JP2006056481A - Method for designing pneumatic tire, and program therefor - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for designing a pneumatic tire capable of greatly reducing manhours for proportionally designing tires of different sizes based on a reference tire. <P>SOLUTION: The grounding length ratio and the grounding pressure dispersion value of the reference tire are defined as input values for optimization computation (4), and a design variable to impart a variation to a tire constitution of a proportionally designed tire, a target function related to the grounding length ratios for the reference tire and the proportionally designed tire, and restricting conditions related to the grounding pressure dispersion value are defined (5). Using an FEM model for the proportionally designed tire, the grounding length ratio and the grounding pressure dispersion value for the proportionally designed tire are determined. By optimization computation, under consideration of the restricting conditions, the value of the design variable to impart the optimum value of the target function is determined in such a way that the grounding length ratio of the proportionally designed tire is closer to that of the reference tire (8-10). The proportionally designed tire is desired based on the design variable to impart the optimum value. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a pneumatic tire design method and a program for the design, and more particularly to a method for proportionally designing tires of different sizes based on a reference tire.

  In the design of pneumatic tires, proportional design is performed in order to provide a product group that provides equivalent tire performance for various tire sizes. In this proportional design, tires of different sizes having performance equivalent to that of a reference tire with respect to a certain tire performance are designed based on the reference tire. Here, the equivalent performance does not require the same performance because the size is different between the reference tire and the proportional design tire, and includes cases where the tire performance has the same tendency and taste. I mean.

  Conventionally, for example, when proportionally designing tires with the same flatness ratio and different tire widths based on the reference tire, the tire shape after trial and error so as to have the same contact length ratio and contact pressure distribution as the reference tire Is determined. This means that if the tire has a complicated internal structure such as a pneumatic tire and the specified load varies depending on the size, simply reducing or expanding the size of the tire shape by proportional calculation with respect to the reference tire. This is because the contact length ratio of the tread and the contact pressure distribution change, and equivalent performance cannot be imparted. In other words, in order to determine the tire shape so as to have the same contact length ratio and contact pressure distribution as the reference tire, there are multiple specifications that define the tire shape. Is required.

  By the way, conventionally, 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, a tire model is created from a tire design proposal, a road surface model to be brought into contact with the tire model is created, and tire performance is predicted based on physical quantities generated in the model due to deformation of the tire model. A method is disclosed in which a value of a design variable that gives an optimum value of an objective function is obtained while considering a condition, and a tire is designed based on the obtained design variable.

  Further, in Patent Document 2, in a tire having a groove continuous in the circumferential direction, the performance related to the contact pressure characteristics in the rib is used as an objective function, and the shape of the arc added to the rib end is actually used as a design variable. A method for obtaining a design variable that gives an optimum value of an objective function that satisfies a constraint condition while predicting tire performance in an environment where the tire is used, and designing the tire from this design variable is disclosed.

All of the techniques disclosed in these patent documents are for designing a tire corresponding to the reference tire in the present invention, and are efficient for achieving the single purpose performance and anti-twist performance of the tire. The present invention relates to tire design, and there is no disclosure or suggestion about using an optimization method based on a finite element method to obtain a tire shape of a proportionally designed tire based on a reference tire.
JP 2001-50848 A JP 2001-287516 A

  The present invention has been made in view of the above points, and in the case of proportionally designing tires of different sizes based on a reference tire, a pneumatic tire design method capable of significantly reducing design man-hours and therefore The purpose is to provide a program.

  A method for designing a pneumatic tire according to the present invention is a method for designing proportionally designed tires having different sizes and having performance equivalent to that of a reference tire with respect to a certain tire performance, and (a) the tire performance of the reference tire is Defining a physical quantity to be represented as an input value for optimization calculation; (b) defining a design variable that changes a tire configuration of the proportionally designed tire; and defining the physical quantity of the reference tire and the tire for the proportionally designed tire Defining an objective function representing a relationship with a physical quantity representing performance; (c) creating a finite element model of the proportionally designed tire; and (d) defining the physical quantity of the proportionally designed tire using the finite element model. In addition to calculating, the physical quantity of the proportionally designed tire is made closer to the physical quantity of the reference tire by optimization calculation. Determining a value of the design variable which gives the optimum value of the objective function, and is intended to include the step of designing a proportional designed tire based on the design variable which gives the (e) the optimum value.

  In the present invention, the step (a) includes the steps of inputting specifications defining the reference tire, creating a finite element model of the reference tire, and using the finite element model of the reference tire. And calculating a physical quantity representing tire performance and defining the calculated physical quantity as an input value for optimization calculation.

  Further, the present invention is a method for proportionally designing a plurality of tires having different sizes, and (f) a step of selecting a tire to be designed, in order of size from a tire having a size closer to a reference tire. A step of selecting a proportionally designed tire to design, (g) for the proportionally designed tire selected in step (f), after determining the value of the design variable that gives the optimum value of the objective function in step (d), A step of determining whether or not a design target tire remains; and (h) when it is determined in step (g) that the design target tire remains, the immediately previous proportional design tire is updated as a reference tire in the next proportional design The step of performing may be further included.

  Furthermore, in the present invention, in the step (b), a constraint condition that restricts the relationship between the reference tire and the proportionally designed tire with respect to another physical quantity for performance evaluation is determined, and in the step (d), the constraint condition is determined. The value of the design variable that gives the optimum value of the objective function may be obtained in consideration of the above.

  In this case, the physical quantity related to the objective function includes a contact length ratio between the center and the end of the tread portion, and the performance evaluation physical quantity related to the constraint condition includes a contact pressure dispersion value of the tread portion. The constraint condition includes a condition that the contact pressure dispersion value of the proportionally designed tire is equal to or less than the contact pressure dispersion value of the reference tire.

  A program for designing a tire according to the present invention is a program for designing a proportionally designed tire of a different size having performance equivalent to that of a reference tire with respect to a certain tire performance. Defining a physical quantity representing the tire performance as an input value for optimization calculation; (b) defining a design variable that changes a tire configuration of the proportional design tire; and defining the physical quantity of the reference tire and the proportional design Defining an objective function representing a relationship with a physical quantity representing the tire performance of the tire; (c) creating a finite element model of the proportionally designed tire; and (d) using the finite element model The physical quantity of the proportionally designed tire is calculated and the physical quantity of the proportionally designed tire is calculated by optimization calculation. Is a program for executing the steps of obtaining a value of the design variable which gives the optimum value of the objective function closer to the physical quantity of the reference tire.

  According to the present invention, an optimization calculation is performed so that a physical quantity representing a certain tire performance in a proportionally designed tire approaches the physical quantity of a reference tire to obtain an optimal solution of a design variable, that is, a proportional design solution, and based on this Since the design tire is designed, tires of different sizes having the same tire performance as the reference tire can be efficiently designed, and the design man-hour required for proportional design can be greatly reduced.

  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 embodiment, which can be implemented using a computer. More specifically, the design method of this embodiment can be implemented by creating a program for causing a computer to execute the following steps and using a computer that stores (installs) the program in a hard disk or the like. it can. In addition, since such a program can be stored in various storage media such as a CD-ROM, DVD, MD, and MO, a drive device for such a storage medium is connected to the computer main body, You may make it run a program via a drive device.

  The design method of the present embodiment is to proportionally design a plurality of tires having different sizes with the same aspect ratio with respect to a reference tire. More specifically, as shown in FIG. This relates to a case where a tire of / 50R16 is used as a reference tire and 10 types of tires (sizes 1 to 10) having the same flatness ratio (that is, flatness ratio = 50%) and different tire widths (cross-sectional widths) are proportionally designed. Note that the present invention is not limited to the case of proportionally designing tires having different cross-sectional widths with the same flatness ratio. For example, the present invention is also applied to the case of proportionally designing tires having the same cross-sectional width and different flatness ratios. can do. Moreover, the present invention is not limited to the case where a plurality of tires are proportionally designed, and can be applied to the case where one type of tire is proportionally designed.

  As shown in FIG. 1, in this embodiment, first, in step 1, specifications for defining a reference tire are input. More specifically, specifications that define the shape of the tire, such as the outer diameter, cross-sectional width, rim diameter, crown radius, and side radius of the reference tire, and the belt layer and carcass layer that are required to create a finite element model, etc. Enter the specifications that define the internal structure of the tire and the physical properties of materials such as tread rubber and sidewall rubber.

  Next, in step 2, a finite element model (hereinafter referred to as FEM model) of the reference tire is created based on the specifications input in step 1. More specifically, a tire cross-sectional shape in a natural equilibrium state is set as a reference shape, and this reference shape is modeled by a finite element method (FEM) to represent a tire cross-sectional shape including an internal structure and divided into a plurality of elements by mesh division. A tire FEM model as shown in FIG. 3 is created.

  In the next step 3, data for the number of proportionally designed tires is input. Here, as the data to be input, only the outer diameter, the cross-sectional width, and the rim diameter are input as specifications for defining the tire shape. Regarding the specifications that define the tire internal structure and the physical properties of the materials, the proportionally designed tire basically has the same structure as the reference tire. The original can be used as it is. On the other hand, as for the dimensional specifications related to the tire internal structure, values obtained by simple proportional calculation with respect to each specification of the reference tire may be used, or alternatively, the standard internal structure of each tire size may be used. The dimensions may be used as they are. In addition, in the case where dimensional specifications relating to the tire internal structure such as the belt width are also defined as design variables in Step 5 described later, all other items except the specifications relating to the tire dimensional standards such as the outer diameter, the cross-sectional width and the rim diameter are used. Regarding the specifications, the specifications of the reference tire can be used as they are.

Next, in step 4, a physical quantity representing a certain tire performance is calculated for the reference tire and defined as an input value for optimization calculation. In this embodiment, in order to provide the same performance for the reference tire and the proportionally designed tire, the ground contact shape is the same for the reference tire and the proportionally designed tire for the wet performance and the wear performance, which are braking performance on the wet road surface. And the proportional design tire is designed to have a uniform contact pressure distribution equal to or higher than that of the reference tire. More specifically, as a grounding shape, a grounding length ratio (Ls / Lc) which is a ratio of a grounding length ratio between the center part and the end part of the tread part, that is, a grounding length Lc of the tread central part and a grounding length Ls of the tread shoulder part. ) As the first physical quantity (see FIG. 4). Here, the contact length Lc at the center of the tread is a contact length on the tread equator line, and the contact length Ls of the tread shoulder is a contact length in the tire circumferential direction 10 mm inside from the position in the width direction contact end. Further, as the contact pressure distribution, the contact pressure dispersion value in the tread portion, that is, the tread is set as the second physical quantity. Here, the ground pressure dispersion value pv is defined by the following equation (1).

  In the equation, pi is the i-th node contact pressure of the tire, pav is the average contact pressure of the tire, and N is the number of nodes having a finite value of the contact pressure.

  Therefore, in Step 4, using the FEM model of the reference tire created in Step 2, the model is assembled on a virtual rim, given predetermined calculation conditions such as air pressure and load, and the contact length ratio of the reference tire is set. (Ls / Lc) and ground pressure dispersion value (pv) are calculated. Then, the obtained contact length ratio and contact pressure dispersion value are defined as input values in the optimization calculation described later.

  In the next step 5, design variables for changing the tire configuration of the proportionally designed tire are defined, and an objective function and constraint conditions are defined.

  As design variables, in the present embodiment, among the items that define the tire shape, the items other than the outer diameter, the cross-sectional width, and the rim diameter that are input in Step 3, such as the crown radius and the side portion radius, can be cited. . In addition, since the tire cross-sectional width (W: see FIG. 6) has a predetermined range according to the standard for each tire size, the cross-sectional width can be set as a design variable by changing within the range. Moreover, the tire cross-section upper side height (H: refer FIG. 6) which is a cross-sectional height above the maximum width of a tire cross section can also be made into a design variable. In addition to the specifications that define the tire shape, the internal configuration such as the belt width and the carcass hoisting height can be used as a design variable.

  In the present embodiment, the objective function is determined based on the difference between the reference tire and the proportionally designed tire with respect to the contact length ratio, which is the first physical quantity, and specifically, the following equation (2) Given by.

Objective function = (rat (cur) −rat (base)) ² / (rat (base)) ² (2)
(However, rat (cur) = Ls (cur) / Lc (cur), rat (base) = Ls (base) / Lc (base))
Here, rat (cur) is the contact length ratio of the proportionally designed tire, and rat (base) is the contact length ratio of the reference tire. Ls (cur) is the contact length of the tread shoulder portion of the proportional design tire, and Lc (cur) is the contact length of the center portion of the tread of the proportional design tire. Ls (base) is a contact length of the tread shoulder portion of the reference tire, and Lc (base) is a contact length of the center portion of the tread of the reference tire. Then, by minimizing the objective function of this equation (2), it means that the contact length ratio of the proportionally designed tire approaches that of the reference tire.

In the present embodiment, the constraint condition is given by the following equation (3) using the ground pressure dispersion value that is the second physical quantity described above.

  Here, pv (cur) is the contact pressure dispersion of the proportionally designed tire, and pv (base) is the contact pressure dispersion of the reference tire. Pi (cur) is the i-th nodal contact pressure of the proportionally designed tire, and pav (cur) is the average contact pressure of the proportionally designed tire. Also, pi (base) is the i-th node contact pressure of the reference tire, and pav (base) is the average contact pressure of the reference tire.

  This constraint condition means that the proportional design tire is designed to be equal to or lower than the contact pressure dispersion value of the reference tire with respect to the degree of uniformity of the contact pressure. This is because, in general, a tire preferably has a ground pressure dispersion value that is as low as possible, so that not only a tire having a ground pressure dispersion value equivalent to that of a reference tire but also a lower ground pressure dispersion value is allowed. is there. Since the reference tire used for proportional design is originally designed to have a low contact pressure dispersion value, a second objective function is defined to bring the contact pressure dispersion value closer to the reference tire together with the above objective function related to the contact length ratio. Thus, it may be an optimization problem that minimizes both.

  As the constraint condition, in addition to the above-described contact pressure dispersion value, a condition for limiting the range allowed as the tire shape or the like as the design variable may be set.

  In the next step 6, all the tires including the tire to be proportionally designed and the reference tire are rearranged in order of increasing cross-sectional width, and are classified into a tire smaller than the reference tire and a large tire. Specifically, in the present embodiment, as shown in FIG. In that case, the reference tire is located between size 6 and size 7. The tire is divided into two groups, a tire having a smaller cross-sectional width than the reference tire (sizes 1 to 6) and a tire having a larger cross-sectional width than the reference tire (sizes 7 to 10). Perform optimization calculations for each of the groups on the side.

  In the group on the small size side, in the next step 7, a tire to be subjected to proportional design is selected. At that time, proportional design tires are selected so that the tires are designed in order starting from a tire having a cross-sectional width closer to that of the reference tire. Therefore, first, a tire of size 6 having the closest cross-sectional width on the small size side with respect to the reference tire is selected.

  Then, in the next step 8, an FEM model is created for the size 6 tire to be designed, and in the next step 9, optimization calculation is executed. The optimization calculation is not particularly limited as long as it is a method capable of obtaining an optimal solution that minimizes the objective function while satisfying the above-described constraint conditions. In the present embodiment, the optimization calculation is performed as follows.

  First, as shown in FIG. 2, in step 90, the initial value of the tire shape of the proportionally designed tire is defined. In the present embodiment, the input value in step 3 is defined for the outer diameter, the cross-sectional width, and the rim diameter, and the specifications of the reference tire are defined as initial values for the other tire shape specifications.

  Next, in step 91, initial values of the objective function and the constraint condition are calculated. When calculating the initial values of the objective function and constraint conditions, the FEM model of the proportional design tire created in Step 8 is used to rim the model into a virtual rim and given predetermined calculation conditions such as air pressure and load. Then, the contact length ratio (Ls / Lc) of the proportionally designed tire and the contact pressure dispersion value (pv) are calculated. Then, the initial values of the objective function and the constraint conditions are calculated by substituting the obtained values into the above formulas (2) and (3) together with the ground contact length ratio and the ground pressure dispersion value defined in step 4 To do.

After obtaining the initial value of the objective function in this way, sensitivity analysis is performed in step 92. 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 (4).

  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 amount of change of the objective function to the unit change of the design variable according to the above equation (4). The function sensitivity is calculated for each design variable to find the direction with the steepest sensitivity gradient.

  Next, in step 93, while considering the constraint conditions, a one-dimensional search is performed to determine how much the design variable should be changed in a direction in which the gradient is steep, and the design variable solution that can minimize the objective function is obtained. And the value of the objective function is calculated from the solution of the design variable.

  In step 94, the initial value of the objective function obtained in step 91 is compared with the value of the objective function obtained in step 93, and the difference between the two is compared with a predetermined threshold value to compare the objective function. It is determined whether or not the value of has converged. If it is determined that the difference between the two is larger than the threshold value, and therefore the value of the objective function has not converged, the initial value is updated in step 95, that is, the solution of the design variable obtained in step 93 and Steps 92 to 94 are repeatedly executed with the value of the objective function as an initial value. In step 94, when the difference between the two is smaller than the predetermined threshold value and the improvement width of the objective function is small, it is determined that the value of the objective function has converged. In step 10, the design variable at this time is determined. Is determined as an optimal solution that gives an optimal value to the objective function, that is, a proportional design solution.

  After obtaining the proportional design solution for the tire of size 6 in this way, it is determined in step 11 whether or not the tire to be designed remains. The proportionally designed tire (that is, the tire of size 6) is updated as the reference tire, and the process returns to Step 7. That is, the proportional design tire for which the proportional design solution is obtained is defined as a reference tire in the next proportional design. In step 7, a tire of size 5 having the closest cross-sectional width on the small size side is selected as the next proportional design tire, and optimization calculation is performed in the same manner as described above to obtain a proportional design solution. Desired. Thereafter, in the same manner, proportional design solutions are sequentially obtained for tires of size 4, size 3, size 2, and size 1.

  The group on the large size side is the same as that on the small size side. First, in step 13, a tire to be subjected to proportional design is selected (first size 7 tire, then size 8, size 9, size 10). ), A FEM model of a proportional design tire is created in step 14, optimization calculation is executed in step 15, a proportional design solution is obtained in step 16, and a design is performed in step 17. It is determined whether the target tire remains, and the optimization calculation is repeated while updating the reference tire at any time in step 18 until proportional design solutions are obtained for all tires.

  If proportional design solutions for all size tires are obtained in both the small size group and the large size group, the process proceeds to step 19 and the optimization calculation is completed. Each proportional design tire is designed based on the proportional design solution thus obtained.

  In the present embodiment described above, when a plurality of tires having the same aspect ratio and different cross-sectional widths are proportionally designed, a tire having the same tire performance as that of the reference tire can be efficiently obtained by using an optimization method. The design man-hours required for proportional design can be greatly reduced.

  In this embodiment, a tire whose size is closest to a tire to be proportionally designed and for which a proportional design solution has already been obtained is defined as a reference tire, and the reference tire is updated each time an individual proportional design solution is obtained. ing. In the optimization calculation, the tire shape specifications other than the input data necessary for the proportional design are defined with the reference tire values as initial values. Therefore, a solution can be obtained more efficiently. This is because the closer the tire size is, the smaller the change width of the ground contact shape of the tire is, so that the change in the design variable is generally small and the objective function can be converged quickly.

  Further, in this embodiment, it is divided into two groups of the small size side and the large size side with respect to the reference tire, and is proportional so that the small size side sequentially decreases and the large size side sequentially increases. Since the design tire is selected and the optimization calculation is executed, it is easy to search for the design variable, and the solution can be efficiently obtained from this point. In the above embodiment, the design target tire exists on both the small size side and the large size side as viewed from the reference tire, but the design target tire may exist only on one side. In this case, proportional design may be performed only for the size on the one side.

  An example in which a proportionally designed tire is designed by performing a simulation using the optimization method of the above-described embodiment will be described. In this example, 10 types of tires (sizes 1 to 10) shown in FIG. 5 were proportionally designed by the optimization method of the above embodiment. At that time, the objective function is as in the above equation (2), the constraint condition is as in the above equation (3), and the design variable is defined by two circular arcs in the tread portion as shown in FIG. For the tire, the radii of curvature R1 (mm) and R2 (mm) of the two arcs and the angles θ1 and θ2 between the two arcs were used.

  Here, for the reference tire (205 / 50R16), R1 = 1350 mm, R2 = 600 mm, θ1 = 1.5 deg, and θ2 = 2 deg. Using this reference tire, a size 6 tire (195 / 50R15) was proportionally designed by the method of the above embodiment, and R1 = 900 mm, R2 = 500 mm, θ1 = 2 deg, and θ2 = 2 deg.

For comparison, tires of size 3, size 6, size 7, size 8 and size 9 in FIG. 5 were proportionally designed by a conventional method using trial and error. Table 1 shows the design man-hours required by the method of the embodiment and the conventional method, and the contact length ratio and contact pressure dispersion value of each designed tire for these five types of tires. The design man-hour is indicated by an index with the design man-hour when the size 6 tire is designed by the conventional method as 100. A smaller index value means less design man-hours.

  As shown in Table 1, with the method of the present embodiment, the design man-hours are greatly reduced while securing the same value as the conventional method for the contact length ratio and the contact pressure dispersion value of the reference tire. It was confirmed that an efficient proportional design can be achieved.

  The present invention can be used to proportionally design a pneumatic tire.

It is a flowchart which shows the flow of the tire design method which concerns on embodiment. It is a flowchart which shows the flow of optimization calculation. It is a figure of the FEM model which divided a tire section into a plurality of elements. It is a schematic diagram of the contact shape of a tire. It is a graph which shows the relationship between the cross-sectional width of a reference tire and a proportional design tire, and an outer diameter. It is a mimetic diagram showing an outline line of a tire.

Claims (6)

A method for designing proportionally designed tires of different sizes having the same performance as a reference tire with respect to a certain tire performance,
(A) defining a physical quantity representing the tire performance for the reference tire as an input value for optimization calculation;
(B) Define a design variable that changes the tire configuration of the proportionally designed tire, and define an objective function that represents the relationship between the physical quantity of the reference tire and the physical quantity that represents the tire performance of the proportionally designed tire. Step,
(C) creating a finite element model of the proportionally designed tire;
(D) The physical quantity of the proportionally designed tire is calculated using the finite element model, and an optimal value of the objective function is given by the optimization calculation so that the physical quantity of the proportionally designed tire is close to the physical quantity of the reference tire. Obtaining values of design variables; and
(E) designing a proportionally designed tire based on a design variable that gives the optimum value;
A pneumatic tire design method including: The step (a)
Inputting specifications defining the reference tire;
Creating a finite element model of the reference tire; and
Calculating a physical quantity representing the tire performance using a finite element model of the reference tire, and defining the calculated physical quantity as an input value for optimization calculation;
The pneumatic tire design method according to claim 1, further comprising: A method of proportionally designing a plurality of tires of different sizes,
(F) a step of selecting a tire to be designed, the step of selecting a proportional design tire so as to design in order of size from a tire having a size close to that of a reference tire;
(G) For the proportionally designed tire selected in step (f), after determining the value of the design variable that gives the optimum value of the objective function in step (d), determining whether the design target tire remains; and ,
(H) a step of updating the immediately preceding proportional design tire as a reference tire in the next proportional design when it is determined in the step (g) that the design target tire remains.
The method for designing a pneumatic tire according to claim 1, further comprising: In the step (b), a constraint condition for restricting a relationship between the reference tire and the proportionally designed tire with respect to another physical quantity for performance evaluation is determined.
The design of the pneumatic tire according to any one of claims 1 to 3, 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. Method.   5. The physical quantity related to the objective function is a contact length ratio between a center portion and an end portion of the tread portion, and the physical quantity for performance evaluation related to the constraint condition is a contact pressure dispersion value of the tread portion. Pneumatic tire design method. A program for designing proportionally-designed tires of different sizes having the same performance as a standard tire with respect to a certain tire performance,
(A) defining a physical quantity representing the tire performance for the reference tire as an input value for optimization calculation;
(B) Define a design variable that changes the tire configuration of the proportionally designed tire, and define an objective function that represents the relationship between the physical quantity of the reference tire and the physical quantity that represents the tire performance of the proportionally designed tire. Step,
(C) creating a finite element model of the proportionally designed tire; and
(D) The physical quantity of the proportionally designed tire is calculated using the finite element model, and an optimal value of the objective function is given by the optimization calculation so that the physical quantity of the proportionally designed tire is close to the physical quantity of the reference tire. Determining the value of a design variable;
A program for running

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