JP5406749B2 - Pneumatic tire simulation method - Google Patents

Description

  The present invention relates to a pneumatic tire simulation method for predicting the life of a pneumatic tire with high accuracy and efficiency.

  The life of a pneumatic tire (hereinafter also referred to as a tire) is affected by cracks generated in the rubber member of the tire. The progress of this crack is greatly influenced by the oxidative deterioration of the rubber member of the tire. Therefore, as a simulation method for predicting the oxygen concentration contained in the rubber member of the tire, the applicant of the present application described in Japanese Patent Application No. 2009-010690, the shape of the tire, the internal structure of the tire, the material of the member constituting the tire, It has been proposed to simulate the oxygen concentration distribution in three dimensions using a diffusion equation with a reaction term due to oxidation of rubber, using the tread pattern of the tire as an element.

  By the way, as a simulation method for predicting a progressing portion of a crack generated in a tire, the applicant of the present invention includes a step of setting the displacement of the overlapping portion of the global model and the local model as the sum of the displacement of each model, and a boundary portion of the local model. Has proposed a method comprising a step of setting the displacement of the local model to zero and a step of predicting the life of the tire by a finite element analysis based on the global model and the local model (Patent Document 1).

JP 2006-113799 A

  In order to predict the oxygen concentration in a specific part of the tire, for example, in the vicinity of the end of the member where the crack of the tire is likely to progress, with high accuracy, it is necessary to subdivide the dividing element (mesh) of this part. However, when the mesh is subdivided by using the three-dimensional oxygen concentration simulation method described in Patent Document 1 described above, the number of elements becomes enormous, which requires a lot of calculation time and is not efficient. It was.

  Accordingly, an object of the present invention is to solve the above-described problems and provide a highly accurate and efficient pneumatic tire simulation method.

The gist of the present invention is as follows.
<1> In a simulation method of oxygen concentration distribution contained in rubber of a pneumatic tire,
Using the diffusion equation with the reaction term due to oxidation of the rubber, using the shape of the tire, the internal structure of the tire, the material of the members constituting the tire, and the tread pattern of the tire as elements, the oxygen concentration distribution is determined. Predict in 3 dimensions,
Select the parts that require detailed forecasts,
Predicting the oxygen concentration distribution of the selected portion in one dimension;
A simulation method characterized by that.

<2> The selection of the portion requiring detailed prediction uses at least one selected from a three-dimensional prediction result of the oxygen concentration distribution, a three-dimensional crack growth simulation result, and an experimental database.
The three-dimensional crack growth simulation
A first step of setting a global model in which a tire is modeled by an assembly of elements capable of numerical analysis and a local model in which a crack generated in the tire is modeled by an assembly of elements capable of numerical analysis When,
A second step in which the displacement of overlapping portions of the global model and the local model set in the first step is a sum of displacements of the respective models;
A third step of setting the displacement of the local model at the boundary portion of the local model set in the first step to zero.
A fourth step of predicting the life of the tire by a finite element method analysis based on the global model and the local model set in the first step to the third step;
The simulation method according to <1>, further comprising:

<3> The simulation method according to <1> or <2>, wherein the finite element method is used for discretizing the space.

<4> The simulation method according to any one of <1> to <3>, wherein an implicit method is used for time integration.

<5> The simulation method according to any one of <1> to <4>, wherein the fiber material used in the tire is modeled by a homogenization method.

<6> The above-mentioned <1> to <5>, wherein a cut boundary model obtained by cutting a tire with a predetermined length in a tire circumferential direction is used, and periodic boundary conditions are given to both cut surfaces of the cut section model. The simulation method according to any one of the above.

  Of the three-dimensional oxygen concentration simulation results of a tire, the portion where cracks are expected to occur is identified, and the portion is analyzed in detail by the one-dimensional oxygen concentration simulation method, thereby predicting the tire life with high accuracy and efficiency. can do.

It is a flowchart of the simulation method of this invention. It is sectional drawing of the width direction of the pneumatic tire used for the simulation method of this invention. It is a partially expanded view of the cross section in the width direction of the pneumatic tire used in the simulation method of the present invention. (A) is a detailed model, (b) is a figure which shows the simple model by the homogenization method. It is a figure which shows a periodic tread pattern. It is a figure which shows the outline of oxygen concentration distribution in the rubber member of a tire.

A flowchart of the simulation method of the present invention is shown in FIG.
In step S1, the distribution of oxygen concentration contained in the rubber of the tire is predicted three-dimensionally. In step S2, the portion of the tire that requires detailed prediction is selected. In step S3, the oxygen concentration of the portion selected in step S2 is selected. Predict the distribution in one dimension. Hereinafter, each step S1-S3 is demonstrated in detail.

(Step S1)
The oxygen concentration distribution is predicted three-dimensionally using a diffusion equation that includes a reaction term due to oxidation of rubber using the tire shape, the tire internal structure, the material of the tire constituting the tire, and the tire tread pattern as elements. .
First, an example of the tire used for the simulation method of this invention is demonstrated using FIG. 2 and FIG.

  FIG. 2 is a cross section in the width direction of a tire used in the simulation method of the present invention. The tire 1 has a carcass 3 extending in a toroidal shape between a pair of bead cores 2 as a skeleton, and on the outer side in the tire radial direction of the carcass 3, a belt 4 including belt layers 4a and 4b of two layers of rubber-coated steel cords and a tread. 5 The belt layers 4a and 4b are so-called intersecting layers, and are inclined belt layers having cord arrangements in which the cords of the belt layers are arranged in different directions across the tire equatorial plane CL and intersect each other.

FIG. 3 is a partially enlarged view of a cross section in the width direction of a tire used in the simulation method of the present invention. Since the internal pressure is applied to the air chamber 10 inside the tire 1, the air concentration is higher than that on the outside of the tire. The rubber constituting the tire 1 (tread rubber, side rubber, rubber covering the belt 4 and the like) is a material in which the air inside the tire 1 is difficult to escape, but the air chamber 10 cannot be completely sealed. Therefore, as shown in FIG. 3, the air 20 permeates to the outside of the tire. When the air 20 permeates the rubber, the air 20 diffuses inside the rubber, and oxygen contained in the air 20 oxidizes the rubber.
In particular, the tire temperature becomes very high while the vehicle is running. Therefore, when the rubber of the tire becomes high in temperature, diffusion, particularly oxidation, which is a chemical reaction, easily occurs. When the oxidation reaction of rubber occurs, the rubber deteriorates, leading to problems such as deterioration of the tire progressing quickly, performance deterioration, and eventually the life of the tire.
Therefore, by analyzing the state of oxygen concentration diffusing and oxidizing from the air chamber 10 to the outside of the tire by numerical simulation, and estimating the oxygen concentration distribution and its change over time, tire deterioration (life) can be reduced. It is necessary to evaluate with high accuracy.

  Accordingly, the present applicant has conceived that the oxygen concentration contained in the rubber of the tire 1 is simulated using a diffusion equation in which a reaction term due to oxidation of the rubber is added. Furthermore, in order to realize a highly accurate simulation, when the simulation is performed, the shape of the tire 1, the internal structure of the tire 1, the material of the member constituting the tire 1, and the tread pattern of the tire 1 are analyzed in three dimensions. To do.

ここで、Ｃは酸素濃度、ｔは時間、ｘは空間配置、Ｄは拡散係数（材料物性）、ｉは次元（１〜３）を表す。 As for the diffusion phenomenon, a diffusion equation represented by the following equation (1) is generally known.

Here, C is oxygen concentration, t is time, x is spatial arrangement, D is a diffusion coefficient (material physical property), and i is a dimension (1 to 3).

Oxidation combines oxygen with the rubber and consumes oxygen. The physical model (formula) is not specified and is simply ω, but ω = kC ⁿ can also be used. Here, ω represents the amount of oxygen consumed per unit time, and k and n represent material properties.
Therefore, the oxygen amount X consumed from a certain time t to the time t + Δt can be obtained by the following equation (2).

The following equation (3), which combines diffusion (equation (1)) with the term ω due to oxidation, is used as the governing equation used in the present invention, and is analyzed by the finite element method.

Next, elements to be considered when performing a three-dimensional simulation will be described. By considering these factors, a simulation model corresponding to an actual tire can be analyzed, and a highly accurate simulation result can be obtained.
Specifically, the shape of the tire 1 is a dimension of a member constituting the tire, such as a flatness ratio, a tread width, and a rim width of the tire 1. In particular, in order to determine the shape of the tire 1, it is necessary to consider the shape of the carcass 3 that is the skeleton of the tire 1.
The internal structure of the tire 1 refers to the thickness of the cords of the carcass 3 and the belt 4, the arrangement angle, and the like.
The material of the member constituting the tire 1 is a rubber material such as a tread, a side, and an inner liner, and a cord material (organic fiber, steel, etc.) of the carcass 3 and the belt 4.
The tread pattern of the tire 1 refers to the width, depth, length, arrangement angle, and the like of each groove (circumferential groove, width direction groove, and inclined groove).

(Step S2)
Next, a portion of the tire 1 that requires detailed prediction, for example, the vicinity of a member end portion where rubber cracks are likely to occur is selected. The member end portion is, for example, an end portion of the carcass 3 or the belt 4 or a joining portion of rubber materials having different materials. Note that the portion requiring detailed prediction is not limited to the vicinity of the end portion of the member where the crack of the rubber is likely to occur, and a tread groove bottom portion or a side portion where the thickness in the cross section is small can be considered.
In the present invention, the selection of the detailed prediction portion is at least one selected from (A) a three-dimensional prediction result of oxygen concentration distribution, (B) a result of three-dimensional crack growth simulation, and (C) an experimental database. It is preferred to use one.
Hereinafter, the above-described (A) to (C) will be described.

(A) Three-dimensional prediction result of oxygen concentration distribution Using the result of the three-dimensional prediction of the oxygen concentration distribution in step S1 described above, a detailed prediction portion can be selected.
The result of the three-dimensional prediction is, for example, a location where the concentration changes greatly (ie, the sensitivity is high) when the deterioration condition (time / temperature) is changed, or in the case of a new structure, the concentration compared with the conventional structure is large. It is a part that is increasing.

(B) Three-dimensional crack growth simulation A detailed prediction portion can be selected using the method described in Patent Document 1 described above. Specifically, a global model in which a tire is modeled by an assembly of elements capable of numerical analysis and a local model in which a part of the tire is modeled by an assembly of elements capable of numerical analysis are set. Here, the local model includes a code model obtained by modeling a cord embedded in a tire and a crack model obtained by modeling a crack generated in the tire. Next, the displacement of the overlapping portion of the global model and the local model is set as the sum of the displacements of the respective models, and the displacement of the local model at the boundary portion of the local model is set to zero. The development of cracks occurring in the tire and the life of the tire are predicted by finite element analysis based on the global model and the local model.

(C) Experimental database The detailed prediction part can be selected using the experimental database that the applicant has constructed from past experiments. The experimental database stores information on the tire size, material and structure, and tire usage environment (temperature, load, usage time, etc.), and the occurrence of cracks in the tire based on this information. It is possible to predict an easy-to-do part.

(Step S3)
Next, the oxygen concentration distribution of the portion selected in step S2 described above is predicted in one dimension. When this selected part is divided into a finite number of elements (mesh division), the oxygen concentration in this selected part can be predicted with high accuracy by subdividing each divided element (mesh).
If the above-described three-dimensional oxygen concentration simulation method is used to predict the oxygen concentration of this portion with high accuracy, the number of division elements becomes enormous, and a great amount of calculation time is required.
Therefore, highly accurate and efficient prediction can be realized by analyzing the oxygen concentration distribution of the selected portion in one dimension.

  Moreover, in step S1 mentioned above, since a finite element method is used for discretization of space, a highly accurate simulation can be realized, which is preferable.

陰解法では、反復計算を行うため、１ステップの計算時間は陽解法より時間がかかるが、Δｔをある程度大きくしても支配方程式を満たすため、陽解法より少ないステップ数で解析することができる。
参考に、陽解法に関して説明する。陽解法では、時刻ｔ＋Δｔにおける濃度を次式（５）から求める。

式（５）の右辺には、時刻ｔでの値しか存在しないため、現在の値から次の時刻の値を予測する。時刻ｔ＋Δｔにおいて、支配方程式を満たしているという保証はなく、Δｔが大きいと、誤差が大きくなり、支配方程式を満たさないため、Δｔを非常に小さい値にする必要がある。よって、陽解法は、通常、衝突解析等の短時間の減少を解析するために用いられる。 Since there is a time derivative on the left side of the above equation (3), time integration is necessary. However, using an implicit method for time integration is preferable because a stable simulation can be realized.
In the implicit method, at time t + Δt, a concentration that satisfies the following equation (4) is obtained by repeated calculation.

In the implicit method, since iterative calculation is performed, the calculation time for one step is longer than that in the explicit method. However, even if Δt is increased to some extent, the governing equation is satisfied, and therefore analysis can be performed with a smaller number of steps than in the explicit method.
For reference, an explicit method will be described. In the explicit method, the concentration at time t + Δt is obtained from the following equation (5).

Since only the value at time t exists on the right side of equation (5), the value at the next time is predicted from the current value. At time t + Δt, there is no guarantee that the governing equation is satisfied. If Δt is large, the error becomes large and the governing equation is not satisfied. Therefore, it is necessary to make Δt very small. Therefore, the explicit method is usually used to analyze a short time decrease such as collision analysis.

In step S1 described above, it is preferable to model the fiber material used in the tire by a homogenization method (particularly, an analytical homogenization method).
The homogenization method is divided into a microscopic structure (microstructure) and a macroscopic structure (macrostructure), and the behavior of the macrostructure and material properties are approximated by obtaining the behavior of the microstructure and material properties. (L. Nasdala, Y. Wei, H. Rothert, “Homogenisation techniques for the analysis of oxygen diffusion and reaction in fiber-reinforced elastomers”, Constitutive Models for Rubber III: Proceedings of the Third European Conference on Constitutive Models for Rubber. (See Ed. Busfield J & Muhr A.) London, UK, 2003, p.85-91).
In the above-mentioned conventional literature, the homogenization method is used as a numerical experiment method. The oxygen concentration is analyzed for the detailed model, the appropriate material properties are given to the simple model, and the analysis is repeated until the equivalent properties are found. We are exploring material properties that give results close to a detailed model. Therefore, the physical properties of the obtained material are approximate values, and there is a problem that it takes a long time to create a model because the matching is performed through experiments.
On the other hand, the homogenization method used in the present invention is a mathematical method and calculates the material properties of an equivalent simple model from the material properties of a detailed model. Therefore, the obtained material physical properties are mathematically equivalent physical properties, and there is an advantage that the time until the equivalent material physical properties are obtained is shorter than that of the above-described conventional literature method.
Specifically, when the detailed model showing one cord 6 and the rubber member 7 shown in FIG. 4A is modeled using a homogenization method, a homogeneous simple model shown in FIG. 4B is obtained. It becomes. This simple model is equivalent to the model of FIG. 4A when viewed macroscopically, and has material properties of the cord 6 and the rubber member 7. For example, even if the cord extends obliquely with respect to the cross section in the tire width direction like an inclined belt layer, the number of elements to be analyzed can be reduced by the homogenization method. It is possible to shorten the creation time.

Moreover, in step S1 mentioned above, it is preferable to use a cut section model obtained by cutting a tire with a predetermined length in the tire circumferential direction, and to give periodic boundary conditions to both cut surfaces of the cut section model.
A tire often has a regular tread pattern as shown in FIG. In such a case, by using a cut section model cut at one pitch and giving periodic boundary conditions to both cut surfaces A and B, the time required for the analysis can be greatly reduced as compared with the case where the entire tire is analyzed. Can do.

Examples of the present invention will be described below.
A cut section model of the pneumatic tire (tire size: 295 / 75R32.5) shown in FIG. 1 is created, and periodic boundary conditions are given to both cross sections. The equivalent properties of the cords of the carcass 3 and the belt 4 are calculated by a homogenization method. Using the implicit finite element method, the diffusion equation (the above equation (3)) with the reaction term due to oxidation is solved.
Next, a specific part in the tire cross section is selected, and the selected part is analyzed with a three-dimensional model (case A) and with a one-dimensional fine mesh model (case B). The results are shown in FIG. FIG. 6 shows an outline of an oxygen concentration distribution in a rubber member of a tire (modeled portion where four kinds of members 1 to 4 are joined).
From FIG. 6, it can be seen that the result of case A overlaps with the result of case B, and almost the same result is obtained. In other words, it was found that even when the calculation was performed with the one-dimensional model, a highly accurate result was obtained as in the case of the calculation with the three-dimensional model.
Further, by performing a one-dimensional detailed analysis, it was found that there was a concentration gradient in each of the members 1 to 4, and further, it was found that the oxygen concentration greatly changed at the member boundaries 1 to 3.
Furthermore, the analysis time for case A was 50 minutes, but the analysis time for case B was 1 minute, and it took more than one month to obtain detailed results equivalent to case B by three-dimensional calculation. I found out that Thus, it has been found that the calculation time can be greatly shortened when the calculation is performed with the one-dimensional model, and the efficiency is improved.
As described above, according to the present invention, it is possible to predict the life of a pneumatic tire with high accuracy and efficiency.

DESCRIPTION OF SYMBOLS 1 Tire 2 Bead core 3 Carcass 4 Belt 4a, 4b Belt layer 5 Tread 6 Cord 7 Rubber member 10 Air chamber 20 Air

Claims (6)

In the simulation method of the oxygen concentration distribution contained in the rubber of the pneumatic tire,
Using the diffusion equation with the reaction term due to oxidation of the rubber, using the shape of the tire, the internal structure of the tire, the material of the members constituting the tire, and the tread pattern of the tire as elements, the oxygen concentration distribution is determined. Predict in 3 dimensions,
Select the parts that require detailed forecasts,
Predicting the oxygen concentration distribution of the selected portion in one dimension;
A simulation method characterized by that. The selection of the portion requiring detailed prediction uses at least one selected from a three-dimensional prediction result of the oxygen concentration distribution, a three-dimensional crack growth simulation result, and an experimental database;
The three-dimensional crack growth simulation
A first step of setting a global model in which a tire is modeled by an assembly of elements capable of numerical analysis and a local model in which a crack generated in the tire is modeled by an assembly of elements capable of numerical analysis When,
A second step in which the displacement of overlapping portions of the global model and the local model set in the first step is a sum of displacements of the respective models;
A third step of setting the displacement of the local model at the boundary portion of the local model set in the first step to zero.
A fourth step of predicting the life of the tire by a finite element method analysis based on the global model and the local model set in the first step to the third step;
The simulation method according to claim 1, further comprising:   3. The simulation method according to claim 1, wherein a finite element method is used for discretizing the space.   The simulation method according to claim 1, wherein an implicit method is used for time integration.   The simulation method according to claim 1, wherein the fiber material used in the tire is modeled by a homogenization method.   The cyclic boundary condition is given to both cut surfaces of the cut section model using a cut section model obtained by cutting the tire at a predetermined length in the tire circumferential direction. Simulation method.

Images