JP4755015B2 - Tire design method - Google Patents

Description

  The present invention relates to a tire design method, a program therefor, and a tire manufacturing method using the design method.

  Conventionally, when designing pneumatic tires, prototypes and tests of tires with different shapes and materials compared to existing tires are made and tested, and the prototypes and tests are repeated until the target performance is achieved for rolling resistance and braking performance. The method was taken. However, such a method has a problem of inefficiency and high cost. For this reason, a method of designing a tire using an optimization method based on FEM (finite element method) analysis has been proposed.

  For example, in Patent Document 1 below, a conversion system that associates a nonlinear correspondence between tire performance and design variables using a neutral network or the like is defined, and using this, mathematical programming, genetic algorithms, etc. A method of designing a tire by obtaining a design variable that gives an optimum value of an objective function by an optimization method is disclosed. In addition, as a method of using these mathematical programming methods, genetic algorithms, neutral networks, etc. for tire design, Patent Document 2 listed below is for predicting performance according to actual tire behavior in the optimization process. An optimization method is proposed, and Patent Literature 3 below proposes a method for optimizing the rib cross-sectional shape. Furthermore, Patent Document 4 below proposes an optimization method using an experimental design method in order to design a tire having excellent braking performance.

  In addition, as a tire design method using an optimization method, the present inventor, for example, in Patent Document 5 below, the entire applied rim is designed so that performance can be improved when mounted on any of a plurality of applied rims. A method for optimizing the objective function is proposed, and in Patent Document 6 below, in order to achieve two tire performances, each of the design variables can be determined from a plurality of design variables using an experimental design method. An optimization method for designing tires by selecting design variables with a high contribution to the objective function is proposed.

In tire design using such conventional optimization techniques, tire configurations with different hair colors such as tire shape such as tire cross section and tire structure such as rubber Young Modulus distribution, cord density, cord angle, etc. It was common to be designed separately.
International Publication No. 99/07543 Pamphlet JP 2001-50848 A JP 2001-287516 A JP 2005-8011 A Japanese Patent Laid-Open No. 2005-112015 JP 2005-225290 A

  On the other hand, when both the tire shape and the tire structure are treated as design variables and optimization is performed for two different objective functions, two methods such as Comparative Example 1 and Comparative Example 2 below are conceivable.

  In Comparative Example 1, optimization calculations of two objective functions are performed in series. That is, in Comparative Example 1, as shown in FIG. 5, first, an initial tire FEM model is created (step 100), a first design variable (design variable 1) related to the tire shape, and a first objective function (objective function). 1) and the first constraint condition (constraint condition 1) are set (step 102), and the optimization calculation of the objective function 1 is performed. That is, the initial value of the objective function 1 is calculated (step 104), the sensitivity analysis is performed (step 106), and then the one-dimensional search is performed to optimize the objective function 1 while considering the constraint condition 1. The value of variable 1 is obtained (step 108), the convergence of objective function 1 is determined (step 110). If not converged, the initial value of design variable 1 is updated (step 112), and the process returns to step 106. If converged, the tire model is updated with the value of the design variable 1 obtained above as the optimum solution 1 (step 114).

  Next, using the tire FEM model updated with the optimal solution 1, the second design variable (design variable 2), the second objective function (objective function 2), and the second constraint condition (constraint condition 2) related to the tire structure are obtained. After setting (step 116), optimization calculation of the objective function 2 is performed. That is, after the initial value of the objective function 2 is calculated (step 118), sensitivity analysis is performed (step 120), and then the one-dimensional search is performed to optimize the objective function 2 while considering the constraint condition 2. The value of variable 2 is obtained (step 122), the convergence of objective function 2 is determined (step 124), and if not converged, the initial value of design variable 2 is updated (step 126) and the process returns to step 120. If converged, the value of the design variable 2 obtained above is set as the optimum solution 2 (step 128).

  As described above, in Comparative Example 1, the tire shape is first determined by optimization calculation, and then the tire internal structure is determined by optimization calculation using the tire model of the determined tire shape. Therefore, the optimization calculation is performed twice, and the calculation cost increases. In addition, since the objective function 2 is optimized using the optimum solution 1 obtained by optimizing the objective function 1 as an initial value, it cannot be said that both the objective function 1 and the objective function 2 have reached extreme values.

  On the other hand, the comparative example 2 performs optimization calculation by synthesizing two objective functions and replacing them with one objective function. That is, in Comparative Example 2, as shown in FIG. 6, first, an initial tire FEM model is created (step 200), and then all the design variables relating to the tire shape and the design variables relating to the tire structure are all in one optimization calculation flow. At the same time as a design variable. Specifically, the first design variable (design variable 1) related to the tire shape, the first objective function (objective function 1), and the first constraint condition (constraint condition 1) are set, and the second design variable related to the tire structure is set. (Design variable 2), second design variable (design variable 2), and second constraint condition (constraint condition 2) are set (step 202). Then, after calculating the initial value of the objective function 1 and the initial value of the objective function 2 (step 204), the weighting coefficients of these two objective functions are defined (step 206), and the objective function 1 and the objective function according to the weighting coefficients are defined. The function 2 is added and replaced with the following one objective function A (step 208).

Objective function A = w1 x (obj1c / obj1) + w2 x (obj2c / obj2)
(Where obj1 is the initial value of the objective function 1, obj1c is the value of the objective function 1 in the optimization calculation flow, obj2 is the initial value of the objective function 2, and obj2c is the value of the objective function 2 in the optimization calculation flow. W1 is a weighting factor of the objective function 1, w2 is a weighting factor of the objective function 2, and 0 ≦ w1, w2 ≦ 1 and w1 + w2 = 1).

  Then, a sensitivity analysis is performed using the objective function A, the design variable 1 and the design variable 2 (step 210), and then a one-dimensional search is performed to determine the objective function A while considering the constraint conditions 1 and 2. The values of design variable 1 and design variable 2 to be optimized are obtained (step 212), the convergence of objective function A is determined (step 214), and if not converged, the initial values of design variable 1 and design variable 2 are determined. Update (step 216), return to step 210, and if converged, the values of the design variable 1 and the design variable 2 obtained above are set as the optimum solutions (step 218).

  As described above, in the comparative example 2, the optimization calculation is performed on the objective function A obtained by synthesizing the objective function 1 and the objective function 2. Therefore, when the relation between the objective function 1 and the objective function 2 is nonlinear, There is a problem that the extreme value is not reached. In addition, the calculation can be performed with one optimization flow as compared with Comparative Example 1, but the number of design variables per flow increases, and thus the calculation cost increases in many cases.

  The present invention has been made in view of the above points, and an object of the present invention is to provide a tire design method capable of achieving both improvement in tire performance and calculation cost.

The tire designing method according to the present invention includes:
(A) creating a tire model in which the tire is divided into a plurality of elements;
(B) determining a first objective function representing a first physical quantity for tire performance evaluation, and a first design variable related to the first objective function, which is a design variable that changes a tire configuration;
(C) determining a second objective function representing a second physical quantity for tire performance evaluation, and a second design variable related to the second objective function, which is a design variable that changes the tire configuration;
(D) The value of the first design variable that optimizes the first objective function based on the sensitivity of the first objective function, which is the ratio of the change amount of the first objective function to the unit change amount of the first design variable. A step of seeking
(E) updating the first design variable with the value of the calculated first design variable;
(F) Using the tire model in which the first design variable is updated, based on the sensitivity of the second objective function, which is the ratio of the change amount of the second objective function to the unit change amount of the second design variable, Obtaining a value of a second design variable for optimizing the second objective function;
(G) updating the second design variable with the value of the obtained second design variable;
(H) The convergence of the second objective function is determined, and when the second objective function is not converged and the number of iterations of the step (f) is less than a predetermined value, the process returns to the step (f), A step of proceeding to the next step (i) when the number of iterations of the step (f) reaches a predetermined number even when the second objective function has converged or has not converged;
(I) When the convergence of the first objective function is determined, and when it is determined that the first objective function has not converged, the process returns to step (d), and when it is determined that the first objective function has converged Includes the step of determining the value of the first design variable obtained in step (d) and the value of the second design variable obtained in step (f) as an optimal solution.

  The present invention also provides a program for designing a tire by a computer, which causes the computer to execute the above steps. The present invention further provides a method for manufacturing a tire characterized by designing and manufacturing a tire using the above-described design method.

  In the present invention, it is preferable that one of the first design variable and the second design variable is a design variable that changes the tire shape, and the other is a design variable that changes the tire structure. In this way, particularly advantageous effects can be achieved when optimization is performed using different hair colors as design variables. The design variables are not limited to these two types. For example, a third objective function related to the third tire performance and a third design variable related thereto are defined and optimized. An optimization calculation flow may be further incorporated.

That is, in the present invention,
(J) determining a third objective function representing a third physical property for tire performance evaluation and a third design variable related to the third objective function, which is a design variable for changing a tire configuration;
(K) Using the tire model in which the second design variable is updated in the step (g), a third objective function that is a ratio of a change amount of the third objective function to a unit change amount of the third design variable. Obtaining a value of a third design variable for optimizing the third objective function based on sensitivity;
(L) updating the third design variable with the value of the determined third design variable;
(M) The convergence of the third objective function is determined, and when the third objective function is not converged and the number of iterations of the step (k) is less than a predetermined value, the process returns to the step (k), A step of proceeding to step (h) when the number of iterations of step (k) reaches a predetermined number even when the third objective function has converged or has not converged;
May further be included.

  In the present invention, another optimization calculation flow (subroutine) is inserted inside one optimization calculation flow (main routine). Then, the solution of the first design variable obtained in the main routine is updated as an initial value to perform optimization calculation of the subroutine, and then the solution of the second design variable obtained in the subroutine is updated as an initial value. The optimization calculation of the next main routine is executed, and the optimization calculation of the main routine and the subroutine is repeated until the first objective function of the main routine finally converges. As described above, since the first objective function and the second objective function are optimized in a weakly coupled manner, the both objective functions are alternately brought close to the optimum values, so that the both objective functions can be effectively improved. it can. Further, the time required to reach the optimal solution can be reduced as compared with the first comparative example in which the optimization calculation is simply performed twice, and the design variable per flow as in the second comparative example. Therefore, the increase in the calculation cost can be suppressed.

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

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

  More specifically, the design method of this embodiment is implemented by creating a program for causing a computer to execute the following steps and using a computer such as a personal computer storing (installing) the program in a hard disk or the like. can do. In other words, the program stored in the hard disk is appropriately read into the RAM at the time of execution, and is calculated by the CPU using various data input from input means such as a keyboard, and the result is displayed by display means such as a monitor. Is displayed. Such a program can be stored in various computer-readable recording media such as a CD-ROM, DVD, MD, and MO. Therefore, a drive device for such a recording medium is provided in the computer. The program may be executed via the drive device.

  If necessary, the design method of the present embodiment includes a second optimization calculation flow (subroutine) that handles design variables related to tire structure inside a first optimization calculation flow (main routine) that handles design variables related to tire shape. ), And the optimal solution of both is obtained by optimization calculation based on mathematical programming. The details are as follows.

  First, in step S10, an initial finite element model (hereinafter referred to as FEM model) of a target pneumatic tire is created. Specifically, a tire shape in a natural equilibrium state is used as a reference shape, and this reference shape is modeled by a method capable of numerically and analytically determining a physical quantity for tire performance evaluation such as FEM, and the tire has an internal structure. The tire initial model divided into a plurality of elements by mesh division is created. As an example, an FEM model having a cross-sectional shape as shown in FIG. 2 is created. Here, modeling refers to digitizing the tire shape and tire structure into an input data format for a computer program created based on a numerical and analytical method.

  In the next step S12, a first objective function (objective function 1) representing a first physical performance evaluation physical quantity, a first design variable (design variable 1) related to the first objective function, and the objective function 1 The first constraint condition (constraint condition 1) that constrains at least one of the design variable 1 and other physical quantities for tire performance evaluation is set. Here, as the design variable 1, one or a plurality of design variables that change the tire shape is selected. For example, the outer shape of a tire cross section such as a tire cross section width, a tread width, a crown radius, and a side portion radius, and a planar shape such as a tread pattern can be given. The objective function 1 is a physical quantity whose value generally changes depending on the tire shape, that is, a function having the design variable 1 as a variable. Examples thereof include a contact area, a contact length ratio between the tread center portion and the shoulder portion. Further, the constraint condition 1 includes an allowable range of the design variable 1, a minimum target performance for the objective function 1, a constraint range for securing a performance exceeding a predetermined value regarding a physical quantity for tire performance evaluation other than the objective function, and the like. Can be mentioned.

  In the next step S14, the initial value of the objective function 1 in the initial value of the design variable 1 is calculated. Specifically, the tire FEM model (initial model) is mounted on the virtual rim, and given calculation conditions such as air pressure and load are applied, and the value of the objective function 1 is calculated.

  Next, in step S16, a second objective function (objective function 2) representing a second physical performance evaluation physical quantity, a second design variable (design variable 2) related to the second objective function, and the objective function 2. A second constraint condition (constraint condition 2) that restricts at least one of the design variable 2 and other physical quantities for tire performance evaluation is set. Here, as the design variable 2, one or a plurality of design variables that change the tire structure is selected. For example, there are various internal structures such as Young modulus of rubber members such as tread rubber and sidewall rubber, material physical properties of reinforcing members such as carcass plies and belts, and the number of ends and angles of the cords. The objective function 2 is generally a physical quantity whose value varies depending on the tire structure, that is, a function having the design variable 2 as a variable. Examples thereof include rolling resistance, average ground pressure, tire rigidity, and inter-cord strain. The constraint condition 2 includes an allowable range of the design variable 2, a minimum target performance for the objective function 2, a constraint range for ensuring a predetermined performance or more with respect to a physical quantity for tire performance evaluation other than the objective function, and the like. Can be mentioned.

  In the present embodiment, in the optimization calculation of the objective function 1, the design variable 2 is not a variable, but only the design variable 1 is treated as a variable. In the optimization calculation of the objective function 2, the design variable 1 is not a variable. Since only the design variable 2 is handled as a variable, the design variable 1 having a small contribution to the objective function 2 is selected, and the design variable 2 having a small contribution to the objective function 1 is selected. However, since the present embodiment optimizes the objective function 1 and the objective function 2 weakly coupled, the design variable 1 contributes to the objective function 2 or the design variable 2 becomes the objective function 1. Even if there is a contribution to, optimization is performed in which those contributions are reflected to some extent.

  In the next step S18, the initial value of the objective function 2 in the initial value of the design variable 2 is calculated. More specifically, a tire FEM model (initial model) is mounted on a virtual rim, given predetermined calculation conditions such as air pressure and load, and the value of the objective function 2 is calculated.

  Next, a main routine which is an optimization calculation flow relating to the objective function 1 and the design variable 1 is entered. First, in step S20, sensitivity analysis is performed. The sensitivity analysis is performed by obtaining the sensitivity of the objective function 1 which is the ratio of the change amount of the objective function 1 to the unit change amount of the design variable 1, that is, one or a plurality of design variables 1 are respectively determined in advance. Change the specified amount little by little and find the direction with the steepest slope.

  More specifically, the sensitivity is generally defined by the following equation (1), each design variable xi is changed by Δxi, the value of the objective function after the change is calculated, and the unit change of the design variable according to equation (1) The sensitivity of the objective function, which is the ratio of the change amount of the objective function to the quantity, is calculated for each design variable, and the direction with the steepest sensitivity gradient is found.

Sensitivity = (f (xi + Δxi) −f (xi)) / Δxi (1)
Where xi: i-th design variable,
Δxi: Change amount of the i-th design variable
f (xi): objective function with design variable xi,
f (xi + Δxi): an objective function at the design variable xi + Δxi.

  Next, in step S22, a one-dimensional search is performed. In other words, based on the sensitivity, the objective function 1 is optimized by determining how much the design variable 1 should be changed in a direction in which the gradient is steep by a one-dimensional search while considering the constraint condition 1. Obtain the solution of design variable 1 to be obtained. The one-dimensional search is to determine the step width (scalar amount), and can be determined by a generally used polynomial approximation method or golden section method.

  In the next step S24, the initial value of the design variable 1 is updated with the solution obtained in the above step S22, and the subroutine which is an optimization calculation flow regarding the objective function 2 and the design variable 2 is entered.

  In the subroutine, first, in step S26, sensitivity analysis of the design variable 2 with respect to the objective function 2 is performed using the FEM model updated with the design variable 1 obtained by the one-dimensional search of the main routine. The method of sensitivity analysis is the same as in step S20, and is based on the sensitivity of the objective function 2 obtained by this, that is, the sensitivity of the objective function 2, which is the ratio of the change amount of the objective function 2 to the unit change amount of the design variable 2. In step S28, a one-dimensional search is performed. That is, by considering how much the design variable 2 should be changed by a one-dimensional search while considering the constraint condition 2, a solution of the design variable 2 that can optimize the objective function 2 is obtained.

  In the next step S30, the initial value of the design variable 2 is updated with the solution obtained in step S28, and the convergence of the objective function 2 is determined in step S32. In determining convergence, the value of the objective function 2 is calculated from the solution of the design variable 2 and is compared with the initial value of the objective function 2 to compare the difference between the two and a predetermined threshold value. Alternatively, whether or not the value of the objective function 2 has converged is determined depending on whether the sign changes such that the difference between the two changes from positive to negative or from negative to positive.

  When it is determined that the objective function 2 has not converged because the difference between the two is greater than the threshold value or the sign has not changed, the subroutine, that is, the number of iterations of steps S26 to S32 is determined. When (ite2) is less than a predetermined value (ite2 <N2), the initial value of the objective function 2 is updated and the process returns to step S26. On the other hand, if the objective function 2 has converged or has not converged, but the number of iterations of the subroutine (ite2) reaches a predetermined number (ite2 ≧ N2), the process returns to the main routine and proceeds to the next step S34.

  Here, the upper limit (N2) of the number of iterations of the subroutine is preferably 1 to 3. In this way, the one-dimensional search loop of the subroutine is not repeatedly performed until the objective function 2 converges, but the control is performed such that the objective function 1 and the objective function 2 are controlled so as to be terminated several times and returned to the main routine. This is because the cost for improvement is not impaired. Also, the calculation time can be reduced by terminating the subroutine in several iterations.

  In the next step S34, the convergence of the objective function 1 is determined. In determining convergence, the objective function 1 is calculated using the FEM model in which the design variable 2 is updated (the design variable 1 is updated in step 24 above), and this is compared with the initial value of the objective function 1. Then, it is determined whether or not the value of the objective function 1 has converged by the same method as in step S32.

  When it is determined that the objective function 1 has not converged, the initial value of the objective function 1 is updated, the process returns to step S20, and steps S20 to S34 are repeatedly executed.

  On the other hand, when it is determined in step S34 that the objective function 1 has converged, in next step S36, the values of the design variable 1 and the design variable 2 at this time, that is, the values of the design variable 1 obtained in the most recent step S22. The value of the design variable 2 obtained in the most recent step S28 is determined as the optimum solution. And based on the optimal solution of the design variable 1 and the design variable 2 determined in this way, a tire shape and a tire structure are determined, and a pneumatic tire is designed.

  A pneumatic tire can be manufactured by vulcanizing and molding the pneumatic tire designed in this manner according to a conventional method, whereby the tire performance according to the objective function 1 and the tire performance according to the objective function 2 can be produced. A pneumatic tire with improved both is obtained.

  In the present embodiment described above, the optimization calculation flow relating to the objective function 2 and the design variable 2 is inserted inside the optimization calculation flow relating to the objective function 1 and the design variable 1, and one time in the former main routine is inserted. The design variable 1 is updated with the solution obtained by the one-dimensional search loop, the optimization calculation of the latter subroutine is performed, and the solution obtained through the one-dimensional search loop once or several times in the subroutine is obtained. It is defined as the initial value in the optimization calculation of the next main routine. Therefore, the objective function 1 and the objective function 2 can be brought close to the optimum values at the same time without increasing the number of design variables per flow of the optimization calculation. Further, by optimizing the objective function 1 and the objective function 2 in a weakly coupled manner, the calculation time can be shortened as compared with the comparative example 1 in which two optimization flows are simply performed in series. One objective function can be effectively improved. Therefore, calculation cost and two tire performance improvements can be made compatible.

  In the above embodiment, the one-dimensional search is performed once in step S22, and then the design variable 1 is updated so as to enter the subroutine. However, the convergence of the objective function 1 is confirmed after the one-dimensional search. Steps S20 to S24 may be repeated a plurality of times (for example, 1 to 3 times) before entering subroutine step S26.

  FIG. 3 is a flowchart showing the flow of the tire designing method according to the second embodiment. This embodiment is characterized in that, in addition to the objective function 1 and the objective function 2 described above, a third optimization calculation flow for defining and optimizing the third objective function is incorporated. That is, in this example, a first subroutine that is an optimization calculation flow related to the objective function 2 and the design variable 2 is incorporated in the main routine that is an optimization calculation flow related to the objective function 1 and the design variable 1, and the first A second subroutine, which is an optimization calculation flow related to the third objective function, is incorporated in the subroutine.

  Specifically, as shown in FIG. 3, after step S18, in step S40, a third objective function (objective function 3) representing a third physical quantity for tire performance evaluation and a third objective function related to the third objective function. A third constraint condition (constraint condition 3) that constrains at least one of three design variables (design variable 3), the objective function 3, the design variable 3, and another physical quantity for tire performance evaluation is set.

  Here, when the second subroutine related to the objective function 3 is incorporated in this way, for example, the design variable that changes the tire structure is divided into two types, the design variable 2 is a variable related to the physical properties of the rubber material, and the design variable 3 is the tire code. It can be an angle or the number of ends. In this case, the objective function 2 includes a physical quantity whose value varies depending on the physical properties of the rubber material, such as an average contact pressure or rolling resistance. The objective function 3 has a value depending on the tire cord angle and the number of ends. Examples include physical quantities that change, such as tire stiffness and strain between cords. The constraint condition 3 includes an allowable range of the design variable 3, a minimum target performance for the objective function 3, a constraint range for securing a performance exceeding a predetermined value for a physical quantity for tire performance evaluation other than the objective function, and the like. Can be mentioned. The design variable 3 is not a variable in the optimization calculation of the objective function 1 and the objective function 2, but is handled as a variable only in the optimization calculation of the objective function 3.

  In the next step S42, the initial value of the objective function 3 in the initial value of the design variable 3 is calculated. More specifically, the tire FEM model (initial model) is mounted on the virtual rim, and predetermined calculation conditions such as air pressure and load are applied, and the value of the objective function 3 is calculated.

  Thereafter, the process proceeds to step S20, and in the same manner as in the above-described embodiment, after entering step S24, the process proceeds to step S30. After proceeding to step S30, in this example, the process proceeds to step S32, not to step S32. That is, after updating the initial value of the design variable 2 with the solution obtained in step S28, the second subroutine which is an optimization calculation flow regarding the objective function 3 and the design variable 3 is entered. In this second subroutine, first, the step In S44, sensitivity analysis of the design variable 3 with respect to the objective function 3 is performed using the FEM model in which the design variable 1 and the design variable 2 have been updated. The method of sensitivity analysis is the same as in step S20, and is based on the sensitivity of the objective function 3 obtained by this, that is, the sensitivity of the objective function 3, which is the ratio of the change amount of the objective function 3 to the unit change amount of the design variable 3. In the next step S46, a one-dimensional search is performed. That is, while considering the constraint condition 3, a solution of the design variable 3 that can optimize the objective function 3 is obtained by determining how much the design variable 3 should be changed by a one-dimensional search.

  In the next step S48, the initial value of the design variable 3 is updated with the solution obtained in step S46, and the convergence of the objective function 3 is determined in step S50. In determining convergence, the value of the objective function 3 is calculated from the solution of the design variable 3 and is compared with the initial value of the objective function 3 to compare the difference between the two and a predetermined threshold value. Alternatively, it is determined whether or not the value of the objective function 3 has converged depending on whether the sign changes such that the difference between the two changes from positive to negative or from negative to positive.

  When the difference between the two is larger than the threshold value or the sign has not changed, it is determined that the objective function 3 has not converged, and the second subroutine, that is, steps S44 to S50. When the number of iterations (ite3) is less than a predetermined value (ite3 <N3), the initial value of the objective function 3 is updated and the process returns to step S44.

  On the other hand, if the number of iterations of the second subroutine (ite3) reaches a predetermined number (ite3 ≧ N3) even if the objective function 3 has converged or has not converged, the process returns to the first subroutine and proceeds to step S32. . Here, the upper limit (N3) of the number of iterations of the second subroutine is preferably 1 to 3.

  Next, in step S32, the convergence of the objective function 2 is determined in the same manner as in the first embodiment. When the objective function 2 has not converged and the number of iterations of the first subroutine (ite2) is less than a predetermined value, (Ite2 <N2), the initial value of the objective function 2 is updated, the process returns to step S26, and the first subroutine and the second subroutine are repeated. On the other hand, if the objective function 2 has converged or has not yet converged, but the iteration number (ite2) of the first subroutine has reached a predetermined number (ite2 ≧ N2), the process returns to the main routine and proceeds to step S34.

  In step S34, the convergence of the objective function 1 is determined. If it is determined that the objective function 1 has not converged, the initial value of the objective function 1 is updated, and the process returns to step S20. S30, S44-50, and S32-S34 are repeatedly executed. On the other hand, when it is determined in step S34 that the objective function 1 has converged, in the next step S36, the values of the design variable 1, the design variable 2, and the design variable 3 at this time, that is, the design obtained in the most recent step S22. The value of variable 1, the value of design variable 2 obtained in the latest step S28, and the value of design variable 3 obtained in the latest step S46 are determined as optimum solutions. Then, a pneumatic tire is designed based on the optimum solution of the design variable 1, the design variable 2, and the design variable 3 determined in this way. Other methods and configurations are the same as those in the first embodiment, and a description thereof will be omitted.

  As described above, the types of the objective function and the design variable are not limited to two types, and three types of the objective function and the design variable can be optimized by incorporating two subroutines as described above. In addition, it is possible to optimize four or more types of objective functions and design variables by incorporating third and fourth subroutines.

  An example of the tire design method using the optimization method according to the first embodiment will be described.

  In this example, the tire size is 205 / 65R15, the use conditions are air pressure: 200 kPa, use rim: 15 × 6.5 JJ, load: 5880 N, the objective function 1 is the contact area (ground shape) 1), the objective function 2 is optimized in accordance with the method of the above embodiment shown in FIG. 1 as minimizing the rolling resistance under the above use conditions. Chemical calculation was performed.

  At that time, the design variable 1 related to the objective function 1 relates to the tire shape, and is set to the maximum value of the tread radius Y coordinate in the tire mold. Here, the maximum value of the Y coordinate means the maximum value of the Y coordinate corresponding to the contact width W measured under the use conditions as shown in FIG. 4, that is, the tire radial direction is defined as the Y coordinate. Is the difference y of the Y coordinate at the contact end position with respect to the Y coordinate at the tread center CL of the tread outline OL.

  The design variable 2 related to the objective function 2 relates to the tire structure, and is the Young modulus of the tire tread rubber portion. Here, the Young's modulus of rubber is obtained by a tensile test method for vulcanized rubber according to JIS K6251.

  Furthermore, the constraint condition 1 sets the constraint range of the design variable 1 to 6.00 mm to 7.00 mm, and the constraint condition 2 sets the constraint range of the design variable 2 to ± 20 for the young modulus of the tread rubber portion of the initial tire. %.

  Further, the upper limit (N2) of the number of iterations of the subroutine in step S32 is three.

  For comparison, optimization calculation was also performed for Comparative Example 1 shown in FIG. 5 and Comparative Example 2 shown in FIG. For the examples and comparative examples 1 and 2, the calculation time required for the optimization calculation is shown in Table 1 below, and the improvement effect of the objective function 1 and the objective function 2 on the control tire before optimization is shown in Table 1 below. Indicated.

The calculation time is expressed as an index with the calculation time required in Comparative Example 1 as 100. The smaller the value, the shorter the calculation time, and the higher the calculation cost. Further, the improvement effect of the objective function is indicated by an index with the initial value of each objective function in the control before optimization as 100. For the objective function 1, the larger the value, the greater the improvement effect, and for the objective function 2, the smaller the value, the greater the improvement effect.

  As shown in Table 1, in the example according to the present invention, the calculation time is shorter than those of Comparative Example 1 and Comparative Example 2, and the improvement effect of the objective function 1 and the objective function 2 is both large. .

  The present invention can be effectively used for designing various tires such as a pneumatic radial tire.

It is a flowchart which shows the flow of the optimization calculation which concerns on 1st Embodiment. It is a half sectional view showing an example of a tire FEM model. It is a flowchart which shows the flow of the optimization calculation which concerns on 2nd Embodiment. It is a schematic diagram which shows the tread radius Y coordinate in a tire metal mold | die. 10 is a flowchart showing a flow of optimization calculation according to Comparative Example 1. 10 is a flowchart showing a flow of optimization calculation according to Comparative Example 2.

Claims (5)

(A) creating a tire model in which the tire is divided into a plurality of elements;
(B) determining a first objective function representing a first physical quantity for tire performance evaluation, and a first design variable related to the first objective function, which is a design variable that changes a tire configuration;
(C) determining a second objective function representing a second physical quantity for tire performance evaluation, and a second design variable related to the second objective function, which is a design variable that changes the tire configuration;
(D) The value of the first design variable that optimizes the first objective function based on the sensitivity of the first objective function, which is the ratio of the change amount of the first objective function to the unit change amount of the first design variable. A step of seeking
(E) updating the first design variable with the value of the calculated first design variable;
(F) Using the tire model in which the first design variable is updated, based on the sensitivity of the second objective function, which is the ratio of the change amount of the second objective function to the unit change amount of the second design variable, Obtaining a value of a second design variable for optimizing the second objective function;
(G) updating the second design variable with the value of the obtained second design variable;
(H) The convergence of the second objective function is determined, and when the second objective function is not converged and the number of iterations of the step (f) is less than a predetermined value, the process returns to the step (f), A step of proceeding to the next step (i) when the number of iterations of the step (f) reaches a predetermined number even when the second objective function has converged or has not converged;
(I) When the convergence of the first objective function is determined, and when it is determined that the first objective function has not converged, the process returns to step (d), and when it is determined that the first objective function has converged Determining the value of the first design variable obtained in step (d) and the value of the second design variable obtained in step (f) as an optimal solution;
Tire design method including:   2. The tire design method according to claim 1, wherein one of the first design variable and the second design variable is a design variable that changes a tire shape, and the other is a design variable that changes a tire structure. (J) determining a third objective function representing a third physical property for tire performance evaluation and a third design variable related to the third objective function, which is a design variable for changing a tire configuration;
(K) Using the tire model in which the second design variable is updated in the step (g), a third objective function that is a ratio of a change amount of the third objective function to a unit change amount of the third design variable. Obtaining a value of a third design variable for optimizing the third objective function based on sensitivity;
(L) updating the third design variable with the value of the determined third design variable;
(M) The convergence of the third objective function is determined, and when the third objective function is not converged and the number of iterations of the step (k) is less than a predetermined value, the process returns to the step (k), A step of proceeding to step (h) when the number of iterations of step (k) reaches a predetermined number even when the third objective function has converged or has not converged;
The tire design method according to claim 1, further comprising:   A tire manufacturing method, wherein the tire is designed and manufactured using the method according to claim 1. A program for designing tires by a computer,
(A) creating a tire model in which the tire is divided into a plurality of elements;
(B) determining a first objective function representing a first physical quantity for tire performance evaluation, and a first design variable related to the first objective function, which is a design variable that changes a tire configuration;
(C) determining a second objective function representing a second physical quantity for tire performance evaluation, and a second design variable related to the second objective function, which is a design variable that changes the tire configuration;
(D) The value of the first design variable that optimizes the first objective function based on the sensitivity of the first objective function, which is the ratio of the change amount of the first objective function to the unit change amount of the first design variable. A step of seeking
(E) updating the first design variable with the value of the calculated first design variable;
(F) Using the tire model in which the first design variable is updated, based on the sensitivity of the second objective function, which is the ratio of the change amount of the second objective function to the unit change amount of the second design variable, Obtaining a value of a second design variable for optimizing the second objective function;
(G) updating the second design variable with the value of the obtained second design variable;
(H) The convergence of the second objective function is determined, and when the second objective function is not converged and the number of iterations of the step (f) is less than a predetermined value, the process returns to the step (f), A step of proceeding to the next step (i) when the number of iterations of the step (f) reaches a predetermined number even when the second objective function has converged or has not converged;
(I) When the convergence of the first objective function is determined, and when it is determined that the first objective function has not converged, the process returns to step (d), and when it is determined that the first objective function has converged Determining the value of the first design variable obtained in step (d) and the value of the second design variable obtained in step (f) as an optimal solution;
A program that causes a computer to execute.

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