Non-pneumatic-tire design device, method, and program

Abstract

In the present invention, a non-pneumatic tire design device comprises: a basic tire model in which a non-pneumatic tire including an inner cylindrical body, an outer cylindrical body, and a connecting member for connecting the inner cylindrical body and the outer cylindrical body is modeled using a finite number of elements; a setting unit for setting an objective function representing tire performance, a limiting condition that limits an allowable range of the tire performance, and a design parameter used to determine the positions of the plurality of control points positioned along the shape of the connecting member in the basic tire model; and a design parameter determination unit that sequentially changes design variables included in the design parameter and determines the design parameter on the basis of the value of the design variable that yields the optimum value of the objective function while fulfilling the limiting condition.

Description

Non-pneumatic tire design device, method, and program

[0001] The present disclosure relates to an apparatus, method, and program for designing a non-pneumatic tire.

[0002] A device has been proposed that simulates tire performance by rolling a basic tire model, in which a tire is modeled using a finite number of elements, on a virtual road surface using a numerical analysis method such as the finite element method. A technology is known in which an airless tire model is used as the tire (see, for example, JP 2022-187341 A).

[0003] As another example of a tire, there is known a technology for designing an airless tire that includes first and second ends on the inside and outside and is connected by blades, taking into consideration performance such as traction (see, for example, JP-A-2016-505448).

[0004] Incidentally, tire performance may be evaluated by actually designing and manufacturing a tire, mounting it on a vehicle, and conducting performance tests. Therefore, if the results of the performance tests are not satisfactory, the design and manufacturing process must be repeated. However, when designing a non-pneumatic tire such as an airless tire and simulating tire performance by modeling the non-pneumatic tire, considering design parameters related to tire performance requires a huge amount of work. Therefore, simulating tire performance requires repeated trial and error regarding the setting of design parameters, etc., which increases the processing load of the device, requiring a huge amount of processing time. Therefore, there is room for improvement in designing non-pneumatic tires while simulating the performance of non-pneumatic tires such as airless tires.

[0005] In consideration of the above facts, the present disclosure makes it possible to provide a non-pneumatic tire design device, method, and program that can reduce the processing load when designing a non-pneumatic tire such as an airless tire.

[0006] An aspect of the technology disclosed herein is a non-pneumatic tire design device including: a basic tire model in which a non-pneumatic tire including an inner cylindrical body, an outer cylindrical body, and a connecting member connecting the inner cylindrical body and the outer cylindrical body is modeled using a finite number of elements; a setting unit that sets an objective function that represents tire performance of the non-pneumatic tire, constraint conditions that restrict an allowable range of the tire performance, and design parameters that are used to determine positions of a plurality of control points arranged along the shape of the connecting member in the basic tire model of the non-pneumatic tire; and a design parameter determination unit that sequentially changes design variables included in the design parameters and determines the design parameters based on the values ​​of the design variables that give an optimal value of the objective function while satisfying the constraint conditions.

[0007] 1 is a block diagram showing a schematic configuration of a tire design device according to a first embodiment. FIG. 2 is a diagram showing an electrical configuration of the tire design device according to the first embodiment. FIG. 3 is a diagram showing a functional configuration of the tire design device according to the first embodiment. FIG. 4 is a diagram showing an operation of the tire design device according to the first embodiment. FIG. 5 is a diagram showing a setting process of an initial structure of a non-pneumatic tire according to the first embodiment. FIG. 6 is a diagram showing a plurality of control points according to the first embodiment. FIG. 7 is a diagram showing a spoke including a plurality of control points according to the first embodiment. FIG. 8 is a diagram showing a tire structure of a non-pneumatic tire according to the first embodiment. FIG. 9 is a diagram showing an example of a plurality of control points according to the first embodiment. FIG. 10 is a diagram showing a state in which a control point according to the first embodiment has been moved. FIG. 11 is a diagram showing a design parameter setting process according to the first embodiment. FIG. 12 is a diagram showing a setting process of an initial structure of a non-pneumatic tire according to the second embodiment. FIG. 13 is a diagram showing a plurality of control points according to the second embodiment. FIG. 14 is a diagram showing a plurality of control points according to the third embodiment. FIG. 15 is a diagram showing a functional configuration of a tire design device according to the fourth embodiment. FIG. 16 is a diagram showing a functional configuration of a tire design device according to the fourth embodiment. FIG. 17 is a diagram showing a configuration of a non-linear calculation unit according to the fifth embodiment. FIG. 18 is a diagram showing a neural network learning process according to the fifth embodiment. FIG. 19 is a diagram showing the operation of the tire design device according to the fifth embodiment. FIG. 20 is a diagram showing details of an optimization process according to the fifth embodiment. FIG. 21 is a diagram showing experimental results of an optimized non-pneumatic tire.

[0008] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. Components and processes that perform the same actions and functions are given the same reference numerals throughout the drawings, and duplicated descriptions may be omitted as appropriate. Furthermore, the present disclosure is not limited to the following embodiments, and can be implemented with appropriate modifications within the scope of the purpose of the present disclosure.

[0009] First Embodiment A non-pneumatic tire design device according to this embodiment calculates design parameters by using mathematical programming. Fig. 1 is a diagram showing a schematic configuration of a tire design device 1 as a non-pneumatic tire design device according to this embodiment.

[0010] As shown in Fig. 1, the tire design device 1 includes an input unit 2, a main unit 3, and a display unit 4. The input unit 2 acquires design parameters including design variables (hereinafter referred to as "design parameters") and may be an input device such as a keyboard or a mouse. The main unit 3 constitutes a design parameter determination unit that determines final design parameters based on design variables that provide optimal values ​​for an objective function while satisfying constraints in accordance with a preset program. The display unit 4 outputs the results of calculations performed by the main unit 3 and may be a display device such as a projection display or a liquid crystal display.

[0011] Here, the objective function is a function for expressing tire performance that indicates the physical properties and capabilities of a non-pneumatic tire, such as belt tension, lateral spring constant, rolling resistance, cornering power, etc., which are used to improve steering stability.

[0012] In this embodiment, the objective functions are the rolling resistance and the energy loss (hysteresis loss) that occurs when a non-pneumatic tire is distorted.

[0013] The constraint condition is a condition that restricts the allowable range of tire performance of a non-pneumatic tire. In this embodiment, the constraint condition is a condition that restricts the allowable range of cornering power.

[0014] The design parameters are parameters used to determine the structure of a basic tire model that models a non-pneumatic tire composed of a finite number of elements, and include parameters used to determine the positions of multiple control points arranged along the spokes that serve as connecting members in the basic tire model. Specifically, the design parameters include parameters used to determine the positions of multiple control points arranged along the shape of the spokes in the basic tire model of a non-pneumatic tire that models a non-pneumatic tire including an inner cylinder, an outer cylinder, and spokes connecting the two. In this case, when the basic tire model is treated two-dimensionally, the design parameters can be parameters used to determine the positions of multiple control points arranged along the tire cross-sectional shape of the basic tire model. Parameters for determining the positions of each control point can include the shape of the spoke (e.g., two-dimensional thickness, such as plate thickness) and the shape of the outer cylinder (e.g., two-dimensional thickness, such as plate thickness) at the position of each control point. When the design parameters include the shape of the spokes and the shape of the outer cylinder, parameters used to determine the thickness of the spokes and the thickness of the outer cylinder at the position of each control point in the tire cross-sectional shape can be applied. The objective function is a function of the design parameters. Therefore, when the design parameters are changed, the objective function is also changed. The positions of the control points are not limited to the positions themselves, but may be physical quantities that enable the positions to be determined. The shape of the spokes may be any shape based on the corresponding control points, and the shape of the outer cylinder may be any shape based on the points where the spokes and the outer cylinder are connected.

[0015] For example, if a plurality of control points (see control point P shown in FIG. 6 , described later) that can deform the spokes in the tire cross-sectional shape are arranged along the spoke shapes, the design parameters include the coordinate values ​​of each control point and values ​​corresponding to those coordinate values. In this embodiment, the design parameters are the coordinates of each control point. The shape of the spokes may be any thickness that indicates the length based on the corresponding control point, and the shape of the outer cylinder may be any thickness that indicates the length based on the point where the spokes are connected to the outer cylinder.

[0016] The design parameters include design variables, and in this embodiment, the design variables include the position of a control point moved by an input operation, the thickness of the spoke relative to the corresponding control point, and the thickness of the outer cylinder body. For example, the position of a control point, which is a design variable, includes the coordinates of the control point moved by an input operation and the amount of movement of the moved control point. The thickness of the spoke includes a thickness indicating the length of the spoke changed relative to the control point, and the thickness of the outer cylinder includes a thickness indicating the length of the changed outer cylinder. In this embodiment, for simplicity of explanation, it is assumed that the position of a control point is moved by an input operation, and the design variables include at least the coordinates of the moved control point.

[0017] Although details will be described later, in this embodiment, as an example of a preferred embodiment, the design variables will be described as including the positions of the control points, the thickness of the spokes, and the thickness of the outer cylinder body. The technology disclosed herein is not limited to applying the positions of the control points, the thickness of the spokes, and the thickness of the outer cylinder body as design variables. For example, at least one of the thickness of the spokes and the thickness of the outer cylinder body may be set to a predetermined value, and the positions of the control points may be used as the design variable, or at least one of the positions of the control points, the thickness of the spokes, and the thickness of the outer cylinder body may be used as the design variable.

[0018] For simplicity of explanation, the following description will be given using an example in which the position of a control point is moved by an input operation, but the technology of the present disclosure is not limited to this. The control point may be any physical position that can be moved during optimization. For example, optimization may be performed as described below without moving the position of the control point from the initial state.

[0019] The above-mentioned objective function or constraint conditions are functions of design variables included in the design parameters. Therefore, the tire design device according to this embodiment determines design parameters (such as the coordinates of the spokes in the tire cross-sectional shape, the thickness of the spokes, and the thickness of the outer cylinder body) that can minimize the rolling resistance (tire performance) while satisfying the constraint conditions.

[0020] In this embodiment, the objective function and constraint conditions are established on the premise of mathematical programming or the like, but since mathematical programming or the like is a common calculation method, detailed explanation thereof will be omitted.

[0021] In this embodiment, the design parameters are determined to minimize the rolling resistance while satisfying the constraints, but the present invention is not limited to this. For example, it is sufficient to determine design parameters that can optimize any objective function, such as a design parameter that can minimize the energy loss (hysteresis loss) that occurs when the tire warps while satisfying the constraints.

[0022] Incidentally, when modeling a non-pneumatic tire to simulate tire performance when designing the tire, it is preferable to consider design parameters related to tire performance so as to reduce the processing load of the device by reducing repetition of trial and error, etc. Therefore, in this embodiment, the non-pneumatic tire is designed by modeling a non-pneumatic tire of an initial structure in which the settings of the design parameters and the like of the non-pneumatic tire are predetermined.

[0023] The initial structure of a non-pneumatic tire is a structure of the non-pneumatic tire that is determined to reduce the processing load required for numerical calculations compared to a case where the computational load required for numerical calculations for control points, etc. used when changing the shape of the non-pneumatic tire is not taken into consideration. The initial structure includes, for example, a structure in which multiple control points that can deform the spokes are arranged along the shape of the spokes. Note that the initial structure can include the positions of the control points arranged along the spokes, the thickness of the spokes, and the thickness of the outer cylinder body.

[0024] Next, a detailed description will be given of the tire design device 1 for a non-pneumatic tire according to this embodiment. Fig. 2 is a diagram showing an example of the electrical configuration of the tire design device 1. The tire design device 1 is configured such that a main body 3 includes a computer as an execution device that executes processes to realize various functions described below.

[0025] The main body 3 includes a computer main body 30, which includes a CPU 30A, a RAM 30B, a ROM 30C, and an I / O 30D, all of which are connected to one another via a bus 30E. An auxiliary storage device 35, which may be implemented by a memory such as a HDD or a nonvolatile flash memory, is connected to the bus 30E. A communication unit 31 for communicating with external devices is connected to the I / O 30D. An input unit 2 and a display unit 4 are also connected to the I / O 30D.

[0026] The auxiliary storage device 35 can store a program 35P for executing processing in the tire design device 1. The computer main body 30 operating as the main body 3 reads the program 35P from the auxiliary storage device 35, loads it into RAM 30B, and executes the processing. As a result, the computer main body 30 that has executed the program 35P operates as a device that performs processing to simulate the tire performance of a non-pneumatic tire using a tire basic model. The program 35P may be provided on a recording medium such as a CD-ROM.

[0027] The auxiliary storage device 35 also stores various data 35D used by the computer main body 30. As will be described in detail later, the data 35D can store data indicating the initial structure, and the data indicating the initial structure stored in the data 35D can be used as template data indicating the initial structure of a non-pneumatic tire.

[0028] The communication unit 31 is capable of exchanging various information (e.g., tire information including various values ​​related to the structure and operation of the tire) with an external device (not shown) via a wired or wireless connection.

[0029] Fig. 3 is a diagram showing an example of the functional configuration of the computer main unit 30. That is, Fig. 3 is a diagram showing an example of a configuration in which operating units implemented by hardware and software related to the operation of the computer main unit 30 (i.e., the processing executed by the computer main unit 30) are expressed as a block configuration.

[0030] 3 , CPU 30A of computer main body 30 operates as the non-pneumatic tire design device of the present disclosure by executing program 35P. CPU 30A includes operating units that operate as an initial structure construction unit 300, a setting unit 302, and a design parameter determination unit 304. Initial structure construction unit 300 and setting unit 302 are examples of the setting unit of the present disclosure, and design parameter determination unit 304 is an example of the design parameter determination unit of the present disclosure.

[0031] The initial structure construction unit 300 constructs a non-pneumatic tire structure including control points used when changing the shape of the non-pneumatic tire, and sets data representing the constructed initial structure as the non-pneumatic tire structure (see step S90 shown in FIG. 4 , which will be described later). The initial structure includes, for example, control points capable of deforming spokes (connecting members), with multiple control points arranged along the shape of the spokes (see FIG. 8 ). Note that the initial structure can use data representing a predetermined structure, and it is possible to use initial values ​​for the positions of the control points, the thickness of the spokes, and the thickness of the outer cylinder body. The initial value of the spoke thickness may be a predetermined value, or a value for each control point position may be used.

[0032] From the shape of the non-pneumatic tire with the above initial structure, the user can set a desired shape of the non-pneumatic tire by performing an input operation, for example, by moving a control point (see FIG. 10 ). In addition, the thickness of the spokes and the shape of the thickness of the outer cylinder body (for example, thickness) may be set to desired values.

[0033] The setting unit 302 sets, for example, a basic tire model in which the tire cross-sectional shape of a non-pneumatic tire is modeled using a finite number of elements, an objective function representing tire performance, constraint conditions that restrict the allowable range of tire performance, and design parameters for determining the modeled tire cross-sectional shape.

[0034] Furthermore, for example, when a control point is moved by an input operation, the setting unit 302 may set the position (e.g., (z3', r3') shown in FIG. 10) of the operation control point (e.g., Pm3 shown in FIG. 10) that is the moved control point, and the position of the operation control point (e.g., P3 shown in FIG. 10) before the movement as design variables and include them in the design parameters (see step S102 shown in FIG. 4, which will be described later).

[0035] In addition, when a control point is moved by an input operation, the setting unit 302 may move other control points other than the moved control point in accordance with the ratio at which the control point is moved. For example, the ratio between the position (e.g., (z3′, r3′) shown in FIG. 10) of the operation control point (e.g., P3′ shown in FIG. 10) that is the moved control point and the position (e.g., (z3, r3) shown in FIG. 10) of the operation control point (e.g., P3 shown in FIG. 10) before the movement may be calculated, and operation-uncontrolled points (e.g., P1 to P2, P4 to P8 shown in FIG. 10) that are control points other than the operation control point may be moved according to the ratio, and the position of the operation control point (e.g., P3′ shown in FIG. 10) after the movement may be set as a design variable and included in the design parameters, and the positions of the operation-uncontrolled points (e.g., P1′ to P2′, P4′ to P8′ shown in FIG. 10) after the movement according to the ratio may be set as design parameters (see S102 shown in FIG. 4, which will be described later).

[0036] The design parameter determination unit 304 sequentially changes the design variables included in the design parameters, and determines the final design parameters based on the design variables that provide the optimal value of the objective function while satisfying the constraints (see steps S106 to S120 shown in FIG. 4 , which will be described later). That is, the design variables that indicate at least one of the control point positions, the spoke thickness, and the outer cylinder body thickness are sequentially changed, and the final design parameters are determined based on the design variables that provide the optimal value of the objective function while satisfying the constraints.

[0037] In this embodiment, the design parameter determination unit 304 calculates design variables that give optimal values ​​of the objective function while satisfying the constraint conditions by mathematical programming using objective function sensitivity, which is the ratio of the amount of change in the objective function to a unit change in the design variable, and constraint condition sensitivity, which is the ratio of the amount of change in the constraint condition to a unit change in the design variable (see, for example, equation (1) described later), and determines final design parameters based on the calculated design variables.

[0038] Next, the operation (tire design method) of the tire design device 1 according to this embodiment will be described. Fig. 4 is a diagram showing the operation of the tire design device 1 according to this embodiment.

[0039] 4, in step S90, the tire design device 1 sets an initial structure as the shape of a non-pneumatic tire. In this embodiment, a case where a tire cross-sectional shape is set as the initial structure will be described as an example. The tire structure can be constructed by expanding the tire cross-sectional shape in the tire width direction.

[0040] Here, the process of setting the initial structure of the non-pneumatic tire in step S90 will be described in detail. Fig. 5 is a diagram showing the flow of the process of setting the initial structure of the non-pneumatic tire. Fig. 6 is a diagram showing a plurality of control points set as the initial structure of the non-pneumatic tire.

[0041] The initial structure of a non-pneumatic tire is set as follows. First, in step S91, a start point P0 is set as a connection point indicating the location where the inner cylinder body Cin of the non-pneumatic tire is connected to the spokes (connecting members) SP, and an end point Pw is set as a connection point indicating the location where the outer cylinder body Cout is connected to the spokes SP. The positions of these start point P0 and end point Pw are set so that a straight line connecting a predetermined position O in the tire radial direction (e.g., the tire rotation center) to the start point P0 forms a predetermined angle θ with a straight line connecting the predetermined position O to the end point Pw. In this case, it is preferable to set the end point Pw at the intersection of a vertical line passing through the predetermined point O and the outer cylinder body Cout.

[0042] Next, in step S92, the position of each of the multiple control points P is set using a straight line Lst connecting the start point P0 and the end point Pw. Specifically, a quadrangle of a predetermined shape (in this embodiment, a square SQ) is defined, with one side being the straight line Lst connecting the set start point P0 on the inner cylinder body Cin side and the end point Pw on the outer cylinder body Cout side. Within the square SQ, a straight line Led on one side opposite the straight line Lst connecting the start point P0 and the end point Pw is set as a reference line. Each of the multiple control points P is set based on its distance from the straight line Led set as the reference line.

[0043] In this embodiment, the straight line Lst connecting the start point P0 and the end point Pw is divided equally into a plurality of parts (in the illustrated example, into nine parts), and the control points P are set to be distributed on the extensions of the straight lines at the boundaries of the divided squares at predetermined distances from the straight line Led. In other words, the control points P are set to be distributed at intervals of a distance Lx obtained by dividing the straight line Lst into nine in the direction of the straight line Lst (or in the direction of the straight line Led), and at a predetermined distance in a direction perpendicular to the straight line Lst.

[0044] The start point P0 is set to the coordinates (Z0, r0), and the end point Pw is set to the coordinates (Zw, rw). The control points are set to P1 (Z1, r1), ..., as coordinates of positions at predetermined distances from the line Led.

[0045] In addition, the multiple control points may be set based on the start point P0 and the end point Pw, with the above-mentioned specified shape (in this embodiment, a square SQ), the number of divisions (or spacing Lx), and the distance LL from the straight line Led as parameters.

[0046] After the setting of the plurality of control points P is completed, the structure of the spokes SP including the plurality of control points P, and the structures of the inner cylinder body Cin and the outer cylinder body Cout are set.

[0047] FIG. 7 is a diagram showing spokes SP including a plurality of control points set as the initial structure of a non-pneumatic tire. As shown in FIG. 7 , the tire design device 1 sets at least the shapes of the spokes SP so that the inner cylinder body Cin and the outer cylinder body Cout are connected to the spokes (connecting members) SP based on the set plurality of control points. Specifically, in step S93 of FIG. 5 , the shapes of the spokes SP and the like, i.e., the shapes of the spokes SP and the shapes of the inner cylinder body Cin and the outer cylinder body Cout connected to the spokes SP, are set. Hereinafter, the spokes SP and the inner cylinder body Cin and the outer cylinder body Cout connected to the spokes SP may be simply referred to as spokes SP. In this embodiment, a case will be described in which the shapes of the inner cylinder body Cin and the outer cylinder body Cout are set to predetermined shapes with cross-sectional thicknesses (tin, tout).

[0048] In setting the shape of the spokes SP, the positions of the multiple control points P are connected by a predetermined curve or a curve derived by an interpolation method (e.g., a spline curve), and the curve is set as the shape of the spoke center line SPc. Furthermore, a predetermined thickness Ti is set in a direction perpendicular to the center line SPc of the spoke SP at each of the multiple control points P, and the thickness distribution of the spokes SP is set by connecting the points indicating the set thickness Ti by a predetermined curve or a curve derived by an interpolation method. Instead of a spline curve, the curves connecting the multiple control points P and the curves connecting the thicknesses may be interpolated using Lagrange interpolation, circular interpolation, a B-spline curve, a Bezier curve, NURBS (weighted B-spline), or the like.

[0049] FIG. 8 is a diagram showing a tire structure set as the initial structure of a non-pneumatic tire. As shown in FIG. 8 , in step S94, the tire design device 1 arranges spokes SP and the like. Specifically, the tire design device 1 arranges multiple spokes SP of a set shape, for example, evenly around the circumference. Note that the shape of the spoke SP and the shapes of the inner cylinder body Cin and outer cylinder body Cout connected to the spoke SP may be considered as one unit, and multiple spokes SP may be arranged, for example, evenly, in the tire rotation direction. The arrangement of the multiple spokes SP is not limited to being evenly arranged. For example, they may be arranged at predetermined intervals. Note that the thicknesses of the inner cylinder body Cin and outer cylinder body Cout may be set as predetermined values ​​in step S94.

[0050] Next, in step S95, the structure of the spokes SP including the plurality of control points P set as described above, and the structures of the inner cylinder body Cin and outer cylinder body Cout are determined as the initial structure of the non-pneumatic tire.

[0051] In this embodiment, a square SQ is used as an example of a quadrangle of a predetermined shape when setting the multiple control points P, but the shape is not limited to a square and may be a rectangle, a parallelogram, or another quadrangle. Furthermore, when a quadrangle such as a rectangle is used, it is preferable to set the distance between the line Lst and the line Led to be greater than the maximum distance from the line Lst to the control point P so that the distance from the line Led to the control point P is on the positive side. This is because the distance is treated as a positive integer.

[0052] Furthermore, in this embodiment, multiple control points are set using a graphic shape having a straight line Lst connecting the start point P0 and the end point Pw as one side, but the setting of multiple control points is not limited to a graphic shape having a straight line Lst as one side. For example, as shown in FIG. 9 , the position of a control point may be set based on the distance to the control point using the straight line Lst connecting the start point P0 and the end point Pw as a reference line. The example shown in FIG. 9 is a diagram illustrating an example of multiple control points set as the initial structure of a non-pneumatic tire. Furthermore, the position of a control point may be set based on the distance to the control point using a straight line Lst' located a predetermined distance away (offset) from the straight line Lst as a reference line.

[0053] Once the above-described setting of the initial structure of the non-pneumatic tire is completed, the tire design device 1 determines an objective function, constraint conditions, and design variables in step S100 shown in Fig. 4. In this embodiment, as will be described later, the tire design device 1 determines the rolling resistance of the tire as the objective function, and determines conditions indicating an allowable range of cornering power generated in the tire as the constraint conditions.

[0054] Objective function OBJ: Rolling resistance Constraint condition G: Cornering power generated in the tire must be at least -3% of the initial shape

[0055] 10 is a diagram showing an example of a state in which a control point has been moved by an input operation. The movement of the control point may be accompanied by a change in at least one of the thickness of the spokes and the thickness of the outer cylinder body, or the movement of the control point may be replaced by a change in at least one of the thickness of the spokes and the thickness of the outer cylinder body. Here, the state in which the control point has been moved will be described.

[0056] If there is a control point (e.g., P3' shown in FIG. 10) that has been moved by an input operation among the control points described below, the tire design device 1 determines the moved control point (e.g., P3' shown in FIG. 10) as a design variable related to the control point. Note that this process only determines which control point is the control point of the design variable, and the content of the design variable, i.e., the position (coordinates) of the control point that has been moved by an input operation, is set in step S102 described below.

[0057] In step 102, the tire design device 1 sets the position (e.g., (z3', r3') shown in FIG. 10) of the control point (e.g., P3' shown in FIG. 10) moved by the input operation as part of the design parameters as the content of the design variable. In addition to this setting, the positions of the other control points are set as design parameters (design parameters other than the design variables) (design parameter setting process).

[0058] Next, the design parameter setting process in step 102 will be described in detail. Fig. 11 is a diagram showing the design parameter setting process in this embodiment. In the design parameter setting process shown in Fig. 11, initial design parameters are determined, and in S122, which will be described later, final design parameters are determined. Here, design parameters related to control points will be described.

[0059] In this embodiment, an example will be described in which a control point Pi (e.g., P3 shown in FIG. 10) before being moved by an input operation is moved, and as a result, each control point other than the control point Pi (e.g., P1 to P2, P4 to P8 shown in FIG. 10) is slid in accordance with the amount of movement of the control point Pi (see step S102B shown in FIG. 11, which will be described later).

[0060] 11 , in step S102A, the tire design device 1 sets the control point Pi' moved by the input operation as the content of the initial design variables. For example, if the control point before being moved by the input operation is P3, the tire design device 1 sets the position (zi', ri') of the control point Pi' after being moved as the content of the design variables.

[0061] Next, in step S102B, the tire design device 1 moves control points other than the control point Pi' that has been moved by the input operation. In this embodiment, if there is a control point Pi' that has been moved by the input operation, the tire design device 1 slides and moves the other control points Pk (here, control points P1 to P2, P4 to P8) in accordance with the ratio between the position of the control point Pi' (here, P3' shown in FIG. 10) and the position of the control point Pi (here, P3) before the movement. For example, the other control points Pk are slid and moved so that the amount of movement decreases as they move away from the moved control point Pi'.

[0062] In the following explanation, the position of control point Pk (here, control points P1 to P2, P4 to P8) other than control point Pi (here, P3) is (zk, rk) {k: number other than i}, and the position of control point Pk' after its movement is (zk', rk').

[0063] In step S102A, the position (zi', ri') of the control point Pmi' is set as the content of the design variable, but the content of this design variable is not limited to one and there may be a plurality of design variables.

[0064] Next, in step S102C, the tire design device 1 sets the design variables set for the control point P and the coordinates of the control points other than the control point Pi' as part of the initial design parameters. For example, if the position of a control point Pk other than the control point Pi (P3 in this case) is (zk, rk) and the position of the control point Pk' after its movement is (zk', rk'), then the position (zk', rk') and the set design variables are included in the initial design parameters.

[0065] In this embodiment and other embodiments, when a design variable is changed, design parameters other than the design variable are also changed accordingly, similar to the processes in steps S102B and S102C.

[0066] In this embodiment, the design variables include the spoke thickness and the outer cylinder thickness. Therefore, the process shown in FIG. 11 can be applied to determining the information indicating the spoke thickness and the outer cylinder thickness as design variables other than the design variables related to the control points. Furthermore, as the content of the information indicating the spoke thickness and the outer cylinder thickness, the spoke thickness and the outer cylinder thickness can be set as part of the design parameters as design variables. Design parameters other than the design variables related to the spoke thickness and the outer cylinder thickness include the position of the control point, which changes when at least one of the spoke thickness and the outer cylinder thickness is changed, and the other of the spoke thickness and the outer cylinder thickness. Furthermore, in step S102C, the content of the information related to the spoke thickness and the outer cylinder thickness, which are part of the design variables, can also be set as design parameters. In this case, the design parameters related to the spoke thickness and the outer cylinder thickness may be fixed to predetermined values.

[0067] 4 , the tire design device 1 sets a basic tire model in which at least the tire cross-sectional shape is modeled with a finite number of elements based on the set design parameters. This tire cross-sectional shape may include the cross-sectional shapes of the inner cylinder body Cin, the outer cylinder body Cout, and the spokes SP, as well as the structures of other components that make up the non-pneumatic tire. Furthermore, modeling refers to the conversion of the tire cross-sectional shape, material, pattern, etc. into numerical values ​​in the form of input data for a computer program capable of executing finite element analysis or the like.

[0068] In this embodiment, the basic shape is the tire cross-sectional shape in a natural equilibrium state (a state in which a non-pneumatic tire is not in contact with the road surface), and a tire basic model is set by modeling this basic shape using a finite number of elements. The tire design device 1 can calculate objective functions such as rolling resistance by performing finite element analysis or the like by rolling the tire basic model on a virtual road surface.

[0069] The basic shape is not limited to the tire cross-sectional shape in a natural equilibrium state, but may also be the tire cross-sectional shape in a state other than the natural equilibrium state. The tire basic model may, of course, be divided into a finite number of elements, including the materials constituting the non-pneumatic tire. Furthermore, although the tire basic model is divided into a finite number of elements, the divided elements may be configured in any shape, such as a triangle, a rectangle, or a cube.

[0070] In step S106, the tire design device 1 calculates an initial value OBJ0 of the objective function and an initial value G0 of the constraint condition by finite element analysis using a basic tire model, based on the initial design parameters set in the process of step S102. The processes from step S106 to step S120 are processes based on so-called mathematical programming.

[0071] In step S108, the tire design device 1 executes a process of changing the design variables. Here, the tire design device 1 changes the design variables (zi', ri') related to the position of the control point P set in the process of step S102 by Δzi' and Δri', respectively.

[0072] In step S110, the tire design device 1 calculates design parameters including coordinate values ​​of the control points after the design variables are changed, and determines the tire cross-sectional shape. Here, the tire design device 1 changes the design parameters excluding the changed design variables (zi'+Δzi', ri'+Δri') by using the process of step S102 described above, based on the changed design variables. That is, the tire design device 1 slides the position of the control point corresponding to the design variables before the change, in accordance with the amount of movement of the control point for the changed design variables (zi'+Δzi', ri'+Δri'). The position of the control point after the slide movement becomes (zk'+Δzk', rk'+Δrk').

[0073] Therefore, the tire design device 1 resets the above positions (zi'+Δzi' (hereinafter referred to as zi'), ri'+Δri' (hereinafter referred to as ri')) as design variables and includes them in the design parameters, and also resets the other positions (zk'+Δzk' (hereinafter referred to as zk'), rk'+Δrk' (hereinafter referred to as rk')) as design parameters.

[0074] Then, based on the reset design parameters, the tire design device 1 calculates a tire cross-sectional shape (here, the cross-sectional shape of the spokes SP) corresponding to the design parameters using a known method. The tire design device 1 also corrects the already set basic tire model using the calculated tire cross-sectional shape.

[0075] In step S112, the tire design device 1 calculates the objective function value OBJ1 and the constraint condition value G1 based on the design parameters including the changed design variables (zi'+Δzi', ri'+Δri') by using the tire basic model corrected in step S110.

[0076] In step S114, the tire design device 1 calculates, for each design variable, objective function sensitivities dOBJ / dzi′, dOBJ / dri′, which are ratios of the change in the objective function to a predetermined change in the design variable, and constraint condition sensitivities dG / dzi′, dG / dri′, which are ratios of the change in the constraint condition to a predetermined change in the design variable, using the following equation (1):

[0077] The slopes of the objective function and the constraint conditions are calculated by calculating these objective function sensitivities and constraint condition sensitivities, and the tire design device 1 can determine whether the current objective function value is trending in a convergence direction based on the slopes of the objective function and the constraint conditions.

[0078] In step S116, the tire design device 1 uses the initial value OBJ0 of the objective function, the initial value G0 of the constraint condition, the initial design variables, the objective function sensitivities dOBJ / dzi′, dOBJ / dri′, and the constraint condition sensitivities dG / dzi′, dG / dri′ to predict, by mathematical programming, the amount of change in the design variables that will bring the current objective function closer to a minimum while satisfying the constraint conditions.

[0079] In step S118, the tire design device 1 again corrects the tire basic model corrected in S110 based on the predicted changes in the design variables, similar to the processing in S110 above. Then, the tire design device 1 calculates the objective function value OBJ using the corrected tire basic model based on the predicted changes in the design variables.

[0080] In step S120, the tire design device 1 determines whether or not the objective function value OBJ calculated in the processing of S118 has converged. For example, if the difference between the objective function value OBJ calculated in the processing of S118 and the initial value OBJ0 of the objective function calculated in the processing of S106 is within a preset threshold range, the tire design device 1 determines that the objective function value OBJ calculated in the processing of S118 has converged, and proceeds to processing of S122.

[0081] On the other hand, if the difference between the objective function value OBJ calculated by the processing of step S118 and the initial value OBJ0 of the objective function calculated by the processing of S106 is not within the range of a preset threshold, the tire design device 1 determines that the objective function value OBJ calculated by the processing of step S118 has not converged, and returns to the processing of step S106. Note that if the processing of S118 returns to the processing of S106 (if NO is determined), the design parameters including the design variables changed by the processing of step S116 are used as initial values.

[0082] In step S122, the tire design device 1 determines the tire cross-sectional shape and the like based on the final design parameters including the design variables changed by the processing in step S116.

[0083] In the above, the tire design device 1 has been described as changing design variables including coordinate values ​​of control points. However, it goes without saying that other design variables, such as the spoke thickness and the design variable related to information indicating the thickness of the outer cylinder body, may also be changed. In this case, the above-described processing may be performed by changing at least one of the design variables related to the control points, the design variable related to the spoke thickness, and the design variable related to the thickness of the outer cylinder body. For example, when changing the design variables of the control points, the spoke thickness, and the outer cylinder body thickness, the above-described processing may be performed for each design variable, or the above-described processing may be performed by changing each design variable simultaneously.

[0084] As described above, according to this embodiment, the tire design device 1 executes a process for setting the initial structure of a non-pneumatic tire. The initial structure of the non-pneumatic tire is set based on a straight line connecting the connection point (start point P0) between the inner cylinder body Cin and the spokes SP and the connection point (end point Pw) between the outer cylinder body Cout and the spokes SP. For example, the tire design device 1 defines a square SQ with a straight line Lst connecting the start point P0 and the end point Pw as one side, and sets the positions of multiple control points based on the distance from the straight line Led, which is the opposing side of the square, as a reference line. This makes it possible to set a tire model for a non-pneumatic tire that is easily deformed without setting a complex structure. This reduces the processing load when designing a non-pneumatic tire.

[0085] In this embodiment, it is also possible to set the thickness of the spokes and the thickness of the outer cylinder body. That is, the tire design device 1 sets the structure of the spokes, including the control points, and sets the thickness of the spokes for the control points and the thickness of the outer cylinder body connected to the spokes, thereby creating the initial structure of the non-pneumatic tire. Therefore, the tire design device 1 does not need to set the complex structure of the non-pneumatic tire from scratch for each structure of the inner cylinder body Cin, the outer cylinder body Cout, and the spokes SP, thereby shortening the overall processing time.

[0086] This allows tire designers to create a special tire cross-sectional shape in a short amount of time with a small number of steps using at least one piece of information about each control point located on the spoke SP, the thickness of the spoke, and the thickness of the outer cylinder body.

[0087] Furthermore, the tire design device 1 gradually changes the initial design variables using mathematical programming so that the value of the objective function approaches the optimal value while satisfying the constraint conditions, and calculates design variables that give the optimal value of the objective function while satisfying the constraint conditions. This allows tire designers to design and develop tires using appropriate design variables that are primarily based on computer-based calculation methods, rather than design variables based on empirical rules, thereby enabling more efficient tire design and development.

[0088] Second Embodiment Next, a second embodiment will be described. The second embodiment is a modified example of the first embodiment. Since the second embodiment has the same configuration as the first embodiment described above, only the differences from the first embodiment will be described below, and a description of the common parts will be omitted.

[0089] In the first embodiment, the tire design device 1 sets a non-pneumatic tire structure by arranging a plurality of spokes in the tire circumferential direction, each of which includes a plurality of control points set using a straight line Lst connecting a start point P0 and an end point Pw. In the second embodiment, a non-pneumatic tire structure is set by arranging a plurality of spoke sets in the tire circumferential direction, each of which includes a plurality of spokes as a spoke set. In the second embodiment, an example of a case in which a non-pneumatic tire structure is set by arranging a plurality of spoke sets in the tire circumferential direction, each of which includes a first spoke and a second spoke that is the same as or different from the first spoke.

[0090] The process of setting the initial structure of the non-pneumatic tire according to the second embodiment will be described in detail.

[0091] Fig. 12 is a diagram showing the flow of a process for setting the initial structure of a non-pneumatic tire according to the second embodiment. In the second embodiment, the tire design device 1 executes the setting process shown in Fig. 12 instead of the setting process shown in Fig. 11 described above. Also, Fig. 13 is a diagram showing a plurality of control points that are set as the initial structure of a non-pneumatic tire according to the second embodiment.

[0092] 12 and 13, in step S96, the tire design device 1 acquires information indicating a predetermined relationship between the first spoke and the second spoke. The information indicating the predetermined relationship includes information indicating the angles θ1 and θ2 of the first and second spokes, respectively, and the relative angle θ3 between the start point P0-1 and the end point Pw-1 that are set by the angle θ1, and the start point P0-2 and the end point Pw-2 that are set by the angle θ2.

[0093] In step S90A, the tire design device 1 sets the shape of the first spoke SP-1, similar to step S90 described above. Specifically, the tire design device 1 sets a first start point P0-1 and a first end point Pw-1 for the first spoke SP-1 so that they form an angle θ1 (S91). Next, a square SQ-1 is defined, with one side being a straight line Lst-1 connecting the first start point P0-1 and the first end point Pw-1, and the positions of multiple control points P for the first spoke SP-1 are set (S92). Next, based on the set multiple control points, the shape of the first spoke SP-1, etc. is set so that the spoke is connected to the inner cylinder body Cin and the outer cylinder body Cout (S93). Here, similar to the above, it is possible to set the shape of the first spoke SP-1, etc., that is, the shape of the first spoke SP-1 and the shapes of the inner cylinder body Cin and the outer cylinder body Cout connected to the first spoke SP-1. Hereinafter, the first spoke SP-1 and the inner cylinder body Cin and outer cylinder body Cout connected to the first spoke SP-1 may be simply referred to as the first spoke SP-1.

[0094] In step S90B, the tire design device 1 sets the shape of the second spoke SP-2, similar to step S90A described above. In step S90B, the tire design device 1 sets the start point P0-2 and the end point Pw-2 at an angle θ2 so that the angle is a relative angle θ3 with respect to the first spoke SP-1 at the angle θ1. That is, the tire design device 1 sets the shape of the second spoke SP-2 by defining a square SQ-2 with one side being a straight line Lst-2 connecting the second start point P0-2 and the second end point Pw-2 so that the square forms the relative angle θ3. Here, similar to the case of spoke SP-1, it is possible to set the shapes of the spoke SP-2, etc., i.e., the shape of the spoke SP-2 and the shapes of the inner cylinder body Cin and the outer cylinder body Cout connected to the spoke SP-2. If the shapes of the inner cylinder body Cin and the outer cylinder body Cout connected to the spokes SP-1 and SP-2 are different, either one may be selected, or a calculated value such as an average value may be used.

[0095] In step S97, the tire design device 1 arranges a plurality of spoke sets, each of which is a combination of first spokes SP-1 and second spokes SP-2 of the set shape, in the circumferential direction of the tire, for example, evenly (at equal intervals). The arrangement of the spoke sets is not limited to being evenly arranged. For example, the spoke sets may be arranged at predetermined intervals.

[0096] Next, in step S98, the tire design device 1 determines, as the initial structure, the structure of the spokes SP including the multiple control points P of the first spokes SP-1 and the second spokes SP-2 set as described above, and the structures of the inner cylinder body Cin and the outer cylinder body Cout.

[0097] After the above-described setting of the initial structure of the non-pneumatic tire is completed, the tire design device 1 determines an objective function, constraint conditions, and design variables in step S100 shown in Fig. 4. In this embodiment, the tire design device 1 determines the rolling resistance of the tire as the objective function, and determines conditions indicating an allowable range of cornering power generated in the tire as the constraint conditions.

[0098] In the example shown in Figure 13, the start point P0-1 and end point Pw-1 of the first spoke SP-1 are determined to form an angle θ1 between them. In this case, it is preferable to set the end point Pw-1 at the intersection of a vertical line passing through the predetermined point O and the outer cylinder body Cout. The angle formed by the end point Pw-2 of the first spoke SP-1 and the end point Pw-2 of the second spoke SP-2 is determined to be a position rotated clockwise by an angle θ3 from the end point Pw-2 of the first spoke SP-1. The end point 2 of the second connecting member is determined to be a position rotated clockwise by an angle θ3 from the vertical line. The determined distance between the first spoke SP-1 and the second spoke SP-2 is defined as one pitch, and they are arranged at equal intervals of N pitches around the circumference.

[0099] According to the second embodiment, a spoke connecting the inner cylinder body Cin and the outer cylinder body Cout can be set using a spoke set that combines a first spoke SP-1 and a second spoke SP-2. Therefore, in addition to the effects of the first embodiment, it is possible to generate non-pneumatic tire structures with a variety of shapes compared to when multiple single spokes are arranged. This increases the degree of freedom when designing non-pneumatic tires. In this way, the tire design device 1 generates non-pneumatic tire structures with a variety of shapes, making it possible to design tires that further improve tire performance.

[0100] <Third Embodiment> Next, a third embodiment will be described. The third embodiment is a modified example of the second embodiment. Since the third embodiment has the same configuration as the first and second embodiments described above, only the differences will be described below, and a description of the common parts will be omitted.

[0101] In the second embodiment, the tire design device 1 forms second spokes SP-2 in a shape similar to the first spokes SP-1, and arranges multiple spoke sets in the tire circumferential direction, each of which includes the first spokes SP-1 and the second spokes SP-2. In other words, the first spokes SP-1 and the second spokes SP-2 do not intersect. In the third embodiment, the tire design device 1 forms second spokes SP-2 in a shape similar to the first spokes SP-1 and symmetrical to the first spokes SP-1. The tire design device 1 arranges multiple spoke sets in the tire circumferential direction, each of which includes the first spokes SP-1 and the second spokes SP-2, so that the first spokes SP-1 and the second spokes SP-2 partially intersect. In other words, the first spokes SP-1 and the second spokes SP-2 intersect at least partially.

[0102] The process of setting the initial structure of the non-pneumatic tire according to the third embodiment will be described in detail.

[0103] FIG. 14 is a diagram showing a plurality of control points set as an initial structure of a non-pneumatic tire according to the third embodiment.

[0104] 12 and 14, in step S96, the tire design device 1 acquires information indicating the predetermined relationship between the first spoke and the second spoke. In this embodiment, the acquired information includes the signs of the angles θ1, θ2, and θ3. In other words, the signs of the angles θ1 and θ2 are opposite to each other. Therefore, the first spoke SP-1 and the second spoke SP-2 are set to have a symmetrical shape.

[0105] The tire design device 1 sets the shape of the first spoke SP-1 in step S90A, and sets the shape of the second spoke SP-2 in step S90B. That is, the tire design device 1 sets the first spoke SP-1 using a square SQ-1, one side of which is a straight line connecting the start point P0-1 and the end point Pw-1 at an angle θ1. Then, the tire design device 1 sets the second spoke SP-2 using a square SQ-2, one side of which is a straight line connecting the start point P0-2 and the end point Pw-2 at an angle θ2, so that the shape is symmetrical to the first spoke SP-1 and has a relative angle θ3. Here, the first spoke SP-1 and the second spoke SP-2 partially intersect.

[0106] In step S97, the tire design device 1 arranges a plurality of spoke sets in the tire circumferential direction, each of which has a shape that combines first spokes SP-1 and second spokes SP-2 of the set shape.

[0107] Next, in step S98, the tire design device 1 determines, as the initial structure, the structure of the spokes SP including the multiple control points P of the first spokes SP-1 and the second spokes SP-2 set as described above, and the structures of the inner cylinder body Cin and the outer cylinder body Cout.

[0108] According to the third embodiment, it is possible to create non-pneumatic tire structures with a greater variety of shapes than when a plurality of single spokes are arranged, as in the second embodiment. Furthermore, by symmetrically arranging the first spokes SP-1 and the second spokes SP-2, it is possible to increase the degree of freedom when designing a non-pneumatic tire.

[0109] <Fourth Embodiment> In the first to third embodiments, the tire design device 1 calculates the final design parameters by using mathematical programming. In contrast, in the fourth embodiment, the tire design device 1 calculates the final design parameters by using a genetic algorithm. Since the fourth embodiment has the same configuration as the first embodiment described above, only the differences from the first embodiment will be described below, and a description of the common parts will be omitted.

[0110] In the fourth embodiment, as in the first embodiment, the objective function is assumed to be rolling resistance. The constraint condition is assumed to be a condition that restricts the allowable range of cornering power. However, the objective function and constraint condition are not limited to these.

[0111] Fig. 15 is a diagram showing an example of the functional configuration of a tire design device 1 in the fourth embodiment. As shown in Fig. 15, the tire design device 1 includes a new design variable generation unit 306 in addition to the configuration in the first embodiment. The setting unit 302 sets set information including design variables that configure each of the tire basic models.

[0112] The new design variable generation unit 306 sequentially selects design variables constituting each of at least two basic tire models from the set information, and executes either or both of the following processes with a predetermined probability: a crossover process in which a part of each of the selected design variables is exchanged with each other to generate new design variables, and a mutation process in which a part of any of the selected design variables is changed to generate new design variables.

[0113] The design parameter determination unit 304 determines the final design parameters based on the design variables that give the optimal value of the objective function while satisfying the constraint conditions, from among the new set information including the generated new design variables and other selected design variables (step S234 shown in FIG. 16 , which will be described later).

[0114] Furthermore, if a predetermined convergence condition is met (YES in S232 shown in FIG. 16 to be described later), the design parameter determination unit 304 determines final design parameters based on the design variables that give the optimal value of the objective function while satisfying the constraint conditions, among the design variables included in the new set information; if the predetermined convergence condition is not met (NO in step S232 shown in FIG. 16 to be described later), the design parameter determination unit 304 sets the new set information as set information and causes the new design variable generation unit 306 to repeatedly execute the same processing.

[0115] Next, a description will be given of the operation of the tire design device 1 in this embodiment. Fig. 16 is a diagram showing the operation of the tire design device 1 in the fourth embodiment.

[0116] 16 , similarly to the first embodiment, the tire design device 1 sets an initial structure as the shape of a non-pneumatic tire in step 90. Next, in step S200, the tire design device 1 determines the rolling resistance of the tire as an objective function, and determines conditions indicating an allowable range of cornering power generated in the tire as constraint conditions.

[0117] Objective function OBJ: Rolling resistance Constraint condition G: Cornering power -3% or more of the initial shape

[0118] The tire design device 1 also sets set information including at least one design variable that configures each of the N tire basic models, where N is input in advance by the tire designer.

[0119] Here, the set information includes N pieces of small set information (first small set information to Nth small set information), each of which corresponds to N tire basic models and includes design parameters including at least one design variable.

[0120] For example, in the processing of step S200, the tire design device 1 determines the design variable as P3' (see FIG. 10), and sets the design parameters including the design variable P3' in the first small set information. Similarly, the tire design device 1 sets the second small set information to the N-th small set information. Note that in the processing of step S200, the position (z3', r3'), which is the content of the design variable, has not yet been set, and will be set in the processing of step S202, which will be described later.

[0121] In step S202, the tire design device 1 sets the contents of the design parameters included in each of the first to Nth small set information (design parameter setting process). For example, if the design variable included in the first small set information is P3', the tire design device 1 sets the position (z3', r3') of P3' as part of the contents of the design parameters. Similarly, the tire design device 1 sets the contents of the design parameters included in each of the second to Nth small set information. Note that the process of step S202 is the same as step S102 in the first embodiment repeated N times, so a detailed description thereof will be omitted.

[0122] In step S204, the tire design device 1 sets first to N-th tire basic models corresponding to the first to N-th small set information, respectively, using the first to N-th small set information set in the processing of step S202. Each of these first to N-th tire basic models is configured with design parameters. Note that the processing of step S204 is similar to the processing of step S104 in the first embodiment, and therefore a detailed description thereof will be omitted.

[0123] In step S206, the tire design device 1 calculates initial values ​​OBJJ of the objective functions and initial values ​​GJ of the constraint conditions corresponding to each of the first to Nth tire basic models (J; 1 to N) by finite element method analysis or the like using the first to Nth tire basic models based on the design parameters for each tire basic model set by the processing of step S202.

[0124] In step S208, the tire design device 1 calculates an adaptive function FJ corresponding to each of the first to Nth tire basic models using the initial values ​​OBJJ of the objective functions and the initial values ​​GJ of the constraint conditions corresponding to each of the first to Nth tire basic models, according to the following equation (2). In this embodiment, it is necessary to minimize rolling resistance. Therefore, the value of the adaptive function (fitness) increases as the rolling resistance decreases.

[0125]

[0126] In step S210, the tire design device 1 uses a commonly known fitness proportional strategy calculation method to select two tire basic models to be crossed from among the N tire basic models based on the fitness function calculated by the processing in step S208. When the fitness proportional strategy calculation method is used, the probability p that a certain tire basic model will be selected from the N tire basic models is calculated by the following equation (3).

[0127] Here, the fitness proportional strategy is a calculation method for selecting a tire base model with a probability proportional to the fitness of each tire base model. Therefore, if the rolling resistance is small (if the objective function is small), the value of the fitness function (fitness) becomes large, and the tire base model having that fitness function has a high probability of being selected by equation (3).

[0128] where FL and FJ are as follows: FL: fitness function of a tire model L among N tire models; FJ: Jth fitness function of N tire models, J=1, 2, 3, ..., N. Note that in this embodiment, the fitness proportional strategy is used, but the present invention is not limited to this. For example, an expected value strategy, a rank strategy, an elite preservation strategy, a tournament selection strategy, or a GENITOR algorithm may also be used (see Genetic Algorithms (edited by Kitano Hiroaki)).

[0129] In step S212, the tire design device 1 determines, with a preset probability, whether or not to cross over the two tire basic models selected in the processing of step S210. If the determination is affirmative, the tire design device 1 proceeds to processing of step S216, and if the determination is negative, the tire design device 1 proceeds to processing of step S214. Here, cross over means exchanging some of the elements constituting the two tire basic models with each other.

[0130] In step S214, the tire design device 1 leaves the two selected tire basic models as they are without intersecting them.

[0131] In step S216, the tire design device 1 crosses over the two selected tire basic models (crossover process). For example, the tire design device 1 exchanges some of the design variables of the selected first tire basic model with some of the design variables of the selected Nth tire basic model (i.e., another tire basic model).

[0132] If the two selected tire basic models are tire basic model a and tire basic model b, the design variables of tire basic model a and tire basic model b are as follows: However, as explained above in FIG. 5 , the position (z, r) of control point P is set in P. Note that the design variables are not limited to information related to the control point, and as mentioned above, it goes without saying that information indicating at least one of the position of the control point, the thickness of the spokes, and the thickness of the outer cylinder body can be applied as the design variable.

[0133] Design variables (vector) of tire basic model a: Pa = (Pa1, Pa2, ..., Pai, Pai+1, Pai+2, ..., Pan-1) Design variables (vector) of tire basic model b: Pb = (Pb1, Pb2, ..., Pbi, Pbi+1, Pbi+2, ..., Pbn-1)

[0134] As described above, crossover processing is a process of exchanging some of the design variables of multiple selected tire base models with each other, and is an example of a process in a processing method known as a genetic algorithm. For example, by exchanging some of the genes that are elements, crossover processing makes it possible to generate a better model than before crossover by multiplying the genetic information of the parent models. As a result, it becomes possible to generate a model similar to the one before crossover.

[0135] For example, a crossover position (position of a design variable) is determined by a random number, and the design variables of the tire basic model a and the design variables of the tire basic model b are crossed at the crossover position determined by the random number. Note that the crossover process is a known process, and therefore a detailed description thereof will be omitted.

[0136] For example, when Pai and Pbi are the crossover positions, the overall design variable Pa′ of the tire basic model a after crossover and the overall design variable Pb′ of the tire basic model b after crossover are as follows:

[0137] Pa'=(Pa1, Pa2,..., Pai, Pbi+1, Pbi+2,..., Pbn-1) Pb'=(Pb1, Pb2,..., Pbi, Pai+1, Pai+2,..., Pan-1)

[0138] It is also possible to use multi-point crossover or uniform crossover as shown in Genetic Algorithm (edited by Kitano Hiroaki).

[0139] Next, in step S218, the tire design device 1 determines, with a preset probability, whether or not to mutate the two tire basic models. If the determination is affirmative, the tire design device 1 proceeds to processing in step S222, and if the determination is negative, the tire design device 1 proceeds to processing in step S220. Here, mutation refers to changing some of the elements that make up each of the two tire basic models (design variables in this embodiment). By performing this mutation, it is possible to increase the probability that optimal design parameters will be included in new set information, which will be described later.

[0140] In step S220, the tire design device 1 leaves the two selected tire basic models as they are without mutating them.

[0141] In step S222, the tire design device 1 mutates the two tire basic models (mutation processing).

[0142] As described above, the mutation process is a process for changing some of the design variables of the basic tire model, and is an example of a process in a processing method known as a genetic algorithm. The mutation process makes it possible to avoid limiting the optimization range within the optimization space where the design variables are optimized. Furthermore, by providing genetic information (design information) that is not present in the parent model, it becomes possible to escape from a local solution.

[0143] For example, a mutation position (position of a design variable) is determined by a random number, and the content of at least one of the design variables of the tire basic model a and the design variables of the tire basic model b is changed at the mutation position determined by the random number. Note that the mutation process is a known process, and therefore a detailed description thereof will be omitted.

[0144] For example, when Pai and Pbi are mutation positions, the overall design variable Pa' after crossover and mutation of the tire basic model a and the overall design variable Pb' after crossover and mutation of the tire basic model b are as follows:

[0145] Pa'=(Pa1, Pa2,..., Pai', Pbi+1, Pbi+2,..., Pbn-1) Pb'=(Pb1, Pb2,..., Pbi', Pai+1, Pai+2,..., Pan-1)

[0146] In step S224, the tire design device 1 uses the two tire basic models obtained in step S220 or step S222 to calculate the values ​​of the objective function and the values ​​of the constraint conditions corresponding to each of the two tire basic models.

[0147] In step S226, the tire design device 1 calculates adaptive function values ​​corresponding to each of the two tire basic models using the objective function values ​​and constraint condition values ​​corresponding to each of the two tire basic models according to the above-described equation (2). The adaptive function values ​​calculated here are used when a negative determination is made in the processing of step S230 or step S232 (described later) and the processing of step S210 is executed again.

[0148] In step S228, the tire design device 1 stores the two tire basic models at the time of this processing as part of new set information.

[0149] In step S230, the tire design device 1 determines whether the number of tire basic models included in the new set information has reached N (a predetermined convergence condition). If the determination is affirmative, the tire design device 1 proceeds to processing in step S232, and if the determination is negative, the tire design device 1 returns to processing in step S210, and repeats this process until the number of tire basic models included in the new set information reaches N.

[0150] In step S232, the tire design device 1 determines whether or not at least one of the following convergence conditions (predetermined convergence conditions) is satisfied. If the determination is affirmative, the tire design device 1 proceeds to processing in step S234, but if the determination is negative, the tire design device 1 sets the N tire basic models included in the new set information as the set information, and repeats the processing from step S210 to step S228.

[0151] Convergence conditions: First condition: When the number of generations (number of iterations) reaches M. Second condition: When the number of small line sequences, which are the values ​​of the objective function, reaches q% or more of the total. Third condition: When the smallest value of the objective function is not updated in the subsequent p generations. Note that M, q, and p are input in advance by the tire designer. In this way, the objective function representing tire performance can be used to determine convergence.

[0152] In step S234, the tire design device 1 selects design variables that minimize the objective function while satisfying the constraints from among the N design variables of the tire model included in the new set information, and determines final design parameters including the selected design variables.The tire design device 1 then determines the tire cross-sectional shape and the like based on the final design parameters.

[0153] As described above, according to this embodiment, the tire design device 1 can generate a variety of design variables by executing either the crossover process or the mutation process, or both processes, with a predetermined probability, and therefore the tire design device 1 can select more appropriate design parameters from among the design parameters that include a variety of design variables.

[0154] Furthermore, since the tire design device 1 sequentially updates the set information and repeats the same process until a predetermined convergence condition is met, the tire design device 1 can increase the probability that the design variables after the crossover process or mutation process are included in the set information each time the same process is repeated, and can select more appropriate design parameters from among design parameters that include a wider variety of design variables.

[0155] The processing in the first embodiment and the processing in the fourth embodiment may be combined. Here, when the objective function and constraints are calculated based on the design variables calculated by the crossover processing or the mutation processing, as described in the literature "Goldberg, DE, "Genetic Algorithms in Search, Optimization and Machine Learning," Addison-Wesley (1988)," the value of the objective function does not fall into a locally optimal solution, but there is a problem in that it is difficult to calculate a true optimal solution. Therefore, in the processing of step S224 in the fourth embodiment, the processing of steps S106 to S120 in the first embodiment is executed, thereby solving the above problem.

[0156] Furthermore, as a method for solving the above problems, simulated annealing (see Genetic Algorithm (edited by Kitano Hiroaki)) may be combined with the fourth embodiment.

[0157] Fifth Embodiment In the first embodiment, the tire design device 1 calculates the final design parameters by using mathematical programming. In the fourth embodiment, the tire design device 1 calculates the final design parameters by using a genetic algorithm. In the third embodiment, the final design parameters are calculated by using, as a conversion system, a trained neural network, which is a nonlinear prediction technology that engineered a neural circuit network of a higher animal. Since the fifth embodiment has a configuration similar to the first and fourth embodiments described above, only the differences from the first and fourth embodiments will be described below, and a description of the common parts will be omitted.

[0158] In this embodiment, as in the first embodiment, the objective function is assumed to be rolling resistance. The constraint condition is assumed to be a condition that restricts the allowable range of cornering power. However, the objective function and constraint condition are not limited to these.

[0159] Fig. 17 is a diagram showing an example of the functional configuration of a tire design device 1 in the fifth embodiment. As shown in Fig. 17, the tire design device 1 includes operating units that operate as an initial structure construction unit 300, a nonlinear calculation unit 312, and an optimization calculation unit 314.

[0160] In this embodiment, the tire design device 1 acquires a plurality of design parameters including the above-mentioned design variables, tire manufacturing conditions, etc., and corresponding experimental data on tire performance. The tire design device 1 also acquires a plurality of design parameters and corresponding experimental data on tire performance.

[0161] The nonlinear calculation unit 312 constitutes a setting unit that sets a conversion system that relates the design parameters acquired by the input unit 2 to the corresponding tire performance by using multiple pieces of learning data including the design parameters and the corresponding experimental data of tire performance.

[0162] Here, the conversion system is a conversion system itself that can perform conversion and inverse conversion so that there is a one-to-one correspondence between design parameters and the corresponding tire performance. When the neural network after training is expressed as a mathematical formula, this conversion system includes the mathematical formula and its coefficients.

[0163] The input unit 2 also acquires optimization item information including an objective function indicating tire performance that should be maximized or minimized, constraint conditions that impose constraints when maximizing or minimizing the objective function, design parameters including the above-mentioned design variables, tire manufacturing conditions, possible ranges of the design parameters / manufacturing conditions, selection of an optimization method for the objective function, parameters required for the selected method, etc. This optimization item information is used by an optimization calculation unit 314, which will be described later.

[0164] Although there are optimization methods such as mathematical programming and genetic algorithms, the present embodiment uses an optimization method that combines the mathematical programming used in the first embodiment with a neural network.

[0165] The optimization calculation unit 314 (design parameter determination unit) includes an objective function / constraint condition calculation unit 314 A and an objective function optimization calculation unit 314 B. The objective function / constraint condition calculation unit 314 A uses the conversion system calculated by the nonlinear calculation unit 312 to convert the design parameters (or manufacturing conditions) (design parameters including new design variables) included in the optimization item information into an objective function that indicates tire performance.

[0166] The objective function optimization calculation unit 314B determines whether the objective function predicted by the objective function / constraint condition calculation unit 314A is one that gives an optimal value while satisfying the constraint conditions, and causes the objective function / constraint condition calculation unit 314A to repeatedly calculate the objective function until the final design parameters that give the optimal value of the objective function while satisfying the constraint conditions are calculated.

[0167] Next, the nonlinear calculation unit 312 in this embodiment will be described. The nonlinear calculation unit 312 has a conversion function that calculates tire performance (objective function) corresponding to design parameters (or manufacturing conditions, etc.) using a conversion system configured by a neural network, and a learning function that makes the conversion system more appropriate.

[0168] Here, the nonlinear calculation unit 312 may have only a conversion function without a learning function. In other words, it is sufficient that the design parameters and the corresponding tire performance are mutually exchangeable. Therefore, the relationship between the design parameters and the corresponding tire performance may be learned in advance by an external neural network, and the conversion coefficients (coupling coefficients or offset values ​​relating the design parameters to the corresponding tire performance) in the learned external neural network may be applied to the neural network of this embodiment. In this way, by configuring the system so that the conversion coefficients in the external neural network can be input, it is sufficient to have only the conversion function, and the learning function is not required.

[0169] Furthermore, a table showing the relationship between the design parameters and the corresponding tire performance may be configured as the conversion system.

[0170] Fig. 18 is a diagram showing the configuration of the nonlinear calculation unit 312 in the fifth embodiment. As shown in Fig. 18, the nonlinear calculation unit 312 includes a neural network configured with an input layer I, an intermediate layer M, an output layer U, and offset units 312A and 312B. The input layer I, the intermediate layer M, the output layer U, and the offset units 312A and 312B, which will be described later, are connected by a synapse SY.

[0171] The input layer I is a layer that acquires each value constituting the design parameters and is composed of a predetermined number of neurons I1, I2, ..., Ip (p > 1). This input layer I is composed of neural circuit elements whose input / output relationships are linear.

[0172] For example, the input layer I acquires each value constituting the design parameters, including the material of the tread rubber or spokes, the coordinate values ​​of each control point arranged along the tire cross-sectional shape, or the tire manufacturing cost. The number of neurons in the input layer I may be set according to the number of each value constituting the design parameters. The input layer I may also be composed of neural network elements that have the characteristic of outputting inputs as they are. The information acquired in the input layer I is not limited to information related to the control points (coordinate values ​​of the control points), and as described above, it goes without saying that information indicating at least one of the coordinate values ​​of the control points indicating the positions of the control points, the thickness of the spokes, and the thickness of the outer cylinder body may also be applied.

[0173] The intermediate layer M is a layer that connects the input layer I and the output layer U, and is composed of a predetermined number of neurons M1, M2, . . . , Mq (q>1).

[0174] The output layer U is a layer that outputs tire performance corresponding to the input design parameters, i.e., each value constituting tire performance related to the objective function and constraint conditions, and is configured with a predetermined number of neurons U1, U2, ..., Ur (r > 1). Note that the number of neurons in the output layer U may be set according to the number of each value constituting the tire performance.

[0175] The intermediate layer M and the output layer U are configured with neural circuit elements whose input / output relationships have sigmoid characteristics, each of which is a sigmoid function. By configuring the input / output relationships of the intermediate layer M and the output layer U to have sigmoid characteristics, the values ​​from the output layer U are real values ​​(positive numbers).

[0176] Moreover, the output values ​​yj of the intermediate layer M and the output layer U can be calculated by the following equation (4).

[0177] That is, in each of the intermediate layer M and the output layer U, the number of synapses on the input side is defined as p, the weight (coupling coefficient) corresponding to the strength of connection of each synapse is defined as wij (1≦i≦p, 1≦j≦N), and each input signal is defined as xi. The virtual internal state variable ui, which corresponds to the average value of the neuron membrane potential, and the output value yj of each of the intermediate layer M and the output layer U can be expressed by the following equation (4).

[0178] where bj is an offset value supplied from the offset unit 312A or 312B, and wij is a coupling coefficient between the ith and jth layers of different layers. As a result, when each value constituting the design parameters is input to the input layer I, the value is multiplied by the coupling coefficient and then an offset value is added to the value, thereby outputting each value constituting the tire performance.

[0179] The offset unit 312A modifies values ​​from the input layer I. The offset unit 312B modifies values ​​from the hidden layer M.

[0180] During learning, when each value constituting an existing design parameter is input to the neural network, the nonlinear calculation unit 312 compares the value output from the neural network with the teacher data, which is each value constituting the tire performance corresponding to the existing design parameter, and updates (learns) each coupling coefficient and offset value so that the difference between the two is minimized.

[0181] After learning, when each value constituting the design parameters included in the optimization item information is input, the nonlinear calculation unit 312 outputs tire performance using the trained neural network.

[0182] In this way, learning is performed and more appropriate coupling coefficients are set for each neuron, which causes each neuron to output more appropriate values, thereby outputting more appropriate tire performance related to the design parameters included in the optimization item information, thereby allowing for more appropriate calculation of the final design parameters.

[0183] Next, the process up to the end of neural network learning in the nonlinear calculation unit 312 will be described in detail (neural network learning process).

[0184] Fig. 19 is a diagram showing the neural network learning process in the fifth embodiment. The neural network learning process shown in Fig. 19 is executed in step S314, which will be described later.

[0185] In this neural network learning process, existing data is used that relates to each value constituting the design parameters and each value constituting the tire performance after a tire prototype is manufactured and evaluated using each value, or existing data that relates to each value constituting the design parameters and each value constituting the tire performance obtained by analyzing the basic tire model corresponding to each value with a computer. In other words, multiple pieces of already collected existing data that consist of each value constituting the design parameters and each value constituting the corresponding tire performance are used for learning the neural network.

[0186] In this embodiment, a predetermined number of the existing data (for example, 90% of the total) is used as training data for training the neural network.

[0187] The remaining data (e.g., the remaining 10%) of the plurality of existing data is used as test data to check whether the neural network has been optimally trained after training.

[0188] In the following, each value constituting the design parameters included in the training data (or test data) is input to an input layer I of the neural network. Here, each value constituting the tire performance included in the training data (or test data) is used as teacher data.

[0189] Then, each value constituting the design parameters contained in the training data (or test data) is input to the input layer I, and the values ​​output from the output layer U are compared with the training data, and the coupling coefficients in the neural network are appropriately updated, thereby training the neural network. The process up to training the neural network will be explained in detail below.

[0190] As shown in FIG. 19, in step S314A, the nonlinear calculation unit 312 reads a plurality of existing data items including learning data and test data stored in advance in the RAM 30B.

[0191] In step S314B, the nonlinear calculation unit 312 sets each of the coupling coefficients (weights) and offset values ​​provided in the neural network to predetermined initial values.

[0192] In step S314C, the nonlinear calculation unit 312 inputs each value constituting the design parameter included in the training data to the input layer I, compares the value output from the output layer U with the teacher data included in the training data, and calculates the error, which is the difference between the two, for each training data. In addition, the nonlinear calculation unit 312 calculates the error of the intermediate layer by error backpropagation or the like using the error between the value output from the output layer U and the teacher data.

[0193] In step S314D, the nonlinear calculation unit 312 updates at least one of the coupling coefficients and the offset value for each piece of training data so as to minimize the error calculated in the process of step S314C.

[0194] In step S314E, the nonlinear calculation unit 312 uses a neural network composed of the updated coupling coefficients and offset values ​​to input test data to the input layer I and output the value output from the output layer I as the test result.

[0195] In step S314F, the nonlinear calculation unit 312 determines whether the test result output by the processing of step S314E satisfies the convergence condition. For example, the nonlinear calculation unit 312 determines whether the test result output by the processing of step S314E falls within a predetermined range (convergence condition), or whether the number of iterations (convergence condition) from step S314C to step S314F has reached a predetermined number. If the determination is affirmative, the nonlinear calculation unit 312 ends this processing, but if the determination is negative, the nonlinear calculation unit 312 returns to the processing of step S314C.

[0196] In this way, the nonlinear calculation unit 312 can update (learn) each of the coupling coefficients and offset values ​​constituting the neural network to more appropriate values ​​by using multiple pieces of known learning data. Then, when the design parameters included in the optimization item information are input, the nonlinear calculation unit 312 uses the learned neural network to calculate final design parameters that provide optimal values ​​for the objective function indicating tire performance while satisfying the constraints (see FIG. 20 described below).

[0197] The neural network learning process may be executed before or during the process shown in Fig. 20, which will be described later. For example, if the neural network learning process is executed before the process shown in Fig. 20, in the neural network learning process, the nonlinear calculation unit 312 causes the neural network to be sufficiently trained, and then stores the coupling coefficients and offset values ​​constituting the trained neural network in RAM 30B. Then, in the process of step S314 shown in Fig. 20, the nonlinear calculation unit 312 uses the neural network (transformation system) configured by the coupling coefficients and offset values ​​stored in RAM 30B.

[0198] Next, the operation of the tire design device 1 in this embodiment will be described in detail. Fig. 20 is a diagram showing the operation of the tire design device 1 in the fifth embodiment.

[0199] As shown in FIG. 20, in the same manner as in the first embodiment, in step 90, the tire design device 1 sets an initial structure as the shape of a non-pneumatic tire.

[0200] Next, in step S300, the tire design device 1 determines the design parameters xi (i = 1 to P), the objective function, the constraints, and the maximum number of analyses. That is, the tire design device 1 determines the objective function and its constraints that indicate the tire performance to be improved, and also determines the number of analyses to be performed until the final design parameters that provide an optimal value for the objective function while satisfying the constraints are determined. In this embodiment, the design parameters xi in step S300 are used as existing data in the processing of step S314, which will be described later, and are used to train the neural network. The objective function OBJ and the constraints G are as follows:

[0201] Objective function OBJ: Rolling resistance Constraint condition G: Cornering power -3% or more of the initial shape

[0202] In step S302, the tire design device 1 sets the allowable range (xiL≦xi≦xiU; xiL is the lower limit value, and xiU is the upper limit value) of the design parameter xi determined by the processing in step S300.

[0203] In step S304, the tire design device 1 initializes M, which indicates the number of analyses, and a variable i, which indicates the ordinal number of the design parameter (M=0, i=1).

[0204] In step S306, the tire design device 1 determines the design variables to be changed from among the design variables that fall within the allowable range of the design parameter xi by using an orthogonal array (or experimental design), etc. For example, the tire design device 1 determines the design variables to be changed from among the design variables that fall within the allowable range of the design parameter xi by using the method described in the literature "Box, GEP, & Draper, NR; "Empirical Model Building and Response Surfaces", John Wiley & Sons, New York."

[0205] In step S308, the tire design device 1 sets n tire basic models configured by each of the design parameters x including the design variables determined in the processing of step S306. Note that the processing up to the formation of the tire cross-sectional shape using the design variables is the same as the processing of step S102 described above, and is executed for each tire basic model n.

[0206] In step S310, the tire design device 1 calculates, using each of the ni tire basic models, the objective function values ​​OBJJ and constraint condition values ​​GJ corresponding to each of the design parameters of the ni tire basic models, and in step S312, stores each design parameter and the objective function values ​​OBJJ and constraint condition values ​​GJ corresponding to each of the design parameters.

[0207] In step S314, the tire design device 1 uses the values ​​constituting the stored design parameters as learning data, and the values ​​constituting the objective function values ​​OBJJ and constraint condition values ​​GJ corresponding to the design parameters as teacher data, thereby causing the neural network to learn. The processing here is similar to the processing shown in Fig. 19 described above, and therefore a detailed description thereof will be omitted.

[0208] In step S316, the tire design device 1 slightly changes the design variables included in the design parameters x to determine whether there are any design parameters x that have little contribution to the objective function. The design variables to be changed are determined by the processing in step S306.

[0209] For example, when each value constituting the design variables included in the design parameter xi is slightly changed, if the change in the value output from the output layer is small, the tire design device 1 determines that the contribution of the design parameter xi to the objective function is small.

[0210] Alternatively, if the change in the value output from the output layer is small when the value output from at least one neuron constituting the input layer is set to 0, the tire design device 1 determines that the contribution of the design parameter xi to the objective function is small.

[0211] Furthermore, if there is a design parameter xi that has a small contribution to the objective function, the tire design device 1 proceeds to processing in step S318, and if there is no design parameter xi that has a small contribution to the objective function, the tire design device 1 proceeds to processing in step S320.

[0212] In step S318, the tire design device 1 deletes design parameters that make little contribution to the objective function, and uses the remaining design parameters to train the neural network again in step S314.

[0213] In step S320, the tire design device 1 stores the coupling coefficients and offset values ​​that constitute the trained neural network.

[0214] In step S322, the tire design device 1 calculates final design parameters based on the design parameters included in the optimization item information (see FIG. 13) by using a neural network (conversion system) configured from the stored coupling coefficients and offset values. This processing will be described in detail in the optimization processing shown in FIG. 21, which will be described later.

[0215] In step S324, the tire design device 1 calculates M=M+1.

[0216] In step S326, the tire design device 1 determines whether M calculated by the processing in step S324 satisfies the relationship M<maximum number of analyses. If this determination is affirmative, the tire design device 1 proceeds to the processing in step S332, and if this determination is negative, the tire design device 1 proceeds to the processing in step S338.

[0217] In step S328, the tire design device 1 calculates i=i+1.

[0218] In step S330, the tire design device 1 resets the allowable range of the design parameter and returns to the processing of step S306. The tire design device 1 resets the allowable range of the design parameter calculated in the processing of step S302 to narrow it using the following equation (5), and then performs the experiment planning again in step S306 based on the narrowed allowable range. By repeating the processing from step S306 in this manner, the design parameter xi calculated in the processing of step S322 ＯＰＴ would be more appropriate.

[0219] However, NN is a coefficient for gradually narrowing the allowable range of the design parameters, and is preferably set to a value of about 1.5 to 5.

[0220] In step S332, the tire design device 1 determines the tire cross-sectional shape and the like based on the final design parameters calculated in the processing of step S322.

[0221] The maximum number of analyses may be set based on the cost of the analysis, the time required to calculate the final design parameters, and so on.

[0222] Next, the details of the optimization process in step S322 will be described with reference to Fig. 21, which is a diagram showing the details of the optimization process in step S322.

[0223] 21 , in step S322A, the tire design device 1 initializes a variable j that indicates the order of the design parameter included in the optimization item information. In step S322B, the tire design device 1 sets the initial value of the design parameter Sj using the following equation (6) based on the design parameter Sj included in the optimization item information.

[0224] where Sj (j=1 to p) is a design parameter. Ｌ ≦Sj≦Sj Ｕ is the range that the design parameter can take. Munit is the number of divisions of the allowable range of the design parameter. k is 0 to Munit and increases by 1 each time the process is repeated. Sj Ｌ , Sj Ｕ is preset.

[0225] Here, if the input values ​​of each design parameter are plotted on a two-dimensional plane and the values ​​of the objective function (tire performance) for each design parameter are plotted in the height direction, the objective function will have multiple peaks in three-dimensional space.

[0226] For this reason, if only one initial value of the design parameter is used, the value of the objective function may fall into a locally optimal solution. Therefore, in this embodiment, since different initial values ​​of the design parameters are sequentially set each time the process of step S322B is repeated, the value of the objective function does not fall into a locally optimal solution, and a true optimal solution can be calculated.

[0227] In step S322C, the tire design device 1 inputs the initial values ​​of the design parameters set by the processing in step S322B into the input layer I of the neural network, and outputs the initial values ​​of the objective function indicating tire performance and the initial values ​​of its constraint conditions from the output layer U.

[0228] In step S322D, the tire design device 1 changes the design variables included in the design parameters Sj by Δsj, and in step S322E, calculates the objective function values ​​OBJj and constraint condition values ​​Gj after the design variables have been changed by Δsj.

[0229] In step S322F, the tire design device 1 calculates, for each design variable, the objective function sensitivity dOBJ / dsj, which is the ratio of the change in the objective function to a predetermined change in the design variable, and the constraint sensitivity dG / dsj, which is the ratio of the change in the constraint to a predetermined change in the design variable, using the following equation (7):

[0230] In step S322G, the tire design device 1 determines whether or not the processes of steps S322E and S322F have been executed for all design parameters Sj. If the determination is affirmative, the tire design device 1 proceeds to the process of step S322H, and if the determination is negative, the tire design device 1 returns to the process of step S322E.

[0231] In step S322H, the tire design device 1 uses the initial value OBJ0 of the objective function, the initial value G0 of the constraint condition, design parameters including the initial design variables, the objective function sensitivity dOBJ / dsj, and the constraint condition sensitivity dG / dsj to predict, by mathematical programming, the amount of change in the design variables that will bring the current objective function closer to a minimum while satisfying the constraint conditions.

[0232] In step S322I, the tire design device 1 corrects the design parameters based on the predicted changes in the design variables using the above-described process. Then, when the values ​​of all the design parameters have been corrected based on the predicted changes in the design variables, the tire design device 1 calculates the value OBJ of the objective function corresponding to each of the corrected design parameters.

[0233] In step S322J, the tire design device 1 determines, for each design parameter, whether the objective function value OBJ calculated by the processing of step S322I has converged. For example, if the difference between the objective function value OBJ calculated by the processing of step S322I and the initial value OBJ0 of the objective function calculated by the processing of step S322C is within a preset threshold range, the tire design device 1 determines that the objective function value OBJ calculated by the processing of step S322I has converged, and proceeds to the processing of step S322K.

[0234] On the other hand, if the determination in step S322J is negative, the tire design device 1 determines that the objective function value OBJ has not converged, and proceeds to the processing of step S322C. Note that if the determination in step S322J is negative, the design parameters corrected by the processing in step S322I are used as initial values.

[0235] In step S322K, the tire design device 1 sets the design parameters corrected by the processing in step S322I.

[0236] In step S322L, the tire design device 1 determines whether the number of times the initial design parameters have been set in the processing of step S322B exceeds a predetermined number {here, (1 + Munit)}. If the determination is affirmative, the tire design device 1 proceeds to the processing of step S322M, and if the determination is negative, the tire design device 1 returns to the processing of step S322B, where the initial design parameters are changed and the same processing is repeatedly executed.

[0237] In step S322M, the tire design device 1 selects, as a final design parameter, the design parameter that has the highest degree of agreement with the following selection condition from among the design parameters set by the processing in step S322K. This final design parameter is the design parameter that satisfies the constraint conditions and provides an optimal value for the objective function.

[0238] [Selection Conditions] Selection Condition 1: Design parameters that reduce the objective function OBJ. However, if the objective function is small, the tire performance is judged to be good. If the objective function is large, the tire performance is good, this is handled by adding a minus sign to the objective function. Selection Condition 2: The objective function and constraints do not change much even if the design parameters are changed slightly around the calculated optimal solution.

[0239] As described above, according to this embodiment, the tire design device 1 uses a conversion system that associates design variables with tire performance, and therefore the tire design device 1 can appropriately determine final design parameters without assuming a function type that associates design variables with tire performance.

[0240] Furthermore, since the tire design device 1 can train a neural network using existing design variables and tire performance, the tire design device 1 can use a conversion system with less arbitrariness and can appropriately determine the final design parameters.

[0241] In this embodiment, mathematical programming (see steps S322C to S322J) and neural network optimization methods are used, but the present invention is not limited to this, and the genetic algorithm in the fourth embodiment and the neural network optimization method in this embodiment may also be used.

[0242] It is also possible to calculate a global optimum value of the objective function as a primary solution by the optimization method using the genetic algorithm in the fourth embodiment, or by the optimization method using the genetic algorithm in the fourth embodiment and the neural network in this embodiment, and then use the primary solution as an initial value to calculate an extreme value near the initial value by the optimization method using mathematical programming, and use this as the final solution.

[0243] In this case, even if the size of the set information is finite in the genetic algorithm, the final design parameters can be made closer to the true design parameters, and furthermore, in the neural network, the error between the values ​​from the output layer and the values ​​of the training data can be made smaller, so that the optimal value of the objective function can be calculated more appropriately.

[0244] [Example] Next, an example of a simulation in which the technology of the present disclosure is applied to the actual design of PCR155 / 70R13 will be described. Fig. 22 shows the simulation results of a non-pneumatic tire having spokes (connecting members) optimized using the technology of the present disclosure. Fig. 22 shows the results of a simulation conducted on the durability, ride comfort, and weight of a non-pneumatic tire having spokes (connecting members) optimized using the technology of the present disclosure, and the results are shown in terms of indices representing stress, longitudinal spring, and gravity. The smaller the stress shown in Fig. 22, the better the durability, and the smaller the longitudinal spring, the better the ride comfort.

[0245] In the examples, the simulation results of a non-pneumatic tire in which an inner cylindrical body and an outer cylindrical body are connected by uniformly formed spokes are used as a comparative example. The simulation results of a non-pneumatic tire optimized by the tire design device of the first embodiment are used as a first example, and the simulation results of a non-pneumatic tire optimized by the tire design device of the third embodiment are used as a second example. The simulation result index is set to 100 for the comparative example, and the simulation results of the first and second examples are shown relative to the comparative example.

[0246] As shown in Figure 22, in the first example, the stress was the same, but the longitudinal spring and weight were reduced, resulting in a tire with better ride comfort and a lighter weight, which was a good result. In the second example, all of these were reduced, resulting in a tire with excellent durability, ride comfort, and weight, which was a good result. Therefore, by applying the technology of the present disclosure, it is possible to optimize at least one of the tire performances, for example, durability, ride comfort, and weight.

[0247] <Other embodiments>

[0248] Although the technology of the present disclosure has been described above using embodiments, the technical scope of the technology of the present disclosure is not limited to the scope described in the above embodiments. Various modifications or improvements can be made to the above embodiments without departing from the gist of the invention, and forms incorporating such modifications or improvements are also included in the technical scope of the disclosed technology. For example, the specific configurations of the above-described components can be modified as appropriate. Furthermore, the configurations of the above-described embodiments can be combined with each other. Furthermore, the actions and effects of the above-described embodiments are merely a list of the most preferable actions and effects resulting from the technology of the present disclosure, and the actions and effects of the technology of the present disclosure are not limited to those described in the above-described embodiments.

[0249] In the above embodiment, the processing is performed by executing a program stored in an auxiliary storage device, but at least a part of the processing of the program may be realized by hardware. The processing flow of the program described in the above embodiment is also an example, and unnecessary steps may be deleted, new steps may be added, or the processing order may be changed within the scope of the gist.

[0250] Furthermore, in order to execute the processing in the above-described embodiment by a computer, a program in which the above-described processing is written in code that can be processed by a computer may be stored on a storage medium such as an optical disk and distributed.

[0251] In the above-described embodiment, a CPU has been used as an example of a general-purpose processor. However, in the above-described embodiment, the term "processor" refers to a processor in a broad sense, and includes general-purpose processors (e.g., CPU: Central Processing Unit, etc.) and dedicated processors (e.g., GPU: Graphics Processing Unit, ASIC: Application Specific Integrated Circuit, FPGA: Field Programmable Gate Array, programmable logic device, etc.).

[0252] Furthermore, the operation of the processor in the above-described embodiments may not only be performed by a single processor, but may also be performed by multiple processors working together, or may be performed by multiple processors located in physically separate locations working together.

[0253] All publications, patent applications, and technical standards mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent application, or technical standard was specifically and individually indicated to be incorporated by reference.

[0254] The disclosure of Japanese Patent Application No. 2024-011147, filed on January 29, 2024, is incorporated herein by reference in its entirety.

[0255] The present disclosure includes the following aspects: A first aspect of the present disclosure is a non-pneumatic tire design device including: a basic tire model in which a non-pneumatic tire including an inner cylindrical body, an outer cylindrical body, and a connecting member connecting the inner cylindrical body and the outer cylindrical body is modeled with a finite number of elements, a setting unit that sets an objective function that represents tire performance of the non-pneumatic tire, constraint conditions that restrict an allowable range of the tire performance, and design parameters that are used to determine positions of a plurality of control points arranged along the shape of the connecting member in the basic tire model of the non-pneumatic tire, and a design parameter determination unit that sequentially changes design variables included in the design parameters and determines the design parameters based on values ​​of the design variables that provide an optimal value of the objective function while satisfying the constraint conditions.

[0256] In a second aspect, in the non-pneumatic tire design device of the first aspect, the plurality of control points enable a shape of the connecting member in the basic tire model to be changed, and the setting unit sets positions of the control points as the design variables by including them in the design parameters.

[0257] In a third aspect, in the non-pneumatic tire design device of the second aspect, the setting unit further sets the shape of the connecting member at the position of the control point and the shape of the outer cylinder body at the position of an end point indicating the connection point where the outer cylinder body and the connecting member are connected as design variables by including them in the design parameters.

[0258] A fourth aspect is the non-pneumatic tire design device of the second or third aspect, wherein the basic tire model is a model representing a tire cross-sectional shape, and the setting unit sets a connection point where the inner cylindrical body and the connecting member are connected as a start point and a connection point where the outer cylindrical body and the connecting member are connected as an end point, and sets the positions of the start point and the end point so that a straight line connecting a predetermined position in the tire radial direction and the start point forms a predetermined angle with a straight line connecting the predetermined position and the end point, uses the straight line connecting the start point and the end point to set each of a plurality of positions on the straight line at a predetermined distance from the straight line as each of the plurality of control points, sets a shape of the connecting member based on the plurality of set control points so that the inner cylindrical body and the outer cylindrical body are connected to the connecting member, and sets a structure of the non-pneumatic tire by arranging a plurality of connecting members of the set shape around the tire.

[0259] In a fifth aspect, in the non-pneumatic tire design device of the fourth aspect, the setting unit defines a quadrangle (square) having a side equal to a straight line connecting the start point and the end point as a first straight line, and sets a side equal to a straight line opposite to the first straight line as a second straight line, and sets each of the positions of the plurality of control points at a predetermined distance from the second straight line.

[0260] In a sixth aspect, in the non-pneumatic tire design device of the fourth or fifth aspect, a curve passing through the plurality of control points is set as a center line of the connecting member, and a shape of the connecting member having a predetermined thickness centered on the set center line of the connecting member is set as a shape of the connecting member.

[0261] A seventh aspect is the non-pneumatic tire design device of any one of the first to sixth aspects, wherein the tire basic model is a model representing a tire cross-sectional shape, and the setting unit: sets a connection point where the inner cylindrical body and a first connecting member that is the connecting member are connected as a first start point, and a connection point where the outer cylindrical body and the first connecting member are connected as a first end point, and sets the positions of the first start point and the first end point so that a straight line connecting a predetermined position in the tire radial direction and the first start point forms a predetermined angle with a straight line connecting the predetermined position and the first end point; uses the straight line connecting the first start point and the first end point to set each of positions at a predetermined distance from each of a plurality of positions on the straight line as each of a plurality of control points of the first connecting member; and sets a shape of the first connecting member so that the inner cylindrical body and the outer cylindrical body are connected to the first connecting member based on the plurality of control points of the first connecting member, setting the positions of a second starting point and a second ending point of a second connecting member, which is a connecting member at a position different from that of the first connecting member; using a straight line connecting the second starting point and the second ending point, setting each of positions at a predetermined distance from each of a plurality of positions on the straight line as each of a plurality of control points of the second connecting member; setting the shape of the second connecting member based on the plurality of control points of the second connecting member so that the inner and outer cylindrical bodies are connected to the second connecting member; and arranging a plurality of connecting member sets made of the first connecting member and the second connecting member having the set shapes around the tire to set the structure of the non-pneumatic tire.

[0262] An eighth aspect is the non-pneumatic tire design device of any one of the first to seventh aspects, wherein the design parameter determination unit calculates the design variables that give the optimal value of the objective function while satisfying the constraint conditions by mathematical programming, using an objective function sensitivity that is a ratio of a change in the objective function to a unit change in the design variable, and a constraint condition sensitivity that is a ratio of a change in the constraint conditions to a unit change in the design variable.

[0263] A ninth aspect is the non-pneumatic tire design device of any one of the first to seventh aspects, wherein the setting unit sets set information including the design variables that constitute each of the tire basic models, and a new design variable generation unit is provided that sequentially selects the design variables that constitute each of at least two of the tire basic models from the set information and executes, with a predetermined probability, either a crossover process that exchanges some of the selected design variables with each other to generate new design variables, or a mutation process that changes some of the selected design variables to generate new design variables, or both of these processes, and the design parameter determination unit determines the final design parameters based on the design variables that give an optimal value of the objective function while satisfying the constraints, from the new set information including the generated new design variables and the other selected design variables.

[0264] In a tenth aspect, in the non-pneumatic tire design device of the ninth aspect, when a predetermined convergence condition is met, the design parameter determination unit determines the final design parameters based on the design variables that give the optimal value of the objective function while satisfying the constraint conditions, among the design variables included in the new set information, and when the predetermined convergence condition is not met, sets the new set information to the set information and causes the new design variable generation unit to repeatedly execute the same process.

[0265] An eleventh aspect is the non-pneumatic tire design device of any one of the first to seventh aspects, wherein the setting unit sets a conversion system that relates a plurality of design variables that have already been collected to the tire performances corresponding to the design variables, and the design parameter determination unit sequentially changes the new design variables set by the setting unit and converts the design variables into the corresponding tire performances using the conversion system, and determines the final design parameters based on the design variables that provide optimal values ​​for the tire performance while satisfying the constraints.

[0266] In a twelfth aspect, in the non-pneumatic tire design device of the eleventh aspect, the conversion system includes a learning model that has been machine-learned to determine a correspondence between the design variables and tire performance corresponding to the design variables.

[0267] In a thirteenth aspect, in the non-pneumatic tire design device of any one of the first to twelfth aspects, when the control point is moved by an input operation, the setting unit calculates a ratio between a position of the moved control point and a position of the control point before the movement, moves control points other than the moved control point according to the ratio, and sets the positions of the control points after the movement as the design variables by including them in the design parameters.

[0268] A fourteenth aspect is a non-pneumatic tire design method, comprising: a processor sets a basic tire model in which a non-pneumatic tire including an inner cylindrical body, an outer cylindrical body, and a connecting member connecting the inner cylindrical body and the outer cylindrical body is modeled using a finite number of elements; an objective function that represents tire performance of the non-pneumatic tire; constraints that restrict an allowable range of the tire performance; and design parameters that are used to determine positions of a plurality of control points that are arranged along the shape of the connecting member in the basic tire model of the non-pneumatic tire; and sequentially changes design variables included in the design parameters, and determines the design parameters based on values ​​of the design variables that provide an optimal value of the objective function while satisfying the constraints.

[0269] A fifteenth aspect is a program that causes a processor to perform the following processing: set a basic tire model in which a non-pneumatic tire including an inner cylindrical body, an outer cylindrical body, and a connecting member that connects the inner cylindrical body and the outer cylindrical body is modeled with a finite number of elements, an objective function that represents tire performance of the non-pneumatic tire, constraint conditions that restrict an allowable range of the tire performance, and design parameters that are used to determine positions of a plurality of control points that are arranged along the shape of the connecting member in the basic tire model of the non-pneumatic tire; and sequentially change design variables included in the design parameters, and determine the design parameters based on the values ​​of the design variables that give an optimal value of the objective function while satisfying the constraint conditions.

[0270] According to the present disclosure, it is possible to reduce the processing load when designing a tire.

Claims

1. A non-pneumatic tire design device comprising: a basic tire model in which a non-pneumatic tire including an inner cylindrical body, an outer cylindrical body, and a connecting member connecting the inner cylindrical body and the outer cylindrical body is modeled using a finite number of elements; a setting unit that sets an objective function that represents tire performance of the non-pneumatic tire, constraint conditions that restrict an allowable range of the tire performance, and design parameters that are used to determine the positions of a plurality of control points arranged along the shape of the connecting member in the basic tire model of the non-pneumatic tire; and a design parameter determination unit that sequentially changes design variables included in the design parameters and determines the design parameters based on the values of the design variables that give an optimal value of the objective function while satisfying the constraint conditions.

2. The non-pneumatic tire design device according to claim 1, wherein the plurality of control points enable the shape of the connecting member in the basic tire model to be changed, and the setting unit sets the positions of the control points as the design variables by including them in the design parameters.

3. The non-pneumatic tire design device according to claim 2, wherein the setting unit further sets the shape of the connecting member at the position of the control point and the shape of the outer cylinder body at the position of an end point indicating the connection point where the outer cylinder body and the connecting member are connected as design variables by including them in the design parameters.

4. The non-pneumatic tire design device according to claim 2, wherein the basic tire model is a model representing a cross-sectional shape of the tire, and wherein the setting unit: sets the position of the start point and the position of the end point so that a connecting point connecting the inner cylindrical body and the connecting member is a start point and a connecting point connecting the outer cylindrical body and the connecting member is an end point, and a line connecting a predetermined position in the radial direction of the tire and the start point forms a predetermined angle with a line connecting the predetermined position and the end point; uses the line connecting the start point and the end point to set each of a plurality of positions on the line at a predetermined distance from each of the plurality of positions on the line as each of the plurality of control points; sets a shape of the connecting member so that the inner cylindrical body and the outer cylindrical body are connected to the connecting member based on the plurality of control points that have been set; and sets a structure of the non-pneumatic tire by arranging a plurality of connecting members of the set shape around the tire.

5. The non-pneumatic tire design device according to claim 4, wherein the setting unit defines a rectangle having a line connecting the start point and the end point as a first line, one side of which is the first line, and defines a line having one side opposite to the first line as a second line, and sets each of the positions at a predetermined distance from the second line as the positions of the plurality of control points.

6. The non-pneumatic tire design device according to claim 4, wherein a curve passing through the plurality of control points is set as the center line of the connecting member, and a shape having a predetermined thickness centered on the set center line of the connecting member is set as the shape of the connecting member.

7. The tire basic model is a model representing a tire cross-sectional shape, and the setting unit: defines a connection point where the inner cylindrical body and a first connecting member, which is the connecting member, as a first starting point, and a connection point where the outer cylindrical body and the first connecting member are connected as a first ending point, and sets the positions of the first starting point and the first ending point so that a straight line connecting a predetermined position in the tire radial direction and the first starting point forms a predetermined angle with a straight line connecting the predetermined position and the first ending point; uses the straight line connecting the first starting point and the first ending point to set each of a plurality of positions on the straight line at a predetermined distance from the straight line as each of a plurality of control points of the first connecting member; sets a shape of the first connecting member so that the inner cylindrical body and the outer cylindrical body are connected to the first connecting member based on the plurality of control points of the first connecting member; and sets each of the positions of a second starting point and a second ending point of a second connecting member, which is a connecting member at a position different from that of the first connecting member; 2. The non-pneumatic tire design device according to claim 1, further comprising: using a straight line connecting the second start point and the second end point, setting each of positions at a predetermined distance from each of a plurality of positions on the straight line as each of a plurality of control points of the second connecting member; setting a shape of the second connecting member based on the plurality of control points of the second connecting member so that the inner cylindrical body and the outer cylindrical body are connected to the second connecting member; and arranging a plurality of connecting member sets made of the first connecting member and the second connecting member having the set shapes around the tire to set a structure of the non-pneumatic tire.

8. The non-pneumatic tire design device according to claim 1, wherein the design parameter determination unit calculates the design variables that give the optimal value of the objective function while satisfying the constraint conditions by mathematical programming using objective function sensitivity, which is the ratio of the amount of change in the objective function to a unit change in the design variable, and constraint condition sensitivity, which is the ratio of the amount of change in the constraint conditions to a unit change in the design variable.

9. The non-pneumatic tire design device according to claim 1, wherein the setting unit sets set information including the design variables that constitute each of the tire basic models, and is equipped with a new design variable generation unit that sequentially selects the design variables that constitute each of at least two of the tire basic models from the set information and executes, with a predetermined probability, either a crossover process that exchanges a portion of each of the selected design variables with another to generate a new design variable, or a mutation process that changes a portion of the selected design variables to generate a new design variable, or both of these processes, and the design parameter determination unit determines the final design parameters based on the design variables that give an optimal value of the objective function while satisfying the constraints, from the new set information that includes the generated new design variables and the other selected design variables.

10. The non-pneumatic tire design device according to claim 9, wherein, when a predetermined convergence condition is met, the design parameter determination unit determines the final design parameters based on the design variables, among the design variables included in the new set information, that give the optimal value of the objective function while satisfying the constraint conditions, and when the predetermined convergence condition is not met, the design parameter determination unit sets the new set information as the set information and causes the new design variable generation unit to repeatedly perform the same process.

11. The non-pneumatic tire design device according to claim 1, wherein the setting unit sets a conversion system relating the design variables to the tire performances corresponding to a plurality of design variables that have already been collected, and the design parameter determination unit sequentially changes the new design variables set by the setting unit and sequentially converts the design variables into the corresponding tire performances using the conversion system, thereby determining the final design parameters based on the design variables that provide optimal values for the tire performances while satisfying the constraints.

12. The non-pneumatic tire design device according to claim 11, wherein the conversion system includes a learning model that has been machine-learned to determine the correspondence between the design variables and the tire performance corresponding to the design variables.

13. The non-pneumatic tire design device according to claim 1, wherein, when the control point is moved by an input operation, the setting unit calculates a ratio between the position of the moved control point and the position of the control point before the movement, moves control points other than the moved control point according to the ratio, and sets the positions of the control points after the movement as the design variables by including them in the design parameters.

14. A non-pneumatic tire design method, comprising: a processor; setting a basic tire model in which a non-pneumatic tire including an inner cylindrical body, an outer cylindrical body, and a connecting member connecting the inner cylindrical body and the outer cylindrical body is modeled using a finite number of elements; an objective function representing tire performance of the non-pneumatic tire; constraints that restrict an allowable range of the tire performance; and design parameters used to determine positions of a plurality of control points arranged along the shape of the connecting member in the basic tire model of the non-pneumatic tire; and sequentially changing design variables included in the design parameters, and determining the design parameters based on the values of the design variables that give an optimal value of the objective function while satisfying the constraints.

15. A program causing a processor to perform the following processing: setting a basic tire model in which a non-pneumatic tire including an inner cylindrical body, an outer cylindrical body, and a connecting member connecting the inner cylindrical body and the outer cylindrical body is modeled using a finite number of elements; an objective function that represents tire performance of the non-pneumatic tire; constraints that restrict an allowable range of the tire performance; and design parameters used to determine positions of a plurality of control points arranged along the shape of the connecting member in the basic tire model of the non-pneumatic tire; and sequentially changing design variables included in the design parameters to determine the design parameters based on the values of the design variables that give the optimal value of the objective function while satisfying the constraints.

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