JP2020067964A - Die shape design method for tire, die shape design device for tire, and program - Google Patents

Abstract

To provide a die shape design method for a tire, a program for implementing the die shape design for the tire, and a die shape design device that can efficiently calculate, as die shape data, a tire cross-sectional shape that considers a physical amount affecting an outline without deteriorating a feature of a shape satisfying a target characteristic.SOLUTION: A tire model enabling numerical analysis is created by setting a problem such as a design variable related to a tire shape. A shape optimization calculation of the tire model is performed based on the problem setting to extract a plurality of nodes forming an outline of a cross-sectional shape of the obtained tire model. An elliptic arc approximating a shape formed by connecting the plurality of nodes is created using a function expressed by a numeric expression. Then, an outline of the tire model including at least the elliptic arc is output as die shape data.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a tire modeled by a computer numerically analyzable element, a tire mold shape designing method using a shape optimization calculation result, a tire mold shape designing apparatus, and a tire mold shape. Regarding a program for executing the design method, in particular, without compromising the characteristics of the tire shape that satisfies the target characteristics, a tire mold shape designing method in which actual manufacturing constraints are added, a tire mold shape designing device, and A program for executing a tire mold shape designing method.

  At present, a method of creating a tire model or the like that can be analyzed by a computer and simulating the performance of the tire or the like has been proposed. In the performance simulation, a tire model obtained by dividing the tire into a finite number of elements is created. The optimum shape of a tire is obtained by performing an optimization calculation using a tire model composed of finite elements. Further, the shape of the tire mold is designed using the calculation result of the optimum shape of the tire.

  For example, in the tire design method of Patent Document 1, a plurality of objective functions, constraints, setting steps for setting 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 of determining a final design parameter based on a design variable giving a value. The plurality of control points enable the shapes 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. Then, the operation control points are included in the design parameters, and when the second member model is moved, the member intervals of the first and second member models are included in the design parameters based on the operation control points. 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 of Patent Document 1 also controls the position of the reinforcing layer. In Patent Document 1, it is stated that the tire cross-sectional shape formed by each control point after movement can be made into a gentle shape without being formed into a wavy shape. When a mold is manufactured using the calculation result of the optimum shape of the tire obtained by the tire designing method of Patent Document 1, the size is indicated by an arc, a straight line, or a combination of the arc and the straight line. It is desirable to adjust the outline of. However, depending on the degree of adjustment of the outline, the characteristic balance of the optimum tire shape may be impaired. In the tire designing method of Patent Document 1, the dimension of the mold is defined by using the calculation result obtained without considering the above problems, and therefore the mold shape is not sufficient.

  An object of the present invention is to eliminate the problems based on the above-mentioned conventional techniques, and to obtain a tire cross-sectional shape in consideration of a physical quantity affected by a contour line on the outer side of the tire without impairing the characteristics of the shape satisfying the target characteristics. It is to provide a program for executing a tire mold shape designing method, a tire mold shape designing apparatus, and a tire mold shape designing method that can be efficiently calculated as shape data.

In order to achieve the above-mentioned object, the first aspect of the present invention is a problem setting step for setting design variables related to a shape, an objective function, constraint conditions, optimal solution determination conditions and node extraction conditions for a tire. For the tire, a creation step of creating a tire model with a computer numerically analyzable element, the design variable set in the problem setting step, the objective function, the constraint condition, the determination condition of the optimal solution and the Based on the extraction conditions of the nodes, a calculation step of performing a shape optimization calculation on the tire model, and from the result of the shape optimization calculation of the calculation step, at least one solution is extracted using a predetermined extraction condition, An extraction process for extracting a plurality of nodes forming the outer contour in the cross-sectional shape of the tire model corresponding to the combination of design variables forming the extracted solution. When the extracted elliptical arc that approximates between said plurality of nodes was, x, and the variable y, generated using a, b, p, q, a function expressed by the equation to the x _0, y ₀ parameter A method for designing a mold shape of a tire, comprising: a creating step; and an output step of outputting the contour line of the tire model including at least the elliptical arc as mold shape data.

In the calculation step, the shape optimization calculation includes a ground contact analysis at a predetermined load, and in the extraction step, the plurality of nodes are extracted in a range from at least a tread center portion to a ground contact end of the tire model, In the creating step, it is preferable that the elliptic arc is created using the nodes in the range of the tire model.
Further, it is preferable that, in the creating step, at least one of the parameters a, b, p, q, x ₀ , and y ₀ of the function is fixed, and the remaining parameters are used to create the elliptic arc.

There is a step of setting a determination condition in the objective function, for the tire model represented by using the elliptic arc created in the creating step, the calculation of the objective function set in the problem setting 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 output in the output step. However, if the error is outside the predetermined range, it is preferable to change the extracted nodes.
In the problem setting step, it is expressed by a combination of a plurality of base shapes that change the shape of the tire model, and it is set such that the domains thereof are included at least as design variables, and an objective function relating to the physical quantity of the tire model is at least 2 It is preferable to set one or more, and in the calculation step, optimization calculation is performed for the tire model.

A second aspect of the present invention relates to a tire, including a model creation unit that creates a tire model with elements that can be numerically analyzed by a computer, design variables, an objective function, constraint conditions, optimal solution determination conditions, and node extraction conditions. A shape for the tire model based on a condition setting unit to be set, the design variable regarding the shape set by the condition setting unit, the objective function, the constraint condition, the optimum solution determination condition, and the node extraction condition. Corresponding to a combination of a calculation unit that performs an optimization calculation and at least one solution from a result of the shape optimization calculation of the calculation unit using a predetermined extraction condition, and a design variable that constitutes the extracted solution. In the cross-sectional shape of the tire model, a plurality of nodes that form the outer contour are extracted, and an elliptic arc that approximates between the plurality of nodes is defined as x and y, and a b, p, q, and x _0, y ₀ was prepared using the function expressed by the equation to the parameter, the data creation unit for outputting a contour line of the tire model which includes at least the elliptical arc as a mold shape data The present invention provides a die shape designing device for a tire, which comprises:

In the calculation unit, the shape optimization calculation includes ground contact analysis at a predetermined load, and in the data creation unit, the plurality of nodes are extracted in the range from at least the tread center to the ground contact end of the tire model, It is preferable that the elliptical arc is created using the nodes of the range of the tire model.
It is preferable that the data creation unit fixes at least one of the parameters a, b, p, q, x ₀ , and y ₀ of the function, and creates the elliptic arc using the remaining parameters.

Calculation of the objective function set by the condition setting unit with respect to the tire model expressed by using the elliptic arc created by the data creating unit by setting a judgment condition on the objective function by the condition setting unit. Is performed by the calculation unit, is created by the model creation unit, in the tire model used to create the elliptical arc, the error with the objective function set by the condition setting unit is calculated by the calculation unit, the error If is within a predetermined range, the mold shape data is output from the data creating unit, and if the error is outside the predetermined range, the data creating unit preferably changes the nodes to be extracted.
The condition setting unit is expressed by a combination of a plurality of base shapes that change the shape of the tire model, and is set so as to include at least the domains thereof as design variables, and an objective function relating to the physical quantity of the tire model is at least 2 It is preferable to set one or more, and the computing unit performs optimization calculation for the tire model.

  A third aspect of the present invention provides a program for causing a computer to execute each step of the tire mold shape designing method of the first aspect of the present invention as a procedure.

  According to the present invention, it is possible to efficiently calculate, as mold shape data, a tire cross-sectional shape that considers a physical quantity that is affected by the contour line on the outside of the tire without impairing the characteristics of the shape that satisfies the target characteristics.

FIG. 1 is a schematic diagram showing a tire mold shape designing device used in a tire mold shape designing method according to an embodiment of the present invention. It is a flowchart which shows the 1st example of the metal mold | die shape design method of the tire of embodiment of this invention in order of process. (A) is a schematic diagram showing an example of a tire model used for a tire mold shape designing method of an embodiment of the present invention, (b) is a schematic diagram showing an example of a method of creating an elliptic arc, (c) [Fig. 4] is a schematic diagram showing another example of a method of creating an elliptic arc. It is a schematic diagram which shows the grounding area of the tire model used for the tire mold shape designing method of the embodiment of the present invention. It is a schematic diagram which shows the 1st example of an elliptic arc based on the metal mold shape designing method of the tire of embodiment of this invention. It is a schematic diagram which shows the 2nd example of an elliptic arc based on the metal mold shape designing method of the tire of embodiment of this invention. It is a flowchart which shows the 2nd example of the tire mold shape designing method of the embodiment of this invention in process order. It is a flowchart which shows the 3rd example of the tire mold shape designing method of the embodiment of this invention in process order. (A) is a schematic diagram showing a tire model of a reference shape, (b) is a schematic diagram showing a tire model of a first base profile, and (c) is a schematic diagram showing a tire model of a second base profile. It is a figure. (A) is a schematic diagram showing a contact pressure distribution of Example 1, and (b) is a schematic diagram showing a contact pressure distribution of Comparative Example 1.

  Hereinafter, based on a preferred embodiment shown in the accompanying drawings, a tire mold shape designing method of the present invention, a tire mold shape designing device, and a tire mold shape designing method for executing the method on a computer or the like. The program will be described in detail.

[Tire mold shape design device]
FIG. 1 is a schematic diagram showing a tire mold shape designing apparatus used in a tire mold shape designing method according to an embodiment of the present invention.
The tire mold shape designing apparatus 10 shown in FIG. 1 is used to execute the tire mold shape designing method of the present embodiment. Hereinafter, the tire mold shape designing device 10 is simply referred to as the designing device 10.

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

The designing device 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 to this, a ROM and the like are provided although not shown.
The processing unit 12 is controlled by the control unit 32. Further, 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, and the condition setting unit 20, the model creation unit 22, the calculation unit 24, and the data creation. The data of the unit 26 is stored in the memory 28.
In the tire mold shape designing method described below, various processing is performed by each unit of the processing unit 12. In the following description, description of various processes performed by the control unit 32 in each unit of the processing unit 12 is omitted, but the control unit 32 controls a series of processes in each unit. The memory 28 also stores various determination conditions described later. The control unit 32 reads the determination condition from the memory 28, compares the determination condition 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 such as a mouse and a keyboard for inputting various information according to an operator's instruction. The display unit 16 displays, for example, results obtained by the tire mold shape designing method, and various known displays are used. The display unit 16 also includes a device such as a printer for displaying various information on an output medium.

  The designing device 10 causes the control unit 32 to execute a program (computer software) stored in a ROM or the like, so that the condition setting unit 20, the model creating unit 22, the computing unit 24, and the data creating unit 26 function. Form. As described above, the designing device 10 may be configured by a computer in which each part functions by executing a program, or may be a dedicated device in which each part is configured by a dedicated circuit.

The tire mold shape designing method of the present embodiment, the tire cross-sectional shape in consideration of the physical quantity influenced by the outer contour of the tire is efficiently treated as mold shape data without impairing the characteristics of the shape satisfying the target characteristics. It is intended to calculate, and relates to a mold shape data creation method using a computer.
In the tire mold shape designing method, an optimum shape is acquired from a shape change having a degree of freedom in advance, and then a process for smoothing the outline is performed, so that a more optimum solution can be acquired. Therefore, it is possible to efficiently calculate, as the mold shape data, the tire cross-sectional shape in consideration of the physical quantity affected by the contour line on the outer side of the tire without impairing the characteristics of the shape satisfying the target characteristics. This makes it possible to obtain mold shape data that does not impair the tire shape characteristics that satisfy the target characteristics.

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

In the condition setting unit 20, a plurality of parameters defined as design variables among the parameters defining the tire and the material forming the tire are set. It should be noted that as parameters of the design variables, variation factors such as loads and boundary conditions, and in the case of products, constraint conditions such as size and mass may be set.
In addition, a plurality of parameters defined as characteristic values (objective functions) are set among the parameters that define the tire and the material forming the tire. As the characteristic value, an index for evaluating the tire and the material forming the tire other than the physical and chemical characteristic values such as cost may be used.
The tire and the material forming the tire may be not only the tire itself, but also the entire system including the tire, such as the parts forming the tire and the tire assembly form, or a part thereof.

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 has a large value, a small value, or a value approaching a predetermined value. Regarding the objective function, in addition to the preferred direction described above, there is also an unfavorable direction opposite to the preferred direction.
The objective function is a characteristic value of the tire. In this case, the characteristic value is a physical quantity that is 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 index of steering stability, and an index of riding comfort. Examples include the primary natural frequency of the tire, rolling resistance as an index of fuel efficiency, lateral spring constant as an index of steering stability, and wear energy of the tire tread part as an index of wear resistance. In addition to these, examples of physical quantities of tires include shape and dimensional values. The shape is, for example, a sectional shape. The dimension value is, for example, the width of the tire, the outer diameter of the tire, or the like. Examples of physical quantities of tires include the amount of deflection, ground pressure, rolling resistance, and cornering characteristics in addition to the shape or dimensional value.

The design variables define the shape of the tire, the internal structure of the tire, the material properties, and the like. The design variables are a plurality of parameters among the material behavior of the tire, the shape of the tire, the sectional shape of the tire, the natural vibration mode of the tire, and the structure of the tire. Design variables include, for example, the radius of curvature that defines the crown shape of the tread portion of the tire, the belt width dimension of the tire that defines the tire internal structure, and the like. In order to obtain mold shape data, the design variables are preferably related to the tire shape.
The constraint condition is a condition for the value of the objective function to satisfy a predetermined range, and a condition for the value of the design variable to satisfy the predetermined range.
Further, the load load of the tire, running conditions including the rolling speed of the tire, road surface conditions on which the tire runs, for example, uneven shape, friction coefficient, etc., information of vehicle specifications for use in vehicle running simulation, etc. Is set.

Further, the condition setting unit 20 is set with information for defining a non-linear response relationship between a plurality of types of design variables and a plurality of types of characteristic values. This non-linear response relationship includes, for example, numerical simulations such as FEM (finite element method) and theoretical formulas.
The condition setting unit 20 sets a model generated by a non-linear response relationship, a boundary condition of the model, a simulation condition and a constraint condition in the simulation when performing a numerical simulation such as FEM.

Furthermore, the conditions for determining the optimum solution are set. The optimum solution determination condition is, for example, an optimization condition for obtaining a Pareto solution, a condition for searching a Pareto solution, or the like. The conditions for the Pareto solution search are the method for searching the Pareto solution and various conditions in the Pareto solution search.
In this embodiment, for example, a genetic algorithm (GA) can be used as a method for searching a Pareto solution. It is generally known that the search ability of a genetic algorithm decreases as the characteristic value (objective function) increases. One of the ways to solve it is to increase the number of individuals.
In addition to this, the domain of the design variable 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, a discrete level value is set for each design variable, and for the remaining design variables, the domain is set as a constant and the combination of design variables is changed by the computer. However, the characteristic value may be calculated and the Pareto solution described below may be extracted.
Further, the extraction condition of the node is set in the condition setting unit 20. The extraction conditions of the nodes are, for example, the number of nodes to be extracted, the range of extracting the nodes, and the like.

  Regarding the shape optimization calculation, the output value is calculated while changing the input variables according to the optimization algorithm such as the method of sequentially searching using the nonlinear relationship (response surface) between the input variable and the output variable and the evolution calculation method. Either method may be used.

  The model creating unit 22 creates a tire model that is modeled by elements that can be numerically analyzed by a computer. The model creating unit 22 creates various calculation models based on the set nonlinear response relationship. As described above, the non-linear response relationship includes numerical simulation such as FEM. In this case, the model creating unit 22 generates a mesh model corresponding to design parameters representing design variables and characteristic value parameters representing characteristic values. To be done. Also, in the case of theoretical formulas and the like, theoretical formulas and the like corresponding to design parameters and characteristic value parameters are created. The calculation unit 24 performs simulation calculation using the tire model.

The tire model created by the model creating unit 22 is created using each type of design parameter set by the condition setting unit 20, but a known creating method can be used to create the tire model. . Note that the tire model also generates at least a road surface model that is a target for rolling the tire model. A tire model may be one that reproduces the rim on which the tire is mounted, the wheel, and the tire rotation axis. Further, if necessary, a model that reproduces the vehicle in which the tire is mounted may be incorporated in the tire model. At this time, it is also 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 a preset boundary condition.
Further, the form of the tire model used for the analysis is not particularly limited, and may be a smooth tire having no groove, only a main groove or having a pattern.

The tire model created by the model creating unit 22 is created using each type of design parameter set by the condition setting unit 20, but a known creating method can be used to create 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 include, for example, a quadrilateral element in a two-dimensional plane, a tetrahedral solid element in a three-dimensional body, a solid element such as a pentahedral solid element, and a hexahedral solid element, a shell such as a triangular shell element, and a quadrangular shell element. Elements that can be analyzed by computer, such as elements and surface elements. In the analysis process, the elements thus divided are specified one by one using the three-dimensional coordinates in the three-dimensional model and the two-dimensional coordinates in the two-dimensional model.

  Each of these models may be a discretized model that can be numerically calculated, and may be, for example, a finite element model for use in a known finite element method (FEM). In addition to the road surface model and the tire model, for example, when a tire design proposal for optimizing tire performance including tire wet performance is obtained using the tire model, inclusions existing on the road surface are reproduced. All you have to do is create a model. For example, as the inclusion model, various models that reproduce water, snow, mud, sand, gravel, ice, etc. on the road surface may be generated as numerically discretized models. The road surface model is not limited to a model that reproduces a road surface having a flat surface, but may be a model that reproduces a road surface shape having irregularities on the surface as necessary.

The calculation unit 24 optimizes the shape of the tire model created by the model creation unit 22 based on the design variables related to the shape set by the condition setting unit 20, the objective function, the constraint conditions, the optimum solution determination conditions, and the node extraction conditions. The calculation is performed. As a result, the 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 by executing a subroutine using a known finite element solver, for example.
The calculation unit 24 calculates the output value (sampling point) in the characteristic value space configured by the values of the plurality of types of design variables and the characteristic value, using the nonlinear response relationship. In addition, the calculation unit 24 creates an approximate model (metamodel) using the design variable and the output value (sampling point) and using the characteristic value that is the output value as the objective function.
The above-mentioned approximate model (metamodel) is a mathematical model that approximates the input / output relationship, and various input / output relationships can be approximated by adjusting the parameters. A polynomial model, Kriging, a neural network, a radial basis function, etc. can be used for the above-mentioned approximate model, for example.

  The calculation unit 24 also executes the shape optimization calculation using the approximate model. It is also one in which the solution (which may include a Pareto solution) extracted from the shape optimization calculation result by the data creating unit 26 is used to execute the actual calculation by using the defined non-linear relation. In addition to this, the calculation unit 24 also applies a boundary condition to a tire model represented by a combination of design variables by using a 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. Examples of the genetic algorithm include, for example, DRMOGA (Divided Range Multi-Objective GA) and NCGA (Neighborhood Cultivation GA) in which a solution set is divided into a plurality of regions along an objective function and a multi-objective GA is performed for each of the divided solution sets. , A known method 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) method. You can

The calculation unit 24 searches for a Pareto solution from the shape optimization calculation result using the approximate model obtained by the calculation unit 24 according to the Pareto solution search condition set by the condition setting unit 20, and finds the Pareto solution. It is also something to extract. The obtained Pareto solution is stored in the memory 28.
Here, the Pareto solution cannot be said to be superior to other arbitrary solutions in a plurality of characteristic values (objective functions) that are in a trade-off relationship, but a solution that does not have a better solution does not exist. Say. Generally, there are a plurality of Pareto solutions as a set. The Pareto ranking method is used to search for Pareto solutions, for example.

  The computing unit 24 performs selection using, for example, vector evaluated genetic algorithms (VEGA), Pareto ranking method, or tournament method. Other than the genetic algorithm (GA), for example, the annealing method (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 by using the design variable is not limited to the simulation such as FEM, but is described above. A theoretical formula or the like can also be used.

The data creation unit 26 extracts at least one solution from the result of the shape optimization calculation of the calculation unit 24 using a predetermined extraction condition. Further, in the cross-sectional shape of the tire model that corresponds to the combination of design variables that form the extracted solution, a plurality of nodes that form the outer contour of the tire model are extracted. An elliptic arc that approximates between the extracted plurality of nodes is created using a function represented by the following mathematical expression, where x and y are variables and a, b, p, q, x ₀ , and y ₀ are parameters. Further, the contour line of the tire model including at least the elliptic arc is output as mold shape data. Details of a method of creating an elliptic arc will be described later.
The parameter a in the following mathematical formula indicates the radius in the x-axis direction, and the parameter b indicates the radius in the y-axis direction. The parameters p and q indicate the order. The parameter x ₀ indicates the x coordinate of the center of the elliptical arc, and the parameter y ₀ indicates the y coordinate of the center of the elliptical arc.

The contour line is an outer line from a bead toe on one side to a bead toe on the opposite side from a bead toe on a tire cross section orthogonal to the equatorial plane of the tire.
The mold shape data is dimensional data indicating the length of a straight line forming the outline, the curvature of the curve, the position coordinates of the straight line, and the position coordinates of the curve. Specifically, for example, it is dimensional data required when a die is manufactured using an NC processing machine. The mold shape data may be the shape of a tire model other than the dimension data, and in this case, the tire model may be modeled by a numerically analyzable element.

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 value of the characteristic value and the result of the shape optimization calculation of the tire model 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 information input via the input unit 14, the tire model, the result of numerical calculation, and the optimum solution. For example, the tire model and the result of the shape optimization calculation of the tire model 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 designing method described below, including the model creation unit 22, the calculation unit 24 of the processing unit 12, And the data creation unit 26.
In the designing device 10, in the input file for changing the shape or structure, the common portion such as the boundary condition and the analysis step and the different portion depending on the individual shape such as the nodal coordinate value, the arrangement angle of the reinforcing material and the initial tension are divided. However, by automating using a file format that can be captured in the common part, that is, by including individual information as an include file, it is possible to easily study the tire shape even when considering many tire shapes. It is possible.

[First Example of Tire Mold Design Method]
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. FIG. 3A is a schematic diagram showing an example of a tire model used in the tire mold shape designing method of the embodiment of the present invention, and FIG. 3B is a schematic diagram showing an example of an elliptic arc creating method. (C) is a schematic diagram which shows the other example of the preparation method of an elliptic arc.

First, as shown in FIG. 2, optimization conditions such as design variables, characteristic values (objective function), and constraint conditions are set for the tire (step S10). Further, in step S10 (problem setting step), optimal solution determination conditions and node extraction conditions are also set. For example, the tire may be a tire having a size of 195 / 65R15.
As the design variable, for example, a design variable that changes the shape of the tire or the sectional shape of the tire is set. The method of setting the design variable is not particularly limited, and for example, the design value of the design variable is set using the Latin hypercube method (Latin hypercube method).
The characteristic values include, for example, tire rigidity, ground pressure, rolling resistance, air resistance, cornering performance, friction energy, and the like as physical characteristics of the tire. For example, two tire physical characteristics of the first characteristic value and the second characteristic value are set as the objective function. The characteristic value set as the objective function may be 1, or 3 or more.

The design variables (input parameters) are parameters of the tire cross-sectional shape, and the characteristic values (output parameters) are two characteristic values that are the tire physical characteristics. The parameter of the sectional shape of the tire and two characteristic values are set in the condition setting unit 20.
In this embodiment, an approximate model is created by the tire mold shape designing method under such setting conditions. A change in the first characteristic value and the second characteristic value depending on the value of the parameter of the sectional shape of the tire is obtained.
Using the information set in the condition setting section 20, the model creating section 22 creates a tire model, for example, a tire model such as a mesh model, using elements that can be numerically analyzed by a computer (creating step).

  Next, the 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 the design variable and the characteristic value is determined. The type of the non-linear response is stored in the memory 28, for example. For example, the relationship between the parameter of the tire cross-sectional shape and the first characteristic value and the second characteristic value is set. When the parameters of the tire cross-sectional shape are 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 parameter of the tire sectional shape as a variable. It is expressed using a non-linear function such as a polynomial. The second characteristic value is expressed using a non-linear function such as a polynomial having a parameter of the tire cross-sectional shape as a variable.

Next, using the non-linear 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, the sampling calculation for calculating the characteristic value that is the output when the design variable is input is executed.
Next, an approximate model is created using the output values obtained by the sampling calculation. That is, the relationship between the design variable and the characteristic value is represented by an approximate model.
Next, the calculation unit 24 executes the shape optimization calculation using the approximate model (step S12).
Regarding the shape optimization calculation in step S12 (computation step), the output value is calculated while sequentially changing the input variables according to a method of searching using a nonlinear relationship (response surface) between the input variables and the output variables or the optimization algorithm. Either of these methods may be used. The shape optimization calculation is also called a 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 (extraction step), the shape (extracted shape) corresponding to the combination of the design variables forming the solution is extracted from the result of the shape optimization calculation, and the tire model 50 (see FIG. 3A) is obtained. You can
In step S14, as the extraction condition to be set, the Pareto solution search unit may extract the Pareto solution to obtain the Pareto solution. Further, not limited to Pareto solutions, solutions may be extracted from all individuals (solutions) using characteristics other than the objective function as constraints.

Next, in the cross-sectional shape of the tire model 50 (see FIG. 3A) corresponding to the combination of design variables that form the extracted solution, a plurality of nodes that form the outer contour are extracted (step S16). In step S16 (extracting step), for example, as shown in FIG. 3B, five points of a node 52a, a node 52b, a node 52c, a node 52d, and a node 52e are extracted.
It is preferable that the plurality of nodes extracted on the outer contour, that is, the plurality of nodes extracted on the outline of the extracted shape, include the nodes at the typical positions of the tire. Taking the tire cross-sectional shape as an example, it is a cap tread center position (tread center part), a tire maximum width position, a tread development width position, a mold dividing position, a bead toe part, a bead heel part, and the like. It should be noted that the extracted plurality of nodes may be the nodes at the representative positions that are not changed, and other nodes may be corrected on the approximate curve, or all the extracted nodes may be corrected on the approximate curve. .

Next, the elliptic arc that approximates the extracted plurality of nodes is calculated by using the above-described function represented by the above mathematical expression with x and y as variables and a, b, p, q, x ₀ , and y ₀ as parameters. Are created (step S18).
In step S18 (creation step), specifically, an elliptic arc 58 that approximates the five extracted nodes 52a, 52b, 52c, 52d, and 52e as shown in FIG. 3B is created. . Note that O (x ₀ , y ₀ ) in FIG. 3B is the center of the elliptic arc 58.
The elliptic arc 58 is an approximation of the five extracted nodes 52a, 52b, 52c, 52d, and 52e, but the elliptical arc 58 and the extracted five nodes 52a, 52b, 52c, and 52c The smaller the distance δ (residual difference) from each of 52d and the node 52e, the higher the accuracy of approximation. It is preferable that the elliptic arc 58 has a high approximation accuracy.
The approximation method is not particularly limited. For example, paying attention to the distance between the node and the elliptic arc, the method of minimizing the residual sum of squares like the least-squares method, and the ellipse arc whose distance δ (residual) at each node has the smallest maximum value. And the like.

For example, as shown in FIG. 3C, an elliptic arc 58 having a minimum distance δ (residual difference) from the four extracted nodes 56a, 56b, 56c and 56d is created. Specifically, it is an elliptic arc that satisfies the following formula. Note that the distance δ (residual error) is not particularly limited, but is defined using the Euclidean distance, the Manhattan distance, or the axial component of the distance (either one of the two orthogonal components of the distance). It is preferable.
In the following formula, r _i is the distance from the center O (x ₀ , y ₀ ) of the elliptic arc 58 to each node 56a to 56d, and r is the distance to the center O (x ₀ , y ₀ ) of the elliptic arc and each node. Is the distance to the intersection of the elliptic arcs.

Regarding the elliptic arc 58, for example, the two nodes 52 and 54 may be fixed points, and the elliptic arc 58 that satisfies the above-described mathematical expression may be searched between the two fixed points. In this case, the elliptic arc 58 may be searched while sequentially changing the values of the parameters a, b, p, q, x ₀ , y ₀ , and one of the fixed points may be the major axis or the minor axis of the ellipse. At least one of the values of the parameters a, b, x ₀ , and y ₀ may be fixed so as to be located on the axis, and the search may be performed while changing the remaining parameters and the values of the parameters p and q.
Although fixed points are not provided for the five nodes 52a to 52e in FIG. 3B, the present invention is not limited to this. For example, elliptic arcs may be created with the nodes at both ends as fixed points. .

  In addition, in the created elliptic arc, if there are circumferential grooves on the tire cross-sectional shape including the target node and it is divided into multiple land parts, the mold shape that was output in consideration of heat shrinkage during manufacturing The heat shrinkage calculation may be performed based on the above, and the obtained result may be used to correct the land shape of each tread to a swollen line at the end of step S18. Specifically, the elliptical arc created above is defined as positive, and the curve that bulges outside the elliptical arc to the outside of the tread and passes through both ends of the land is defined as a function parametrically to minimize the difference from the line after heat shrinkage calculation. The corrected line is defined by incorporating the search for the parameter to be performed into the optimization algorithm and causing the computer to perform the search.

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

Further, the shape optimization calculation (step S12) by the calculation unit 24 may include a ground contact analysis under a predetermined load.
Here, FIG. 4 is a schematic diagram showing a ground contact area of a tire model used in the tire mold shape designing method of the embodiment of the present invention.
In the data creation unit 26, as shown in FIG. 4, a plurality of nodes are extracted from at least the tread central portion 60 of the tire model 50 to the ground contact end 62 (step S16), and at least the tread central portion 60 of the tire model 50 is extracted. It is also possible to create an elliptic arc by using the nodes in the range up to the ground contact end 62.
As shown in FIG. 4, the range from the tread central portion 60 of the tire model 50 to the ground contact end 62 is the ground contact area 64.
In this way, a plurality of elliptic arcs are connected by defining the extraction range for extracting the nodes as the grounding area 64, finding the area to be grounded in advance by calculation, and creating the outer contour line of the tread with one elliptic arc. Is unnecessary, and the adverse effect on the tire characteristics due to the connection point between the arcs can be improved. Therefore, the ground area 64 is preferably approximated by one elliptic arc.

In the tire model 50 shown in FIG. 4, the nodes of the tread central portion 60 and the ground contact end 62 are fixed, and the contour line (tread contour) of the ground contact region 64 is smoothed by an elliptic arc as the fixed point. The part 60 does not have to have a node (fixed point). For example, no node (fixed point) may be provided at a position symmetrical about the tread central portion 60. If the grounding end 62 is included in the elliptic arc, the grounding end 62 does not have to be a node (fixed point).
In the ground contact analysis for a given load, the load is not particularly limited, but, for example, a load equivalent to the maximum load capacity, a load considering the safety factor, or a value equivalent to the axial load of the specified vehicle should be given. Is mentioned.

The tread central portion 60 is a position where the tire cross-section height passing through the tire equatorial plane CL is maximum in the cross-sectional shape of the tire model 50 orthogonal to the tire equatorial plane CL.
The tire equatorial plane CL is a plane that is orthogonal to the rotation axis (not shown) of the tire model 50 and that passes through the center of the tire width of the tire model 50.

It is preferable that the data creation unit 26 fixes at least one of the parameters a, b, p, q, x ₀ , and y ₀ of the above function, and creates an elliptic arc using the remaining parameters. As a result, the number of parameters for creating the elliptic arc can be reduced, that is, the degree of freedom can be reduced and the efficiency of the calculation for creating the elliptic arc can be improved. Note that fixing the parameter means making the parameter a constant.
FIG. 5 is a schematic view showing a first example of an elliptical arc based on the tire mold shape designing method of the embodiment of the present invention, and FIG. 6 is an elliptic arc based on the tire mold shape designing method of the embodiment of the present invention. It is a schematic diagram which shows the 2nd example of. 5 and 6, the same components as those of the tire model 50 shown in FIG. 4 are designated by the same reference numerals, and detailed description thereof will be omitted.
In the elliptic arc 70 shown in FIG. 5, the center O is fixed, and among the parameters a, b, p, q, x ₀ , y ₀ , the parameters b, x ₀ , y ₀ are constants, and the parameters a, p , Q are created by changing the values of q.
The elliptical arc 70 in FIG. 5 approximates the ground area 64 between the tread center 60 and the ground edge 62. Reference numeral 63 indicates a node of the tread central portion 60, and reference numeral 65 indicates a node of the ground contact end 62. In the elliptic arc 70, the parameter b is the value of the distance from the center O to the node 63 of the tread central portion 60. The parameters p and q and the parameter a are adjusted so as to approximate the ground area 64. The elliptical arc 70 can be created using the above-described approximation method.
When the tire cross-sectional shape of the tire model 50 is symmetrical about the tire equatorial plane CL, the center O of the elliptic arc is preferably on the tire equatorial plane CL. In FIG. 5, the center O of the elliptic arc 70 is on the tire equatorial plane CL.

The elliptic arc 70 in FIG. 5 is obtained by changing the values of the parameters a, p, and q, but is not limited to this. For example, among the parameters a, b, p, q, x ₀ , y ₀ , the parameters a, b may be constants and the values of the parameters p, q may be changed. In this case, if the parameters a and b are constants, the center O (x ₀ , y ₀ ) is fixed, and, for example, the elliptic arc 72 shown in FIG. 6 is created. In FIG. 6, the center O of the elliptic arc 72 is on the tire equatorial plane CL.
In the elliptic arc 72, the parameter a is the value of the distance from the center O to the node 67 at the maximum width position 66 of the tire. The parameter b is the value of the distance from the center O to the node 63 of the tread central portion 60. The parameters p and q are adjusted so as to approximate the ground area 64. The elliptical arc 72 can be created using the above-described approximation method.
In this case, instead of minimizing the residual sum of squares of all the nodes between the fixed points and the elliptic arc, weights may be given so as to improve the accuracy of some areas. For example, a method of fixing the position represented by the parameter a to the maximum width position and calculating the values of p and q at which the residual sum of squares between the tread central portion 60 and the ground contact end 62 (ground contact region 64) is the minimum is calculated. You may use.
When the parameters a and b are constants, the parameters a and b are the tire equatorial plane CL, the maximum width represented by the maximum length in the tire width direction, and the tire radial direction from the bead bottom surface to the tire maximum width position. It is specified by the distance (SDH).

  Further, in the above-mentioned function, the domain of the orders of the parameters p and q is not particularly limited, but in order to improve the search efficiency, it is desired to constrain the center of the elliptic arc to the inside of the extracted node group, that is, the axis center side. In this case, it is preferable to give constraint conditions such that p> 1 and q> 1. If the center of the elliptic arc is outside the group of nodes, an asteroid curve may be used. The asteroid-like curve is obtained by giving constraints such that p <1 and q <1.

[Second Example of Tire Mold Design Method]
Next, a second example of the tire mold shape designing method of the present embodiment will be described.
FIG. 7 is a flowchart showing a second example of the tire mold shape designing method of the embodiment of the present invention in the order of steps.
In the second example of the tire mold shape designing method, detailed description of the same steps as those in the first example of the tire mold shape designing method will be omitted. Note that, hereinafter, the second example of the tire mold shape designing method will be simply referred to as the second example.

  The second example is different from the first example of the tire mold shape designing method in that the target characteristics of the modified tire model represented by the elliptic arc are verified, and the other steps are the same. Since it is the same as the first example of the die shape designing method, detailed description thereof will be omitted.

In the second example, a step (step S22) of calculating the objective function set in the problem setting step is performed for the tire model represented by using the elliptic arc created in step S18, that is, for the corrected tire model. Have.
Further, in the tire model used for the shape optimization calculation, the difference between the objective function set in the problem setting process and the objective function set in the corrected tire model in the problem setting process is calculated, and the error is calculated. It has a process (step S24).
If the error does not satisfy the predetermined determination condition (step S26), that is, if the error is outside the predetermined range, a plurality of nodes are extracted again (step S16). An elliptic arc is created again using the extracted nodes (step S18), the objective function is calculated (step S22), the error is calculated (step S24), and it is determined whether the error satisfies a predetermined determination condition (step S26). ) Is repeated.
If the error satisfies a predetermined determination condition (step S26), the outer shape line of the tire model including at least the elliptic arc obtained in step S18 is output as mold shape data (step S30), and the other points are different. Since the steps are the same as those in the first example of the tire mold shape designing method, detailed description thereof will be omitted. When incorporating the step of correcting the bulging shape in consideration of the thermal contraction in the first example, it is preferable to set it to be executed after the determination condition of step S26 is satisfied.

In step S22, the objective function set in the question setting step is calculated by FEM analysis using the tire model including at least the elliptic arc. When a plurality of objective functions are set, at least one objective function may be calculated.
In step S24, the shape optimization calculation is performed in step S12, and the objective function set in the question setting step is calculated. Therefore, the calculation results of the objective functions in step S12 and step S22 are compared to obtain the error.
In step S26, the allowable error is preset according to the objective function, and this allowable error is compared with the error obtained in step S24. If the error obtained in step S24 is smaller than the set allowable error, that is, if the error is within the predetermined range, the contour line data of the tire model including at least the elliptic arc is output as the mold shape data. (Step S30).

In the second example, when the change in the target characteristics becomes large due to the change in the tire shape before and after the formation of the elliptic arc, the range of the plurality of nodes to be extracted and the number of the nodes are changed to impair the target characteristics. It is possible to extract mold shapes without
Note that changing a plurality of extracted nodes is synonymous with changing the range approximated by an elliptic arc.

[Third Example of Tire Mold Design Method]
Next, a third example of the tire mold shape designing method will be described.
FIG. 8 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. 9A is a schematic diagram showing a tire model having a reference shape, FIG. 9B is a schematic diagram showing a tire model having a first base shape, and FIG. 9C is a tire model having a second base shape. It is a schematic diagram which shows.
In the third example of the tire mold shape designing method, detailed description of the same steps as those in the first example of the tire mold shape designing method will be omitted. Hereinafter, the third example of the tire mold shape designing method will be simply referred to as the third example.

In the third example, as compared with the first example of the tire mold shape designing method, before the optimization calculation is executed (step S50), the shape of the tire model is different from the reference shape. Is expressed by a combination of base shapes of (steps S40 and S42), and the domains thereof are set to include at least the design variables (step S44), and at least two or more objective functions regarding the physical quantity of the tire model are set (step S44). S46) is 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 die shape designing method. Detailed description is omitted.
In the third example, for the steps S40 to S48 described above, for example, the methods described in JP2013-189160A and JP2013-191146A can be appropriately used. Further, steps S40 to S48 described above correspond to step S10 of the first example.

In the third example, first, the tire model 100 having the reference shape shown in FIG. 9A is set (step S40). The 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 S42). The base shapes are, for example, the first base shape tire model 102 shown in FIG. 9B and the second base shape tire model 104 shown in FIG. 9C. 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. The number of base shapes is not limited to two as long as it is plural, and needless to say, 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 by elements that can be numerically analyzed by a computer.

Next, the domain of the design variable 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 the difference (displacement) between the position coordinates of the nodes of the base shape and the position coordinates of the corresponding nodes of the reference shape. The weighted addition means weighted addition using the value of the weight strength for the changed portion of each base shape, that is, changing the amount of change. The weighted addition also includes a weighted average obtained by dividing the weighted addition result of the base shape by the sum of the weight strength values used. When creating the trial cross-sectional shape, a weight strength value is given to each of the base shapes. The value of the weight strength is set by the condition setting unit 20. As the value of the weight strength, for example, a known experiment design method, specifically, a design matrix such as a Latin hypercube or an orthogonal table is used to set the value of the weight strength.
The value of the weight strength may be set according to the design matrix or may be changed sequentially within a predetermined range, and the tire cross-sectional shape is created each time the value of the weight strength is changed. In both cases, the tire cross-sectional shape is created by changing the value of the weight strength so as to cover the entire set range evenly. The value of the weight strength is discretely changed so as to be larger or smaller for each fixed size, but the value of the weight strength may be randomly changed.

Next, the 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, the width of the tire, the outer diameter of the tire, the amount of deflection, the contact pressure, the rolling resistance, the cornering characteristics, and the like.
Since the setting of the objective function is the same as the setting of the objective function in step S10 of the first example, detailed description thereof will be omitted.
Next, a non-linear function is set (step S48). Since the setting of the non-linear function is the same as the setting of the non-linear function in step S10 of the first example, detailed description thereof will be omitted.

Next, using the non-linear response relationship set in step S48, the output value in the characteristic value space composed of the values of the plurality of types of design variables and the characteristic value is calculated. That is, the sampling calculation for calculating the characteristic value that is the output when the design variable is input is executed. An approximate model is created using the output values obtained by the sampling calculation. That is, the relationship between the design variable and the characteristic value is represented by an approximate model. Next, the calculation unit 24 executes the optimization calculation using the approximate model (step S50).
The optimization calculation (step S50) 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 set objective functions are different, and therefore detailed description thereof is omitted. .
At least one solution is extracted from the result of the optimization calculation under a predetermined extraction condition (step S52). Since step S52 is the same as extracting at least one solution from the result of the shape optimization calculation using a predetermined extraction condition (step S14), detailed description thereof will be omitted.

Next, in the cross-sectional shape of the tire model corresponding to the combination of the design variables that form the extracted solution, a plurality of nodes that form the outer contour are extracted (step S54). Since step S54 is the same as the extraction of the plurality of nodes (step S16) in the first example, detailed description thereof will be omitted.
Next, the elliptic arc that approximates the extracted plurality of nodes is calculated by using the above-described function represented by the above mathematical expression with x and y as variables and a, b, p, q, x ₀ , and y ₀ as parameters. Are created (step S56). Since step S56 is the same as the elliptic arc creation (step S18) of the first example, detailed description thereof will be omitted.
Next, the outer shape line of the tire model including at least the elliptic arc is output as mold shape data (step S58). In this way, the mold shape data necessary for the tire mold shape design can be obtained.
As described above, steps S50 to S58 are steps corresponding to steps S12 to S20 of the first example.

According to the third example, the optimum tire shape can be obtained by combining the tire shapes. Even in the case of combining tire shapes, it is possible to obtain mold shape data required for tire mold shape design.
Further, according to the third example, by searching for the tire optimum shape by excluding the constraint of the outline, the tire shape satisfying the target characteristics can be obtained from a wide design space, and the actual manufacturing restrictions can be reduced. A tire cross-section shape that takes into consideration, for example, a tire cross-section shape that does not deteriorate the characteristics caused by ground contact, for example, the mold size of the tire cross-section shape that does not deteriorate the characteristics caused by ground contact, using a computer, etc. Can be calculated efficiently.

Also in the third example, the error may be verified for the elliptic arc obtained in step S56 as in the second example.
Also in the third example, a plurality of nodes for obtaining an elliptic arc may be changed as in the second example.
Incidentally. In each of the tire mold shape designing methods of the first to third examples described above, a computer that executes the tire mold shape designing method can cause a computer to execute each step as a procedure.

  The present invention is basically constructed as described above. The tire mold shape designing method, the tire mold shape designing apparatus, and the program of the present invention have been described above in detail, but the present invention is not limited to the above-described embodiments 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 Example 1 described below.

  In this example, a tire model (not shown) having no groove in the tread was used to create Example 1 and Comparative Example 1. The shape of the tire model including the outer contour is obtained by performing shape optimization calculation. In the tire model, the shape of the rim contact portion remains unchanged so that the contact optimization does not occur, and the shape optimization calculation is performed. Further, Example 1 and Comparative Example 1 are different only in the method of correcting the outline, and use the same result as the original shape.

Example 1 is the one in which the tire mold shape designing method of the present invention is applied to a tire model having no groove in the tread portion, and an outer shape line of the tire model is created using an elliptic arc.
In Comparative Example 1, the outer shape line of the tire model was created by combining a tire model having no groove in the tread portion with two types of arcs sharing a tangent line at the connection portion.
As described above, in Example 1, the contour line is configured by an elliptic arc, and in Comparative Example 1, the contour line is configured by combining two types of arcs. Example 1 and Comparative Example 1 are tire model models. The configuration is the same except that the outlines are different, and the FEM analysis has the same configuration except that the outlines of the tire models are different.

FEM analysis was performed on Example 1 and Comparative Example 1, the ground pressure was calculated, and the ground pressure distribution was also obtained. The results are shown in FIGS. 10 (a) and 10 (b). FIG. 10A is a schematic diagram showing the contact pressure distribution of Example 1, and FIG. 10B is a schematic diagram showing the contact pressure distribution of Comparative Example 1. The left-right direction of the drawings in FIGS. 10A and 10B is the tire width direction.
Moreover, the average ground pressure was calculated from the ground pressure. The results are shown in Table 1 below.
The longitudinal rigidity, lateral rigidity, circumferential rigidity, and wear life of Example 1 and Comparative Example 1 were determined by FEM analysis. The results are shown in Table 1 below. The numerical values of longitudinal rigidity, lateral rigidity, circumferential rigidity, average ground pressure, and wear life in Table 1 below are shown as indices with Comparative Example 1 as 100. Numerical values of longitudinal rigidity, lateral rigidity, circumferential rigidity and wear life preferably exceed 100. The average ground pressure is preferably less than 100.

As shown in Table 1 above, in Example 1, high wear life could be obtained while maintaining the performances of longitudinal rigidity, lateral rigidity, circumferential rigidity and average ground pressure.
Further, as shown in FIG. 10A, in Example 1, the pressure difference of the ground pressure is small. On the other hand, in Comparative Example 1 shown in FIG. 10B, there was a region with a high ground pressure at the ground end. In the present invention, in the cross-sectional shape of the tire model, it is possible to improve the local increase in the ground contact pressure due to the rattling of the nodes that form the outer contour, and drop it into the mold shape while maintaining the characteristic balance of the optimum shape of the tire. I was able to. As described above, according to the present invention, it is possible to obtain mold shape data that does not impair the tire shape characteristics that satisfy the target characteristics.

10 Tire mold design device (design device)
12 processing unit 14 input unit 16 display unit 20 condition setting unit 22 model creating unit 24 computing unit 26 data creating unit 28 memory 30 display control unit 32 control unit 50, 100, 102, 104 tire model 52a to 52d, 56a to 56d node 58, 70, 72 Elliptical arc 60 Tread central part 62 Ground contact end 64 Ground contact area 63, 65, 67 Node 66 Maximum width position CL Tire equatorial plane O center δ Distance

Claims (11)

For the tire, a problem setting step of setting design variables related to the shape, objective function, constraint conditions, optimal solution determination conditions and node extraction conditions,
For the tire, a creation process that creates a tire model with elements that can be numerically analyzed by a computer,
Based on the design variables set in the problem setting step, the objective function, the constraint conditions, the determination conditions of the optimal solution and the extraction conditions of the nodes, a calculation step of 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 a combination of design variables forming the extracted solution, An extraction step of extracting a plurality of nodes forming the outer contour,
A creating step of creating an elliptic arc that approximates the extracted plurality of nodes using a function represented by a mathematical expression having x, y as variables and a, b, p, q, x ₀ , y ₀ as parameters. When,
And a step of outputting the contour line of the tire model including at least the elliptical arc as mold shape data.
In the calculation step, the shape optimization calculation includes a ground contact analysis at a predetermined load,
In the extraction step, the plurality of nodes are extracted in the range from at least the tread central portion of the tire model to the ground contact end,
The tire mold shape designing method according to claim 1, wherein in the creating step, the elliptic arc is created using the nodes in the range of the tire model. 3. The creating step fixes at least one of the parameters a, b, p, q, x ₀ , y ₀ of the function, and creates the elliptic arc using the remaining parameters. The method for designing a tire mold shape according to. A step of setting a judgment condition in the objective function,
For the tire model expressed using the elliptical arc created in the creating step, the calculation of the objective function set in the problem setting step is performed,
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. Then
The tire mold shape designing method according to any one of claims 1 to 3, wherein the extracted node is changed if the error is outside a predetermined range. In the problem setting step, it is expressed by a combination of a plurality of base shapes that change the shape of the tire model, and it is set such that the domains thereof are included at least as design variables, and an objective function relating to the physical quantity of the tire model is at least 2 Set one or more,
The mold shape designing method for a tire according to any one of claims 1 to 4, wherein in the calculation step, optimization calculation is performed on the tire model. For the tire, a model creation unit that creates a tire model with elements that can be numerically analyzed by a computer,
A condition setting part that sets design variables, objective functions, constraint conditions, optimal solution determination conditions, and node extraction conditions,
An arithmetic unit that performs a shape optimization calculation for the tire model based on the design variables related to the shape set by the condition setting unit, the objective function, the constraint condition, the determination condition of the optimum solution, and the extraction condition of the node. When,
From the result of the shape optimization calculation of the calculation 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 the design variables constituting the extracted solution, Extract multiple nodes that make up the outer contour,
An elliptic arc that approximates between the plurality of nodes is created using a function represented by a mathematical expression having x, y as variables and a, b, p, q, x ₀ , y ₀ as parameters,
A mold designing apparatus for a tire, comprising: a data creation unit that outputs a contour line of the tire model including at least the elliptical arc as mold shape data.
In the calculation unit, the shape optimization calculation includes a ground contact analysis under a predetermined load,
In the data creation unit, the plurality of nodes are extracted in a range from at least the tread center to the ground contact end of the tire model, and the elliptical arc is created by using the nodes in the range of the tire model. 6. The tire mold shape designing device according to item 6. 7. The data creation unit fixes at least one of the parameters a, b, p, q, x ₀ , and y ₀ of the function, and creates the elliptic arc using the remaining parameters. 7. The tire mold design device according to item 7. Set the judgment condition in the objective function in the condition setting unit,
For the tire model represented by using the elliptic arc created by the data creation unit, the calculation unit calculates the objective function set by the condition setting unit,
In the tire model created by the model creation unit and used for creating the elliptic arc, the error with the objective function set by the condition setting unit is calculated by the calculation unit, and the error is within a predetermined range. For example, output the mold shape data from the data creation unit,
9. The tire mold shape designing apparatus according to claim 6, wherein if the error is outside a predetermined range, the data creation unit changes the extracted node. The condition setting unit is expressed by a combination of a plurality of base shapes that change the shape of the tire model, and is set so as to include at least the domains thereof as design variables, and an objective function relating to the physical quantity of the tire model is at least 2 Set one or more,
The tire mold shape designing apparatus according to any one of claims 6 to 9, wherein the calculation unit performs optimization calculation on the tire model.   A program for causing a computer to execute each step of the tire mold shape designing method according to claim 1 as a procedure.