass 3 Belt 4 Belt cover 10 Base material solid model 10M Base material model 10Ta, 10Tb Both end surfaces 12, 12B, 12D, 22, 122 Mesh 13A, 13B, 13C, 13D Side surface 14, 14B, 14D, 24 Node 15 , 25 Tetrahedral element 20 Stranded solid model 21 Stranded solid model 21M Stranded model 21CS Section 30 Unit cell 30M Twisted structure model 31 Boundary 50 Model creation device (twisted structure model creation device)
50m storage unit 50p processing unit 51 solid model creation unit 52 model synthesis unit 53 mesh division unit 54 element division unit

Claims (9)

An analysis model of the twisted structure that can be analyzed by a computer with respect to a twisted structure that is combined with a base material and a twisted wire obtained by twisting a plurality of monofilament strands and is embedded in the structure to reinforce the structure In creating
A step of creating a solid wire model that is a solid model of the plurality of monofilament wires and a base material solid model that is a solid model of the base material;
The computer incorporates a stranded solid model composed of a plurality of the strand solid models inside the matrix solid model;
The computer divides the surface of the solid solid model with a plurality of meshes composed of a plurality of nodes, and the plurality of meshes existing on one surface of the opposing surfaces of the base material solid model are divided into the other. Dividing the surface of the base material solid model with a plurality of meshes composed of a plurality of nodes such that the nodes of the mesh on one surface overlap the nodes of the mesh on the other surface when projected onto the surface of ,
The computer creates a wire model by dividing the interior of the wire solid model into a plurality of tetrahedral elements composed of a plurality of nodes using a mesh of the surface of the wire solid model, and A matrix model is created by dividing the interior of the matrix solid model into a plurality of tetrahedral elements composed of a plurality of nodes using a mesh of the surface of the matrix solid model, and the wire model and the matrix Creating a twisted structure model composed of the model;
A method for creating a twisted structure model, comprising: An analysis model of the twisted structure that can be analyzed by a computer with respect to a twisted structure that is combined with a base material and a twisted wire obtained by twisting a plurality of monofilament strands and is embedded in the structure to reinforce the structure In creating
A step of creating a solid wire model that is a solid model of the plurality of monofilament wires and a base material solid model that is a solid model of the base material;
The computer divides the surface of the solid solid model with a plurality of meshes composed of a plurality of nodes, and the plurality of meshes existing on one surface of the opposing surfaces of the base material solid model are divided into the other. Dividing the surface of the base material solid model with a plurality of meshes composed of a plurality of nodes such that the nodes of the mesh on one surface overlap the nodes of the mesh on the other surface when projected onto the surface of ,
The computer creates a wire model by dividing the interior of the wire solid model into a plurality of tetrahedral elements composed of a plurality of nodes using a mesh of the surface of the wire solid model, and A procedure for creating a base material model by dividing the inside of the base material solid model with a plurality of tetrahedral elements composed of a plurality of nodes using a mesh of the surface of the base material solid model;
The computer incorporates a plurality of the wire models inside the base material model to create a twisted structure model composed of the wire model and the base material model;
A method for creating a twisted structure model, comprising:   The strand according to claim 1 or 2, wherein the strand solid model has the same shape between a plurality of cross sections orthogonal to a central axis in a twisted state of the monofilament strand constituting the strand. How to create a structure model.   4. The twisted structure model according to claim 1, wherein at least one condition among fixing, peeling, and contact is given between the wire model and the base material model constituting the twisted structure model. A method for creating a twisted structure model according to any one of the above items.   2. The mesh created on the surface of the solid wire model is present on a cross section orthogonal to the central axis in the twisted state of the monofilament wire constituting one of the sides of the mesh. 5. A method for creating a twisted structure model according to any one of items 1 to 4.   6. The tetrahedron element on the surface of the base material model has a larger dimension than the tetrahedron element on the surface of the wire model in a cross section orthogonal to the longitudinal direction of the twisted structure model. A method for creating a twisted structure model according to the item.   The method for creating a twisted structure model according to any one of claims 1 to 6, wherein the base material is rubber.   The method for creating a twisted structure model according to any one of claims 1 to 6, wherein periodic boundary conditions are given to opposing surfaces of the twisted structure model.   A computer program for creating a twisted structure model, which causes a computer to execute the method for creating a twisted structure model according to any one of claims 1 to 8.

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