JP2007034728A - Cord and method for preparing finite element model of its complex - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for preparing a finite element model, capable of considering twist torque generated by the twist of a cord and analyzing a finite element method. <P>SOLUTION: The cord A is divided into a solid element 1 forming the entity of the cord A, an axial truss element 2a for adjusting the extension amount in the longitudinal direction of the cord A to tension acting on the cord A, and a helical truss element 2b which is a truss element 2 in a helical shape inclined in the circumferential direction of the cord A to the longitudinal direction of the cord A for generating component force in the circumferential direction of the cord A at nodes 3 on the outer surface of the cord A to the tension acting on the cord A, and modeling is executed. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a method of creating a finite element model of a cord and a method of creating a finite element model of a composite made of a cord and an elastomer.

In products that use elastomer as the main component, in order to secure strength against external forces such as axial load and air pressure, belts for transmission or conveyance, tires, etc. are reinforced by embedding cords as cords in the elastomer. Is done. Then, a finite element method (FEM) is applied to a composite made of such a cord and an elastomer to analyze and predict the behavior of the composite (see, for example, Patent Document 1, Patent Document 2, etc.). ).
JP 2003-94916 A JP-A-2005-78556

  In belts and tires, reinforcing cords are made by twisting fibers of metal, glass, and other polymer materials, so that when the tensile load acts as tension, twisting torque is generated in the direction of untwisting. . For this reason, the behavior of the composite is affected, for example, a phenomenon occurs in which deviation occurs during traveling due to this torsional torque.

  However, when simulating the mechanical behavior of belts and tires by finite element analysis, most of the cords are modeled as finite elements as materials that are strong in the tensile direction.

  For this reason, it has been impossible to verify the deviation or deformation of the belt or tire during traveling, which is considered to be caused by the torsion torque generated in the cord, by finite element analysis.

  The present invention has been made in view of the above points, and provides a method for creating a finite element model in which finite element method analysis can be performed in consideration of torsional torque generated by twisting a cord. It is the purpose.

  The method for creating a finite element model of a cord according to the present invention adjusts the amount of elongation in the longitudinal direction of the cord with respect to the tension applied to the cord, the solid element forming the substance of the cord, and the solid element. An axial truss element and a spiral truss element held in the solid element and inclined in the circumferential direction of the cord with respect to the longitudinal direction of the cord, and a node on the outer surface of the cord against the tension acting on the cord And a spiral truss element that generates a component force in the circumferential direction of the cord.

  The composite finite element model creation method according to the present invention is a method of creating a composite finite element model in which a code array in which codes are arranged is covered with an elastomer. An axial truss element that adjusts the longitudinal extension of the cord against the tension acting on the cord, held by the solid element, and tilted in the circumferential direction of the cord with respect to the longitudinal direction of the cord held by the solid element A spiral truss element that is divided into a spiral truss element that creates a circumferential component of the cord at a node on the outer surface of the cord against tension acting on the cord; And a step of creating a finite element model of the complex using the finite element model of this code.

  In the above finite element model creation method, the cord is composed of S-twisted or Z-twisted twisted cord.

  As the truss element, the shaft truss element that adjusts the longitudinal extension of the cord with respect to the tension acting on the cord, and the cord is inclined in the circumferential direction of the cord with respect to the cord longitudinal direction and acts on the cord. A spiral truss element that generates a circumferential force of the cord at the nodal point on the outer surface of the cord against the tension to be applied. In this spiral truss element, the torsional torque generated by the twisting of the cord is taken into consideration It is possible to perform the finite element method analysis.

  Hereinafter, the best mode for carrying out the present invention will be described.

  The cord A is produced by twisting a plurality of single yarns 10. Depending on the twist direction, the cord A of S twist (right twist) as shown in FIG. 2 (a) and the cord A of FIG. 2 (b) There is such a Z-twisted (left-twisted) cord A.

  The code A is composed of two types of finite elements, the solid element 1 and the truss element 2. Here, the truss element 2 is a linear element having no bending rigidity and having rigidity only in the length direction of the element.

  The contour shape of the code A is formed by using the solid element 1, and the contour of the code A is divided into meshes by the solid element 1 as shown in FIG. In the embodiment of FIG. 1 (a), mesh division is performed with pentahedral solid elements, but of course, the invention is not limited to this. Thus, the solid element 1 occupies the entire area of the code A and forms the substance of the code A. By varying the material property value (elastic modulus, etc.) of the solid element 1, the bending rigidity of the code A can be increased. It can be adjusted.

  In the present invention, the truss element 2 is composed of an axial truss element 2a and a helical truss element 2b. The axial truss element 2a and the spiral truss element 2b are not distinguished as finite elements, and are merely changed in name due to the difference in arrangement.

  The axial truss element 2a is a linear truss element 2 arranged along the longitudinal direction of the central axis of the cord A, and the solid element 1 at the center of the cord A as shown in FIG. The nodes 3 are connected and held by the solid element 1. Since the elastic modulus of the solid element 1 is adjusted in accordance with the bending rigidity of the cord A, the solid element 1 alone is too stretched with respect to the tension acting on the cord A. For this reason, the axial truss element 2a having higher rigidity than the solid element 1 is arranged while being held by the solid element 1, and the tension in the longitudinal direction of the cord A is adjusted by sharing the tension with the axial truss element 2a. is there.

  The spiral truss 2b is a truss element 2 that is spirally wound around the outer circumference of the cord A so as to be inclined in the circumferential direction of the cord A with respect to the longitudinal direction of the cord A, and is arranged in one or more. As shown in FIG. 1 (c), the nodes 3 of the solid element 1 on the outer surface of the code A are connected and held by the solid element 1. If the truss element 2 is only the shaft truss element 2a, the influence of torsional torque generated by twisting the cord A is not taken into consideration. For this reason, the spiral truss element 2b is arranged while being held by the solid element 1, and a part of the tension applied to the cord A acts on the spiral truss element 2b, whereby the cord 3 A component force in the circumferential direction is generated, and the torsional torque is adjusted by the component force in the circumferential direction. The direction of the spiral of the spiral truss 2b is set in accordance with the S twist and the Z twist of the cord A.

  As described above, the code A can be divided into the solid element 1, the axial truss element 2a, and the spiral truss element 2b, and a finite element model can be created by modeling. In this finite element model of code A, the solid element 1, the axial truss element 2a, and the spiral truss element 2b are subjected to mechanical behavior such as elongation and generated torsion torque when the tension is applied to the actual code A. Set the parameters such as the elastic modulus and the cross-sectional area of the truss element 2 that match, and simulate / predict the behavior considering the torsional torque generated by the twisting of the code A by simulating with the finite element method analysis software It is something that can be done.

  The cord A is used by embedding a plurality of cords as cords for reinforcement in an elastomer B such as rubber in a transmission or conveyance belt, a tire, or the like. In applying the finite element method to a composite D composed of an array B and an elastomer C in which a plurality of codes A as shown in FIG. 4 are arranged in parallel, and analyzing and predicting the behavior of the composite, First, a finite element model in which the code A is divided into the solid element 1, the axial truss element 2a, and the spiral truss element 2b by the above steps is created. Next, the outline of the elastomer C that covers the array B of codes A is mesh-divided with the solid elements 4. In this step, after the elastomer C is modeled by the solid element 4 as shown in FIG. 3A, the array B in which the finite element model of the code A is arranged in the finite element model of the elastomer C is joined at the nodes 3 to each other. The finite element model of the complex D as shown in FIG. 3B can be created by taking the steps of arranging in the above state.

  In the finite element model of the composite D, various parameters are set for each element 1, 2a, 2b of the code A and the solid element 4 of the elastomer C, and the code A is simulated by finite element method analysis software. It is possible to analyze and predict the behavior of the composite D in consideration of the torsional torque generated by twisting.

  First, for twisted cord A made of polyethylene terephthalate, a torsion torque test, a tensile test, and a bending test were performed, and data was taken at a load of 12N. The results are shown in Table 1. The torsional torque is an average value of the S-twisted cord A and the Z-twisted cord A. The elastic modulus given in Table 1 is given to the solid element 1 of code A, and the elastic modulus given to the axial truss element 2a and the spiral truss element 2b with the value of torsional torque and the value of elongation as target values, the axial truss element 2a, The cross-sectional area of the spiral truss element 2b is determined as a parameter of the code A finite element model.

  On the other hand, in the finite element model of code A, the solid element 1 is created by dividing into 8 parts in the circumferential direction and 2 mm pitch in the longitudinal direction, and is arranged through the axial truss element 2a at the axis center of the code A. A spiral truss element 2b was spirally wound around the outer periphery of A. Four spiral truss elements 2b are arranged at equal intervals in the circumferential direction, and each spiral truss element 2b is wound by 90 ° in the circumferential direction by one solid element 1 so that the helical pitch Is set to 8 mm for four solid elements 1.

Then, using “MSC.Marc” manufactured by MSC Software Co., Ltd. as the finite element method analysis software, the value of the elastic modulus (1200 MPa) of Table 1 obtained in the test is given to the solid element 1 of the code A, and the code When the finite element model of A is pulled in the longitudinal direction with a load of 12 N, a part of the force is distributed to the four spiral truss elements 2b and a torsion torque is generated. The remaining force is distributed to the solid element 1 and the shaft truss element 2a, and the cord A extends. Here, when the elastic modulus of the solid element 1 and the elastic modulus of the truss element 2 (common to the shaft truss element 2a and the spiral truss element 2b) are fixed values, the spiral truss element 2b increases as the cross-sectional area of the spiral truss element 2b increases. The torsional torque increases as the force distribution increases. Accordingly, the torsion torque value (0.0693 N · mm) in Table 1 is used as a target value, and simulation is performed so as to determine the cross-sectional area of the spiral truss element 2b. In this embodiment, the total of the cross-sectional areas of one axial truss element 2a and four helical truss elements 2b is fixed to 1 mm ² so that the target value of the torsion torque can be obtained. Calculation is performed to adjust the cross-sectional area ratio of the element 2b. Further, by adjusting the cross-sectional area ratio of the spiral truss element 2b in this way, the elongation of the cord A is the target value (0.24%) in Table 2 even if the torsional torque value becomes the target value. Not exclusively. Therefore, for the elongation, the elastic modulus of the truss element 2 (common to the shaft truss element 2a and the spiral truss element 2b) is adjusted to match the target elongation value. However, if the elastic modulus of the truss element 2 is changed, the value of the torsional torque is also slightly shifted, so it is necessary to repeatedly adjust the torsion torque. In actual adjustment, the adjustment of the elongation and the torsional torque is performed simultaneously. To do.

  As a result of several calculations in this way, the parameters given to each element of the finite element model of code A could be determined as shown in Table 2.

  Next, the tensile test of the composite D of FIG. 4 was simulated using the finite element model of the above code A, and the practicality was verified. The code A of the composite D is as described above, and the composite D is formed by embedding an array B in which two cords A are arranged in parallel in the elastomer C. Elastomer C is ethylene / propylene / diene rubber (EPDM), and the measured value of the elastic modulus is 9.1 MPa. The dimensions of this composite D are shown in FIG. 4 (the unit of dimensions in FIG. 4 is mm).

Then, as shown in FIG. 3, the finite element model of the complex D is created by incorporating the finite element model of the code A into the finite element model in which the elastomer C is modeled by the solid element 4, and the finite element method analysis software As a parameter, an elastic modulus of 9.1 MPa was given to the solid element 4 of the elastomer C, and as shown in Table 2, the solid element 4 of the code A was assigned to the solid element 4 of the code A. An elastic modulus of 1200.0 MPa is given to each of the axial truss element 2a and the helical truss element 2b, and a cross sectional area of 0.92638 mm ² is given to the axial truss element 2a. giving 0.01840Mm ^2, respectively, to simulate the tensile test of the complex D, and finite element analysis It is to determine the torsional torque.

  Here, as the two cords A of the composite D, one is S-twisted and the other is Z-twisted (this is referred to as “SZ”), and both are Z-twisted (this is referred to as “ZZ”). The above finite element method analysis was performed for each.

  On the other hand, the composite D of FIG. 4 was subjected to a tensile test using a tensile tester, and the torsional torque was measured. In addition to SZ and ZZ, this test was also performed on two cords A in which both strands are S twisted (this is referred to as “SS”).

  And the result of a finite element method (FEM) analysis and the result of the test by a tensile testing machine are compared, and it shows in FIG. The difference between the S-twisted cord and the Z-twisted cord A in the finite element method analysis is only the direction in which the torsion torque is generated and the absolute value is the same. Therefore, in the finite element method analysis, only the ZZ is calculated, The absolute values of SS and ZZ in the test according to the above were compared with the averaged results.

  As seen in FIG. 5, the result of the finite element method (FEM) analysis is in good agreement with the result of the test by the tensile tester, and it was verified that the present invention has high practicality. When the combination of cords A is SZ, the torsional torques of both cords A cancel each other, and the overall torsional torque is zero.

BRIEF DESCRIPTION OF THE DRAWINGS It shows an example of embodiment of this invention, (a) is a perspective view which shows a solid element, (b) is a perspective view which shows arrangement | positioning of an axial truss element, (c) shows arrangement | positioning of a spiral truss element. It is a perspective view. The cord is shown, (a) is a schematic diagram of the S twist cord, (b) is a schematic diagram of the Z twist cord. BRIEF DESCRIPTION OF THE DRAWINGS It shows an example of embodiment of this invention, (a) is a perspective view which shows the solid element of a composite_body | complex, (b) is a perspective view which shows arrangement | positioning of the axial truss element and spiral truss element of a cord. The composite is shown, in which (a) is a front view and (b) is a plan view. It is the graph which compared the result of the finite element method analysis of the torsion torque of a composite, and the test result measured with the testing machine.

Explanation of symbols

1 Solid Element 2 Truss Element 2a Axial Truss Element 2b Spiral Truss Element 3 Node 4 Solid Element

Claims (4)

  A method for creating a finite element model of a cord, wherein the cord is a solid element that forms the substance of the cord, and an axial truss that is held by the solid element and adjusts the longitudinal elongation of the cord against the tension acting on the cord And a spiral truss element held by the solid element and inclined in the circumferential direction of the cord with respect to the longitudinal direction of the cord, and cords at the nodes on the outer surface of the cord against the tension acting on the cord A method for creating a finite element model of a code, characterized in that the model is divided into spiral truss elements that generate a component force in the circumferential direction.   The method for creating a finite element model of a cord according to claim 1, wherein the cord is an S-twisted or Z-twisted twisted cord.   A method of creating a finite element model of a composite in which a code array in which codes are arranged is covered with an elastomer, the code being divided into solid elements that form the substance of the code and tensions that are held in the solid elements and act on the codes An axial truss element that adjusts the longitudinal extension of the cord and a spiral truss element that is held by the solid element and is inclined in the circumferential direction of the cord with respect to the longitudinal direction of the cord, acting on the cord The step of modeling the spiral truss element that generates a component force in the circumferential direction of the cord at a node on the outer surface of the cord with respect to the tension, and the finite element model of the complex using the finite element model of this cord And a step of creating an element model. 4. The method for creating a finite element model for a composite according to claim 3, wherein the cord is an S-twisted or Z-twisted twisted cord.

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