Tire model creation method, tire model creation device, and tire model creation program

Abstract

The tire model manufacturing apparatus includes: a modeling unit that separately models a shell and a pattern representing a patterned tire using a spline function; a surface coupling unit that couples a surface of a housing model, which is a model of the housing, and a surface of a pattern model, which is a model of the pattern; a calculation point arrangement unit that arranges, on a coupling surface between the surface of the housing model and the surface of the pattern model, calculation points for calculating the restoring force of the coupling surface; and a restoring force calculation unit that calculates a restoring force on the basis of the arranged calculation points.

Description

Technical Field

[0001] The present invention relates to a tire model making method, a tire model making device and a tire model making program. Background Art

[0002] Conventionally, the ground contact behavior of a tire has been analyzed using the finite element method (FEM) etc. In numerical analysis using FEM, the tire shape is created using CAD (Computed Aided Design) and then element segmentation is performed.

[0003] In addition, IGA (Isogeometric Analysis) is known as a numerical analysis method that replaces FEM (for example, refer to non-patent document 1 (JA Cottrell, TJR Hughes, and Y. Bazilevs, "Isogeometric Analysis Toward Integration of CAD and FEA." Wiley, 2009.)). IGA is a method that is more compatible with CAD than FEM. When expressing the shape of an object, FEM expresses it through straight lines (first-order basis functions), while IGA expresses it through spline functions. In addition, a method of applying IGA to the analysis of tires is disclosed in non-patent document 2 (Garcia, MA, and Kaliske, M., "Isogeometric Analysis for Tire Simulation at Steady-State Rolling", Tire Science and Technology, TSTCA, Vol. 47, No. 3, July-September, pp. 174-195.).

[0004] In addition, Patent Document 1 (Japanese Patent Application Laid-Open No. 2013-6491) discloses a method of using a spline function in a simulation for predicting the contact area between a tire and a road surface. This method generates a tire model by dividing the tire into a finite number of elements, divides the nodes that are vertices of the elements on the outer peripheral surface of the tire model into contact nodes included in the contact portion that contacts the road surface and non-contact nodes included in the non-contact portion that does not contact the road surface, and calculates the contact area using at least the position information of the non-contact nodes. Summary of the invention

[0005] Problem that the invention aims to solve

[0006] In addition, in numerical analysis using FEM, element segmentation is performed after the tire shape is created by CAD, so the element segmentation takes time and effort. Therefore, it can be considered that by using IGA, which is highly compatible with CAD, instead of FEM in numerical analysis of tires, not only can the time and effort spent on element segmentation be reduced, but also the shape expressed by CAD can be directly analyzed, so the tire shape reproducibility becomes higher and the analysis accuracy can be improved.

[0007] The above-mentioned Non-Patent Document 2 discloses a method of applying IGA to tire analysis, but does not mention analysis of treaded tires. In addition, the above-mentioned Patent Document 1 does not disclose a specific method of using spline functions in simulation.

[0008] The present disclosure aims to provide a tire model making method, a tire model making device, and a tire model making program that can achieve high tire shape reproducibility and improved analysis accuracy when making a model of a treaded tire.

[0009] Solutions for solving problems

[0010] In order to achieve the above object, a first method is a tire model making method for simulating the performance of a tire with a tread pattern, the tire model making method comprising:

[0011] Using a spline function to separately model a shell and a tread representing the treaded tire;

[0012] coupling a surface of a shell model serving as a model of the shell with a surface of a pattern model serving as a model of the pattern;

[0013] configuring a calculation point for calculating the restoring force of the coupling surface between the surface of the shell model and the surface of the pattern model; and

[0014] The restoring force is calculated based on the configured calculation points.

[0015] A second aspect is, in the tire model making method of the first aspect,

[0016] At a reference time, there is a gap between the surface of the shell model and the surface of the pattern model.

[0017] A third aspect is, in the tire model making method of the second aspect,

[0018] The restoring force is calculated using the coefficient of the restoring force, the time increment, the shape function of the shell model, the shape function of the pattern model, the parameterized coordinates of the calculation points, the coordinates of the control points at the current moment, the coordinates of the control points at the reference moment, the area of ​​the coupling surface, and the variable representing the gap.

[0019] A fourth aspect is a tire model making method according to any one of the first to third aspects, wherein

[0020] The spline function is a T-spline function.

[0021] A fifth aspect is, in the tire model making method of any one of the first to third aspects,

[0022] The housing includes a membrane member,

[0023] The spline function is a T-spline function,

[0024] The membrane member is modeled using the T-spline function.

[0025] A sixth aspect is a tire model making device for simulating the performance of a tire with a tread pattern, the tire model making device comprising:

[0026] a modeling unit that separately models a casing and a pattern representing the treaded tire using a spline function;

[0027] a surface coupling unit for coupling a surface of a shell model serving as a model of the shell with a surface of a pattern model serving as a model of the pattern;

[0028] a calculation point configuration unit configured to configure calculation points for calculating a restoring force of a coupling surface between a surface of the shell model and a surface of the pattern model; and

[0029] A restoring force calculation unit calculates the restoring force based on the arranged calculation points.

[0030] A seventh aspect is a tire model making program for simulating the performance of a treaded tire, the tire model making program causing a computer to execute the following processing:

[0031] Using a spline function to separately model a shell and a tread representing the treaded tire;

[0032] coupling a surface of a shell model serving as a model of the shell with a surface of a pattern model serving as a model of the pattern;

[0033] configuring a calculation point for calculating the restoring force of the coupling surface between the surface of the shell model and the surface of the pattern model; and

[0034] The restoring force is calculated based on the configured calculation points.

[0035] Effects of the Invention

[0036] According to the present disclosure, when a model of a treaded tire is produced, the tire shape reproducibility is high and the analysis accuracy can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a block diagram showing an example of the electrical configuration of the tire model creating device according to the first embodiment.

[0038] Figure 2 It is a schematic cross-sectional view showing an example of main members constituting the treaded tire according to the embodiment.

[0039] Figure 3 This is a block diagram showing an example of the functional structure of the tire model creating device according to the first embodiment.

[0040] Figure 4 It is a diagram schematically showing an example of a shell model and a pattern model according to the embodiment.

[0041] Figure 5 This is a diagram for explaining the modeling of the tied contact according to the embodiment.

[0042] Figure 6 This is a flowchart showing an example of the flow of processing of the tire model creation program according to the first embodiment.

[0043] Figure 7 A diagram for explaining an analysis example of a shell model and a pattern model.

[0044] Figure 8 A diagram for explaining an analysis example of a shell model and a pattern model.

[0045] Fig. 9 A diagram for explaining an analysis example of a shell model and a pattern model.

[0046] Fig.10 A diagram for explaining an analysis example of a shell model and a pattern model.

[0047] Fig.11 This is a diagram showing the ground contact pressure distribution result when the performance prediction of the treaded tire is performed using the IGA analysis.

[0048] Fig.12 A diagram for explaining the difference between NURBS and T-spline.

[0049] Fig.13 This is a diagram showing an example of the cross-sectional shape of a tire produced using T-splines.

[0050] Fig.14 This is a diagram showing the vicinity of the belt end after reducing the control points using T-splines.

[0051] Fig.15 FIG. 1 is a diagram showing an example of the positions and weights of control points for expressing a perfect circle.

[0052] Fig.16 FIG. 1 is a diagram showing an example of a tire model developed in the circumferential direction.

[0053] Fig.17 1 is a diagram showing an example of a tire model that is thinned and divided again in the circumferential direction.

[0054] Fig.18 It is a diagram showing an example of a film member and a virtual entity.

[0055] Fig.19 It is a diagram showing a comparative example of the results of film analysis based on IGA and FEM.

[0056] Fig. 20 FIG. 1 is a diagram schematically showing a state where control points are arranged at the mesh boundary. DETAILED DESCRIPTION

[0057] Hereinafter, embodiments for realizing the technology of the present disclosure will be described in detail with reference to the drawings.

[0058] In addition, for components and processes that have the same role and function, the same reference numerals are sometimes marked in all drawings and repeated descriptions are appropriately omitted. In addition, the present disclosure is not limited to the following embodiments and can be implemented with appropriate changes within the scope of the purpose of the present disclosure. In addition, in the present disclosure, the estimation of physical quantities for nonlinearly deformed components is mainly described, but of course it can also be applied to the estimation of physical quantities for linearly deformed components.

[0059] In addition, in each embodiment described below, "shape reproducibility" includes reproducing the shape change over time. "Casing" is also called "base tire", which means the part of the tire other than the tread part, and "pattern" means the tread part of the tire where the tread pattern is formed. "FEM" is the abbreviation of Fenite Element Method, and "IGA" is the abbreviation of Isogeometric Analysis.

[0060] [First embodiment]

[0061] Figure 1This is a block diagram showing an example of the electrical configuration of the tire model creating device 10 according to the first embodiment.

[0062] like Figure 1 As shown, the tire model making device 10 according to the present embodiment includes a CPU (Central Processing Unit) 11, a ROM (Read Only Memory) 12, a RAM (Random Access Memory) 13, an input / output interface (I / O) 14, a storage unit 15, a display unit 16, an operation unit 17, and a communication unit 18. In the tire model making device 10, for example, a general-purpose computer device such as a personal computer (PC) or a server computer is applied.

[0063] The CPU 11, ROM 12, RAM 13 and I / O 14 are connected to each other via a bus. The I / O 14 is connected to each functional unit including a storage unit 15, a display unit 16, an operation unit 17 and a communication unit 18. These functional units are configured to be able to communicate with the CPU 11 via the I / O 14.

[0064] The control unit is composed of CPU 11, ROM 12, RAM 13 and I / O 14. The control unit can be configured as a sub-control unit that controls the operation of a part of the tire model making device 10, or can be configured as a part of the main control unit that controls the overall operation of the tire model making device 10. A part or all of the blocks of the control unit, for example, use an integrated circuit such as LSI (LargeScale Integration) or an IC chipset. Each of the above blocks can use a separate circuit or a circuit that integrates a part or all of them. The above blocks can be set as one piece, or a part of the blocks can be set separately. In addition, in each of the above blocks, a part of it can also be set separately. The integration of the control unit is not limited to the use of LSI, and a dedicated circuit or a general-purpose processor can also be used.

[0065] As the storage unit 15, for example, a HDD (Hard Disk Drive), an SSD (Solid State Drive), a flash memory, etc. are used. The storage unit 15 stores a tire model creation program 15A for executing the tire model creation process involved in this embodiment. In addition, the tire model creation program 15A may also be stored in the ROM 12.

[0066] The tire model making program 15A may be pre-installed in the tire model making device 10, for example. The tire model making program 15A may be stored in a non-volatile storage medium or distributed via a network and appropriately installed in the tire model making device 10. Examples of the non-volatile storage medium include a CD-ROM (Compact Disc Read Only Memory), a magneto-optical disk, a HDD, a DVD-ROM (Digital Versatile Disc Read Only Memory), a flash memory, a memory card, and the like.

[0067] The display unit 16 uses, for example, a liquid crystal display (LCD), an organic EL (ElectroLuminescence) display, etc. The display unit 16 may also have a touch panel integrally. The operation unit 17 is provided with a device for operation input, such as a keyboard and a mouse. The display unit 16 and the operation unit 17 receive various instructions from the user of the tire model making device 10. The display unit 16 displays various information such as the result of the processing executed according to the instruction received from the user and the notification of the processing.

[0068] As an example, the communication unit 18 is connected to a network such as the Internet, a LAN (Local Area Network), or a WAN (Wide Area Network), and can communicate with external devices via the network.

[0069] Figure 2 It is a schematic cross-sectional view showing an example of main components constituting the treaded tire 40 according to the present embodiment.

[0070] like Figure 2 As shown, the treaded tire 40 has a carcass ply 42 for maintaining the internal pressure shape. The carcass ply 42 uses, for example, organic fiber cords to form the skeleton of the tire 40. The carcass ply 42 is also called a carcass or a ply, and the carcass ply 42 is hereinafter referred to as a ply 42.

[0071] The carcass layer 42 is folded back by a bead core 44 for fixing the treaded tire 40 to a rim (not shown). In the treaded tire 40, a bead rubber 46 is arranged at a position on the inner side of the bead core 44 in the tire radial direction, thereby forming a bead portion 48 at the front end portion on the inner side of the tire radial direction. In the treaded tire 40, a bead filler 50 for maintaining the rigidity of the bead portion 48 is arranged in a triangular area formed by the folded back carcass layer 42, and a sidewall tread 52 for protecting the carcass layer 42 is arranged on the outer side of the carcass layer 42. In addition, in the treaded tire 40, a belt layer 54 is arranged on a position on the outer side of the carcass layer 42 in the tire radial direction, and a tread 56 is arranged on the outer side of the belt layer 54 in the tire radial direction. In the tread 56, the area where the pattern (tread pattern) is formed is a tread portion 58. In addition, a tubeless tire is used as an example as the tread tire 40 , and an inner liner layer (not shown) for maintaining an airtight inner pressure is arranged inside the carcass layer 42 .

[0072] In addition, when performing numerical analysis on patterned tires, by using IGA, which is highly compatible with CAD, instead of FEM, not only can the time and labor spent on element segmentation be reduced, but the shape expressed by CAD can also be directly analyzed. Therefore, it is believed that the shape reproducibility of the tire is improved, and the analysis accuracy can also be improved.

[0073] Therefore, the tire model making device 10 involved in this embodiment uses IGA to simulate the performance of a treaded tire. When modeling a treaded tire, it is difficult to model the casing (base tire) and the pattern at the same time, so when implementing the performance prediction of the treaded tire, a spline function is used to model the casing and the pattern separately, and couple them (bound contact) when performing the analysis.

[0074] Specifically, the CPU 11 of the tire model making device 10 according to the present embodiment writes the tire model making program 15A stored in the ROM 12 or the storage unit 15 into the RAM 13 and executes the program. Figure 3 The parts shown perform their functions.

[0075] Figure 3 This is a block diagram showing an example of the functional configuration of the tire model creating device 10 according to the first embodiment.

[0076] like Figure 3 As shown, the CPU 11 of the tire model creating device 10 according to the present embodiment functions as a modeling unit 11A, a surface coupling unit 11B, a calculation point arranging unit 11C, and a restoring force calculating unit 11D.

[0077] The modeling unit 11A uses a spline function to separately model the shell and pattern representing the patterned tire. The spline function used in the modeling is not particularly limited, and for example, Bezier curves, T-splines, B-splines, etc. can be used. A Bezier curve is an N-1 degree curve obtained based on N control points. T-spline is a type of mathematical model used in the generation of free-form surfaces in computer graphics, and has T-shaped control points. B-spline is a smooth curve defined by a given plurality of control points and node vectors. In addition, the shell represents the portion of the patterned tire 40 other than the tread portion 58, and the pattern represents the tread portion 58 formed with a tread pattern.

[0078] Figure 4 It is a diagram schematically showing an example of a shell model and a pattern model according to the present embodiment.

[0079] Figure 4 The shell model shown is obtained by modeling the portion of the tread tire 40 except the tread portion 58. Figure 4 The pattern model shown is a model of a tread portion 58 on which a tread pattern is formed.

[0080] The surface coupling unit 11B couples (binds and contacts) the surface of the shell model as the model of the shell obtained by the modeling unit 11A and the surface of the pattern model as the model of the pattern.

[0081] The calculation point arrangement unit 11C arranges calculation points for calculating the restoring force (tied contact force) of the coupled surface between the surface of the shell model and the surface of the pattern model coupled by the surface coupling unit 11B.

[0082] The restoring force calculation unit 11D calculates the restoring force (binding contact force) based on the calculation points arranged by the calculation point arrangement unit 11C.

[0083] Next, refer to Figure 5 The modeling of bonded contact will be described in detail.

[0084] Figure 5 This is a diagram for explaining the modeling of the binding contact according to the present embodiment.

[0085] There are several methods that can be considered for modeling the binding contact, but in this embodiment, the binding contact is modeled by introducing a restoring force (binding contact force) when the surfaces are separated or overlapped. First, Figure 5 As shown, calculation points for calculating the restoring force (binding contact force) are configured on the coupling surface (binding contact surface).

[0086] For example, the restoring force (binding contact force) is calculated by the following formula. g Represents the restoring force (binding contact force).

[0087]

[0088] Here, K represents the coefficient of the restoring force (binding contact force), and Δt represents the time increment. In addition, N1 and N2 represent the shape functions of object 1 and object 2, respectively, and r1 and r2 represent the parameterized coordinates of the calculation points of object 1 and object 2, respectively. In addition, object 1 corresponds to a shell model, for example, and object 2 corresponds to a pattern model, for example. In addition, x and X represent the coordinates of the control point at the current time and the coordinates of the control point at the reference time, respectively, and S represents the area of ​​the coupling surface (binding contact surface). Here, g g It is a variable introduced to maintain the gap when there is a gap between the surfaces at the reference time. The forces f1 and f2 at the control points of the objects 1 and 2 are calculated by the following formulas, respectively.

[0089]

[0090] Next, refer to Figure 6 The operation of the tire model creating device 10 according to the first embodiment will be described.

[0091] Figure 6 This is a flowchart showing an example of the flow of processing of the tire model creation program 15A according to the first embodiment.

[0092] When the CPU 11 of the tire model creation device 10 instructs to execute the processing of the tire model creation program 15A, the CPU 11 executes the processing by writing the tire model creation program 15A stored in the ROM 12 or the storage unit 15 into the RAM 13 .

[0093] exist Figure 6 In step S101, the CPU 11 receives settings of analysis conditions (eg, boundary conditions, initial conditions, material settings, etc.).

[0094] In step S102, the CPU 11 creates a shell model using a spline function. In addition, the order of step S101 and step S102 may be reversed.

[0095] In step S103 , the CPU 11 deletes the pattern portion (tread portion) from the casing model created in step S102 .

[0096] On the other hand, in step S104, the CPU 11 extracts the outer shape of the pattern portion (tread portion) from the casing model created in step S102.

[0097] In step S105 , the CPU 11 creates a pattern model using a spline function for the outer shape of the pattern portion (tread portion) extracted in step S104 .

[0098] In step S106, CPU 11 performs IGA analysis, couples the surface of the shell model produced above with the surface of the pattern model (binding contact), and configures calculation points for calculating the restoring force (binding contact force) on the coupling surface (binding contact surface). As an example, the above-mentioned formula (1) is used to calculate the restoring force (binding contact force) based on the configured calculation points.

[0099] In step S107, the CPU 11 calculates the following equation of motion based on the restoring force calculated in step S106. The equation of motion is expressed by the following equation.

[0100] ma+F int =F ext -F tied …(3)

[0101] Here, m is mass, a is acceleration, and F is int is the internal force, F ext is the external force, F tied is the binding contact force.

[0102] In step S108 , the CPU 11 updates the time.

[0103] In step S109, the CPU 11 determines whether the calculation is completed. If it is determined that the calculation is completed (in the case of affirmative determination), the process proceeds to step S110, and if it is determined that the calculation is not completed (in the case of negative determination), the process returns to step S106 and repeats the process.

[0104] In step S110 , the CPU 11 processes the analysis result of the IGA and ends a series of processes of the tire model creation program 15A.

[0105] Next, refer to Figure 7 to Figure 10 An analysis example of a tensile analysis performed as verification of the validity of the tire model according to the present embodiment will be described.

[0106] Figure 7 to Figure 10 It is a diagram for explaining an analysis example of the shell model M1 and the pattern model M2.

[0107] like Figure 7As shown, the object 1 representing the shell and the object 2 representing the pattern are modeled separately and set as the shell model M1 and the pattern model M2, and the meshes do not match at the coupling surface. The control points are only shared at the ends. It can be seen that they are separated in "no binding contact" and coupled in "binding contact".

[0108] In addition, Figure 8 2 shows the analysis result when there is a gap between the objects at the reference time. It can be seen that the analysis can be performed without any problem even if there is a gap between the shell model M1 and the pattern model M2.

[0109] In addition, Fig. 9 The three-dimensional analysis result is shown in . It can be seen that the analysis can be performed without any problem even when the surfaces of the shell model M1 and the pattern model M2 are coupled to each other.

[0110] In addition, if Fig.10 As shown, it can be known that the restoring force (binding contact force) is not only defined as from the shell model M1 to the pattern model M2, or from the pattern model M2 to the shell model M1, but can also be stably analyzed by simultaneously defining from the shell model M1 to the pattern model M2 and from the pattern model M2 to the shell model M1.

[0111] Fig.11 This is a diagram showing the ground contact pressure distribution result when the performance prediction of the treaded tire is performed using the IGA analysis.

[0112] exist Fig.11 In the example of , the case where the shell and the pattern are modeled separately and the surface of the shell model and the surface of the pattern model are coupled (bound contact) are shown. By comparing with FEM, it is confirmed that the same ground pressure distribution can be obtained.

[0113] As described above, according to the present embodiment, when a model of a treaded tire is prepared, the IGA analysis is used, so that the shape reproducibility of the tire including the reproduction of the shape change over time is high, and the analysis accuracy can be improved.

[0114] Furthermore, compared with the case where a tire model is created by FEM analysis, a tire model can be created with prediction performance equal to or higher than that required while reducing the time and effort required to complete the creation of the tire model.

[0115] [Second Embodiment]

[0116] In the second embodiment, a method of applying a T-spline function as a spline function used for modeling will be described.

[0117] Fig.12A diagram for explaining the difference between NURBS and T-spline.

[0118] IGA can handle various splines such as Bezier curves and NURBS (Non-Uniform Rational B-Spline). Bezier curves and B-splines cannot strictly represent circles, while NURBS and T-splines can strictly represent circles. Fig.12 As shown, T-splines can reduce the number of control points compared to NURBS. IGA using T-splines is described in, for example, "Y. Bazilevs et al., "Isogeometric analysis using T-splines", Computer Methods in Applied Mechanics and Engineering, vol. 199, no. 5-8, pp. 229-263, 2010." Therefore, it can be said that IGA using T-splines is most suitable for tire analysis.

[0119] Fig.13 : is a diagram showing an example of the cross-sectional shape of a tire made by T-splines. Fig.14 This is a diagram showing the vicinity of the belt end after reducing the control points using T-splines.

[0120] like Fig.13 and Fig.14 As shown in the figure, T-splines in three-dimensional space are expressed by orthogonal R-axis, S-axis, and T-axis in parameterized space. The cross-sectional shape of the tire is created using T-splines in two-dimensional space expressed by R-axis and S-axis. By using T-splines instead of NURBS, control points can be reduced, and model creation and analysis can be performed efficiently.

[0121] Fig.15 FIG. 1 is a diagram showing an example of the positions and weights of control points for expressing a perfect circle.

[0122] like Fig.15 As shown, the T-axis direction of the T-spline is used as the circumferential direction to expand the above Fig.13 and Fig.14The shape of the cross section produced in . The basis function in the T-axis direction is set to be quadratic or higher. First, divide the circumference of the tire into four regions: 0 degrees to 90 degrees, 90 degrees to 180 degrees, 180 degrees to 270 degrees, and 270 degrees to 360 degrees (=0 degrees). In addition, the radius of the tire is set to r, and the weight of the control point is set to w. If the basis function is set to quadratic and C0 is set to be continuous at 0 degrees, 90 degrees, 180 degrees, and 270 degrees, the node vector in the T-axis direction is [0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4]. In addition, by setting the weights of the control points of the T-spline (=w) at 45 degrees, 135 degrees, 225 degrees, and 315 degrees The rest is 1, which can represent a perfect circle.

[0123] Fig.16 FIG. 1 is a diagram showing an example of a tire model that has been circumferentially developed.

[0124] like Fig.16 As shown, by setting the start point and the end point to the same control point, a tire model of one circle can be created.

[0125] Fig.17 1 is a diagram showing an example of a tire model that is thinned and divided again in the circumferential direction.

[0126] In the above Fig.16 The circumferential segmentation in the example above would be too coarse. Fig.17 As shown, it is assumed that the elements are divided by performing T-spline thinning. Thinning refers to a technique of re-dividing without changing the shape of the spline. For example, in the above-mentioned non-patent document 1, NURBS thinning is described, but T-spline thinning can be performed by the same idea.

[0127] As described above, according to the present embodiment, by applying the T-spline function as the spline function used for modeling, it is possible to reduce the number of control points compared to NURBS, thereby making it possible to more efficiently create and analyze a model.

[0128] [Third Embodiment]

[0129] In the third embodiment, a method of modeling the membrane members (carcass plies, belt layers, etc.) constituting the tire using a T-spline function will be described.

[0130] Fig.18 2 is a diagram showing an example of a membrane member and a virtual entity. The membrane member (also referred to as "membrane" or "shell") mentioned here includes the above-mentioned carcass layer 42, belt layer 54, and the like.

[0131] Here, there are two main types of membrane component formulation. The first type (the former) is a method based on two-dimensional elements and processed two-dimensionally within the elements and then mapped to three-dimensional space. The second type (the latter) is a method based on three-dimensional space from the beginning. The former is mainly used in the modeling of membrane components based on IGA, but the formulation becomes complicated. Therefore, in this embodiment, the latter method is used, that is, for Fig.18 The membrane member (hatched portion) shown is a method of modeling the membrane member by creating a virtual entity by perturbing each node by the plate thickness. This method is hereinafter referred to as degeneration type formulation.

[0132] For example, the normal at the control points constituting the T-spline is calculated, and the virtual entity is created by perturbing the control points. Here, as shown in the following equations (4) to (6), the tangent vector t is calculated by using the differential of the T-spline, and the normal vector n is calculated based on the tangent vector t, thereby being able to calculate the normal vector with high accuracy.

[0133]

[0134] Where r represents the parameterized coordinate, R represents the coefficient of each control point of the T-spline, and x represents the coordinate of the control point. Fig.19 2 shows the results of tensile analysis of the film using the film model prepared by this method.

[0135] Fig.19 It is a diagram showing a comparative example of the results of film analysis based on IGA and FEM.

[0136] like Fig.19 As shown in the figure, it can be seen that the membrane analysis based on IGA obtains the same results as those of FEM for "cord angle 30°" and "cord angle 60°".

[0137] Next, a method of embedding a T-spline of a film model into a rubber (solid) is described. In order to analyze a tire, it is necessary to embed film models of the belt 54, the carcass 42, etc. into a solid. For embedding into a solid, for example, the following two methods can be considered.

[0138] (1) Embedding to the T-spline boundary

[0139] Since control points exist at the T-spline boundaries, it is possible to create a virtual T-spline entity without any problem.

[0140] (2) Embedding into the interior of the T-spline (grid boundary)

[0141] When the degree of T-spline is higher than two, there are no control points at the mesh boundary. Therefore, it is not possible to create a virtual T-spline entity by perturbing the control points. Fig. 20 As shown in FIG. 1 , regarding the mesh boundary where the film is embedded, the control points are arranged at the mesh boundary by overlapping the nodes. Thus, the film can be embedded at the mesh boundary.

[0142] Fig. 20 FIG. 1 is a diagram schematically showing a state where control points are arranged at the mesh boundary.

[0143] like Fig. 20 As shown, when there are no control points configured at the mesh boundary, it is impossible to create a virtual T-spline entity by perturbing the control points. On the other hand, when control points are configured at the mesh boundary by overlapping nodes, a virtual T-spline entity can be created by perturbing the control points, thereby enabling the membrane to be embedded at the mesh boundary.

[0144] As described above, according to the present embodiment, the membrane members (carcass plies, belt layers, etc.) constituting the tire can be modeled using the T-spline function.

[0145] In addition, the technical scope of the present disclosure is not limited to the scope described in the above embodiment. Various changes or improvements can be added to the above embodiment within the scope not departing from the gist, and the forms obtained by adding such changes or improvements are also included in the technical scope of the present disclosure.

[0146] Contribution to the United Nations-led Sustainable Development Goals (SDGs)

[0147] In order to realize a sustainable society, SDGs are advocated. One embodiment of the present invention is considered to be a technology that can contribute to "No. 9_Industry, Innovation, and Infrastructure" and the like.

[0148] The disclosure of Japanese Patent Application No. 2022-144096 filed on September 9, 2022 is incorporated herein by reference in its entirety. All documents, patent applications, and technical standards described in this specification are incorporated herein by reference to the same extent as if each document, patent application, and technical standard were specifically and individually described as being incorporated by reference.

Claims

1. A tire model manufacturing method for simulating the performance of a tire with a tread pattern, the tire model manufacturing method comprising: Using a spline function to separately model a shell and a tread representing the treaded tire; coupling a surface of a shell model serving as a model of the shell with a surface of a pattern model serving as a model of the pattern; Configuring a calculation point for calculating the restoring force of the coupling surface between the surface of the shell model and the surface of the pattern model; as well as The restoring force is calculated based on the configured calculation points.

2. The tire model making method according to claim 1, wherein: At a reference time, there is a gap between the surface of the shell model and the surface of the pattern model.

3. The tire model making method according to claim 2, wherein: The restoring force is calculated using the coefficient of the restoring force, the time increment, the shape function of the shell model, the shape function of the pattern model, the parameterized coordinates of the calculation points, the coordinates of the control points at the current moment, the coordinates of the control points at the reference moment, the area of ​​the coupling surface, and the variable representing the gap.

4. The tire model making method according to claim 1, wherein: The spline function is a T-spline function.

5. The tire model making method according to claim 1, wherein: The housing includes a membrane member, The spline function is a T-spline function, The membrane member is modeled using the T-spline function.

6. A tire model making device for simulating the performance of a tire with a tread pattern, the tire model making device comprising: a modeling unit that separately models a casing and a pattern representing the treaded tire using a spline function; a surface coupling unit for coupling a surface of a shell model serving as a model of the shell with a surface of a pattern model serving as a model of the pattern; A calculation point configuration unit, which configures calculation points for calculating the restoring force of the coupling surface between the surface of the shell model and the surface of the pattern model; as well as A restoring force calculation unit calculates the restoring force based on the arranged calculation points.

7. A tire model making program for simulating the performance of a tire with a tread pattern, the tire model making program being used to cause a computer to perform the following processing: Using a spline function to separately model a shell and a tread representing the treaded tire; coupling a surface of a shell model serving as a model of the shell with a surface of a pattern model serving as a model of the pattern; Configuring a calculation point for calculating the restoring force of the coupling surface between the surface of the shell model and the surface of the pattern model; as well as The restoring force is calculated based on the configured calculation points.

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