JP2005112015A - Pneumatic tire designing method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a pneumatic tire designing method capable of enhancing the performance even when a pneumatic tire is mounted on a plurality of applicable rims. <P>SOLUTION: An FEM model of a tire is prepared, and design variables to give changes to the tire configuration, an objective function to express the physical quantity for evaluating the tire performance, and a plurality of applicable rims to be combined with the FEM model are determined (100, 102 and 104). The value of the objective function is operated in each applicable rim by respectively combining the FEM model with the plurality of applicable rims. The value of the objective function on the entire applicable rims is obtained by integrating the result of the operations, and the operation is repeated until the objective function is converged (106-120). The value of the design variables to give the optimum value of the objective function on the entire applicable rims is obtained (122), and the tire is designed based on the design variables to give the optimum value. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a method for designing a pneumatic tire.

  Conventionally, as a tire design method that considers physical properties, tires with different shapes and materials compared to existing tires are prototyped and tested, and prototypes and tests are performed until the target performance is achieved for rolling resistance, spring constant, etc. The technique of repeating was taken. However, such a method has problems such as inefficiency and high cost. For this reason, a method for designing a tire using an optimization method based on FEM (finite element method) analysis has been proposed.

  For example, Patent Document 1 describes a tire basic model that represents a tire cross-sectional shape including an internal structure and is divided into a plurality of elements, an objective function that represents a physical quantity for tire performance evaluation, and a design that determines physical properties of a rubber member and a reinforcing material. A variable, a step of defining a constraint that restricts at least one of the physical properties of the rubber member and the reinforcing material, a physical quantity for performance evaluation, and a tire size, and a design variable that gives an optimum value of the objective function while taking the constraint into consideration A method for designing a pneumatic tire is disclosed that includes a step of obtaining a value and a step of designing a tire based on a design variable that provides an optimum value of an objective function.

Further, Patent Document 2 represents a step of determining a conversion system that relates a nonlinear correspondence between a tire cross-sectional shape including an internal structure or a tire design parameter representing the tire structure and the performance of the tire, and represents the performance of the tire. A step of defining an objective function and a constraint condition that restricts an allowable range of at least one of the performance of the tire and the manufacturing condition of the tire; and using the conversion system, the objective function and the objective condition based on the constraint condition A method for designing a pneumatic tire is disclosed, including the step of determining a tire design parameter that provides an optimal value of the function and designing the tire based on the tire design parameter.
JP-A-7-164815 International Publication No. 99/07543 Pamphlet

  In the tire design method using the conventional optimization method described above, FEM analysis is performed with a standard rim width or a rim width used for an experiment as a guideline for tire design.

  However, there are generally several types (for example, 3 to 7 types) of applicable rims for individual tire sizes described in standards such as JATMA (Japan Automobile Tire Association) yearbook. Therefore, even if it can be confirmed that the target performance is satisfied by FEM analysis with a rim width of a certain applied rim, the target performance may be deteriorated when the rim is mounted on another different applied rim.

  The present invention has been made in view of the above points, and an object of the present invention is to provide a pneumatic tire design method capable of improving performance when mounted on any of a plurality of applicable rims. .

  A pneumatic tire design method according to the present invention includes (a) a step of creating a tire model representing a tire cross-sectional shape including an internal structure, and (b) a design variable for changing a tire configuration, and a tire performance evaluation. Determining an objective function representing a physical quantity for use, (c) determining a plurality of application rims to be combined with the tire model, and (d) combining each of the tire models with the plurality of application rims, Calculating the value of the objective function, obtaining the value of the objective function in the entire application rim by combining the calculation results, and obtaining the value of the design variable that gives the optimum value of the objective function in the entire application rim; (E) designing a tire based on a design variable that gives the optimum value.

  In the present invention, in the step (d), it is preferable that the value of the objective function in the entire application rim is obtained by an average value of the values of the objective function in each application rim.

  Further, in the step (b), a constraint condition that restricts at least one of the design variable, the objective function, and another physical quantity for tire performance evaluation is defined, and in the step (d), the constraint condition is taken into consideration. A design variable value that gives an optimum value of the objective function may be obtained.

  Further, the constraint condition may be that the value of the objective function at each application rim satisfies a predetermined performance, or alternatively, the objective function at each application rim as the constraint condition. The variance of the values may be limited.

  In the step (c), the plurality of application rims may be all application rims defined in the specification of the destination of the tire, or alternatively, specified in the specification of the destination of the tire. Of all the applicable rims that are used, there may be three types, one with the largest rim width, one with the smallest rim width, and one with the median value.

  According to the present invention, it is possible to design a pneumatic tire capable of improving performance when mounted on any of a plurality of applied rims, and the performance is extremely deteriorated when the applied rim to be mounted is changed. Tire production can be avoided in advance.

  Embodiments of the present invention will be described below with reference to the drawings.

  FIG. 1 is a flowchart showing a flow of optimization calculation for realizing the tire designing method according to the embodiment, which can be implemented using a computer.

  In this optimization calculation, first, in step 100, a tire FEM model representing a tire cross-sectional shape including the internal structure is created for a target tire. More specifically, a tire cross-sectional shape in a natural equilibrium state is used as a reference shape, and this reference shape is modeled by a method capable of obtaining a physical quantity for tire performance evaluation numerically and analytically, such as FEM. An initial tire model is created that represents a tire cross-sectional shape including the above and is divided into a plurality of elements by mesh division. Here, modeling means that the tire shape, structure, material, and pattern are digitized into an input data format to a computer program created based on numerical and analytical methods. In the present embodiment, as shown in FIG. 2, an FEM model in which a tire cross section is divided into a plurality of elements is created.

  In the next step 102, a constraint that restricts at least one of a design variable that changes the tire configuration, an objective function that represents a physical quantity for tire performance evaluation, and the design variable, the objective function, and another physical quantity for tire performance evaluation Set conditions.

  Here, examples of the design variable include a tire shape and physical properties of a tire material such as a rubber member and a reinforcing member. Examples of the objective function include strain energy in a specific region, rolling resistance, tire rigidity, and the like. Furthermore, as a constraint condition, a range that is allowed as a design variable such as a tire shape and material physical properties, a minimum target performance with respect to an objective function, and a physical performance evaluation physical quantity other than the objective function are ensured to exceed a predetermined level. For example, there is a restriction range.

  In the next step 104, a plurality of application rims to be combined with the FEM model in the optimization calculation are set. Specifically, check the applicable rim described in the standard of the destination of the target tire. For example, in the case of 185 / 65R15 for Japan, there are four types of applicable rims from the JATMA Yearbook: 5J, 51 / 2JJ, 6JJ, 61 / 2JJ. The data is input to the computer.

  It is preferable to combine all applicable rims stipulated in the standard with the FEM model in order to improve calculation accuracy. However, from the viewpoint of shortening the calculation time, some of all applicable rims are selected. It is also possible to perform optimization calculation. In this case, for example, it is preferable to perform optimization calculation for three types of rim widths having the maximum, minimum, and median values among all applicable rims defined in the standard. In addition, about the thing which takes a median, when the total number of application rims is an even number, you may select either of the center two application rims.

  In the next step 106, the initial value of the objective function in the initial value of the design variable is calculated. Specifically, the tire FEM model (initial model) is mounted on each of the above-described applied rims (virtual rims in the FEM analysis), and calculation conditions (for example, air pressure, load, slip angle around the vehicle, etc.) Alignment or the like) is applied to the FEM model, and the force and displacement for each element obtained thereby are calculated for each applied rim (1) to (N) (steps 108a, 108b, and 108c). Then, from the calculation result, the values of the objective functions (1) to (N) at each application rim are calculated (steps 110a, 110b, and 110c), and the calculation results are combined to calculate the objective function of the entire application rim. An initial value is calculated (step 112). The calculation for each application rim and the calculation of the objective functions (1) to (N) may be performed in parallel for the number of types of application rims, or the calculation is sequentially performed for a plurality of application rims. It can also be done.

すなわち、適用リム全体での目的関数ＯＢＪは、各適用リムでの目的関数ＯＢＪ（ｉ）の平均値により求められる。 Here, the objective function OBJ in the entire applied rim is expressed by the following equation (1), where the number of applied rims = N and the objective function in each applied rim = OBJ (i) (where i = 1 to N). Defined in

That is, the objective function OBJ for the entire applied rim is obtained from the average value of the objective function OBJ (i) for each applied rim.

After obtaining the initial value of the objective function OBJ in this way, sensitivity analysis is performed in step 114. Sensitivity analysis is to change each design variable little by little by a predetermined amount and find the direction with the steepest slope. Generally, sensitivity is defined by the following equation (2).

  Specifically, by changing each design variable xi by Δxi and calculating the value of the objective function after the change, the objective is the ratio of the change amount of the objective function to the unit change amount of the design variable according to the above equation (2). The function sensitivity is calculated for each design variable to find the direction with the steepest sensitivity gradient. The value of the objective function calculated at that time is the value of the objective function OBJ in the entire applied rim, and the average value of the objective function in the N applied rims is calculated in the same manner as in step 106 above.

  Next, in step 116, a design variable capable of maximizing or minimizing the objective function OBJ in the entire applied rim by determining how much the design variable should be changed in a direction in which the gradient is steep by a one-dimensional search. And the value of the objective function OBJ in the entire applied rim is calculated from the solution of the design variable. The value of the objective function OBJ for the entire applied rim here is also calculated as the average value of the objective functions for the N applied rims, as in step 106 described above.

  In the next step 118, the value of the objective function OBJ in the entire applied rim in the initial model obtained in step 106 is compared with the value of the objective function OBJ in the entire applied rim obtained in step 116. Then, it is determined whether or not the value of the objective function OBJ has converged by comparing the difference between them and a predetermined threshold value.

  If it is determined that the difference between the two is larger than the threshold value, and therefore the value of the objective function OBJ has not converged, in step 120, the initial model is replaced with the corrected model obtained this time, ie, step Steps 114 to 118 are repeatedly executed with the solution of the design variable obtained in 116 and the value of the objective function OBJ as initial values. Note that, when repeatedly executing in this way, in step 118, the convergence is obtained by comparing the value of the objective function OBJ calculated from the previously obtained solution with the value of the objective function OBJ calculated from the solution obtained this time. Judging.

  On the other hand, when the difference between the two is smaller than the predetermined threshold value in step 118 and the improvement width of the objective function OBJ is small, it is determined that the value of the objective function OBJ has converged. Is determined as an optimal solution that gives an optimal value to the objective function OBJ.

  When optimizing the objective function in this manner, it is preferable to consider the above-mentioned constraint conditions. For example, whether the objective function OBJ calculated in step 116 satisfies the target performance, It can also be determined whether or not the tire performance evaluation physical quantity satisfies a predetermined performance or more. Further, when the solution of the design variable is obtained by the one-dimensional search in step 116, the allowable range for the tire shape and material physical properties as the above-described constraint conditions is taken into consideration, and the solution is obtained within the range.

  Further, as a constraint condition, it is determined whether or not the values of the objective functions OBJ (1) to (N) in each applied rim satisfy the predetermined target performance, and the minimum value is obtained in all the applied rims. The performance may be guaranteed. Alternatively, as a constraint condition, the variance of the value of the objective function OBJ (1) to (N) at each application rim (for example, the sum of the squares of deviations from the objective function OBJ over the entire application rim, which is an average value) is free. It is also possible to reduce the variation in performance due to the difference in the applied rims by restricting the degree (degree divided by (N-1)) to a predetermined value or less.

  In the optimization method based on mathematical programming, when the design variable that maximizes the objective function, such as tire stiffness, is an optimal solution, the sensitivity of the objective function is positive and steep in the sensitivity analysis in step 114. Find a direction with a slope. On the other hand, when the design variable that minimizes the objective function is an optimal solution, such as an improvement in durability performance, the sensitivity analysis in step 114 may find a direction in which the sensitivity of the objective function has a negative steep slope. For example, the optimization can be performed instead of the maximization problem by adding a negative sign to the objective function or replacing the objective function with an inverse number.

  As described above, it is possible to design a tire in which the value of the objective function OBJ is optimized by the optimum solution of the design variable calculated in step 122.

  Next, an example of a tire design method for improving durability performance by performing simulation using the optimization method of the above-described embodiment will be described.

また、設計変数は、タイヤ最大幅およびトレッド幅とし、制約条件は、カーカスのペリフェリ長さが初期形状のそれの３％を越えないこととした。 In this example, the tire size was 185 / 65R15, the air pressure was 240 kPa, and the load was 7683 N. The objective function was the tire circumferential amplitude of the strain energy density at the carcass winding end. More specifically, since the region that affects the durability performance at the carcass winding end is a range surrounded by the frame 10 in FIG. 3, it is assumed that there are k elements of the FEM model in this range (example in FIG. 3). Then two). Then, assuming that the circumferential amplitude of the strain energy density of the i-th element is E (i), the objective function is expressed by the following equation (3). Therefore, optimization calculation may be performed so as to minimize this. .

The design variables were the maximum tire width and tread width, and the constraint condition was that the peripheral length of the carcass did not exceed 3% of that of the initial shape.

  Furthermore, the virtual rims used for the FEM analysis were all applicable rims defined in the JATMA yearbook, that is, 5J, 51 / 2JJ, 6JJ, 61 / 2JJ. For comparison, the applied rim combined with the FEM model was only 51 / 2JJ, and the others were optimized in the same manner as in the example as a comparative example.

  The optimum solution of the design variable was obtained by the optimization calculation of the example, and the tire was actually made as an optimum solution 1 and an indoor durability performance test was performed. Table 2 below shows the value of the objective function at each applicable rim calculated by the optimal solution 1 and the result of the durability of the tire manufactured based on the optimal solution 1, and the control (tire before optimization) is 100. The index was displayed. In either case, the smaller the index, the better the result.

  In addition, the optimal solution of the design variable (optimal solution obtained when the rim size is fixed to 51/2 JJ) is obtained by the optimization calculation of the comparative example, and the tire is actually made as an optimum solution 0, and the indoor durability performance is obtained. The test was conducted. In Table 2 below, the value of the objective function at each applicable rim calculated with the optimal solution 0 and the result of the durability of the tire prototyped based on the optimal solution 0 are shown as indices with the control being 100, respectively.

  Moreover, about each tire of a control, an Example, and a comparative example, each mold shape was shown in FIG.

In the indoor durability performance test, under the test conditions defined in JIS D 4230, a method of increasing the load step by step was adopted in order to promote early failure after test stage 3. The relationship between the test time and the load is as shown in Table 1 below, and the durability was evaluated by the length of time until failure. In Table 2, the reciprocal of the time until failure is taken, and the control is taken as an index of 100.

  As shown in Table 2, in the tires of the comparative examples, the durability was improved for the rim widths 51 / 2JJ, 6JJ, and 61 / 2JJ, but the durability was deteriorated for the rim width 5J. It was. On the other hand, in the tire of the example, the durability was improved even when the tire was mounted to any rim width of the applicable rim width.

  In the above-described embodiment, the optimization method based on mathematical programming has been described. However, the present invention is not limited to this, and various optimizations such as a genetic algorithm and a statistical optimization method can be used. It can be applied to the method.

  In the above embodiment, a method for optimizing a physical quantity of one tire performance as an objective function has been described. However, in the present invention, an objective function related to two tire performances can be optimized at a time. In this case, for example, if the objective function to be maximized like tire rigidity is OBJa and the objective function to be minimized like durability mentioned above is OBJb, OBJ = OBJa + (− OBJb) is defined and the above optimization calculation is performed so as to maximize it. When optimizing an objective function obtained by synthesizing a plurality of objective functions in this way, the numerical order of each objective function may be different. In such a case, it is preferable to make each objective function non-dimensional, and a general method for non-dimensionalization includes dividing by an objective function of an initial value. In addition, various specific methods can be adopted as long as the technical idea of the present invention is not impaired.

  The present invention can be used for an efficient design of a pneumatic tire capable of improving performance with respect to a plurality of applied rims.

It is a flowchart which shows the flow of the optimization calculation in embodiment. It is a figure of the FEM model which divided a tire section into a plurality of elements. It is a figure of the FEM model which expands and shows carcass winding end vicinity. (A) is the mold shape of the tire of a control, (b) is the figure of the mold shape of the tire of an Example, (c) is a figure which shows the mold shape of the tire of a comparative example, respectively.

Claims (7)

(A) creating a tire model representing a tire cross-sectional shape including an internal structure;
(B) determining design variables that change the tire configuration, and determining an objective function that represents a physical quantity for tire performance evaluation;
(C) determining a plurality of application rims to be combined with the tire model;
(D) The tire model is combined with each of the plurality of application rims, and the value of the objective function at each application rim is calculated. Obtaining a value of a design variable that gives an optimum value of the objective function in the entire applied rim;
(E) designing a tire based on a design variable that gives the optimum value;
A pneumatic tire design method including:   The method for designing a pneumatic tire according to claim 1, wherein, in the step (d), the value of the objective function in the entire applied rim is obtained by an average value of the value of the objective function in each applied rim. In the step (b), a constraint condition that restricts at least one of the design variable, the objective function, and another physical quantity for tire performance evaluation is defined.
The method for designing a pneumatic tire according to claim 1 or 2, wherein, in the step (d), a value of a design variable that gives an optimum value of the objective function is obtained in consideration of the constraint condition.   The method for designing a pneumatic tire according to claim 3, wherein the constraint condition is that each of the values of the objective function at each applicable rim satisfies a predetermined performance.   The pneumatic tire design method according to claim 3, wherein, as the constraint condition, dispersion of a value of an objective function at each application rim is limited.   The pneumatic tire according to any one of claims 1 to 5, wherein in the step (c), the plurality of application rims are all application rims defined in a specification of a destination of the tire. Design method.   In the step (c), the plurality of application rims take the median value of the maximum, minimum, and minimum rim widths of all the applicable rims defined in the destination specification of the tire. The method for designing a pneumatic tire according to any one of claims 1 to 5, wherein:

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