Airless tire simulation method

Abstract

To provide a simulation method enabling performance of an airless tire to be evaluated.SOLUTION: Provided is a simulation method for an airless tire having a tread ring, a hub, and a plurality of spokes. The simulation method includes: a model input step S1 of inputting to a computer an airless tire model including a tread ring model obtained by discretizing each of the tread ring, the hub, and the plurality of spokes with a finite number of elements, a hub model, and a plurality of spoke models; and a simulation step S2 in which the computer provides an external force to the airless tire model, and calculates a physical quantity acting on the airless tire model. The simulation step S2 includes a step of, for each of the plurality of spoke models, calculating a force acting on such a predetermined reference plane that cuts a length of the spoke model in a tire radial direction.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present invention relates to a method for simulating an airless tire.

Background Art

[0002] Patent Document 1 below describes a tire including a tread and spokes. In this document, in order to evaluate the peak strain energy density generated by the bending of the spokes, a model (mesh) of the non-deflected state of the spokes is created, and FEA (Finite Element Analysis) for bending the model is performed.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] In an airless tire, it is desirable that the weight of the vehicle is supported by the tension of the spokes located on the side not in contact with the ground (i.e., the upper side of the hub). Also, in order to mitigate the impact from the ground when in contact, it is also desirable to reduce the compression rigidity of the spokes. However, the magnitude of the tension such as tension or compression applied to each spoke varies among the plurality of spokes arranged in the tire circumferential direction, and the magnitude has not been sufficiently studied. Therefore, in order to evaluate the performance of an airless tire, it is important to consider these forces.

[0005] The present invention has been devised in view of the above actual situation, and the main object thereof is to provide a simulation method capable of evaluating the performance of an airless tire.

Means for Solving the Problems

[0006] The present invention relates to a method for simulating a non-pneumatic tire having an annularly extending tread ring, a hub concentrically arranged on the inner side in the tire radial direction of the tread ring, and a plurality of spokes extending in the tire radial direction between the tread ring and the hub. The method includes a model input step of inputting, to a computer, a non-pneumatic tire model including a tread ring model, a hub model, and a plurality of spoke models, which are obtained by discretizing the tread ring, the hub, and the plurality of spokes with a finite number of elements respectively, and a simulation step of applying an external force to the non-pneumatic tire model by the computer to calculate physical quantities acting on the non-pneumatic tire model. The simulation step includes a step of calculating, for each of the plurality of spoke models, a force acting on a predetermined reference plane that cuts the length of the spoke model in the tire radial direction.

[0007] In the method for simulating the non-pneumatic tire according to the present invention, the reference planes of the plurality of spoke models may be at the same position in the tire radial direction.

[0008] In the method for simulating the non-pneumatic tire according to the present invention, the reference planes of the plurality of spoke models may be planes orthogonal to the tire radial direction.

[0009] In the method for simulating the non-pneumatic tire according to the present invention, the nodes of the elements may be defined on the reference planes of the plurality of spoke models.

[0010] In the method for simulating the non-pneumatic tire according to the present invention, the model input step may include a step of inputting a first part model and a second part model, which are obtained by discretizing a first part and a second part of each of the plurality of spokes with the reference plane, and a step of setting the plurality of spoke models in which the nodes are defined on the reference plane by coupling the first part model and the second part model via the reference plane respectively.

[0011] In the simulation method of the airless tire according to the present invention, the step of inputting the first partial model and the second partial model may include the step of making the positions of the respective nodes on the reference plane of the first partial model and the second partial model coincide with each other.

[0012] In the simulation method of the airless tire according to the present invention, the model input step may include the step of setting the plurality of spoke models by discretizing, with the elements, a first part and a second part obtained by dividing each of the plurality of spokes by the reference plane.

[0013] In the simulation method of the airless tire according to the present invention, the calculating step may calculate at least one of a vertical force and a shear force acting on the reference plane.

Effect of the Invention

[0014] By adopting the above steps, the simulation method of the airless tire of the present invention can evaluate the performance of the airless tire.

Brief Description of the Drawings

[0015]

Figure 1

Figure 2

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Figure 8

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Figure 10

Figure 11

Figure 12

Figure 13

Mode for Carrying Out the Invention

[0016] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. It should be understood that the drawings include exaggerated expressions and expressions different from the dimensional ratios of actual structures in order to assist in understanding the present invention. Also, when there are a plurality of embodiments, the same or common elements are denoted by the same reference numerals throughout the specification, and redundant descriptions are omitted. Furthermore, the specific configurations shown in the embodiments and the drawings are for understanding the content of the present invention, and the present invention is not limited to the specific configurations shown.

[0017] In the simulation method of the airless tire of the present embodiment (hereinafter, sometimes simply referred to as "simulation method"), the performance of the airless tire is evaluated. In the simulation method of the present embodiment, a computer is used.

[0018] [Computer] FIG. 1 is a perspective view showing an example of a computer 1 for executing a simulation method of a non-pneumatic tire. The computer 1 is configured to include, for example, a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. In the main body 1a, for example, an arithmetic processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2 are provided. The storage device stores in advance software for executing the simulation method of the present embodiment. Therefore, the computer 1 is configured as a simulation device for a non-pneumatic tire.

[0019] [Non-pneumatic tire] FIG. 2 is a side view showing an example of a non-pneumatic tire 2 to be analyzed. The non-pneumatic tire 2 of the present embodiment is exemplified as a passenger car tire, but is not particularly limited. The non-pneumatic tire 2 may be used, for example, for a two-wheeled vehicle, a heavy load such as a truck or a bus, etc. Note that whether the non-pneumatic tire 2 is real or not is not questioned.

[0020] The non-pneumatic tire 2 has an annularly extending tread ring 3, a hub 4 concentrically arranged on the inner side in the tire radial direction of the tread ring 3, and a plurality of spokes 5 extending in the tire radial direction between the tread ring 3 and the hub 4.

[0021] [Tread ring] The tread ring 3 is an annular rubber member. The tread ring 3 is formed of, for example, vulcanized rubber. The outer peripheral surface of the tread ring 3 in the tire radial direction is formed as a ground contact surface 3a for contacting the ground (road surface). Various drainage grooves (not shown) may be formed in the ground contact surface 3a. The spokes 5 are joined to the inner peripheral surface 3b of the tread ring 3 in the tire radial direction (in this example, via the outer ring portion 6).

[0022] [Hub] The hub 4 is for fixing an axle (not shown). The hub 4 of the present embodiment is made of a metallic material. The hub 4 integrally includes, for example, a disk portion 4a and a cylindrical portion 4b formed on the outer side in the tire radial direction thereof.

[0023] [Spoke] The plurality of spokes 5 extend in the tire radial direction between the tread ring 3 and the hub 4 and integrally connect them. These spokes 5 can, for example, relieve the impact input to the tread ring 3 by flexing during running.

[0024] The plurality of spokes 5 of the present embodiment are respectively joined to the tread ring 3 via an annular outer ring portion 6 joined to the inner peripheral surface 3b of the tread ring 3. Note that the plurality of spokes 5 may be directly joined to the inner peripheral surface 3b of the tread ring 3.

[0025] The plurality of spokes 5 of the present embodiment are respectively joined to the hub 4 via an annular inner ring portion 7 joined to the outer peripheral surface (more specifically, the outer peripheral surface of the cylindrical portion 4b) 4e of the hub 4. Note that the plurality of spokes 5 may be directly joined to the outer peripheral surface 4e of the hub 4.

[0026] The plurality of spokes 5 of the present embodiment are made of the same material (for example, a resin or an elastomer material) as the outer ring portion 6 and the inner ring portion 7. The plurality of spokes 5, the outer ring portion 6, and the inner ring portion 7 are integrally formed.

[0027] [Method for Simulating an Airless Tire] Next, an example of the processing procedure of the simulation method of the present embodiment will be described. FIG. 3 is a flowchart showing an example of the processing procedure of the simulation method of the airless tire.

[0028] [Model Input Step (First Embodiment)] In the simulation method of this embodiment, first, a non-pneumatic tire model is input to the computer 1 (model input step S1). FIG. 4 is a side view showing an example of the non-pneumatic tire model 12.

[0029] In this embodiment, a non-pneumatic tire model 12 including a tread ring model 13, a hub model 14, and a plurality of spoke models 15, in which the tread ring 3, the hub 4, and the plurality of spokes 5 shown in FIG. 2 are discretized by a finite number of elements F(i), respectively, is input. FIG. 5 is a flowchart showing an example of the processing procedure of the model input step S1.

[0030] [Tread Ring Model Input Step] In the model input step S1 of this embodiment, first, a tread ring model 13 (shown in FIG. 4) in which the tread ring 3 (shown in FIG. 2) is discretized by a finite number of elements F(i) is input (step S11).

[0031] In the step S11 of this embodiment, based on information about the tread ring 3 (shown in FIG. 2) (for example, CAD data, etc.), the contour of the tread ring 3 is discretized using a finite number of elements F(i) (i = 1, 2,...) that can be handled by a numerical analysis method. Thereby, in the step S11, the tread ring model 13 is set. As the numerical analysis method of this embodiment, the finite element method is adopted, but for example, the finite volume method, the difference method, or the boundary element method may be adopted. For the above-mentioned discretization, for example, general meshing software (for example, "ICEM CFD" of ANSYS) is used.

[0032] For the element F(i), for example, a tetrahedral solid element, a pentahedral solid element, or a hexahedral solid element is used. Each element F(i) has a plurality of nodes 18. Numerical data such as an element number, a number of the node 18, and a coordinate value of the node 18 are defined for each element F(i).

[0033] Numerical data such as the material properties (e.g., density, Young's modulus, attenuation coefficient, loss tangent (tanδ), and / or complex elastic modulus E*, etc.) of the tread ring 3 shown in FIG. 2 are defined for each element F(i). The tread ring model 13 is input into the computer 1 (shown in FIG. 1).

[0034] [Hub Model Input Step] Next, in the model input step S1 of the present embodiment, a hub model 14 (shown in FIG. 4) obtained by discretizing the hub 4 (shown in FIG. 2) with a finite number of elements F(i) is input (step S12). In step S12 of the present embodiment, based on information about the hub 4 (e.g., CAD data, etc.), the hub 4 (its contour) is discretized using the above-mentioned finite number of elements F(i). Thereby, in step S12, the hub model 14 is set up.

[0035] Numerical data such as the material properties (e.g., density, Young's modulus, attenuation coefficient, loss tangent (tanδ), and / or complex elastic modulus E*, etc.) of the hub 4 shown in FIG. 2 are defined for each element F(i). In the hub model 14 of the present embodiment, only the cylindrical portion 4b of the hub 4 (shown in FIG. 2) is modeled. Furthermore, the hub model 14 is formed thinner than the cylindrical portion 4b. Thereby, in the present embodiment, the number of elements F(i) and the number of nodes 18 of the hub model 14 can be reduced, so that the calculation target in the simulation step S2 described later can be reduced. Therefore, in the simulation method of the present embodiment, the calculation time can be shortened. The hub model 14 is input into the computer 1 (shown in FIG. 1).

[0036] [Spoke Model Input Step (First Embodiment)] Next, in the model input step S1 of the present embodiment, a spoke model 15 obtained by discretizing each of the plurality of spokes 5 (shown in FIG. 2) with a finite number of elements F(i) is input (spoke model input step S13). FIG. 6(a) is an enlarged view of one spoke 5. FIG. 6(b) is an enlarged view of one spoke model 15.

[0037] In the present embodiment, for each of the plurality of spoke models 15, a predetermined reference plane 20 that cuts the length of the spoke model 15 in the tire radial direction (i.e., between the outer end 15a and the inner end 15b of the spoke model 15 in the tire radial direction) is set. These reference planes 20 are for calculating the forces acting on the spoke model 15 in the simulation step S2 described later. The forces calculated by these reference planes 20 are used to evaluate the performance of the non-pneumatic tire 2 (shown in FIG. 2).

[0038] In the plurality of spoke models 15 (spokes 5), each reference plane 20 can be set as appropriate. The reference plane 20 of the present embodiment is set on the inner end 15b side in the tire radial direction of the spoke model 15, but is not limited to such a mode. For example, it may be set on the outer end 15a side. Note that it is desirable that the reference planes 20 are at the same position as each other in the tire radial direction. Thereby, in the present embodiment, in each spoke model 15 (shown in FIG. 4), the forces acting at the same position in the tire radial direction can be calculated respectively, and they can be compared. FIG. 7 is a flowchart showing an example of the processing procedure of the spoke model input step S13.

[0039] In the spoke model input step S13 of the present embodiment, first, the first partial model 31 and the second partial model 32 (shown in FIG. 6(b)) are input (step S31). The first partial model 31 and the second partial model 32 are obtained by discretizing the first part 21 and the second part 22 (shown in FIG. 6(a)) obtained by dividing each of the plurality of spokes 5 by the reference plane 20 with the above-described element F(i).

[0040] As shown in FIG. 6(a), the first part 21 of the present embodiment is a part arranged on the outer side in the tire radial direction with respect to the reference plane 20 (indicated by a two-dot chain line) in each spoke 5. On the other hand, the second part 22 is a part arranged on the inner side in the tire radial direction with respect to the reference plane 20 in each spoke 5. These first part 21 and second part 22 can be specified based on information (such as CAD data) regarding each spoke 5.

[0041] In step S31, for each of the plurality of spokes 5, the first part 21 (outline) and the second part 22 (outline) are discretized using the finite number of elements F(i) described above. As a result, in step S31, the first part model 31 and the second part model 32 (shown in FIG. 6(b)) are respectively set.

[0042] In the present embodiment, the first part 21 and the second part 22 (shown in FIG. 6(a)) divided by the reference plane 20 are discretized independently of each other. Therefore, for example, even if the reference plane 20 is set at a portion where the shape change of the spoke 5 is large (for example, a corner portion at the inner end of the spoke 5), it is possible to easily discretize them.

[0043] FIG. 8 is a partial perspective view showing an example of each reference plane 20 of the first part model 31 and the second part model 32. In FIG. 8, in order to illustrate both the reference plane 20 of the first part model 31 and the reference plane 20 of the second part model 32, a state in which the first part model 31 is tilted with respect to the second part model 32 is shown.

[0044] At the reference plane (division plane) 20 of the first part model 31 and the reference plane (division plane) of the second part model 32, the nodes 18 of the element F(i) are respectively set by the above-described discretization. The first part model 31 and the second part model 32 are stored in the computer 1.

[0045] Next, in the spoke model input step S13 of the present embodiment, a plurality of spoke models 15 (shown in FIG. 6(b)) in which the first partial model 31 and the second partial model 32 are respectively combined via the reference plane 20 are set (step S32). In step S32, for each of the spokes 5 (shown in FIG. 2), the first partial model 31 and the second partial model 32 that model the first part 21 and the second part 22 (shown in FIG. 6(a)) are respectively combined via the reference plane 20. As a result, in step S32, a plurality of spoke models 15 (shown in FIG. 4) in which each of the plurality of spokes 5 is discretized by the above-described element F(i) are set. The plurality of spoke models 15 are stored in the computer 1.

[0046] The first partial model 31 and the second partial model 32 (shown in FIG. 6(b)) can be combined as appropriate. Such combination can be realized, for example, by constraining (defining constraint conditions) the relative positions of the respective nodes 18 of the first partial model 31 facing each other at the reference plane 20 shown in FIG. 8 and the respective nodes 18 of the second partial model 32. Note that the first partial model 31 and the second partial model 32 may be combined by sharing (merging) the respective nodes 18 of the first partial model 31 and the second partial model 32 facing each other at the reference plane 20.

[0047] In order to easily constrain or share the respective nodes 18, 18 facing each other at the reference plane 20, step S31 may include a step of making the positions of the respective nodes 18 on the reference plane 20 of the first partial model 31 and the second partial model 32 shown in FIG. 8 coincide with each other. Here, "making the positions of the respective nodes 18 coincide with each other" means making the positions (coordinate values) of the respective nodes 18 formed on the reference plane 20 and the number of nodes 18 the same when the first partial model 31 and the second partial model 32 are opposed via the reference plane 20. In this way, in order to make the positions of the respective nodes 18 coincide with each other, for example, constraint conditions such as the number of nodes 18 on the reference plane 20 and their coordinate values can be set in the above-described meshing software prior to the discretization of the element F(i), and thus it can be easily realized.

[0048] In this way, by aligning the positions of the respective nodes 18 of the first partial model 31 and the second partial model 32 facing each other at the reference plane 20, in step S32, it becomes possible to easily share or constrain the nodes 18, 18 facing each other at the reference plane 20. Furthermore, the shapes of the elements F(i) at the reference plane 20 of the first partial model 31 and the second partial model 32 can be made to coincide. As a result, even if large deformations are calculated in the simulation step S2 described later for each spoke model 15, the first partial model 31 and the second partial model 32 constituting them can smoothly follow the deformed shapes via the reference plane 20. Therefore, in the present embodiment, even when the spoke model 15 composed of the first partial model 31 and the second partial model 32 is used, the simulation accuracy does not decrease.

[0049] [Punctureless Tire Model Input Step] Next, in the model input step S1 of the present embodiment, as shown in FIG. 4, the tread ring model 13, the hub model 14, and a plurality of spoke models 15 are combined to define a punctureless tire model 12 (step S14). The combination of the tread ring model 13, the hub model 14, and the plurality of spoke models 15 can be appropriately performed by constraining the nodes 18 and sharing the nodes 18 as described above.

[0050] In the punctureless tire model 12 of the present embodiment, an outer ring model 16 in which the outer ring portion 6 (the contour thereof) shown in FIG. 2 is discretized by a finite number of elements F(i) is arranged between the tread ring model 13 and the plurality of spoke models 15. Note that the outer ring model 16 may be omitted.

[0051] On the other hand, although the plurality of spoke models 15 are coupled to the hub model 14, it is not necessarily limited to such an aspect. For example, an inner ring model (not shown) modeling the inner ring portion 7 shown in FIG. 1 may be arranged between the plurality of spoke models 15 and the hub model 14.

[0052] In the model input step S1 of the present embodiment, the tread ring model 13, the hub model 14, and the plurality of spoke models 15 are each discretized independently, but it is not limited to such a mode. For example, models outside the tire radial direction from the reference plane 20 (shown in FIG. 6(b)) (for example, the tread ring model 13, the outer ring model 16, and the first partial model 31 (shown in FIG. 6(b))) may be discretized together. Further, models inside the tire radial direction from the reference plane 20 (for example, the second partial model 32 (shown in FIG. 6(b)) and the hub model 14) may be discretized together. The airless tire model 12 is stored in the computer 1.

[0053] [Simulation Step] Next, in the simulation method of the present embodiment, the computer 1 applies an external force to the airless tire model 12 and calculates the physical quantity acting on the airless tire model 12 (simulation step S2). FIG. 9 is a flowchart showing an example of the processing procedure of the simulation step S2. FIG. 10 is a side view showing an example of the airless tire model 12 and the road surface model 23. In FIG. 10, the element F(i) shown in FIG. 4 is omitted.

[0054] In the simulation step S2 of the present embodiment, first, an external force is applied to the airless tire model 12 (step S21). The external force to the airless tire model 12 can be appropriately applied based on the performance to be evaluated. In the present embodiment, an external force is applied to the airless tire model 12 based on a predetermined load condition L.

[0055] In the present embodiment, in order to apply an external force to the airless tire model 12, a road surface model 23 that models the road surface (not shown) on which the tread ring 3 shown in FIG. 2 contacts the ground is used. The road surface model 23 can be appropriately set. In the present embodiment, the road surface (not shown) is discretized using a finite number of elements (not shown) that can be handled by a numerical analysis method (in the present embodiment, the finite element method). The element is defined, for example, as a rigid plane element set to be non-deformable.

[0056] In step S21 of this embodiment, first, the tread ring model 13 of the non-pneumatic tire model 12 and the road surface model 23 are brought into contact with each other. Next, a load condition L directed toward the non-pneumatic tire model 12 is defined for the road surface model 23 in a state where the degree of freedom of the rotation axis 12s (indicated by a two-dot chain line) of the non-pneumatic tire model 12 is constrained. As a result, in step S21, an external force is applied to the non-pneumatic tire model 12. The load condition L can be set as appropriate. The load condition L may be set, for example, based on the normal load of a pneumatic tire replaced by the tire size of the non-pneumatic tire 2.

[0057] The "normal load" is the load defined for each tire in a standard system including the standards on which the tire is based. Therefore, the normal load is, for example, "maximum load capacity" in the case of JATMA, the maximum value described in the table "TIRE LOAD LIMITS AT VARIOUS COLD INFLATION PRESSURES" in the case of TRA, and "LOAD CAPACITY" in the case of ETRTO.

[0058] The deformation calculation of the non-pneumatic tire model 12 is performed based on the shapes and material properties of the respective elements F(i) shown in FIG. 4, and the mass matrix, stiffness matrix, and damping matrix of each element F(i) are created. Further, these matrices are combined to create the matrix of the entire system. Then, the equations of motion are created by applying the various conditions, and these are calculated for each small time (unit time T(x) (x = 0, 1,...)). As a result, the deformation calculation of the non-pneumatic tire model 12 is performed. The unit time T(x) is set as appropriate according to the required simulation accuracy. Further, for the deformation calculation, a commercially available finite element analysis application software such as LS-DYNA manufactured by LSTC is used.

[0059] As shown in FIG. 10, in step S21 of this embodiment, a state in which a plurality of spoke models 15 are deformed into different shapes is calculated by the external force (load condition L) applied to the non-pneumatic tire model 12.

[0060] Next, in the simulation step S2 of the present embodiment, for each of the plurality of spoke models 15, the force acting on the reference plane 20 (shown in FIGS. 6(b) and 8) is calculated (step S22). In the present embodiment, the force acting on the node 18 defined on the reference plane 20 is calculated. When a plurality of nodes 18 are defined on the reference plane 20, for example, the average value or the total value of the forces of each node 18 may be obtained, or the maximum value or the minimum value may be obtained.

[0061] In the present embodiment, as the force acting on the reference plane 20, at least one of the vertical force acting on the reference plane 20 and the shear force is calculated (output). Note that, in step S22, physical quantities (forces) different from these may be calculated. The vertical force includes the tension of tension or compression acting in the tire radial direction at the node 18 of the reference plane 20.

[0062] As shown in FIG. 10, the tension F1 of tension is the tension toward the rotation axis 12s with respect to the tread ring model 13. Such a tension F1 of tension mainly acts on the spoke model 15 located on the side not in contact with the road surface model 23 (that is, the upper side of the hub model 14). On the other hand, the compression tension F2 is the tension toward the side opposite to the rotation axis 12s (tread ring model 13). Such a compression tension F2 mainly acts on the spoke model 15 located on the side in contact with the road surface model 23 (that is, the lower side of the hub model 14). The shear force (not shown) is calculated as the shear force acting parallel to the reference plane 20 at the node 18 of the reference plane 20 shown in FIG. 6(b). The force acting on each reference plane 20 is stored in the computer 1.

[0063] In order to effectively calculate the above vertical force and shear force, each reference plane 20 (shown in FIG. 6(b)) is preferably a plane orthogonal to the tire radial direction. Thereby, in step S22, it becomes possible to calculate the vertical force acting in the tire radial direction and the shear force acting in the direction orthogonal to the tire radial direction over the entire area of each reference plane 20.

[0064] As shown in FIG. 10, in the simulation step S2 of the present embodiment, in order to apply an external force to the airless tire model 12, the airless tire model 12 is brought into contact with the road surface model 23, and the load condition L is defined, but it is not limited to such a mode. In the simulation step S2, for example, a state in which the airless tire model 12 rolls on the road surface model 23 may be calculated.

[0065] [Evaluation Step] Next, in the simulation method of the present embodiment, the performance of the airless tire is evaluated based on the force acting on the reference surface 20 (step S3). In step S3, the evaluation of the performance of the airless tire 2 may be performed by the computer 1 or may be performed by an operator or the like.

[0066] FIG. 11 is a graph showing an example of the relationship between the identification number of the spoke model 15 and the vertical force. FIG. 12 is a graph showing an example of the relationship between the identification number of the spoke model 15 and the shear force. The identification number is based on one spoke model 15 selected from the plurality of spoke models 15 shown in FIG. 10 (the identification number is "1"), and is sequentially assigned to the spoke models 15 arranged on one side in the tire circumferential direction from that reference. The vertical force is such that the tension (tensile tension F1) toward the rotation axis 12s shown in FIG. 10 is a positive value, and the tension (compressive tension F2) toward the side opposite to the rotation axis 12s is a negative value. The shear force is such that the shear force acting on one side in the tire circumferential direction is a positive value, and the shear force acting on the other side in the tire circumferential direction is a negative value.

[0067] As described above, in the simulation step S2, due to the external force (load condition L) applied to the airless tire model 12 shown in FIG. 10, the deformed shapes of the plurality of spoke models 15 are different from each other. Therefore, as shown in FIGS. 11 and 12, the magnitude of the force (such as vertical force and shear force) applied to one spoke model 15 is different for each of the plurality of spoke models 15 arranged in the tire circumferential direction. In the present embodiment, since the forces (such as vertical force and shear force) applied to each spoke model 15 are calculated respectively, it is possible to evaluate the performance considering them.

[0068] In the present embodiment, based on a predetermined reference plane 20, the forces applied to each spoke model 15 are calculated (output). For this reason, in step S3, based on a certain standard, those forces can be compared, so that it is possible to appropriately evaluate the performance of the airless tire. Further, in the present embodiment, each reference plane 20 (shown in FIG. 6(b)) is set at the same position in the tire radial direction. For this reason, in step S3, in each spoke model 15, the forces acting at the same position in the tire radial direction can be accurately compared, and it is possible to evaluate the performance of the airless tire.

[0069] In step S3 of the present embodiment, it is determined whether the tensile tension, compressive tension, or shear force of each spoke model 15 is equal to or less than a predetermined threshold value. And in step S3, if those values are equal to or less than the threshold value, it is determined that the performance of the airless tire 2 is good.

[0070] The threshold value is appropriately set based on, for example, the performance (such as durability and riding comfort) required for the airless tire 2 (shown in FIG. 2). The threshold value may be set for each of the tensile tension, compressive tension, or shear force.

[0071] In step S3, if it is determined that the performance of the non-pneumatic tire is good (i.e., "Y" in step S3), based on the design factors used in the setting of the non-pneumatic tire model 12, the non-pneumatic tire 2 (shown in FIG. 2) is manufactured (step S4). On the other hand, in step S3, if it is determined that the performance is not good (i.e., "N" in step S3), the design factors of the non-pneumatic tire model 12 are changed (step S5), and the model input steps S1 to S3 are performed again. Thus, with the simulation method of the present embodiment, it is possible to reliably design and manufacture the non-pneumatic tire 2 with good performance.

[0072] In step S3 of the present embodiment, it is determined whether the tensile stress, compressive stress, or shear stress of each spoke model 15 is equal to or less than a predetermined threshold value, but the present invention is not limited to such an aspect. For example, the performance of the non-pneumatic tire may be evaluated based on the ratio of the number of spoke models 15 subjected to tensile stress to the number of spoke models 15 subjected to compressive stress.

[0073] [Model Input Step (Second Embodiment)] In the model input step S1 (spoke model input step S13) of the previous embodiments, the first partial model 31 and the second partial model 32 shown in FIGS. 6(b) and 8 are coupled via the reference plane 20, but the present invention is not limited to such an aspect. FIG. 13 is a flowchart showing an example of the processing procedure of the spoke model input step S13 according to another embodiment of the present invention. In this embodiment, the same components as those in the previous embodiments may be denoted by the same reference numerals, and the description thereof may be omitted.

[0074] [Spoke Model Input Step (Second Embodiment)] In the spoke model input step S13 of this embodiment, for each of the plurality of spokes 5 (shown in FIG. 2), a first portion 25 and a second portion 26 (shown in FIG. 6(a)) divided by the reference plane 20 are specified (step S33). The first portion 25 is a portion (region) arranged on the outer side in the tire radial direction with respect to the reference plane 20 in each spoke 5. On the other hand, the second portion 26 is a portion (region) arranged on the inner side in the tire radial direction with respect to the reference plane 20 in each spoke 5. In this embodiment, in each spoke 5, without being divided into a first portion 21 and a second portion 22 (for example, shown in FIG. 8), the contour of each spoke 5 is virtually divided, whereby the first portion 25 and the second portion 26 are specified. These first portion 25 and second portion 26 can be specified based on information (for example, CAD data, etc.) regarding each spoke 5.

[0075] Next, in the spoke model input step S13 of this embodiment, each of the first portion 25 and the second portion 26 is discretized using the element F(i) shown in FIG. 6(b) (step S34). In step S34, since the contour of the first portion 25 and the contour of the second portion 26 are discretized independently, the element F(i) does not straddle the reference plane 20. Therefore, in step S34, the node 18 can be defined on the reference plane 20.

[0076] In this embodiment, since each spoke 5 is not divided into a first portion 25 and a second portion 26 and their regions are discretized by the element F(i), it is not necessary to combine the first portion model 31 and the second portion model 32 (shown in FIG. 8) as in the previous embodiments. Therefore, in this embodiment, the spoke model 15 can be defined in an even shorter time.

[0077] In step S34, in each spoke model 15, a step of matching the positions of each node 18 on the reference planes 20 on the first part 21 side and the second part 22 side may be included. Thereby, even if large deformations are calculated in the above-described simulation step S2 for each spoke model 15, the deformed shapes of the parts corresponding to the first part 25 and the second part 22 can be smoothly followed via the reference plane 20.

[0078] As described above, the particularly preferred embodiments of the present invention have been described in detail. However, the present invention is not limited to the illustrated embodiments and can be implemented in various forms.

Example

[0079] Based on the processing procedure shown in FIG. 3, simulations for evaluating the performance of the non-pneumatic tire were carried out (Example 1 and Example 2). In Example 1 and Example 2, a non-pneumatic tire model including a tread ring model, a hub model, and a plurality of spoke models in which the tread ring, the hub, and the plurality of spokes were each discretized into a finite number of elements was input. For each of these non-pneumatic tire models, a predetermined reference plane that cuts the length of the spoke model in the tire radial direction was set for each of the plurality of spoke models.

[0080] In Example 1, based on the processing procedure shown in FIG. 5, a first part model and a second part model in which each of the plurality of spokes was divided by a reference plane and discretized into elements were input. Then, in Example 1, by connecting the first part model and the second part model via the reference plane, a plurality of spoke models in which nodes were defined on the reference plane were set. In Example 1, the positions of each node on the reference plane of the first part model and the second part model were made to coincide with each other.

[0081] In Example 2, based on the processing procedure shown in FIG. 13, a plurality of spoke models were set by discretizing, with elements, a first portion and a second portion obtained by dividing each of the plurality of spokes by a reference plane. In Example 2, the positions of the respective nodes on the reference planes on the first portion side and the second portion side were made to coincide with each other.

[0082] In Example 1 and Example 2, each reference plane set in the plurality of spoke models was set at the same position as each other in the tire radial direction. Further, each reference plane was set as a plane orthogonal to the tire radial direction.

[0083] Then, a simulation process was performed in which an external force (load condition) was applied to each of the airless tire model of Example 1 and the airless tire model of Example 2, and physical quantities acting thereon were calculated. In this simulation process, for each of the plurality of spoke models, the force acting on the reference plane was calculated. The common specifications are as follows. Tire dimensions (unloaded state): Tread ring: Outer diameter: 528 mm Width: 94 mm Thickness: 25 mm Inner diameter of the disk portion of the hub: 328 mm Spokes: Length in the tire radial direction: 68 mm Number: 48 Reference plane: Same position as each other in the tire radial direction External force (load condition L): 2.2 kN

[0084] FIG. 11 is a graph showing an example of the relationship between the identification number of the spoke model of Example 1 and the vertical force. FIG. 12 is a graph showing an example of the relationship between the identification number of the spoke model of Example 1 and the shear force. In Example 2, like in Example 1, the vertical force and the shear force were obtained.

[0085] In Example 1 and Example 2, in the non-pneumatic tire model to which an external force was applied, for each of the plurality of spoke models, the force acting on each spoke model could be considered. Therefore, Example 1 and Example 2 were able to evaluate the performance of the non-pneumatic tire.

[0086] Unlike Example 2, in Example 1, since the first part and the second part obtained by dividing the spoke by the reference plane were discretized respectively, even if the reference plane was set at the part where the shape change of the spoke was large, it could be easily discretized. On the other hand, in Example 2, unlike Example 1, since it was not necessary to combine the divided first part model and the second part model, the spoke model could be defined in a short time.

Explanation of Signs

[0087] S1 Model Input Process S2 Simulation Process

Claims

1. A method for simulating a non-pneumatic tire having an annularly extending tread ring, a hub concentrically arranged radially inside the tire of the tread ring, and a plurality of spokes extending in the tire radial direction between the tread ring and the hub, a model input step of inputting, into a computer, a non-pneumatic tire model including a tread ring model, a hub model, and a plurality of spoke models, each of which discretizes the tread ring, the hub, and the plurality of spokes with a finite number of elements; a simulation step in which the computer applies an external force to the non-pneumatic tire model and calculates physical quantities acting on the non-pneumatic tire model, the simulation step including, for each of the plurality of spoke models, a step of calculating a force acting on a predetermined reference plane that cuts the length of the spoke model in the tire radial direction, the model input step including a step of inputting a first partial model and a second partial model, which are obtained by dividing each of the plurality of spokes by the reference plane and discretizing them with the elements; a step of setting the plurality of spoke models in which nodes of the elements are defined on the reference plane by coupling the first partial model and the second partial model via the reference plane, when the first partial model and the second partial model are opposed to each other via the reference plane, coordinate values of each node formed on the reference plane of the first partial model and the second partial model, and the number of the nodes are the same, A method for simulating a non-pneumatic tire.

2. The method for simulating a non-pneumatic tire according to claim 1, wherein the reference planes of the plurality of spoke models are at the same position as each other in the tire radial direction.

3. The method for simulating a non-pneumatic tire according to claim 1 or 2, wherein the reference planes of the plurality of spoke models are planes orthogonal to the tire radial direction.

4. The method for simulating a non-pneumatic tire according to any one of claims 1 to 3, wherein the reference plane is set between the outer end and the inner end of the spoke model in the tire radial direction. **Claim 5**: The simulation process according to any one of claims 1 to 4, wherein the simulation process includes a step of defining a load condition L directed to the airless tire model on a road surface model obtained by modeling a road surface while restricting the degree of freedom of the rotation axis of the airless tire model. **Claim 6** The step of inputting the first partial model and the second partial model according to claim 5, wherein the step includes a step of matching the positions of the respective nodes on the reference plane of the first partial model and the second partial model with each other. **Claim 7** The model input step according to claim 4, wherein the model input step includes a step of setting a plurality of spoke models by discretizing, by the elements, a first part and a second part obtained by dividing each of the plurality of spokes by the reference plane. **Claim 8** The step of calculating according to any one of claims 1 to 7, wherein the step of calculating calculates at least one of a vertical force and a shear force acting on the reference plane.

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