JP2003094916A - Method and device for manufacturing finite element model of composite body - Google Patents

Abstract

PROBLEM TO BE SOLVED: To increase the analyzing accuracy of a composite body. SOLUTION: In this method of manufacturing a finite element model of the composite body, the finite element model Fa for analyzing the numerical values of the composite body is formed of the composite body F formed by covering a cord arranged body 9 having a cord c arranged thereon with a rubber g. The method comprises the steps of modeling the rubber g with a solid element e1 and modeling the cord arranged body 9 with a film element e2 for which anisotropy with different Young's moduli is defined between the longitudinal direction j of the cord c and a direction k orthogonal to the longitudinal direction j. At least the Young's modulus of the film element e2 in the longitudinal direction j of the cord comprises the Young's modulus for compression used for calculation when a compressed stress acts thereon and Young's modulus for tension used for calculation when a tensile stress acts thereon. The Young's modulus for compression is made smaller than the Young's modulus for tension.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and apparatus for producing a finite element model of a composite which is useful for improving the analysis accuracy of the composite of a cord and rubber.

[0002]

2. Description of the Related Art In recent years,
The finite element method is widely used for development and design of industrial products, and is preferably used for simulation for tire development, for example. When performing analysis by the finite element method, it is necessary to create a model for numerical analysis by replacing the analysis target with a finite number of elements.

On the other hand, in a tire, as schematically shown in FIG. 2A, a composite body F in which a cord array 9 in which cords c are arranged substantially in parallel is covered with a rubber g for topping is laminated. Thereby, a skeleton portion such as a carcass ply or a belt ply is formed. Such a composite F has different rigidity in the longitudinal direction j of the cord c and the direction orthogonal to the longitudinal direction (anisotropic). Further, when the complex F is replaced with a finite element method model, if the code c is modeled for each one, the elements will be miniaturized and the number will be enormous, so the calculation time required for the analysis will be large. It becomes extremely large.
This is not practical with current computer capabilities.

Therefore, as shown in an exploded view of FIG. 2B, the composite F is a membrane element e2 having anisotropy for the code array 9 and a solid element e for the rubber g.
1 and e1 are modeled respectively, and these are overlaid and approximately modeled to obtain an analysis result which is substantially equivalent to the actual machine in the simulation while significantly reducing the number of elements.

By the way, the conventional membrane element e2 is
The same Young's modulus is set for compression. However, since the cord c is formed by twisting a plurality of thin fibers (strands), when the tensile force acts, the twisted strands come into close contact with each other, and the rigidity of each strand remains almost unchanged. Since it contributes to the rigidity of the entire cord, it exhibits high rigidity, but when a compressive force is applied, the interval between the twisted wires can be widened, and the rigidity becomes low.

In general use of the tire, since the tensile stress is applied to the cord c due to the filling of air pressure, the difference in rigidity between compression and tension is unlikely to be a problem, but even when the internal pressure is zero. When analyzing a run flat tire or the like that can travel at a predetermined speed, a compressive force may act on the code c. Further, in the case of a tire having a large tread surface curvature such as a motorcycle tire, the tread ground contact portion may be locally largely deformed when a load is applied, and the cord c of this portion may receive a compressive force. Therefore, in the conventional membrane element, in the situation where the compression force acts on the cord c,
As a result different from the actual deformation behavior, there is a problem that an accurate analysis result cannot be obtained.

The present invention has been devised in view of the above problems, and basically sets the Young's modulus for compression of the membrane element to be smaller than the Young's modulus for tension.
It is an object of the present invention to provide a finite element model creating method and apparatus for a composite useful for improving the analysis accuracy of the composite composed of a cord and rubber.

[0008]

According to a first aspect of the present invention, a finite element model for numerical analysis of a composite is prepared from a composite in which a code array in which codes are arranged is covered with rubber. A method for creating a finite element model of a composite, wherein the step of modeling the rubber with a solid element and the cord array has different Young's moduli in the longitudinal direction of the cord and the direction orthogonal to the longitudinal direction. Modeling with a membrane element having a defined anisotropy, and at least the Young's modulus in the longitudinal direction of the cord of the membrane element is the Young's modulus for compression used in the calculation during compression and the calculation in tension. And the Young's modulus for tension used for the above, and the Young's modulus for compression is determined to be smaller than the Young's modulus for tension.

The invention according to claim 2 is the method for producing a finite element model of a composite according to claim 1, characterized in that the Young's modulus for compression is 0.

According to a third aspect of the present invention, the Young's modulus for compression is calculated by multiplying the Young's modulus for tension by a coefficient larger than 0 and smaller than 1. Is a method of creating a finite element model of the complex of.

According to a fourth aspect of the present invention, the membrane element has at least a Young's modulus for compression in the longitudinal direction of the cord,
The first membrane element in which the Young's modulus for tension is set to the same value (≠ 0) is geometrically overlapped by sharing a node with the first membrane element, and the cord is compressed in the longitudinal direction. A finite element model creating method for a composite according to claim 1 or 3, characterized in that the Young's modulus for use with the second membrane element is set to 0.

According to a fifth aspect of the present invention, the value of the Young's modulus of the first membrane element is set so as to approximate to the Young's modulus of the cord array when compressed, and the second membrane element is also set. Is set to a value obtained by subtracting the Young's modulus of the first membrane element from the Young's modulus when the cord array is pulled, and a method for creating a finite element model of a composite. .

The invention according to claim 6 is an apparatus including a computer, which is characterized by executing the method for creating a finite element model of a complex according to claims 1 to 5.

[0014]

BEST MODE FOR CARRYING OUT THE INVENTION An embodiment of the present invention will be described below with reference to the drawings. FIG. 1 shows a cross-sectional view of a pneumatic tire T which is an analysis target of this embodiment. Pneumatic tire T
Is a carcass ply 6A folded back from the tread portion 2 through the sidewall portion 3 and the bead core 5 of the bead portion 4.
And a belt layer 7 composed of two outer and inner belt plies 7A and 7B arranged on the outer side in the tire radial direction of the carcass 6 and inside the tread portion 2.

The carcass ply 6A and the belt ply 7
As shown in part (A) of FIG. 2, each of A (or 7B) is a ply in which both sides of the cord array 9 in which the cords c are arranged are covered with the rubber g for topping, that is, the composite F.
Composed of. The cord c is a stranded wire formed by twisting strands or fiber materials, and includes various cords such as a steel cord, an organic fiber cord or an inorganic fiber cord.

FIG. 3 shows a complex finite element model creating apparatus for creating a finite element model Fa for numerical analysis of the complex from the complex F as described above. For this device,
For example, the computer 10 is used. Computer 1
Reference numeral 0 is configured to include a CPU as an arithmetic processing unit, a ROM in which processing procedures of the CPU are stored in advance, a RAM as a working memory of the CPU, an input / output port, and a bus connecting these. ing. In the input / output port,
In this example, an input unit I such as a keyboard and a mouse for inputting and setting predetermined information, a display capable of displaying the input result, an output unit O such as a printer, and an external storage such as a magnetic disk or a magneto-optical disk. The device D is connected. Further, the external storage device D stores programs and data such as the procedure of the method of the present embodiment.

FIG. 4 shows an example of the processing procedure of the method for creating a finite element model of a complex according to this embodiment. As shown in FIGS. 4 and 2B, in the present embodiment, first, the rubber g is modeled by the solid element e1 (step S).
1). The “solid element” is an element that can three-dimensionally define a modeling target. In this example, the solid element e1 uses a hexahedral solid element, but other than this, a tetrahedral solid element, a pentahedral solid element, or the like can be used.

In modeling, the rubber g portion of the composite F is divided into appropriate sizes, and the divided regions are sequentially modeled into solid elements e1. In this example, the rubber g on the upper side and the lower side of the cord array 9 are respectively
The lower solid elements e1 and e1 are modeled.
The thickness t1 of each solid element e1 is set to be substantially equal to the rubber thickness tg between the virtual straight lines N, N contacting the cord contour inside and outside the cord array 9 in the complex F and the outer surface of the complex, for example. It

The adjacent codes c of the code array 9 are
The amount of rubber filled between c is small and contributes little to rigidity, so it is ignored in this embodiment. Further, the solid element e1 is defined based on the rubber g of the composite F such as coordinates of each node n, material characteristics (elastic modulus, specific gravity) and the like.

Next, in this embodiment, the code array 9 is
Is modeled by a membrane element e2 in which anisotropy is defined in which Young's moduli differ in the longitudinal direction j of the code c and the direction k orthogonal to the longitudinal direction j (step S2).

The "membrane element" is an element that transmits only in-plane force, that is, tension, compression, and shear in a direction along the plane, and in this example, a quadrilateral membrane element is illustrated. However, for example, a triangular membrane element or the like can also be appropriately used. Such a membrane element e2 is particularly suitable for the longitudinal direction j of the cord.
It is suitable for expressing the characteristics of a composite material that has a significantly low bending rigidity when bending along a cord with respect to the rigidity of.

Further, as shown in FIG. 8, the composite body F can be modeled in the thickness direction by one solid element e1 and one membrane element e2. At this time,
The solid element e1 has a thickness (2 × t) in FIG.
g + D) is given. The membrane element can be handled without regard to its thickness. Generally, the rubber g on the upper side and the lower side of the cord array 9 has a small thickness of about 0.5 to 1.2 mm.
It can be made larger than that of (B), and it is possible to prevent deterioration of calculation accuracy due to deterioration of aspect ratio of elements.

As schematically shown in FIG. 5, the Young's modulus E1 along the longitudinal direction j of the cord of the membrane element e2 is the Young's modulus E1c for compression used in the calculation when the compressive stress is applied, and the Young's modulus E1c when the tensile stress is applied. Young's modulus for tension E1t used for calculation
It is set including and. In this example, the Young's modulus E1t for tension is set to a value close to the Young's modulus of the actual cord c at the time of tension. On the other hand, the Young's modulus E1 for compression
c is set to be smaller than the Young's modulus E1t for pulling.

Thus, by setting the Young's modulus E1c for compression to be smaller than the Young's modulus E1t for tension,
It is possible to set the compressive rigidity of the membrane element e2 by approximating the deformation behavior of the cord array 9 of the composite F, and approximate the characteristics when the code array 9 is actually subjected to tensile and compressive loads. It becomes possible to obtain the analysis result. Therefore,
More accurate analysis is possible.

The Young's modulus E1c for compression is not particularly limited as long as it is smaller than the Young's modulus E1t for tension, but the value can be set to 0, for example. In this case, when a compressive force acts on the model Fa of the composite F, the membrane element e2 becomes a solid element e that models the rubber g.
1 and e1 are displaced together, but internal stress is not generated in the membrane element, and the calculation is performed assuming that the compressive stress acts only on the solid element e1 that models the rubber portion having a large Poisson's ratio. This is useful for obtaining an analysis result closer to that of the actual machine than the conventional one.

When the Young's modulus of the membrane element e2 is made to differ between the compression side and the tension side in this way, when calculating the stress, it is determined whether the deformation occurring in the element is the tension side or the compression side. It is necessary to judge Young's modulus for compression and tension based on the result of judgment individually, which may seem like a hassle. However, when the membrane element e2 is in a compressed state, it is not necessary to calculate the stress for the membrane element e2, so that the problem of an increase in calculation steps does not substantially occur.

When it is desired to analyze the actual behavior of the composite F with higher accuracy, the Young's modulus E1c for compression of the membrane element is set lower than the Young's modulus E1t for take-up and is larger than 0. Set to the value of. In this case, the characteristics of the cord material itself, which is a constituent element of the tire, can be better reproduced, and as a result, the behavior such as the flexure of the tire can be more accurately reproduced. The material of the cord c is roughly classified into organic fiber and metal fiber.
The difference in rigidity between the tension side and the compression side is particularly large in the case of the organic fiber and is relatively small in the case of the metal fiber. Therefore, the embodiment in which the Young's modulus E1c for compression is set to 0 as described above is suitable when modeling the cord c made of an organic fiber material, for example.

The cord array 9 is composed of
The rigidity difference at the time of compression and tension also changes depending on the number of hammers and the like. Therefore, in order to further improve the analysis accuracy of the composite F, it is desirable that the difference between the Young's modulus E1c for compression and the Young's modulus E1t for tension can be arbitrarily set. For example, the Young's modulus E1c for compression can be calculated by multiplying the Young's modulus E1t for tension by a coefficient G larger than 0 and smaller than 1. The coefficient G is a twisting method, a twisting pitch,
It can be obtained empirically according to the number of twists, etc., or can be calculated from the results of various experiments. Such a method is preferable in that the tensile / compression rigidity can be changed at an arbitrary ratio. Further, it is desirable that the processing for changing the Young's modulus of the element as described above is defined as, for example, a subroutine and incorporated into the calculation process of generally commercially available finite element method analysis software.

FIG. 6 shows another embodiment of the present invention. In this embodiment, the membrane element e2 modeling the cord array 9 has a Young's modulus E1c 'for compression and a Young's modulus E for tension at least in the longitudinal direction j of the cord c.
The first membrane element e2a in which both 1t 'are defined to have the same value (≠ 0) and the first membrane element e2a share a node n geometrically and overlap in the longitudinal direction j of the cord. The second film element e2b having a Young's modulus for compression defined as 0 is shown.

The values of the Young's modulus E1c 'for compression and the Young's modulus E1t' for tension of the first membrane element e2a are defined by being approximated to the actual Young's modulus of the cord array 9 during compression. . On the other hand, the Young's modulus E1c ″ for tension of the second membrane element e2b is obtained by subtracting the Young's modulus E1c ′ for tension of the first membrane element e2a from the Young's modulus of the actual cord array 9 in tension. Value, and membrane element e
The deformation calculation of 2 is performed by the first and second membrane elements e2a and e2.
It is treated as the one in which b is integrally laminated, that is, the two membrane elements are deformed while keeping the sharing of the node n. This makes it possible to easily express the characteristics of the actual material.

In this embodiment, the Young's modulus of the first membrane element e2a is set to the same value for tension and compression. Therefore, it is not necessary to judge whether the deformation of the membrane element e2a is compression or tension, while on the other hand, the second membrane element e2b.
, The Young's modulus differs between tension and compression, so the membrane element e2b
It is necessary to judge whether the deformation of is compression or tension,
In the case of compression, it is not necessary to calculate stress. Therefore,
Although the calculation cost is slightly increased, it is preferable in that there is no need to create a new user subroutine as compared with the case where the coefficient is multiplied.

In each of the above-mentioned embodiments, the membrane element has been described by taking the Young's modulus different in the cord arranging direction j as an example, but the direction k orthogonal to the cord arranging direction is described.
With regard to, since the rigidity does not substantially change between tension and compression, the Young's modulus may be the same between tension and compression. The specific value can be appropriately determined with reference to the value of the complex F as an example. For example, the Young's modulus in tension of the actual composite F in the cord arrangement direction j is X, the Young's modulus in tension in the direction k orthogonal to the cord arrangement direction is Y, the Young's modulus of the model in the direction j is X1, and the model is When the Young's modulus in the direction k of Y is Y1, the Young's modulus Y1 in the direction k may be calculated by Y · X1 / X.

Although the embodiments of the present invention have been described above, the present invention is not limited to the above-mentioned embodiments and can be variously modified. For example, the execution order of step S1 and step S2 may be exchanged, or they may be processed in parallel.

[0034]

[Example] Size P225 / 60 having a puncture resistant structure
A finite element model was created from R16 runflat tires based on the use of Table 1. The tire has a carcass ply formed of a composite using organic fiber cords,
The belt ply is composed of a composite using a metal cord. Then, the carcass ply and the belt ply were modeled into a finite element model according to the present invention, and a tire analysis model as shown in FIG. 7 was created.

In this tire analysis model, internal pressure filling conditions (200 kPa, rim 7JJ, longitudinal load 5.0 kN) and puncture conditions (0 kPa, rim 7JJ, longitudinal load 5.0 k) were used.
N) was set for each and a simulation for calculating the vertical deflection amount of the tire was performed. The simulation uses general-purpose explicit software LS-DYNA as analysis software,
As the hardware, a computer SX-4 manufactured by NEC Corporation was used. Further, actual tires were also tested under the same conditions to evaluate the difference between the actual machine and the analytical model. The test results and the like are shown in Table 1, and the Young's modulus is an index display with the value of the conventional example as 100. In addition, each example and comparative example were prepared by the following procedure.

(Conventional example) A code array is modeled by one membrane element. The Young's modulus for compression and the Young's modulus for tension are both set to the same value.

(Example 1) The code array is modeled by one membrane element. The Young's modulus for compression is set to 0 for both the array of organic fiber cords (carcass ply) and the array of metal cords (corresponding to claim 2).

(Example 2) The code array is modeled by one membrane element. The Young's modulus for compression is calculated by multiplying the Young's modulus for tension by a coefficient. A user subroutine for executing such processing is defined (corresponding to claim 3).

(Embodiment 3) The code array is modeled by the first and second membrane elements. The value of the Young's modulus of the first membrane element is defined by approximating the Young's modulus of the code array when compressed. The Young's modulus of the second membrane element in tension is defined as a value obtained by subtracting the Young's modulus of the first membrane element from the Young's modulus of the cord array body in tension (corresponding to claim 5).
Table 1 shows the test results and the like.

[0040]

[Table 1]

As a result of the test, it can be confirmed that in the comparative example and the example, an analysis result very close to the actual machine is obtained under the internal pressure filling condition. However, under the puncture condition in which the compressive stress acts on the cord, it is understood that the comparative example has a large difference from the actual machine and the accuracy is deteriorated. On the other hand, in the analytical models of Examples 1 to 3, good results close to those of the actual machine were obtained even under the puncture condition. Also, the computer calculation time required for the analysis is not much different from that of the comparative example.

[0042]

As described above, according to the first aspect of the invention, in the membrane element that models the code array, the Young's modulus for compression is set to be smaller than the Young's modulus for tension. It is possible to set the compression rigidity of the element by approximating the compression behavior of the actual code array. Therefore, it becomes possible to obtain an analysis result that is similar to the characteristic when the cord array is actually subjected to tensile and compression loads, which is useful for improving the analysis accuracy.

Further, the method of setting the Young's modulus for compression to 0 as in the second aspect of the invention makes it unnecessary to calculate the stress when the membrane element is compressed and deformed, and therefore is useful for shortening the deformation calculation time. In addition, it can be suitably used without causing a large error in modeling a cord made of an organic fiber having a relatively large rigidity difference between the tension side and the compression side.

According to a third aspect of the invention, the Young's modulus for compression is greater than 0 and 1 for the Young's modulus for tension.
When it is obtained by multiplying by a smaller coefficient, the Young's modulus for compression can be obtained by a simple method, and the Young's modulus for compression can be set to a value closer to the actual machine according to the twist of the cord and the like.

According to the invention described in claims 4 and 5,
The compression rigidity of the membrane element can be approximated to the compression rigidity of the cord array by superimposing the membrane element on the first and second membrane elements and regulating the Young's modulus of compression and tension of each membrane element. It becomes possible to set.

[Brief description of drawings]

FIG. 1 is a sectional view of a tire.

FIG. 2A is a cross-sectional perspective view of a composite ply,
(B) is an exploded perspective view of the finite element model.

FIG. 3 is a block diagram showing an example of a computer device that performs the processing of the present invention.

FIG. 4 is a flowchart showing an example of processing of the present invention.

FIG. 5 is a perspective view illustrating a membrane element.

FIG. 6 is an exploded perspective view of a membrane element showing another embodiment of the present invention.

FIG. 7 is a perspective view of a finite element model.

FIG. 8 is an exploded perspective view of a finite element model showing another embodiment of the present invention.

[Explanation of symbols]

9 Code array c code g rubber F complex Finite element model of Fa complex

Claims (6)

[Claims] 1. A method for creating a finite element model of a composite, which comprises creating a finite element model for numerical analysis of the composite from a composite in which a code array in which codes are arranged is covered with rubber. Modeling with an element, and modeling the code array with a membrane element in which anisotropy is defined in which Young's moduli are different in the longitudinal direction of the code and the direction orthogonal to the longitudinal direction. At the same time, at least the Young's modulus in the longitudinal direction of the cord of the membrane element includes the Young's modulus for compression used in the calculation during compression and the Young's modulus for tension used in the calculation during tension, and Is set to be smaller than the Young's modulus for tension, which is a method for creating a finite element model of a composite. 2. The method for producing a finite element model of a composite according to claim 1, wherein the Young's modulus for compression is 0. 3. The finite element model of a composite according to claim 1, wherein the Young's modulus for compression is calculated by multiplying the Young's modulus for tension by a coefficient larger than 0 and smaller than 1. How to make. 4. The first membrane element, wherein at least the Young's modulus for compression and the Young's modulus for tension in the longitudinal direction of the cord are both set to the same value (≠ 0), and the first membrane element. 5. A second membrane element which geometrically overlaps with the membrane element of (1) and which has a Young's modulus for compression in the longitudinal direction of the cord set to 0, and which is geometrically overlapped. A method for creating a finite element model of a complex described in. 5. The value of the Young's modulus of the first membrane element is
The Young's modulus for tension of the second membrane element is set to be close to the Young's modulus of the cord array for compression, and the Young's modulus of the first membrane element for tension is determined from the Young's modulus of the cord array for tension. A method for creating a finite element model of a complex, characterized by being set to a value obtained by subtracting a rate. 6. An apparatus including a computer for executing the method for creating a finite element model of a complex according to claim 1.