JP2017045105A - Method and device for designing die shape of tire, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method and a device for designing the die shape of a tire capable of obtaining die shape data which does not impair characteristics of the tire shape satisfying objective characteristics, and a program for executing the method for designing the die shape of a tire.SOLUTION: The method for designing the die shape of a tire includes creating a tire model by an element numerically analyzable by a computer for a tire, and performing shape optimization computation for the tire model on the basis of a design variable, an objective function and a constraint condition relating to the set shape. At least one solution is extracted according to the result of the shape optimization computation, and at least two nodes constituting the outer profile are extracted in the cross-sectional shape of the tire model corresponding to a combination of design variables constituting the extracted solution. At least two nodes are set as a fixed point, an arc is created so that the shortest distance to the respective nodes between the fixed points becomes minimum and the outline of the tire model including the arc at least is outputted as die shape data.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a tire mold shape design method, a tire mold shape design apparatus, and a tire mold shape using a shape optimization calculation result in a tire modeled by elements that can be numerically analyzed by a computer. With regard to a program for executing a design method, in particular, a tire mold shape design method, a tire mold shape design apparatus, and a tire mold shape design apparatus in consideration of actual manufacturing constraints without impairing characteristics of a tire shape that satisfies target characteristics, and The present invention relates to a program for executing a tire mold shape design method.

  Currently, a method of creating a tire model that can be analyzed by a computer and simulating the performance of the tire has been proposed. In the performance simulation, a tire model obtained by dividing a tire into a finite number of elements is created. An optimal shape of a tire is obtained by performing optimization calculation using a tire model composed of finite elements. In addition, the shape of the tire mold is designed using the calculation result of the optimum shape of the tire.

  For example, the tire design method of Patent Document 1 includes a setting step for setting a plurality of objective functions, constraint conditions, and design parameters used for determining positions of a plurality of control points in the tire basic model, and optimization of the objective function. A design parameter determining step for determining a final design parameter based on a design variable giving a value. The plurality of control points allow the shape of the first member model and the second member model to be changed, and the setting step moves the operation non-control point based on the operation control point when the first member model is moved. The operation control point is set to be included in the design parameter, and when the second member model is moved, the member interval of the first and second member models is set to be included in the design parameter based on the operation control point. To do. A curve (for example, a B-spline curve) along each control point can define the tire cross-sectional shape.

JP 2014-148196 A

  The tire design method disclosed in Patent Document 1 also controls the position of the reinforcing layer. In Patent Document 1, it is said that a tire cross-sectional shape formed by each control point after movement can be formed into a gentle shape without forming a wave shape. In the case of producing a mold using the calculation result of the optimum shape of the tire obtained by the tire design method of Patent Document 1, the dimensions are indicated by an arc, a straight line, or a combination of an arc and a straight line. It is desirable to adjust the outline of the. However, depending on the degree of adjustment of the outline, the characteristic balance of the optimum tire shape may be impaired. In the tire design method of Patent Document 1, the dimensions of the mold are defined using the calculation results obtained without considering the above-described problem, and therefore the mold shape is not sufficient.

  An object of the present invention is to solve the problems based on the prior art described above, and to obtain a mold shape data that does not impair the characteristics of the tire shape that satisfies the target characteristics, and a tire mold shape design method and tire Is to provide a program for executing the mold shape designing apparatus and the tire mold shape designing method.

  In order to achieve the above-mentioned object, the first aspect of the present invention is a problem setting step for setting design variables, objective functions and constraint conditions related to the shape of the tire, and numerical analysis of the tire by a computer. A creation step of creating a tire model with elements, a calculation step of performing shape optimization calculation on the tire model based on the design variables, objective functions and constraint conditions set in the problem setting step, and the shape of the calculation step At least one solution is extracted from a result of the optimization calculation using a predetermined extraction condition, and an outer contour is formed in the cross-sectional shape of the tire model corresponding to the combination of design variables constituting the extracted solution. An extraction step for extracting at least two nodes, and setting the extracted at least two nodes as fixed points, between the fixed points A tire comprising: a creation step for creating an arc having a minimum shortest distance to each node; and an output step for outputting an outline of the tire model including at least the arc as mold shape data. The mold shape design method is provided.

In the creation step, when creating a plurality of arcs, it is preferable that at least one fixed point shares a tangent with an adjacent arc.
A step of setting a determination condition in the objective function, and the objective function set in the problem setting step is calculated for the tire model expressed using the arc created in the creation step. In the tire model used in the calculation step, an error with the objective function set in the problem setting step is calculated, and if the error is within a predetermined range, the mold shape data is calculated in the output step. It is preferable to output and change the fixed node if the error is outside a predetermined range.

In the creation step, when creating a plurality of arcs, a predetermined threshold is provided for the radius of curvature of the arc, and in the outline of the tire model represented by the plurality of arcs, the radius of curvature is greater than the threshold. In this case, it is preferable to make a straight line between the fixed points for setting the arc.
In the problem setting step, the objective model is expressed by a combination of a plurality of base shapes that change the shape of the tire model and includes at least the definition domain as a design variable. It is preferable to set one or more, and the calculation step performs multi-objective optimization calculation for the tire model.

  According to a second aspect of the present invention, for a tire, a model creation unit that creates a tire model with elements that can be numerically analyzed by a computer, a condition setting unit that sets design variables, an objective function, and constraint conditions, and the condition setting unit Based on the design variables, objective function, and constraint conditions related to the shape set in step 1, a calculation unit that performs shape optimization calculation on the tire model, and using a predetermined extraction condition from the result of the shape optimization calculation of the calculation unit And extracting at least two nodes constituting the outer contour in the cross-sectional shape of the tire model corresponding to the combination of design variables constituting the extracted solution, and extracting the extracted nodes. Is set as a fixed point, an arc having the shortest distance from each node between the fixed points is created, and the tag including at least the arc is created. The outline of Yamoderu is to provide a die shape designing device of a tire characterized by having a die data creation unit for outputting as a mold shape data.

In the mold data creation unit, when creating a plurality of arcs, it is preferable that at least one fixed point shares a tangent with an adjacent arc.
A determination condition is set for the objective function in the condition setting unit, and for the tire model expressed using the arc created by the mold data creation unit, the objective function set by the condition setting unit The calculation unit performs the calculation, and the calculation unit calculates an error from the objective function set in the condition setting unit in the tire model created by the model creation unit and used for creating the arc. If the error is outside the predetermined range, the mold data creation unit may change the node to be fixed. preferable.

When creating a plurality of arcs in the mold data creation unit, the mold data creation unit provides a predetermined threshold value for the radius of curvature of the arc in the outline of the tire model represented by the plurality of arcs. In the case where the arc has a radius of curvature larger than a threshold value, it is preferable that the mold data creation unit form a straight line between the fixed points where the arc is set.
The condition setting unit is expressed by a combination of a plurality of base shapes that change the shape of the tire model, and the definition area thereof is set so as to include at least as a design variable, and an objective function related to a physical quantity of the tire model is set to at least 2 It is preferable to set one or more, and the calculation unit performs multi-objective optimization calculation for the tire model.

  According to a third aspect of the present invention, there is provided a program for causing a computer to execute each step of the tire mold shape designing method according to the first aspect of the present invention as a procedure.

  According to the present invention, it is possible to obtain mold shape data that does not impair the characteristics of the tire shape that satisfies the target characteristics.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic diagram showing a tire mold shape design apparatus used in a tire mold shape design method according to an embodiment of the present invention. It is a flowchart which shows the 1st example of the mold shape design method of the tire of embodiment of this invention in process order. (A) is a schematic diagram which shows an example of a tire model, (b) is a schematic diagram which shows the preparation method of a circular arc. (A) is a schematic diagram which shows an example of the optimal shape of a tire model, (b) is a schematic diagram which expands and shows a tread shoulder part, (c) is a graph which shows the example of the interpolation between nodes. . (A) is a schematic diagram which shows an example of the optimal shape of a tire model, (b) is a schematic diagram which expands and shows a tread center part. It is a flowchart which shows the 2nd example of the metal mold | die shape design method of the tire of embodiment of this invention in process order. (A) And (b) is a schematic diagram which shows the change method of the fixed point of circular arc, (c) is a schematic diagram which shows the change method of the node between the fixed points of circular arc. (A) is a schematic diagram which shows an example of a tire model, (b) is a principal part enlarged view of a tire model. It is a flowchart which shows the 3rd example of the metal mold | die shape design method of the tire of embodiment of this invention in process order. (A) is a schematic diagram showing a tire model having a reference shape, (b) is a schematic diagram showing a tire model having a first base shape, and (c) is a schematic diagram showing a tire model having a second base shape. FIG. It is typical sectional drawing which shows the cross section of a tire model. (A) is a schematic diagram showing the ground pressure distribution of Example 1, (b) is a schematic diagram showing the ground pressure distribution of Comparative Example 1, and (c) is a schematic diagram showing the ground pressure distribution of Comparative Example 2. FIG.

Hereinafter, based on a preferred embodiment shown in the accompanying drawings, a tire mold shape designing method, a tire mold shape designing apparatus, and a tire mold shape designing method according to the present invention are executed by a computer or the like. Describe the program in detail.
FIG. 1 is a schematic diagram showing a tire mold shape design apparatus used in a tire mold shape design method according to an embodiment of the present invention.

  A tire mold shape design apparatus 10 shown in FIG. 1 is used for execution of the tire mold shape design method of the present embodiment. Hereinafter, the tire mold shape design apparatus 10 is simply referred to as a design apparatus 10.

  The design apparatus 10 is configured using hardware such as a computer. As described above, the tire mold shape design method of the present invention uses the design apparatus 10 shown in FIG. 1, and the tire mold shape design method is executed by using hardware such as a computer and software. If possible, it is not limited to the design apparatus 10.

The design apparatus 10 includes a processing unit 12, an input unit 14, and a display unit 16. The processing unit 12 includes a condition setting unit 20, a model creation unit 22, a calculation unit 24, a data creation unit 26, a memory 28, a display control unit 30, and a control unit 32. In addition, although not shown, it has a ROM and the like.
The processing unit 12 is controlled by the control unit 32. In the processing unit 12, the condition setting unit 20, the model creation unit 22, the calculation unit 24, and the data creation unit 26 are connected to the memory 28. The condition setting unit 20, the model creation unit 22, the calculation unit 24, and the data creation are performed. Data of the unit 26 is stored in the memory 28.
In the tire mold shape designing method described below, various processes are performed in each part of the processing unit 12. In the following description, the description that various processes are performed by each unit of the processing unit 12 by the control unit 32 is omitted, but a series of processes of each unit is controlled by the control unit 32. The memory 28 also stores various determination conditions described later. The control unit 32 reads the determination condition from the memory 28, compares it with the result obtained by the calculation unit 24, determines the operation of each unit based on the determination result, and operates each unit based on the determined operation.

  The input unit 14 is various input devices for inputting various information such as a mouse and a keyboard in accordance with an operator instruction. The display unit 16 displays, for example, the results obtained by the tire mold shape design method, and various known displays are used. The display unit 16 also includes a device such as a printer for displaying various types of information on an output medium.

  The design apparatus 10 executes the program (computer software) stored in the ROM or the like by the control unit 32, thereby functioning each part of the condition setting unit 20, the model creation unit 22, the calculation unit 24, and the data creation unit 26. Form. As described above, the design apparatus 10 may be configured by a computer in which each part functions by executing a program, or may be a dedicated apparatus in which each part is configured by a dedicated circuit.

The tire mold shape design method of the present embodiment is intended to obtain a mold shape faithful to a tire model without impairing characteristics, and relates to a mold shape data creation method using a computer.
In the tire mold shape design method, an optimum shape is acquired from a shape change having a degree of freedom in advance, and then a process of smoothing the outline is performed, so that a more optimal solution can be obtained. For this reason, it is possible to efficiently calculate the tire cross-sectional shape taking into consideration the actual manufacturing restrictions without impairing the feature of the shape that satisfies the target characteristics. Thereby, mold shape data that does not impair the characteristics of the tire shape that satisfies the target characteristics can be obtained.

  The condition setting unit 20 of the design apparatus 10 sets design variables, objective functions, and constraint conditions necessary for the shape optimization calculation of the tire model. In addition, various conditions and information necessary for calculating the shape optimization of the tire model are input and set. Design variables, objective functions, constraint conditions, various conditions, and information are input via the input unit 14. Design variables, objective functions, constraint conditions, various conditions, and information set by the condition setting unit 20 are stored in the memory 28.

The condition setting unit 20 is set with a plurality of parameters determined as design variables among parameters defining the tire and the material constituting the tire. The design variable parameters may be set with variation factors such as load and boundary conditions, and in the case of products, constraints such as size and mass.
In addition, a plurality of parameters determined as characteristic values (objective functions) among the parameters defining the tire and the material constituting the tire are set. As the characteristic value, an index for evaluating the tire and the material constituting the tire other than the physical and chemical characteristic values such as cost may be used.
The tire and the material constituting the tire may be a whole system including the tire, such as a part constituting the tire, a tire assembly form, or a part thereof, instead of the tire alone.

The plurality of types of characteristic values set in the condition setting unit 20 are physical quantities to be evaluated, that is, objective functions. The objective function has a preferable direction in terms of performance, and the value increases, decreases, or approaches a predetermined value. As for the objective function, there is an unfavorable direction opposite to the preferred direction in addition to the above-mentioned preferable direction.
The objective function is the characteristic value of the tire. In this case, the characteristic value is a physical quantity to be evaluated as tire performance, for example, CP (cornering power) which is a lateral force in the vicinity of zero slip angle, which is an indicator of steering stability, and an indicator of riding comfort. Examples thereof include a primary natural frequency of a tire, rolling resistance as an index of rolling resistance, a lateral spring constant as an index of steering stability, wear energy of a tire tread member as an index of wear resistance, and fuel efficiency. Other than this, examples of the physical quantity of the tire include a shape and a dimensional value. The shape is, for example, a cross-sectional shape. Examples of the dimension value include a tire width and a tire outer diameter. Examples of the physical quantity of a tire include a deflection amount, contact pressure distribution, rolling resistance, cornering characteristics, and the like in addition to the shape or dimensional value.

The design variable defines the shape of the tire, the internal structure of the tire, the material characteristics, and the like. The design variables are a plurality of parameters among the tire material behavior, the tire shape, the tire cross-sectional shape, the tire natural vibration mode, and the tire structure. Examples of the design variable include a radius of curvature that defines a crown shape in a tread portion of the tire, a belt width dimension of the tire that defines a tire internal structure, and the like. In addition to this, for example, a filler dispersion shape that defines material characteristics in the tread portion, a filler volume ratio, and the like can be given. In order to obtain mold shape data, the design variable is preferably related to the shape of the tire.
The constraint condition is a condition for constraining the value of the objective function to a predetermined range or constraining the value of the design variable to a predetermined range.
In addition, information on vehicle specifications to be used for vehicle running simulation, such as tire load load, tire rolling speed and other running conditions, road surface conditions on which the tire runs, for example, uneven shape, friction coefficient, etc. Is set.

In addition, information for determining a nonlinear response relationship between a plurality of types of design variables and a plurality of types of characteristic values is set in the condition setting unit 20. This nonlinear response relationship includes, for example, a numerical simulation such as FEM (finite element method), a theoretical formula, and the like.
The condition setting unit 20 sets a simulation condition and a constraint condition in the simulation when performing a numerical simulation such as a model generated by a nonlinear response relationship, a boundary condition of the model, and FEM.

Furthermore, optimization conditions for obtaining a Pareto solution, for example, conditions for searching for a Pareto solution may be set. The conditions for the Pareto solution search are a method for searching for the Pareto solution and various conditions in the Pareto solution search. In the present embodiment, for example, a genetic algorithm (GA) can be used as a method for searching for a Pareto solution. In general, it is known that the search ability of a genetic algorithm decreases as the characteristic value (objective function) increases. One way to solve this is to increase the number of individuals.
In addition to this, a design variable definition area is set in the condition setting unit 20. The domain of the design variable may be a discrete level value or a constant. Since there are multiple types of design variables, discrete level values are set for all design variables, and the computer changes the combination of design variables with the domain defined as the constant for the remaining design variables. The characteristic value may be calculated while extracting a Pareto solution described later.

  For shape optimization calculations, output values are calculated while changing input variables in accordance with optimization algorithms such as the sequential search using evolutionary techniques and the nonlinear search (response surface) between input and output variables. Any of the searching methods may be used.

  The model creation unit 22 creates a tire model modeled with elements that can be numerically analyzed by a computer. The model creation unit 22 creates various calculation models based on the set nonlinear response relationship. As described above, the nonlinear response relationship includes a numerical simulation such as FEM. In this case, the model creation unit 22 generates a mesh model corresponding to a design parameter representing a design variable and a characteristic value parameter representing a characteristic value. Is done. Also in the case of a theoretical formula or the like, a theoretical formula or the like corresponding to the design parameter or characteristic value parameter is created. The calculation unit 24 performs a simulation calculation using the tire model.

The tire model created by the model creation unit 22 is created using each type of design parameters set by the condition setting unit 20, and a known creation method can be used for creating the tire model. . The tire model also generates at least a road surface model that is a target for rolling the tire model. A tire model that reproduces a rim on which a tire is mounted, a wheel, and a tire rotation axis may be used. Further, if necessary, a model that reproduces a vehicle to which a tire is attached may be incorporated into the tire model. At this time, it is possible to create a model in which the tire model, the rim model (wheel model), and the tire rotation axis model are integrated based on preset boundary conditions.
Moreover, the form of the tire model used for the analysis is not particularly limited, and may be a smooth tire without a groove, only a main groove, or with a pattern.

The tire model created by the model creation unit 22 is created using each type of design parameters set by the condition setting unit 20, and a known creation method can be used for creating the tire model. .
For example, a tire model is created by dividing a tire into a finite number of elements composed of a plurality of nodes.
The elements constituting the tire model are, for example, a quadrilateral element in a two-dimensional plane, a solid element such as a tetrahedral solid element, a pentahedral solid element, and a hexahedral solid element in a three-dimensional body, and a shell such as a triangular shell element and a rectangular shell element. Elements that can be analyzed by a computer, such as elements and surface elements. In the process of analysis, the elements divided in this way are identified one by one using three-dimensional coordinates in the three-dimensional model and using two-dimensional coordinates in the two-dimensional model.

  Each of these models may be a discretized model capable of numerical calculation, such as a finite element model for use in a known finite element method (FEM). In addition to the road surface model and the tire model, the inclusions existing on the road surface are reproduced, for example, when a tire design plan that optimizes tire performance such as tire wet performance is obtained using the tire model. Generate a model. For example, as an inclusion model, various models that reproduce water, snow, mud, sand, gravel, ice, and the like on the road surface may be generated as a discretized model that can be numerically calculated. The road surface model is not limited to a model that reproduces a road surface with a flat surface, and may be a model that reproduces a road surface shape having irregularities on the surface as necessary.

The calculation unit 24 calculates the characteristic value using the tire model created by the model creation unit 22. Thereby, a characteristic value (output value) for the design variable is obtained. The obtained output value (output value) is stored in the memory 28. The calculation unit 24 functions, for example, by executing a subroutine using a known finite element solver.
The computing unit 24 calculates an output value (sampling point) in a characteristic value space composed of a plurality of types of design variable values and characteristic values using a non-linear response relationship. The computing unit 24 uses the design variable and the output value (sampling point) to create an approximate model (meta model) using the characteristic value that is the output value as an objective function.
The above approximate model (meta model) is a mathematical model that approximates the input / output relationship, and various input / output relationships can be approximated by adjusting parameters. For example, a polynomial model, kriging, a neural network, a radial basis function, or the like can be used as the above approximate model.

  The calculation unit 24 also performs shape optimization calculation using the approximate model. Using the solution (which may include a Pareto solution) extracted by the data creation unit 26 from the shape optimization calculation result, the actual calculation is executed using the specified nonlinear relationship. In addition to this, the calculation unit 24 directly gives a boundary condition to the tire model expressed from the combination of design variables by using the finite element method without using an approximate model, and directly calculates a characteristic value. As the shape optimization calculation method, for example, a genetic algorithm (GA) which is one of evolution calculation methods is used. Genetic algorithms include, for example, DRMOGA (Divided Range Multi-Objective GA), NCGA (Neighborhood Cultivation GA), which divides a solution set into a plurality of regions along an objective function and performs multi-objective GA for each divided solution set. , Using known methods such as DCMOGA (Distributed Cooperation model of MOGA and SOGA), NSGA (Non-dominated Sorting GA), NSGA2 (Non-dominated Sorting GA-II), and SPEAII (Strength Pareto Evolutionary Algorithm-II) Can do.

The computing unit 24 searches for the Pareto solution from the shape optimization calculation result using the approximate model obtained by the computing unit 24 according to the Pareto solution search conditions set by the condition setting unit 20, and finds the Pareto solution. It is also what is extracted. The obtained Pareto solution is stored in the memory 28.
Here, a Pareto solution cannot be said to be superior to any other solution in a plurality of characteristic values (objective functions) in a trade-off relationship, but a solution that has no other superior solution exists. Say. In general, there are a plurality of Pareto solutions as a set. For the Pareto solution search, for example, the Pareto ranking method is used.

  In the calculation unit 24, selection using a vector evaluation genetic algorithm (VEGA), a Pareto ranking method, or a tournament method is performed, for example. Other than the genetic algorithm (GA), for example, annealing (SA) or particle swarm optimization (PSO) may be used as the same evolutionary calculation method.

  In the present invention, the non-linear response relationship defined between the design variable and the characteristic value, that is, the one used when the characteristic value is obtained using the design variable is not limited to the simulation such as FEM. A theoretical formula or the like can also be used.

  The data creation unit 26 extracts at least one solution from the shape optimization calculation result of the calculation unit 24 using a predetermined extraction condition. Then, at least two nodes constituting the outer contour are extracted from the cross-sectional shape of the tire model corresponding to the combination of design variables constituting the extracted solution. The extracted nodes are set as fixed points, and an arc having the shortest distance from each node between the fixed points is created. In the tire model, an outline including at least an arc is output as mold shape data. Details of the arc creation method will be described later.

The outline is an outer line from one bead toe to the opposite bead toe in the tire cross section orthogonal to the tire equator plane.
The mold shape data is dimension data indicating the length of a straight line constituting the outline, the curvature of a curve, the position coordinates of the line, and the position coordinates of the curve. Specifically, for example, it is dimension data necessary for producing a mold using an NC processing machine. In addition to the dimension data, the mold shape data may be data represented by the shape of a tire model. In this case, the tire model may be modeled by an element capable of numerical analysis, for example.

The display control unit 30 causes the display unit 16 to display various parameters such as design variables and characteristic values set in the condition setting unit 20, output values obtained by the calculation unit 24, and a tire model. For example, the characteristic value and the result of the tire model shape optimization calculation are read from the memory 28 and displayed on the display unit 16.
The display control unit 30 can also cause the display unit 16 to display various types of information, tire models, numerical calculation results, and optimal solutions input via the input unit 14. For example, the tire model and the result of the tire model shape optimization calculation are read from the memory 28 and displayed on the display unit 16.

As described above, the control unit 32 controls the processing unit 12, and performs various processes performed by the tire mold shape design method described below, including the model creation unit 22, the calculation unit 24, and the processing unit 12. And the data creation unit 26.
In the design apparatus 10, in the input file when changing the shape or structure, common portions such as boundary conditions and analysis steps are divided from different portions according to individual shapes such as node coordinate values, the placement angle of the reinforcing material, and initial tension. However, by automating using a file format that is captured in the common part, that is, by converting individual information into an include file, even when examining a large number of tire shapes, the tire shape can be easily examined. Is possible.

Next, a first example of the tire mold shape designing method of the present embodiment will be described.
FIG. 2 is a flowchart showing a first example of a tire mold shape designing method according to an embodiment of the present invention in the order of steps.
First, as shown in FIG. 2, optimization conditions such as design variables, characteristic values (objective functions), and constraint conditions are set for the tire (step S10). For example, a tire having a size of 195 / 65R15 can be used as the tire.
As the design variable, for example, a design variable that changes the shape of the tire or the cross-sectional shape of the tire is set. The design variable setting method is not particularly limited. For example, the design value of the design variable is set using the Latin hypercube method (Latin hypersquare method).
The characteristic values include, for example, tire rigidity, rolling resistance, air resistance, cornering performance, friction energy, and the like as tire physical characteristics. For example, two tire physical characteristics of a first characteristic value and a second characteristic value are set as objective functions. The characteristic value set as the objective function may be 1 or 3 or more.

The design variable (input parameter) is a parameter of the tire cross-sectional shape, and the characteristic value (output parameter) is two characteristic values that are tire physical characteristics. Parameters for the tire cross-sectional shape and two characteristic values are set in the condition setting unit 20.
In the present embodiment, an approximate model is created by the tire mold shape design method under such setting conditions. A change in the first characteristic value and the second characteristic value depending on the parameter value of the tire cross-sectional shape is obtained.
Using the information set in the condition setting unit 20, the model creation unit 22 creates a tire model such as a mesh model.

  Next, a non-linear response used when obtaining the characteristic value from the design variable is set in the condition setting unit 20. That is, the relationship between design variables and characteristic values is determined. The type of this nonlinear response is stored in the memory 28, for example. For example, the relationship between the tire cross-sectional shape parameter and the first characteristic value and the second characteristic value is set. When the tire cross-sectional shape parameter is input and the first characteristic value and the second characteristic value are output, the relationship to be set is, for example, that the first characteristic value uses the tire cross-sectional shape parameter as a variable. It is expressed using a nonlinear function such as a polynomial. In addition, the second characteristic value is expressed using a nonlinear function such as a polynomial having a tire cross-sectional shape parameter as a variable.

Next, using the nonlinear response relationship set in step S10, an output value in a characteristic value space composed of a plurality of types of design variable values and characteristic values is calculated. That is, sampling calculation is performed to calculate a characteristic value that is an output when a design variable is input.
Next, an approximate model is created using the output value obtained by sampling calculation. That is, the relationship between the design variable and the characteristic value is expressed by an approximate model.
Next, the calculation unit 24 executes shape optimization calculation using the approximate model (step S12).
For shape optimization calculation, either the search method using the nonlinear relationship (response surface) between the input variable and the output variable or the search method by calculating the output value while sequentially changing the input variable according to the optimization algorithm May be used. The shape optimization calculation is also called multi-objective optimization calculation if a plurality of objective functions are set.

Next, at least one solution is extracted from the result of the shape optimization calculation using a predetermined extraction condition (step S14).
In step S14, as an extraction condition to be set, a Pareto solution may be obtained by extracting a Pareto solution by a Pareto solution search unit. In addition, the solution may be extracted from all individuals (solutions) using characteristics other than the objective function as a constraint condition.

Next, in the cross-sectional shape of the tire model 50 (see FIG. 3A) corresponding to the combination of design variables constituting the extracted solution, at least two nodes constituting the outer contour are extracted (step S16). ).
It is preferable that at least two points constituting the outer contour to be extracted are representative positions of the tire. Taking the tire cross-sectional shape as an example, there are a cap tread center position, a tire maximum width position, a tread deployment width position, a mold division position, a bead toe portion, a bead heel portion, and the like.

Next, as shown in FIG. 3B, the extracted nodes are set as fixed points 52 and 54. A circular arc 58 having the shortest distance from each of the nodes 56a to 56d between the fixed points 52 and 54 is created (step S18).
Specifically, in step S18, the arc satisfies the following mathematical formula. The r In the following equation the radius of curvature of the arc 58, the _{r i} is that the center O of the arc 58 of the distance to each node 56a to 56d.
For the arc 58, for example, an arc having the maximum curvature radius is set between the fixed points 52 and 54, and the arc 58 is searched by changing the curvature so as to satisfy the following formula. In this case, a straight line may be set as the arc having the maximum curvature radius between the fixed points 52 and 54.
In addition to the above, the arc 58 may be searched while sequentially changing the radius of curvature, or the arc having the shortest distance may be searched after the radius of curvature is set discretely. When searching, it is preferable to search based on the radius of curvature of the arc passing through the three fixed points and the node closest to the center point between the fixed points.

  Next, as shown in FIG. 2, the outline of the tire model including at least the arc 58 is output as mold shape data (step S20). In this way, mold shape data necessary for designing the mold shape of the tire can be obtained.

  4A is a schematic diagram showing an example of the optimum shape of the tire model, FIG. 4B is a schematic diagram showing an enlarged tread shoulder portion, and FIG. 4C is a graph showing an example of interpolation between nodes. It is. In FIG. 4A, reference numeral 62 indicates a tread shoulder portion, and reference numeral 64 indicates a tread portion.

The tire model 60 (see FIG. 4A) having the optimum shape obtained by the shape optimization calculation has an outline 68 represented by a set of nodes 66 as shown in FIG. 4B. The outline 68 of the tire model causes minute backlash at the node 66. When this occurs on the tread surface, there is a concern about deterioration of wear resistance performance such as uneven wear, and therefore it is desirable that the outline is smoothly connected.
On the other hand, it is desirable to adjust the outline because the dimensions are indicated by a combination of arcs or straight lines when creating the mold shape. However, depending on how the tire is shaped, the characteristic balance of the optimum shape may be impaired.
An example in which the node 66 of the tread portion 64 is interpolated is shown in FIG. The contour line 70 by Lagrange interpolation and the contour line 72 by spline interpolation shown in FIG. 4C always pass through the nodes 66, so that the minute rattling on the contour lines 70 and 72 cannot be solved. In the present invention, since the arc 58 does not necessarily pass through the node 66, it is possible to obtain a contour line faithful to the tire shape obtained by the optimization calculation.

In step S18, the number of arcs 58 is not limited to one and may be plural. For example, there may be two arcs.
Here, FIG. 5A is a schematic diagram showing an example of the optimum shape of the tire model, and FIG. 5B is a schematic diagram showing an enlarged tread center portion.
In the tire model 61 shown in FIG. 5A, reference numeral 80 denotes a fixed point (node) of the tread center portion, and reference numeral 82 denotes a fixed point (node) of the tread end portion. Reference numeral 86 indicates an outline from the fixed point 80 (node) of the tread center portion to the fixed point (node) 82 of the tread end portion.

As shown in FIG. 5B, the fixed point 84 (node) at the tread end portion is not set as one arc from the fixed point 80 (node) at the tread center portion, but a fixed point 84 is set in the middle. The first arc 86a and the second arc 86b are set with this fixed point 94 in common. The first arc 86a and the second arc 86b are adjacent to each other. By making the fixed point 84 common, the first arc 86a and the second arc 86b adjacent to the first arc 86a also share a tangent.
Since the method of obtaining the first arc 86a is the same as that of the arc 58 described above, detailed description thereof is omitted. Incidentally, FIG. 5 reference numeral _{O 1} of the (b) shows a center of the first arc 86a, reference numeral _{O 2} denotes the center of the second circular arc 86b. Reference numeral 88 in FIG. 5B indicates a node. The center O ₁ of the _first arc 86 a and the center O 2 of the second arc 86 _b are on the same straight line 89. Therefore, when the first arc 86a on the center side is defined and an arbitrary fixed point 84 is selected, the second arc 86b is uniquely determined.

  By using a plurality of arcs, the nodes can be smoothly connected, the outline of the tire can be smoothed, and performance and appearance defects occurring in the tire can be suppressed. Examples of a preferable example of smoothly connecting the nodes include a cap tread from the viewpoint of wear resistance performance, and a sidewall portion from the viewpoint of improving the appearance.

Next, a second example of the tire mold shape designing method of the present embodiment will be described.
FIG. 6 is a flowchart showing a second example of the tire mold shape designing method according to the embodiment of the present invention in the order of steps. FIGS. 7A and 7B are schematic views showing a method for changing a fixed point of an arc, and FIG. 7C is a schematic diagram showing a method for changing a node between fixed points of the arc.
In the second example of the tire mold shape design method, detailed description of the same steps as those of the first example of the tire mold shape design method described above will be omitted. 7A to 7C, the same components as those in FIG. 3B are denoted by the same reference numerals, and detailed description thereof is omitted. Hereinafter, the second example of the tire mold shape designing method is simply referred to as a second example.

  The second example differs from the first example of the tire mold shape design method in that the formed arc is verified, and the other steps are the first of the tire mold shape design method. Since it is the same as that of an example, the detailed description is abbreviate | omitted.

In the second example, for the tire model expressed using the arc created in step S18, the step of calculating the objective function set in the problem setting step (step S22), the tire used for the shape optimization calculation A step of calculating an error from the objective function set in the problem setting step in the model (step S24). If the error does not satisfy a predetermined determination condition (step S26), the node to be fixed is changed (step S28). ), An arc is created again using the changed fixed point (step S18), the objective function is calculated (step S22), the error is calculated (step S24), and whether the error satisfies a predetermined determination condition (step S22). Step S26) is repeated.
If the error satisfies a predetermined determination condition (step S26), the outline of the tire model including at least the arc 58 obtained in step S18 is output as mold shape data (step S30). Since this step is the same as the first example of the tire mold shape designing method, its detailed description is omitted.

In step S22, the objective function set in the objective setting step is calculated by, for example, FEM analysis using a tire model including at least the arc 58. If a plurality of objective functions are set, at least one objective function may be calculated.
In step S24, shape optimization calculation is performed in step S12, and the objective function set in the objective setting step is calculated. For this reason, the calculation results of the objective functions in step S12 and step S22 are compared to determine the error.
In step S26, an error is preset according to the objective function, and this error is compared with the error obtained in step S24. If the error obtained in step S24 is smaller than the set error, the outline data of the tire model including at least the arc 58 is output as mold shape data (step S30).

  As shown in FIG. 7A, when two fixed points 52 and 54 are set and an arc 58 is formed, the objective function set in the problem setting process is calculated (step S22) and set in the problem setting process. When the error from the objective function is calculated (step S24) and the error does not satisfy the predetermined determination condition (step S26), the fixed point 54 is replaced with the fixed point 52 as shown in FIG. It changes to the fixed point 54a on the side (step S28). Then, an arc 58a is created. The above steps S22 to S26 are repeated for the arc 58a. The process is repeated until the error satisfies a predetermined determination condition.

In the second example, when the change in the target characteristic becomes large due to the change in the tire shape that occurs before and after the arc formation, by changing the fixed point, the outline of the tire model before correction is changed without impairing the characteristic. A shape expressed by an arc can be extracted. When there is a constraint condition for connecting with an arc, since the arc to be contacted is uniquely determined, a minute difference in shape may affect the characteristic value, which is very suitable for eliminating the risk.
The changing method of the fixed node in step S28 is not particularly limited to changing to the fixed point 52 side, and may be changed to the node on the fixed point 54 side.
As shown in FIG. 7C, the nodal positions in the tire model after the correction in step S28 are the intersection points 59 of the straight line L passing through the nodal points 56a to 56d and the center O of the arc 58 and the arc 58 formed. It is desirable that the objective function is calculated with an offset. As a result, the node can be moved on the arc while minimizing the amount of movement from the original node position, and correction that does not change the original shape as much as possible is possible. For this reason, it is possible to suppress a decrease in mesh quality such as the shape of the constituent elements.

In addition, when creating multiple arcs, set a predetermined threshold for the radius of curvature of the arc, and set the arc when the arc has a radius of curvature larger than the threshold in the outline of the tire model represented by multiple arcs. It is preferable to make a straight line between the fixed points.
FIG. 8A is a schematic diagram showing an example of a tire model, and FIG. 8B is an enlarged view of a main part of the tire model.
In the tire model 90 shown in FIG. 8A, for example, as shown in FIG. 8B, a fixed point 96 is provided in the middle between the fixed point 92 and the fixed point 94 to create two arcs. In this case, a predetermined threshold is set for the radius of curvature of each arc. When the radius of curvature of the arc is larger than the threshold radius of curvature, a straight line is set between the fixed points where the arc is set. When the curvature radius calculated according to the target performance or position is equivalent to a straight line, it is possible to output mold shape data with a clear and simplified dimension indication.
In FIG. 8B, the radius of curvature between the fixed point 92 and the fixed point 94 is smaller than the threshold and is an arc 98a. When a circular arc is formed between the fixed point 96 and the fixed point 94, the radius of curvature is larger than the threshold value, and a straight line 98b is set. For example, if the radius of curvature of the arc is 4000 mm or more, it is a straight line.

Next, a third example of the tire mold shape designing method will be described.
FIG. 9 is a flowchart showing a third example of the tire mold shape designing method according to the embodiment of the present invention in the order of steps. FIG. 10A is a schematic diagram showing a tire model having a reference shape, FIG. 10B is a schematic diagram showing a tire model having a first base shape, and FIG. 10C is a diagram showing a tire model having a second base shape. It is a schematic diagram shown.
In the third example of the tire mold shape design method, detailed description of the same steps as those in the first example of the tire mold shape design method is omitted. Hereinafter, the third example of the tire mold shape designing method is simply referred to as a third example.

The third example is different from the first example of the tire mold shape design method in that the shape of the tire model is different from the reference shape before the multi-objective optimization calculation is executed (step S50). It is expressed by a combination of a plurality of base shapes (steps S40 and S42), their definition areas are set so as to include at least as design variables (step S44), and at least two objective functions related to physical quantities of the tire model are set ( Step S46) is further different in that a non-linear function of the design variable and the objective function is set (Step S48), and the other steps are the same as those in the first example of the tire mold shape designing method. Detailed description thereof is omitted.
In the third example, for the above-described steps S40 to S48, for example, methods described in JP2013-189160A and JP2013-191146A can be appropriately used. The above-described steps S40 to S48 correspond to step S10 of the first example.

In the third example, first, a tire model 100 having a reference shape shown in FIG. 10A is set (step S50). Data of the tire model 100 having the reference shape is stored in the memory 38, for example.
Next, a plurality of base shapes are set (step S52). The base shape is, for example, a first base shape tire model 102 shown in FIG. 10B and a second base shape tire model 104 shown in FIG. The data of the first base shape tire model 102 and the second base shape tire model 104 are stored in the memory 38, for example. Of course, the number of base shapes is not limited to two as long as it is plural, and may be three or more.
The tire model 100 having the reference shape, the tire model 102 having the first base shape, and the tire model 104 having the second base shape are all modeled with elements capable of numerical analysis.

Next, a domain for defining weights (design variables) is set (step S44).
When combining the first base shape and the second base shape, for example, weighted addition of the changed portion is performed. In step S44, the weight at this time is set.
Here, the changed portion refers to a difference (displacement) between the position coordinates of the node of the base shape and the position coordinates of the corresponding node of the reference shape. The weighted addition refers to weighted addition using the value of the weight intensity for the changed portion of each base shape, that is, changing the amount of change. The weighted addition includes a weighted average obtained by dividing the addition result of the weighted base shape by the sum of the weight intensity values used. When creating the trial cross-sectional shape, a value of the weight intensity is given to each of the base shapes. The value of the weight intensity is set by the condition setting unit 20. The weight intensity value is set using, for example, a known experimental design technique, specifically, a design matrix such as a Latin hypercube or an orthogonal table.
The value of the weight strength may be set according to the planning matrix or may be sequentially changed within a predetermined range, and the tire cross-sectional shape is created each time the weight strength value is changed. In either case, the tire cross-sectional shape is created by changing the weight strength value so as to cover the entire set range evenly. For example, the weight strength value is changed so as to increase or decrease by a certain amount, but the weight strength value may be changed at random.

Next, an objective function is set (step S46). The objective function set in step S46 relates to the physical quantity of the tire, and at least two of these are set. The physical quantity of the tire is, for example, a tire width, a tire outer diameter, a deflection amount, a contact pressure distribution, a rolling resistance, a cornering characteristic, and the like.
The setting of the objective function is the same as the setting of the objective function in step S10 in the first example, and thus detailed description thereof is omitted.
Next, a nonlinear function is set (step S48). Since the setting of the nonlinear function is the same as the setting of the nonlinear function in step S10 of the first example, detailed description thereof is omitted.

Next, using the nonlinear response relationship set in step S48, an output value in a characteristic value space composed of a plurality of types of design variable values and characteristic values is calculated. That is, sampling calculation is performed to calculate a characteristic value that is an output when a design variable is input. An approximate model is created using the output value obtained by sampling calculation. That is, the relationship between the design variable and the characteristic value is expressed by an approximate model. Next, multi-objective optimization calculation using the approximate model is executed by the calculation unit 24 (step S50).
Since the multi-objective optimization calculation is the same as the shape optimization calculation (step S12) of the first example except that the type of objective function and the number of objective functions set are different, detailed description thereof will be omitted.
At least one solution is extracted from the result of the multi-objective optimization calculation under a predetermined extraction condition (step S52).

Next, in the cross-sectional shape of the tire model corresponding to the combination of design variables constituting the extracted solution, at least two nodes constituting the outer contour are extracted (step S54).
Next, the extracted nodes are set as fixed points, and an arc having the shortest distance between the fixed points and the respective nodes is created (step S56).
Next, the outline of the tire model configured to include at least an arc is output as mold shape data (step S58). In this way, mold shape data necessary for designing the mold shape of the tire can be obtained.
Steps S52 to S58 correspond to steps S12 to S20 of the first example, and detailed description thereof is omitted.

According to the third example, an optimum tire shape can be obtained by combining tire shapes. Even when the tire shapes are combined, the mold shape data necessary for designing the mold shape of the tire can be obtained.
In addition, according to the third example, by searching for the optimum tire shape excluding the restriction of the outline, the tire shape that satisfies the target characteristics is obtained from a wider design space, and the actual manufacturing restriction is obtained. Can be calculated efficiently by using the mold dimensions of the tire cross-sectional shape in consideration of the above.

Also in the third example, as in the second example, the error may be verified with respect to the outline including the arc formed by the nodes (fixed points) fixed with respect to the arc obtained in step S56.
Also in the third example, the fixed point for obtaining the arc may be changed as in the second example. Moreover, there may be a plurality of arcs. Furthermore, when the radius of curvature of the arc is larger than the threshold value, it may be a straight line instead of the arc.

  The present invention is basically configured as described above. As described above, the tire mold shape designing method, the tire mold shape designing apparatus, and the program according to the present invention have been described in detail. However, the present invention is not limited to the above-described embodiment, and does not depart from the gist of the present invention. Of course, various improvements or changes may be made.

Examples of the tire mold shape designing method of the present invention will be specifically described below.
In this example, the effects of the tire mold shape designing method of the present invention were confirmed using Example 1 and Comparative Examples 1 and 2 shown below.

  In this example, a tire model 110 having a cross-sectional shape shown in FIG. 11 was used. Since the tire model 110 in FIG. 11 is symmetrical with respect to the tire equator line C, only half of the tire model 110 is shown. In FIG. 11, reference numerals 112a, 112b, and 112c represent nodes to be fixed (fixed points). Reference numerals 114a to 114d denote shared fixed points. Reference numeral 116 indicates a node. Reference numerals R1 to R7 indicate sections for obtaining arcs. In the tire model 110, the shape of the rim contact portion is unchanged so as not to cause poor contact. The tire model 110 is obtained by performing shape optimization calculation.

In Example 1, the tire mold 110 according to the present invention is used for the tire model 110 shown in FIG.
Comparative Example 1 remains the tire model 110 shown in FIG. It is the state before the process of Example 1. FIG.
In Comparative Example 2, the operator manually corrects the tire model 110 shown in FIG.
Example 1, Comparative Example 1, and Comparative Example 2 have the same configuration except that the outline of the tire model is different. The FEM analysis also has the same configuration except that the outline of the tire model is different.

FEM analysis was performed on Example 1, Comparative Example 1, and Comparative Example 2, and the contact pressure distribution was calculated. The results are shown in FIGS. 12A shows the ground pressure distribution of Example 1, FIG. 12B shows the ground pressure distribution of Comparative Example 1, and FIG. 12C shows the ground pressure distribution of Comparative Example 3.
Further, with respect to Example 1, Comparative Example 1, and Comparative Example 2, longitudinal rigidity, lateral rigidity, circumferential rigidity, rolling resistance, and wear life were determined by FEM analysis. The results are shown in Table 1 below. In addition, each numerical value of the longitudinal rigidity, the lateral rigidity, the circumferential rigidity, the rolling resistance, and the wear life in the following Table 1 is an index with Comparative Example 1 being 100. The longitudinal stiffness, lateral stiffness, circumferential stiffness and wear life are preferably greater than 100. The rolling resistance is preferably a numerical value of less than 100.

As shown in Table 1 above, Example 1 was able to obtain a high wear life while maintaining the performances of longitudinal rigidity, lateral rigidity, circumferential rigidity, and rolling resistance.
In Comparative Example 2, the rolling resistance was increased and the wear life was shortened.
Further, as shown in FIG. 12A, in Example 1, the pressure distribution difference of the ground pressure is small. On the other hand, Comparative Example 1 shown in FIG. 12B and Comparative Example 2 shown in FIG. 12C had a region where the ground pressure was high at the ground end. As described above, in the present invention, it is possible to obtain mold shape data that does not impair the characteristics of the tire shape that satisfies the target characteristics.

DESCRIPTION OF SYMBOLS 10 Tire mold shape design apparatus 12 Processing part 14 Input part 16 Display part 20 Condition setting part 22 Model creation part 24 Calculation part 26 Mold data creation part 28 Memory 30 Display control part 32 Control part 50, 60, 61, 90 , 100, 102, 104, 110 Tire models 52, 54, 54a, 80, 82, 92, 94, 96 Fixed points 56a to 56d, 66 Nodes 62 Tread shoulder 64 Tread 68, 86 Outline

Claims (11)

A problem setting process for setting design variables, objective functions, and constraints related to the shape of the tire,
For the tire, a creation process for creating a tire model with elements that can be numerically analyzed by a computer,
Based on the design variables, objective functions, and constraints set in the problem setting step, a calculation step for performing shape optimization calculation for the tire model;
From the result of the shape optimization calculation of the calculation step, at least one solution is extracted using a predetermined extraction condition, and in the cross-sectional shape of the tire model corresponding to the combination of design variables constituting the extracted solution, An extraction step of extracting at least two nodes constituting the outer contour;
A step of setting the extracted at least two of the nodes as fixed points, and creating an arc having a minimum shortest distance between each of the nodes between the fixed points;
A tire mold shape design method, comprising: outputting an outline of the tire model including at least the arc as mold shape data.   2. The tire mold shape designing method according to claim 1, wherein when creating a plurality of arcs in the creating step, at least one fixed point shares a tangent with an adjacent arc. Setting a determination condition in the objective function,
For the tire model expressed using the arc created in the creation step, the objective function set in the problem setting step is calculated,
In the tire model used in the calculation step, an error with the objective function set in the problem setting step is calculated, and if the error is within a predetermined range, the mold shape data is output in the output step And
The tire mold shape designing method according to claim 1 or 2, wherein a node to be fixed is changed if the error is outside a predetermined range.   In the creation step, when creating a plurality of arcs, a predetermined threshold is provided for the radius of curvature of the arc, and in the outline of the tire model represented by the plurality of arcs, the radius of curvature is greater than the threshold. In this case, the mold shape designing method for a tire according to any one of claims 1 to 3, wherein a straight line is formed between the fixed points for setting the arc. In the problem setting step, the objective model is expressed by a combination of a plurality of base shapes that change the shape of the tire model and includes at least the definition domain as a design variable. Set one or more
The tire mold shape design method according to claim 1, wherein the calculation step performs multi-objective optimization calculation for the tire model. About the tire, a model creation unit that creates a tire model with elements that can be numerically analyzed by a computer,
A condition setting unit for setting design variables, objective functions and constraints;
Based on design variables, objective functions, and constraint conditions related to the shape set in the condition setting unit, a calculation unit that performs shape optimization calculation for the tire model;
From the result of the shape optimization calculation of the arithmetic unit, at least one solution is extracted using a predetermined extraction condition, and in the cross-sectional shape of the tire model corresponding to the combination of design variables constituting the extracted solution, Extract at least two nodes that make up the outer contour,
Set the extracted nodes as fixed points, create an arc that minimizes the shortest distance between each fixed point between the fixed points,
A mold shape design apparatus for a tire, comprising: a mold data creation unit that outputs an outline of the tire model including at least the arc as mold shape data.   The tire mold design apparatus according to claim 6, wherein in the mold data creation unit, when creating a plurality of arcs, at least one fixed point shares a tangent with an adjacent arc. In the condition setting unit, a determination condition is set for the objective function,
For the tire model expressed using the arc created by the mold data creation unit, calculation of the objective function set by the condition setting unit is performed by the calculation unit,
The calculation unit calculates an error with the objective function set in the condition setting unit in the tire model created by the model creation unit and used for creating the arc, and if the error is within a predetermined range Output the mold shape data from the mold data creation unit,
The tire mold shape designing apparatus according to claim 6 or 7, wherein if the error is outside a predetermined range, the mold data creation unit changes a node to be fixed. When creating a plurality of arcs in the mold data creation unit, the mold data creation unit provides a predetermined threshold value for the radius of curvature of the arc in the outline of the tire model represented by the plurality of arcs. ,
The tire mold shape design according to any one of claims 6 to 8, wherein when the arc has a radius of curvature larger than a threshold value, the mold data creation unit sets a straight line between fixed points for setting the arc. apparatus. The condition setting unit is expressed by a combination of a plurality of base shapes that change the shape of the tire model, and the definition area thereof is set so as to include at least as a design variable, and an objective function related to a physical quantity of the tire model is set to at least 2 Set one or more,
The tire mold shape design apparatus according to any one of claims 6 to 9, wherein the calculation unit performs multi-objective optimization calculation for the tire model.   The program for making a computer perform as a procedure each process of the metal mold | die shape design method of the tire of any one of Claims 1-6.