Simulation method, simulation device and program

Abstract

To provide a simulation method, a simulation device and a program which find temperature of a tire model.SOLUTION: A simulation method includes steps of: executing contact analysis between a tire model composed of elements which can be numerically analyzed by a computer and a road surface model; obtaining stress in a tire circumferential direction in each element of the tire model and a strain waveform; performing Fourier transformation of the stress and the strain waveform, and obtaining spectrums of the stress and the strain for each element; obtaining a heat generation amount of each element of the tire model, by using stress amplitude, phase difference of the stress, strain amplitude, phase difference of the strain, and phase lag, and element volume of the tire model, Fourier degree, and deformation mode; obtaining temperature of each element of the tire model by heat conduction analysis using a heat conduction equation; and correcting the stress amplitude and the phase lag of each element of the tire model by using the temperature of the tire model. Until preset conditions are satisfied, the correction of the stress amplitude and the phase lag is repeated.SELECTED DRAWING: Figure 7

Description

[Technical field]

[0001] The present invention relates to a simulation method, a simulation device, and a program for simulating a tire model and a road surface model using elements that can be numerically analyzed by a computer, and more particularly to a simulation method, a simulation device, and a program for calculating the temperature of a tire model by heat conduction analysis. [Background technology]

[0002] Currently, tire simulations are carried out using computer-based numerical analysis such as the finite element method (FEM) in order to predict and evaluate tire performance without making prototypes. Specifically, the simulation involves filling a tire model, which is modeled using the finite element method, with internal pressure, and then performing a static contact analysis in which the tire is brought into contact with a road surface model at a set load, or a dynamic rolling analysis in which the tire model is rolled.

[0003] It is known that when a tire is brought into contact with a road surface or rolled on the road surface, a viscoelastic energy loss (heat generation) occurs in the tire. For example, Patent Document 1 derives the heat generation energy of the entire rotating body including a viscoelastic material. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 3969821 A Summary of the Invention [Problem to be solved by the invention]

[0005] The above-mentioned viscoelastic energy loss (heat generation) caused by the rolling of the tire is a cause of rolling resistance. In the above-mentioned Patent Document 1, the heat generation energy of the entire rotating body including the viscoelastic material is derived, and the heat generation of the tire is obtained. When heat is generated in a tire, a temperature distribution is formed inside the tire due to heat conduction to the rubber and reinforcing materials that make up the tire. When the temperature inside the tire changes, the properties of the rubber that makes up the tire also change, so temperature changes inside the tire affect the tire properties. Therefore, predicting the temperature inside the tire is extremely important in improving the accuracy of tire simulations. However, in the current simulation, the temperature of the tire model is not obtained. An object of the present invention is to provide a simulation method, a simulation device, and a program for determining the temperature of a tire model. [Means for solving the problem]

[0006] In order to achieve the above-mentioned object, the invention [1] includes a first step of performing a contact analysis between a tire model, which is composed of elements that can be numerically analyzed by a computer, and a road surface model, which is composed of elements that can be numerically analyzed by a computer, which represents a road surface; a second step of obtaining stress and strain waveforms in the tire circumferential direction for each element of the meridian section of the tire model; a third step of Fourier transforming the stress and strain waveforms in the tire circumferential direction for each element of the tire meridian section obtained in the second step to obtain a stress and strain spectrum for each element of the tire meridian section; and a method for calculating a contact spectrum based on the stress and strain spectrum obtained in the third step. The simulation method includes a fourth step of calculating the amount of heat generated in each element of the meridian section of the tire model using the stress amplitude, stress phase difference, strain amplitude, strain phase difference, and phase lag, as well as the element volume, Fourier order, and deformation mode of the tire model; a fifth step of calculating the temperature of each element of the tire model by heat conduction analysis using a heat conduction equation; and a sixth step of correcting the stress amplitude and phase lag of each element of the meridian section of the tire model using the temperature of the tire model calculated in the fifth step, and the fourth step, the fifth step, and the sixth step are repeatedly performed until a preset condition is reached.

[0007] Invention [2] is the simulation method according to invention [1], in which the stress amplitude and phase lag corrected in the sixth step are corrected using a function of temperature or a mathematical table relative to temperature. Invention [3] is the simulation method according to invention [1], in which the stress amplitude corrected in the sixth step is corrected using a value normalized by the value of the complex modulus when the complex modulus becomes a constant value as a function of temperature or in a mathematical table. Invention [4] is a simulation method according to any one of Inventions [1] to [3], comprising a step of integrating the heat generation amount in each element of a meridian section of the tire model calculated in the fourth step over the entire tire model, and dividing the total heat generation amount obtained by the integration by the distance traveled by the tire model per rotation to calculate the rolling resistance of the tire model.

[0008] Invention [5] is a simulation method according to any one of Inventions [1] to [4], wherein the heat transfer conditions imparted to the outer surface of the tire model in the heat conduction analysis in the fifth step are values ​​calculated using one or more of the following physical quantities: a function of the distance from the tire rotation axis to each element of the outer surface of the tire model, a curvature of the tire model surface, a groove width of the tire model, a groove depth of the tire model, a groove volume of the tire model, a contact length of the tire model, a contact width of the tire model, and a surface roughness of the outer surface of the tire model. The invention [6] is the simulation method according to any one of the inventions [1] to [5], in which the tire model is axially symmetric. Invention [7] is a simulation method according to any one of Inventions [1] to [6], in which the thermal conduction analysis in the fifth step is performed at a preset time interval, the time interval being in the range of 1 to 300 seconds.

[0009] The invention [8] is the simulation method according to any one of the inventions [1] to [6], in which the heat conduction analysis in the fifth step is a steady-state heat conduction analysis. Invention [9] is a simulation method according to any one of Inventions [1] to [8], in which tire characteristics are calculated using a modified tire model in which the elasticity or viscoelasticity of each element of the tire model is modified using a temperature distribution of the tire model obtained by repeatedly performing the fourth step, the fifth step, and the sixth step until a preset condition is reached. Invention

[10] is a simulation method according to any one of Inventions [1] to [9], which includes, before the first step, a step of creating a tire model representing the tire and composed of elements that can be numerically analyzed by a computer, and a road surface model representing the road surface and composed of elements that can be numerically analyzed by a computer.

[0010] The invention

[11] has an analysis unit that performs a contact analysis between a tire model that represents a tire and is composed of elements that can be numerically analyzed by a computer, and a road surface model that represents a road surface and is composed of elements that can be numerically analyzed by a computer, and a calculation unit that obtains stress and strain waveforms in the tire circumferential direction in each element of a meridian section of the tire model, performs a Fourier transform on the obtained stress and strain waveforms in the tire circumferential direction in each element of the tire meridian section, and obtains stress and strain spectra for each element of the tire meridian section, and the calculation unit calculates stress amplitude, stress phase difference, strain amplitude, strain phase difference, and phase difference based on the obtained stress and strain spectra. This simulation device calculates the amount of heat generated in each element of the meridian cross section of the tire model using the phase lag, the element volume, Fourier order, and deformation mode of the tire model, and calculates the temperature of each element of the tire model by heat conduction analysis using a heat conduction equation.The calculated temperature of the tire model is used to correct the stress amplitude and phase lag of each element of the meridian cross section of the tire model, and repeatedly calculates the amount of heat generated in each element of the meridian cross section of the tire model, calculates the temperature of each element of the tire model, and corrects the stress amplitude and phase lag of each element of the meridian cross section of the tire model until a preset condition is reached.

[0011] The invention

[12] is the simulation apparatus according to the invention

[11] , in which the corrected stress amplitude and phase lag are corrected using a function of temperature or a mathematical table relative to temperature. Invention

[13] is the simulation device according to invention

[11] , wherein the corrected stress amplitude is corrected using a value normalized by the value of the complex modulus when the complex modulus becomes a constant value as a function of temperature or in a mathematical table. Invention

[14] is the simulation device according to any one of Inventions

[11] to

[13] , wherein the calculation unit calculates the rolling resistance of the tire model by integrating the calculated heat generation amount in each element of the meridian section of the tire model over the entire tire model and dividing the total heat generation amount obtained by the integration by the distance traveled by the tire model in one rotation.

[0012] Invention

[15] is the simulation device according to any one of Inventions

[11] to

[14] , wherein the heat transfer conditions applied to the outer surface of the tire model for the heat conduction analysis are values ​​calculated using one or more of the following physical quantities: a function of the distance from the tire rotation axis to each element of the outer surface of the tire model, a curvature of the tire model surface, a groove width of the tire model, a groove depth of the tire model, a groove volume of the tire model, a contact length of the tire model, a contact width of the tire model, and a surface roughness of the outer surface of the tire model. The invention

[16] is the simulation device according to any one of the inventions

[11] to

[15] , wherein the tire model is axially symmetric. The invention

[17] is a simulation device according to any one of the inventions

[11] to

[16] , wherein the thermal conduction analysis is performed at a preset time interval, the time interval being in the range of 1 to 300 seconds.

[0013] The invention

[18] is the simulation device according to any one of the inventions

[11] to

[16] , wherein the heat conduction analysis is a steady-state heat conduction analysis. Invention

[19] is a simulation device according to any one of Inventions

[11] to

[18] , wherein the calculation unit calculates tire characteristics using a modified tire model in which elasticity or viscoelasticity is modified for each element of the tire model, using a temperature distribution of the tire model after a preset condition is reached. Invention

[20] is a simulation device according to any one of Inventions

[11] to

[19] , having a model creation unit that creates a tire model representing a tire and composed of elements that can be numerically analyzed by a computer, and a road surface model representing the road surface and composed of elements that can be numerically analyzed by a computer.

[0014] The invention

[21] is a program for causing a computer to execute, as a procedure, each step of the simulation method according to any one of the inventions [1] to

[10] . Effect of the Invention

[0015] According to the present invention, the temperature of a tire model can be obtained. [Brief description of the drawings]

[0016] [Figure 1] FIG. 1 is a schematic diagram showing a simulation device used in a simulation method according to an embodiment of the present invention. [Diagram 2] FIG. 2 is a schematic perspective view showing a state in which a tire model and a road surface model are in contact with each other according to the embodiment of the present invention. [Diagram 3] 1 is a graph showing the relationship between phase lag and temperature. [Figure 4] Graph (a) shows the relationship between the complex modulus and temperature, and graph (b) shows the relationship between the normalized complex modulus and temperature. [Diagram 5] FIG. 2 is a schematic diagram showing an example of heat generation distribution in a tire model obtained by the simulation method according to an embodiment of the present invention. [Figure 6] FIG. 2 is a schematic diagram showing an example of temperature and heat distribution in a tire model obtained by the simulation method according to an embodiment of the present invention. [Figure 7] 1 is a flowchart showing an example of a simulation method according to an embodiment of the present invention in the order of steps. [Figure 8] 11 is a flowchart showing another example of a simulation method according to an embodiment of the present invention in the order of steps. [Figure 9]FIG. 2 is a schematic diagram showing a tire model used in a simulation. [Figure 10] 13 is a graph showing rolling resistance results. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0017] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A simulation method, a simulation device, and a program according to the present invention will be described in detail below based on preferred embodiments shown in the accompanying drawings. It should be noted that the drawings described below are illustrative for explaining the present invention, and the present invention is not limited to the drawings shown below. In addition, unless otherwise specified, the term "orthogonal" includes a generally acceptable error range in the relevant technical field. Furthermore, unless otherwise specified, the values ​​indicating various lengths and other sizes include a generally acceptable error range in the relevant technical field. Furthermore, unless otherwise specified, the physical properties such as speed, temperature, heat transfer coefficient, thermal conductivity, and specific heat include a generally acceptable error range in the relevant technical field. Unless otherwise specified, the time also includes a generally acceptable error range in the relevant technical field. In addition, the term "process" includes not only an independent process, but also a process that cannot be clearly distinguished from other processes, as long as the intended purpose of the process is achieved.

[0018] [Simulation device] Fig. 1 is a schematic diagram showing a simulation device used in a simulation method according to an embodiment of the present invention, Fig. 2 is a schematic perspective view showing a state in which a tire model and a road surface model according to an embodiment of the present invention are in contact with each other. The simulation device and simulation method of the present embodiment are intended to obtain the temperature of a tire model. The simulation device and simulation method predict the temperature inside the tire model by coupling a simulation for predicting heat generation inside the tire model with a heat conduction analysis inside the tire model. The simulation device can obtain heat generation and heat distribution of the tire model, as well as temperature and temperature distribution of the tire model, and can also obtain rolling resistance and tire characteristics.

[0019] The simulation device 10 has a processing unit 12, an input unit 14, and a display unit 16. The processing unit 12 has a model creation unit 20, an analysis unit 22, a calculation unit 24, a display control unit 26, a memory 27, and a control unit 28. The simulation device 10 also has a ROM (Read Only Memory) and the like, which are not shown in the figure. The processing unit 12 is controlled by a control unit 28. In the processing unit 12, the model creation unit 20, the analysis unit 22, the calculation unit 24, and the display control unit 26 are connected to a memory 27, and data of the model creation unit 20, the analysis unit 22, and the calculation unit 24 is stored in the memory 27. The simulation device 10 may be configured using hardware such as a computer that functionally forms each of the parts of the model creation unit 20, analysis unit 22, and calculation unit 24 by executing a program (computer software) stored in a ROM or the like in the control unit 28, or it may be a dedicated device in which each part is configured with a dedicated circuit, or it may be configured as a server to be executed on the cloud. The memory 27 is not particularly limited, and may be a physical storage medium such as a hard disk drive (HDD), a solid state drive (SSD), and a dynamic random access memory (DRAM), or may be a storage area located on a cloud connected via the Internet.

[0020] In the simulation device 10 described below, various processes are performed in each part of the processing unit 12. In the following description, a description of the various processes performed in each part of the processing unit 12 by the control unit 28 is omitted, but a series of processes in each part are controlled by the control unit 28.

[0021] The input unit 14 is a variety of input devices such as a mouse and a keyboard for inputting various information according to instructions from an operator. The display unit 16 displays, for example, the amount of heat generated and the heat distribution of the tire model obtained by the simulation method, the temperature and the temperature distribution of the tire model, the rolling resistance results, the tire characteristic results, the simulation results obtained by the simulation method, etc., and various known displays are used for this purpose. The display unit 16 also includes a device such as a printer for displaying various information on an output medium.

[0022] The model creation unit 20 of the simulation device 10 creates a tire model 30 (see FIG. 2) that represents a tire and is composed of elements that can be numerically analyzed by a computer, and also creates a road surface model 32 (see FIG. 2) that represents a road surface and is composed of elements that can be numerically analyzed by a computer.

[0023] Regarding the tire model, data on the shape and size of the model and elasticity or viscoelasticity are input to the model creation unit 20 via the input unit 14, for example, and the tire model is created in the model creation unit 20. For the road surface model, data representing the model's shape, size, and road surface, as well as physical property data indicating that it is a rigid body, are input to the model creation unit 20, for example, via the input unit 14, and the road surface model is created in the model creation unit 20. The tire model and the road surface model may be stored in advance in the memory 27 via, for example, the input unit 14. In this case, the model creation unit 20 reads out the tire model and the road surface model stored in the memory 27 from the memory 27 and sets the tire model and the road surface model. Here, Fig. 2 shows a state in which the tire model 30 and the road surface model 32 are in contact with each other. In Fig. 2, the symbol DL indicates the rolling direction, and the symbol Dw indicates the width direction. The rolling direction DL and the width direction Dw are perpendicular to each other.

[0024] A known method can be used to create the tire model and the road surface model. For example, the tire model and the road surface model are each divided into a finite number of elements each consisting of a plurality of nodes to create the tire model and the road surface model. The tire model and the road surface model include node information. The node information is information about the nodes (vertices) of each element (mesh) that can be numerically analyzed by a computer, and includes position information of the nodes. In the case of graphic data, the data is converted into data modeled with elements that can be numerically analyzed by a computer. The tire model and road surface model modeled with elements that can be numerically analyzed by a computer may be discrete models that can be numerically calculated, and may be, for example, mesh data used in numerical simulations such as FEM, or design data such as CAD data.

[0025] The tire model 30 is not particularly limited as long as it is composed of elements that can be numerically analyzed by a computer, and is, for example, a three-dimensional finite element model that is mesh-divided into a finite number of elements. There are no particular limitations on the road surface model 32 as long as it is made up of elements that can be numerically analyzed by a computer, and it may be, for example, a finite element model that is divided into a finite number of mesh elements. The elements constituting the tire model or road surface model are elements that can be analyzed by a computer, such as solid elements such as tetrahedral solid elements, pentahedral solid elements, and hexahedral solid elements, shell elements such as triangular shell elements and quadrilateral shell elements, and membrane elements.

[0026] The tire model may be one in which elasticity or viscoelasticity is imparted to each element, or a tire model may be created by modeling rubber having a predetermined viscoelastic property. In this case, the model creation unit 20 imparts elasticity or viscoelasticity to each element of the tire model. The method of imparting elasticity and viscoelasticity to the tire model is not particularly limited, and any method used in numerical analysis software can be used as appropriate. Viscoelasticity includes, for example, the Prony series and parallel rheology frameworks. As for elasticity, it is preferable to use a hyperelastic model (Neo-Hookean, Yoeh, etc.).

[0027] The tire model may be a model of the tread rubber of the tire that comes into contact with the road surface. In this case, it is preferable to add information on the physical properties of the tread rubber of the tire to the tire model. The physical properties of the tread rubber are viscoelasticity and elasticity characteristics according to the composition of the tread rubber. The tread rubber contains, for example, a rubber component, silica, carbon black, and a silane coupling agent. Examples of the rubber component include natural rubber (NR), isoprene rubber (IR), butadiene rubber (BR), styrene butadiene rubber (SBR), acrylonitrile-butadiene copolymer rubber (NBR), butyl rubber (IIR), halogenated butyl rubber (Br-IIR, Cl-IIR), and chloroprene rubber (CR).

[0028] Since an actual road surface is considered to be harder than rubber and less likely to deform, it is preferable that the road surface model has physical characteristics in which the entire model or the portion in contact with the tire model is a rigid body. Here, a rigid body means that when the tire model comes into contact with the road surface model and the tire model and the road surface model are subsequently moved relatively, the deformation of the road surface model is zero. The actual road surface means the actual road surface.

[0029] In the road surface model 32, the surface 32a may be, for example, a flat surface, a curved surface, or a model having projections and recesses that reproduce an actual road surface. By making the surface 32a of the road surface model 32 a curved surface, for example, a drum test machine can be reproduced. For example, a part of the road surface model 32 may be modeled using a curved line. By modeling the surface 32a of the road surface model 32 using a curved line, the surface 32a of the road surface model 32 becomes smooth, the contact with the tire model 30 becomes stable, and numerical calculations such as FEM can be efficiently performed. The modeled curve is not particularly limited, and examples include a circular arc, a sine wave, a cosine wave, a spline curve, and a Bezier curve.

[0030] When the road surface model 32 is a model having projections and recesses that reproduces an actual road surface, it is also possible to model it using displacements or coordinate values ​​obtained by measuring the surface shape of the actual road surface. The method of modeling using the displacement or coordinate values ​​obtained by measuring the surface shape of the actual road surface is not particularly limited, and examples thereof include the following methods. For example, first, the surface shape of the actual road surface to be modeled into the road surface model 32 is measured by a laser displacement meter. Next, the surface shape data obtained by measuring with the laser displacement meter is Fourier transformed to calculate the spectrum of the road surface irregularity amplitude and the irregularity period (road surface period), thereby obtaining the road surface model 32.

[0031] The analysis unit 22 performs a contact analysis between the tire model and the road surface model. The contact analysis is not particularly limited as long as it can obtain stress and strain waveforms in the tire circumferential direction in each element (not shown) of the meridian section Ac (see FIG. 2) of the tire model 30. For example, a static ground contact analysis is used in which the tire model is brought into contact with the road surface model with a predetermined load. In addition, for example, a dynamic rolling analysis is used in which the tire model and the road surface model are moved relatively at a predetermined speed while in contact with each other, for example, the tire model rolls one revolution on the road surface model. Steady-state transportation analysis is also used. The contact analysis is performed in a virtual space such as inside a computer. Furthermore, prior to the contact analysis, the analysis unit 22 determines analysis conditions such as the load and the relative moving speed in the contact analysis between the tire model and the road surface model. In the contact analysis, for example, a tire model is brought into contact with a road surface model under a prescribed load while the internal pressure of the tire model is at a prescribed internal pressure. In addition, in the contact analysis, an internal pressure filling process is performed on the tire model. The internal pressure filling process reproduces the process of assembling a tire onto a rim of a rim size specified by JATMA, ETRTO, TRA, etc. and filling the tire with internal pressure, and is a process of applying a pressure equivalent to the internal pressure of the tire model to the inner surface of the tire model that faces the tire cavity region.

[0032] Here, the specified internal pressure refers to the "maximum air pressure" specified by JATMA, the maximum value of the "TIRE LOAD LIMITS A TVARIOUS COLD DINFLATION PRESSURES" specified by TRA, or the "INFLATION PRESSURES" specified by ETRTO. The specified load refers to the "maximum load capacity" specified by JATMA, the maximum value of the "TIRE LOAD LIMITS AT VARIOUS COLLIDING PRESSURES" specified by TRA, or the "LOAD CAPACITY" specified by ETRTO. However, in JATMA, for passenger car tires, the specified internal pressure is 180 kPa, and the specified load is 88% of the maximum load capacity. The relative movement speed is not particularly limited, and is set to, for example, 1 to 30 m / s. In addition, when the tire model and the road surface model are moved relatively, either the tire model or the road surface model may be moved. Furthermore, the direction of the relative movement of the tire model and the road surface model is not particularly limited, but may be, for example, the rolling direction DL. The tire model 30 is rotated one rotation around the rotation axis C of the tire model.

[0033] The load and relative movement speed in the contact analysis between the tire model 30 and the road surface model 32, as well as which of the tire model 30 and the road surface model 32 is to be moved and the movement direction, are stored, for example, in the memory 27. The analysis unit 22 may store the load and relative movement speed, and which of the tire model 30 and the road surface model 32 is to be moved and the movement direction in the memory 27 and read them out from the memory 27. Furthermore, the load and relative movement speed in the contact analysis between the tire model and the road surface model may be inputted from the input unit 14 and set in the analysis unit 22 . The tire model 30 and the road surface model 32 to be moved and the direction of movement may be input from the input unit 14 and set in the analysis unit 22 . Moreover, in the memory 27, simulation conditions such as contact analysis in the analysis unit 22 are set.

[0034] The calculation unit 24 obtains heat generation of the tire model, heat generation distribution of the tire model, temperature of the tire model, and temperature distribution of the tire model. Furthermore, the calculation unit 24 obtains rolling resistance of the tire model and tire characteristics of the tire model. In addition, in the above-mentioned analysis unit 22 and calculation unit 24, a software program such as Abaqus is used for numerical analysis (simulation) such as the finite element method. The heat generation and heat generation distribution of the tire model are obtained using, for example, the method described in Japanese Patent No. 3969821. The heat generation in the tire model, the heat generation distribution in the tire model, the temperature in the tire model, the temperature distribution in the tire model, the rolling resistance of the tire model, and the tire characteristics of the tire model are obtained by numerical analysis performed in a virtual space such as within a computer.

[0035] After performing a contact analysis between the tire model and the road surface model, the calculation unit 24 obtains stress and strain waveforms in the tire circumferential direction Dc (see FIG. 2) at each element (not shown) of the meridian cross section Ac (see FIG. 2) of the tire model 30. The stress and strain waveforms in the tire circumferential direction are obtained by the contact analysis and are stored in the memory 27, for example. The calculation unit 24 then performs a Fourier transform on the obtained stress and strain waveforms in the tire circumferential direction in each element of the tire meridian cross section to obtain a stress and strain spectrum for each element of the tire meridian cross section. The stress and strain spectrum for each element of the tire meridian cross section is stored in the memory 27, for example. The calculation unit 24 further obtains the stress amplitude, the stress phase difference, the strain amplitude, the strain phase difference, and the phase lag from the acquired stress and strain spectra. These are stored in the memory 27, for example.

[0036] The calculation unit 24 further calculates the heat generation amount in each element of the meridian section of the tire model using the stress amplitude, stress phase difference, strain amplitude, strain phase difference, and phase lag based on the acquired stress and strain spectra, and the element volume, Fourier order, and deformation mode of the tire model, and then calculates the temperature of each element of the tire model by heat conduction analysis using the heat conduction equation. Furthermore, the calculation unit 24 corrects the stress amplitude and phase lag of each element in the meridian section of the tire model using the calculated temperature of each element of the tire model. Furthermore, the calculation unit 24 repeatedly calculates the heat generation amount in each element of the meridian cross section of the tire model, calculates the temperature of each element of the tire model, and corrects the stress amplitude and phase lag of each element of the meridian cross section of the tire model until a preset condition is reached. This will be explained in more detail below.

[0037] As described above, when the tire model and road surface model are brought into contact with each other, or when the tire model is rotated once on the road surface model, the elements of the meridian section of the tire model receive a force from the road surface model in the tire circumferential direction Dc (see FIG. 2), causing deformation, etc. At this time, stress waveforms and strain waveforms in the tire circumferential direction are obtained for each element of the meridian section of the tire model. It is known that in a viscoelastic body, the phase of strain lags relative to stress. It is also known that the area of ​​the hysteresis loop of a viscoelastic body is the viscoelastic loss energy. The viscoelastic loss energy corresponds to heat energy. If the stress amplitude, strain amplitude, and phase lag are known, it is possible to calculate the viscoelastic loss energy, i.e., the heat energy. For this reason, for the elements of the meridian cross section that make up the tire model, the stress and strain waveforms in the tire circumferential direction Dc (see Figure 2) are obtained by numerical analysis such as the finite element method in the above-mentioned contact analysis.

[0038] The phase lag mentioned above refers to the phase difference (δ of tan δ) between strain and stress measured in a dynamic viscoelasticity test. It is also known that the stress amplitude and phase lag are temperature dependent. The obtained stress and strain waveforms in the tire circumferential direction in each element of the tire meridian cross section are then Fourier transformed, thereby obtaining a stress and strain spectrum for each element of the tire meridian cross section. As described above, by Fourier transforming the stress and strain waveforms of each element, the stress amplitude, stress phase difference, strain amplitude, strain phase difference, and phase lag can be obtained for each Fourier order, which allows the area of ​​the hysteresis loop to be calculated for each Fourier order. The degree of Fourier transformation is preferably 10 to 100, more preferably 20 to 50, and if the degree is 10 to 100, the accuracy is good.

[0039] The heat generation (viscoelastic loss energy) of each element of the tire model can be calculated by the following formula (1). This gives the amount of heat generation in each element of the meridian section of the tire model.

[0040]

number

[0041] In the above formula (1), Q is heat generation (viscoelastic loss energy). Viscoelastic loss energy represents heat generation. A m σ is the stress amplitude. Stress amplitude A m σ is the stress amplitude after Fourier transformation of the element stress and has temperature dependence. B m σ is the phase difference of the stress. m σ is the phase difference of the stress after Fourier transformation of the element stress. A m ε is the strain amplitude. Strain amplitude A m ε is the strain amplitude after Fourier transform of the element strain. B m ε is the strain phase difference. Strain phase difference B m εis the strain phase difference after Fourier transform of the element strain. δ is the phase lag. The phase lag δ is the δ of tan δ measured in the dynamic viscoelasticity test described above, and has temperature dependency. V is the element volume of the tire model. n is the Fourier order, and N is the maximum value of the Fourier order. m is the deformation component. In a three-dimensional tire model, there are six independent deformation components, so m is six, and six viscoelastic loss energies (heat generation) Q can be calculated.

[0042] According to the above formula (1), the heat generation amount of the tire model and the heat generation distribution of the tire model can be obtained. The obtained data of the heat generation amount of the tire model and the data of the heat generation distribution of the tire model are stored in the memory 27. In addition, the obtained data of the heat generation amount of the tire model and the heat generation distribution of the tire model can also be displayed on the display unit 16 together with the tire model. Furthermore, the temperature of each element of the tire model is calculated from the heat generation amount obtained by the above formula (1) by heat conduction analysis using the heat conduction equation of the following formula (2). In this way, the heat generation distribution of the tire model can be obtained. The obtained temperature data of each element of the tire model and the temperature distribution data of the tire model are stored in memory 27. In addition, the obtained temperature data of each element of the tire model and the temperature distribution of the tire model can also be displayed on display unit 16 together with the tire model. In the following formula (2), Q is the viscoelastic loss energy (heat generation), T is the temperature, α is the thermal diffusion coefficient, ρ is the density, and Cp is the specific heat at constant pressure.

[0043]

number

[0044] As described above, the stress amplitude and phase lag are temperature dependent, so the calculation unit 24 corrects the stress amplitude and phase lag of each element in the meridian section of the tire model using the temperature of each element of the tire model calculated based on the above formula (2). Specifically, the stress amplitude and phase lag of each element are corrected using a function of temperature or a numerical table with respect to temperature. Information on the physical properties of various materials is attached to the elements. For this reason, for example, a function of stress amplitude as a function of temperature and a numerical table with respect to temperature are created in advance for each material. For the phase lag, a function of phase lag as a function of temperature and a numerical table with respect to temperature are also created for each material. This is preferable because it makes it possible to efficiently correct the stress amplitude and phase lag of each element for various materials. The above-mentioned function is preferably created using actual measured values ​​of the stress amplitude and the phase lag, which can be obtained by a dynamic viscoelasticity test. From the measured value of the phase lag, for example, a function of tan δ and temperature represented by curve 34 as shown in Figure 3 can be obtained. For example, the phase lag is corrected for temperature using the function of tan δ and temperature as shown in Figure 3. 3 is expressed as a function of tan δ and temperature as shown in the following formula (3): In the following formula (3), T is temperature, and a, p, and q are fitting parameters.

[0045]

number

[0046] Also, a conversion formula such as the WLF (Williams-Landel-Ferry) conversion formula can be used to convert the temperature into a function of frequency or a numerical table. By using this, for example, the relationship between the elastic modulus and temperature can be replaced with the relationship between the elastic modulus and frequency, and the function of the frequency of the elastic modulus can be used as the function of the temperature of the elastic modulus to correct the stress amplitude and phase lag of each element.

[0047] In addition, it is preferable to correct the stress amplitude using a value normalized by the value of the complex modulus of elasticity when the complex modulus of elasticity becomes a constant value as shown in FIG. 4(a) in a function of temperature or a numerical table (see FIG. 4(b)). Here, FIG. 4(a) is a graph showing the relationship between the complex modulus of elasticity and temperature, and FIG. 4(b) is a graph showing the relationship between the normalized complex modulus of elasticity and temperature. FIG. 4(a) shows the temperature dependence of the complex modulus of elasticity, and shows a curve 36 showing the relationship between the complex modulus of elasticity and temperature. The temperature dependence of the complex modulus of elasticity can be measured experimentally. FIG. 4(b) shows the complex modulus of elasticity E * The complex modulus E as a function of temperature * The complex modulus E at a constant temperature of 80°C * An example of normalization is shown in Fig. 4(b). Curve 37 shown in Fig. 4(b) is a constant value when the temperature exceeds 80°C. Curve 36 showing the relationship between the complex modulus and temperature in Fig. 4(a) is normalized to obtain curve 37 shown in Fig. 4(b).

[0048] As described above, the exponent of the complex modulus versus temperature can be obtained by normalizing the complex modulus value. For example, in Fig. 4(b), the exponent is 1 at a temperature of 80°C, and the exponent is greater than 1 when the temperature is lower than 80°C. For example, when the temperature changes from 20°C to 80°C, the elastic modulus of the elements of the tire model decreases. For example, in the example of FIG. 4(b), the index is 1 at a temperature of 80°C, but is 2 at a temperature of 20°C. When the temperature changes from 20°C to 80°C, the complex elastic modulus is halved, so the value according to the index is set as the stress amplitude A in the above formula (1). m σ Multiplying by 20°C, the stress amplitude A is half that of 20°C. m σ Correct the following. As described above, the complex elastic modulus is approximately constant when the temperature is high, and the complex elastic modulus is large when the temperature is low. By using this to correct the stress amplitude, the accuracy of calculating the viscoelastic loss energy, i.e., the accuracy of calculating the amount of heat generated, is improved. As a result, for example, the accuracy of the rolling resistance calculated using the amount of heat generated is improved. Moreover, since the stress amplitude can be easily corrected, the time required for calculation can be shortened. The stress amplitude obtained by the Fourier transform is the stress amplitude in the tire model and is different from the complex elastic modulus. However, it is useful to correct the stress amplitude by correcting the elastic modulus of the element that changes with temperature using the index shown in Fig. 4(b) as described above. In the above, a graph showing the relationship between the complex elastic modulus and the temperature is used, but this is not limited to this. The stress amplitude can be corrected in the same manner as the graph by using a numerical table showing the relationship between the complex elastic modulus and the temperature.

[0049] As described above, the calculation unit 24 repeatedly calculates the heat generation amount in each element of the meridian section of the tire model, calculates the temperature of each element of the tire model, and corrects the stress amplitude and phase delay of each element of the meridian section of the tire model until a preset condition is reached. This allows a plurality of calculations of the temperature of the tire model to be performed, and the temperature of the tire model can be obtained in time series, thereby obtaining the time series change in the temperature of the tire model. The preset condition is, for example, a preset number of repetitions, which refers to the number of repetitions of the calculation of the heat generation amount in each element of the meridian cross section of the tire model, the calculation of the temperature of each element of the tire model, and the correction of the stress amplitude and the phase delay of each element of the meridian cross section of the tire model. In addition, when the heat conduction analysis is a non-steady analysis, the preset condition is the calculation end time. In this case, the temperature of the tire model from the time when the tire model contacts the road surface model until a predetermined time has elapsed is obtained. Furthermore, when the heat conduction analysis is a steady-state analysis, the preset condition is a threshold value using the maximum value of the temperature difference in the tire model, or the maximum value of the heat generation difference or the maximum value of the heat generation change rate, etc. In this case, when the temperature or heat generation change in the tire model becomes small, the correction of the stress amplitude and phase lag of each element based on the temperature of the tire model is terminated.

[0050] (Rolling resistance of tire model) The calculation unit 24 can calculate the rolling resistance of the tire model by integrating the calculated heat generation amount in each element of the meridian section of the tire model over the entire tire model and dividing the total heat generation amount obtained by the integration by the distance traveled by the tire model during one rotation. Specifically, the heat generation (viscoelastic loss energy) of each element of the tire model obtained by the above formula (1) is integrated to obtain the total heat generation (viscoelastic loss energy) of all elements of the tire model, and the total heat generation amount is obtained. This total heat generation amount is Qt. The distance traveled by the tire model during one rotation is Lt. When the rolling resistance of the tire model is RR, RR = Qt / Lt. The distance Lt traveled by the tire model during one rotation is preferably an actual measurement value or a simulation value. Furthermore, the distance Lt traveled by the tire model during one rotation can be calculated from the tire radius (static contact radius or dynamic load radius). For example, the outer radius of the tire model when no load is applied is R0. The load radius when a load is applied in the contact analysis, i.e., the distance between the rotation axis C (see FIG. 2) of the tire model and the surface 32a (see FIG. 2) of the road model 32 (see FIG. 2) is R1. In this case, the distance Lt traveled by the tire model 30 during one rotation can be calculated by Lt=2π(K(R1-R0)+R0). By using the heat generation amount that takes into account the temperature distribution inside the tire, the accuracy of the calculated rolling resistance of the tire model is improved. In addition, it is also possible to calculate unsteady rolling resistance.

[0051] The amount of heat generated in each element of the meridian section of the tire model is corrected based on the temperature change associated with heat generation. The heat generation (viscoelastic loss energy) is corrected according to the changing temperature of the tire model. By using the corrected heat generation (viscoelastic loss energy) to calculate the rolling resistance, it is possible to calculate the rolling resistance according to the temperature of the tire model, and obtain the change in rolling resistance that accompanies the temperature change of the tire model.

[0052] In the heat conduction analysis, the heat transfer conditions applied to the outer surface of the tire model are preferably values ​​calculated using one or more of the following physical quantities: a function of the distance from the tire rotation axis to each element of the outer surface of the tire model, the curvature of the tire model surface, the groove width of the tire model, the groove depth of the tire model, the groove volume of the tire model, the contact length of the tire model, the contact width of the tire model, and the surface roughness of the outer surface of the tire model. This improves the accuracy of the heat conduction analysis and improves the calculation accuracy of the temperature distribution in the tire model. The heat transfer conditions applied to the outer surface of the tire model in the heat conduction analysis are, for example, that the heat transfer coefficient is made higher in the area corresponding to the contact width than on the surface outside the area corresponding to the contact width, and the heat transfer coefficient is made smaller as the groove depth of the tread portion increases. In the heat conduction analysis, the heat transfer coefficient of the outer surface of the tire model may be changed according to the distance from the rotation axis C (see FIG. 2) of the tire model. For example, the heat transfer coefficient of the tread part is made higher than that of the side part. The value calculated using a plurality of physical quantities is, for example, a value calculated from the ratio of the contact length of the tire model to the outer circumferential length of the tire in a tread portion defined as a function of the distance from the tire rotation axis to the contact area of ​​the tread as a heat transfer condition of the tread portion.

[0053] In addition, it is preferable to use an axisymmetric tire model for the heat conduction analysis because it can shorten the calculation time for the heat conduction analysis. Therefore, it is preferable that the tire model is axisymmetric. Here, the axisymmetric tire model is, for example, a model that is symmetric with respect to the tire equatorial plane CL (see FIG. 2). The tire equatorial plane CL (see FIG. 2) is a plane that is perpendicular to the rotation axis C (see FIG. 2) of the tire model 30 (see FIG. 2) and passes through the center of a region of the tire model 30 that corresponds to the tire width.

[0054] The heat conduction analysis is performed, for example, at a preset time interval, which is in the range of 1 to 300 seconds. This allows the temperature of the tire model to be calculated at the time interval, and the temperature of the tire model can be obtained in time series at the time interval. A time step width in the range of 1 to 300 seconds is preferable because it enables calculation of the heat generation distribution of the tire model, the temperature distribution of the tire model, and the rolling resistance of the tire model in a non-steady state. The heat conduction analysis may be a steady-state heat conduction analysis, which makes it possible to quickly calculate the heat distribution of the tire model in a steady state, the temperature distribution of the tire model, and the rolling resistance of the tire model. Steady-state heat conduction analysis can be achieved by setting the left side of the above equation (2) to 0, that is, by using the following equation (4).

[0055]

number

[0056] The calculation unit 24 can also calculate tire characteristics using a modified tire model in which the elasticity or viscoelasticity is modified for each element of the tire model, using the temperature distribution of the tire model after a preset condition is reached. By calculating the temperature of the tire model, the phase lag and stress amplitude of each element are corrected based on the temperature. Therefore, the phase lag and stress amplitude of the elements of the modified tire model are corrected. The modified tire model is obtained by imparting elasticity or viscoelasticity to the elements that match the corrected phase lag and stress amplitude. The tire characteristics are obtained by performing known simulations such as static contact analysis, rolling analysis, and steady-state transport analysis using a modified tire model. The tire characteristics are not particularly limited, and examples thereof include stress distribution, strain distribution, cornering power, and cornering force.

[0057] The display control unit 26 causes the display unit 16 to display the tire model and road surface model created by the model creation unit 20, information on the determined load and relative movement speed, the moving object and movement direction, the simulation status and simulation results using the finite element method or the like in the calculation unit 24, the heat distribution of the tire model, the temperature distribution of the tire model, etc. The display control unit 26 can also cause the display unit 16 to display various types of information input via the input unit 14.

[0058] The control unit 28 controls the processing unit 12 as described above, and causes the model creation unit 20, analysis unit 22, and calculation unit 24 of the processing unit 12 to perform various steps in the simulation method described below. From the above, the simulation device 10 can obtain a heat generation distribution 40 of the tire model as shown in Fig. 5. Furthermore, a temperature and heat distribution 42 of the tire model can be obtained as shown in Fig. 6. The temperature distribution is formed by the heat generated by viscoelastic loss energy being conducted within the tire model. Depending on the physical properties of the elements of the tire model and the shape of the tire model, there are areas where heat is easily conducted, areas where heat is not easily conducted, and areas where heat is easily dissipated, and the temperature tends to decrease over time. For this reason, the temperature distribution does not necessarily match the heat generation distribution.

[0059] [Simulation method] Next, the simulation method will be specifically described. The simulation method can obtain heat generation and heat distribution of the tire model, as well as temperature and temperature distribution of the tire model, in the same manner as the simulation device. Furthermore, rolling resistance and tire characteristics can be obtained. The simulation method of the present embodiment is carried out, for example, by using a simulation device 10 shown in FIG. As described above, the simulation method is implemented, for example, by using the simulation device 10 shown in Fig. 1, but as long as the simulation method can be executed using hardware and software such as a computer, it is not limited to the simulation device 10, and may be a program for causing a computer to execute each step of the simulation method as a procedure. Furthermore, the simulation device 10 is not limited to the configuration shown in Fig. 1. In the simulation method described below, various processes are performed in each part of the processing unit 12 of the simulation device 10 shown in Fig. 1. In the following explanation, the various processes performed in each part of the processing unit 12 by the control unit 28 are omitted, but a series of processes in each part are controlled by the control unit 28. FIG. 7 is a flowchart showing an example of a simulation method according to an embodiment of the present invention.

[0060] First, before the first process (step S12), for example, a tire model 30 (see FIG. 2) representing a tire and composed of elements that can be numerically analyzed by a computer, and a road surface model 32 (see FIG. 2) representing a road surface and composed of elements that can be numerically analyzed by a computer are created (step S10). The tire model 30 and the road surface model 32 in step S10 are created by the model creation unit 20. Data of the tire model 30 and the road surface model 32 created in step S10 are output to and stored in, for example, the memory 27. As described above, the tire model 30 is, for example, a three-dimensional finite element model that is divided into a finite number of mesh elements. The viscoelastic properties of the tire model 30 use the Prony series and parallel rheology framework described above. Moreover, the above-mentioned hyperelastic model (Neo-Hookean, Yoeh, etc.) is used as the elasticity of the tire model 30. Note that the tire model 30 may be provided with information on the physical properties of the tire tread rubber as described above.

[0061] As described above, the road surface model 32 is a finite element model that is divided into a finite number of mesh elements. As described above, the road surface model 32 has physical characteristics such as the entire model being a rigid body or the part in contact with the tire model being a rigid body. As described above, the surface 32a of the road surface model 32 is, for example, a flat surface, but it may be a curved surface like a drum testing machine, or may be a model that reproduces the shape of a road surface having projections and recesses.

[0062] In step S10, the tire model 30 and the road surface model 32 are created, but this is not limited to the above. The tire model 30 and the road surface model 32 may be created in separate steps, and the tire model 30 and the road surface model 32 may be created in either order, and the order of creation is not particularly limited. The tire model 30 and the road surface model 32 may be prepared in advance and input to the model creation unit 20 from the input unit 14. Alternatively, the tire model 30 and the road surface model 32 may be prepared in advance and stored in the memory 27, and the model creation unit 20 may read out the tire model 30 and the road surface model 32 from the memory 27. For this reason, step S10 is not necessarily required.

[0063] Next, a contact analysis between the tire model and the road surface model is performed (step S12 (first process)). Step S12 (first process) is performed by the analysis unit 22. In step S12, before the contact analysis, analysis conditions such as the load, the relative movement speed, etc. are determined. The data of the load and the relative movement speed set in step S12 is output to the memory 27 and stored therein, for example. In the contact analysis, a determined load, for example, a specified load is applied to a road surface model when the internal pressure of a tire model is at a specified internal pressure. In the contact analysis, the tire model may be moved in the rolling direction DL (see FIG. 2) by rolling the tire model one rotation on the road surface model at a determined relative moving speed while maintaining the contact state.

[0064] In step S14, the tire model 30 and the road surface model 32 are maintained in contact with each other under the set load. At this time, pressure is applied to the contact portion between the tire model 30 and the road surface model 32 shown in Fig. 2, causing strain in the tire circumferential direction Dc in each element (not shown) of the meridian cross section Ac of the tire model 30, and stress acts on the tire. The calculation unit 24 performs a numerical analysis such as the finite element method to obtain stress and strain waveforms in the tire circumferential direction Dc in each element of the meridian cross section Ac of the tire model 30 (step S14 (second process)). The data of the stress and strain in the tire circumferential direction and the stress and strain waveforms in each element of the meridian section of the tire model obtained in step S14 (second step) are output to and stored in the memory 27, for example.

[0065] Next, the stress and strain waveforms in the tire circumferential direction in each element of the meridian section of the tire model obtained in step S14 are Fourier transformed by the calculation unit 24 to obtain stress and strain spectra for each element of the meridian section of the tire model (step S16 (third step)). The data of the stress and strain spectrum for each element of the meridian section of the tire model is output to and stored in, for example, the memory 27. By the Fourier transform in step S16 (third process), the stress amplitude, the stress phase difference, the strain amplitude, the strain phase difference, and the phase lag are obtained for each Fourier order.

[0066] Next, the heat generation amount in each element of the meridian section of the tire model is calculated using the stress amplitude, stress phase difference, strain amplitude, strain phase difference, and phase lag based on the stress and strain spectrum acquired in step S16 (third step), as well as the element volume, Fourier order, and deformation mode of the tire model (step S18 (fourth step)). In step S18 (fourth step), the heat generation (viscoelastic loss energy) of each element of the tire model is calculated by the above formula (1) as described above. The data of the heat generation (viscoelastic loss energy) of each element of the tire model is output to and stored in the memory 27, for example. Next, the temperature of each element of the tire model is calculated by heat conduction analysis using the heat conduction equation (step S20 (fifth step)). As a result, the temperature of each element of the tire model is obtained, and the temperature distribution of the tire model can be obtained. The temperature data of each element of the tire model is output to and stored in, for example, memory 27.

[0067] Next, it is determined whether a preset condition is met (step S22). In step S22, if the preset condition is reached, the tire characteristics are calculated using a modified tire model in which the elasticity or viscoelasticity is modified for each element of the tire model using the temperature distribution of the tire model after the preset condition is reached (step S24). In step S24, a simulation such as a rolling analysis is performed using the modified tire model to obtain tire characteristics. This allows tire characteristics to be obtained with high accuracy. As described above, the tire characteristics include, for example, stress distribution, strain distribution, cornering power, and cornering force.

[0068] On the other hand, if the preset condition is not reached in step S22, the stress amplitude and phase lag of each element of the meridian section of the tire model are corrected using the temperature of the tire model calculated in step S20 (fifth step) (step S26 (sixth step)). The correction of the stress amplitude and phase lag of each element is as described above.

[0069] After step S26 (sixth step), the process returns to step S18 (fourth step), and step S18 (fourth step) is executed using the stress amplitude and phase lag corrected in step S26 (sixth step). This allows heat generation (viscoelastic loss energy) based on the corrected stress amplitude and phase lag to be obtained. The heat generation (viscoelastic loss energy) can be obtained with high accuracy. The corrected heat generation (viscoelastic loss energy) data is output to and stored in memory 27, for example. Next, the corrected heat generation (viscoelastic loss energy) is used to perform a heat conduction analysis using a heat conduction equation to calculate the temperature of each element of the tire model (step S20 (fifth step)). This allows the temperature of each element of the tire model based on the corrected heat generation (viscoelastic loss energy) to be obtained. The temperature data of each element of the tire model based on the corrected heat generation (viscoelastic loss energy) is output to and stored in, for example, memory 27.

[0070] Next, it is determined whether a preset condition is met (step S26 (sixth step)). In the simulation method, the fourth step (step S18), the fifth step (step S20), and the sixth step (step S26) are repeatedly executed until a preset condition is reached. The third step (step S16), the fourth step (step S18), the fifth step (step S20), the calculation of tire characteristics (step S24), and the sixth step (step S26) are performed by the calculation unit 24.

[0071] The simulation method is not limited to the method shown in FIG. Fig. 8 is a flow chart showing another example of the simulation method according to the embodiment of the present invention. Note that in the simulation method shown in Fig. 8, detailed explanations of the same steps as those in the simulation method shown in Fig. 7 will be omitted. The simulation method shown in FIG. 8 differs from the simulation method shown in FIG. 7 in that rolling resistance is calculated, but otherwise the steps are the same as those of the simulation method shown in FIG.

[0072] In the simulation method shown in FIG. 8, after step S18 (fourth step), it is determined whether or not to obtain the rolling resistance (step S30). In step S30, if the rolling resistance is not obtained, from step S18 (fourth step) onwards, each step is carried out in the same manner as in the simulation method shown in FIG. On the other hand, when the rolling resistance is calculated in step S30, the heat generation amount in each element of the meridian section of the tire model calculated in step S18 (fourth process) is integrated over the entire tire model to calculate the total heat generation amount (step S32). Next, the total heat generation amount obtained by integration is divided by the distance traveled by the tire model during one rotation. In this way, the rolling resistance of the tire model is calculated (step S34). The method of calculating the rolling resistance is as described above. In the simulation method, it is sufficient if the temperature of the tire model can be obtained. Therefore, although the above-mentioned simulation method shown in Fig. 7 and the simulation method shown in Fig. 8 calculate the tire characteristics using the modified tire model (step S24), the calculation of the tire characteristics using the modified tire model (step S24) is not necessarily required and may not be required.

[0073] The simulation method described above can be implemented by causing a computer to execute each step of the simulation method as a procedure using a program for executing the simulation method.

[0074] The present invention is basically configured as described above. Although the simulation method, the simulation device, and the program of the present invention have been described in detail above, the present invention is not limited to the above-mentioned embodiments, and various improvements and modifications may be made without departing from the spirit and scope of the present invention. EXAMPLES

[0075] Hereinafter, an embodiment of the simulation method of the present invention will be specifically described. In this example, the rolling resistance was obtained to confirm the effect of the simulation method of the present invention. A 3D tire model with the shape of the meridian section shown in Fig. 9 was used as the tire model. The size of the tire model elements was automatically determined when the 3D tire model was created. The tire size was 195 / 65R15. The road surface model was a flat model. In the contact analysis, the internal pressure was set to 210 kPa and the load was set to 4.82 kN. The tire model was subjected to an internal pressure filling process based on the internal pressure conditions. The internal pressure filling process reproduced the above-mentioned situation where a tire was mounted on a rim of a specified rim size specified by JATMA, ETRTO, and TRA and the tire was filled with internal pressure.

[0076] The boundary conditions in the heat conduction analysis were that the inside 52 of the tire model 50 shown in Fig. 9 was insulated. The temperature of the atmosphere around the tire model 50 was 25°C. The heat transfer coefficient of the tire model outer surface 53a within 270 mm from the rotation axis (not shown) of the tire model 50 is set to 1×10 -4 (W / (mm 2 The heat transfer coefficient of the tire model outer surface 53b at a position 270 mm or more away from the rotation axis (not shown) of the tire model 50 was set to 1×10 -3 (W / (mm 2 9 is a line indicating a position 270 mm away from the rotation axis (not shown) of the tire model 50. The thermal properties of the tire model in the heat conduction analysis are thermal conductivity of 0.2 (W / (m K)) and density of 1.1 to 1.2 × 10 -9 (kg / mm 3 ) and the specific heat was set to 1880 (J / (kg J)). The thermal conduction analysis was performed as a non-steady analysis, with a time step size of 10 seconds and a calculation end time of 2000 seconds. Abaqus / Standard was used for the simulation.

[0077] In Example 1, the rolling resistance was calculated by correcting the stress amplitude and phase lag in the simulation method of the present invention. In Comparative Example 1, the rolling resistance was calculated using heat generation (viscoelastic loss energy) without correcting the stress amplitude and phase lag. In addition, the rolling resistance was measured for an actual tire that corresponds to the tire model. This was used as a reference example. The results are shown in FIG. 10 below. In FIG. 10, reference numeral 50 indicates Example 1, reference numeral 52 indicates Comparative Example 1, and reference numeral 54 indicates the Reference Example. As shown in FIG. 10, in terms of rolling resistance, Example 1 obtained results close to those of the Reference Example (actual measured values). On the other hand, Comparative Example 1 deviated from the Reference Example (actual measured values). In this way, it was confirmed that the simulation method of the present invention, which determines the temperature of a tire model and corrects the stress amplitude and phase lag, can obtain rolling resistance with high accuracy. [Explanation of symbols]

[0078] 10 Simulation device 12 Processing Unit 14 Input section 16 Display section 20 Model Creation Department 22 Analysis Department 24 Arithmetic section 26 Display control section 27 Memory 28 Control Unit 30, 50 tire models 32 Road surface model 32a surface 40 Fever distribution 42 Temperature heat distribution 52 Inside 53a, 53b Tire model outer surface Ac meridian section C Rotational Axis CL Tire Equatorial Plane DL Rolling direction Dc Tire circumferential direction Dw Width direction

Claims

1. a first step of performing a contact analysis between a tire model, which represents a tire and is constituted by elements that can be numerically analyzed by a computer, and a road surface model, which represents a road surface and is constituted by the elements that can be numerically analyzed by a computer; A second step of obtaining stress and strain waveforms in a tire circumferential direction in each element of a meridian section of the tire model; a third step of performing a Fourier transform on the stress and strain waveforms in the tire circumferential direction in each element of the tire meridian cross section obtained in the second step, and acquiring a stress and strain spectrum for each of the elements of the tire meridian cross section; a fourth step of calculating a heat generation amount in each element of a meridian section of the tire model by using a stress amplitude, a stress phase difference, a strain amplitude, a strain phase difference, and a phase lag based on the stress and strain spectra acquired in the third step, and an element volume, a Fourier order, and a deformation mode of the tire model; a fifth step of calculating a temperature of each element of the tire model by a heat conduction analysis using a heat conduction equation; and a sixth step of correcting the stress amplitude and the phase lag of each element of a meridian section of the tire model by using the temperature of the tire model calculated in the fifth step, The simulation method further comprises repeatedly performing the fourth step, the fifth step, and the sixth step until a preset condition is reached.

2. The simulation method according to claim 1 , wherein the stress amplitude and the phase lag corrected in the sixth step are corrected using a function of temperature or a mathematical table relative to temperature.

3. 3. The simulation method according to claim 2, wherein the stress amplitude corrected in the sixth step is corrected using a value normalized by a value of a complex elastic modulus when the complex elastic modulus becomes a constant value in the function of temperature or in the numerical table.

4. 2. The simulation method according to claim 1, further comprising a step of integrating the heat generation amount in each element of a meridian section of the tire model calculated in the fourth step over the entire tire model, and dividing the total heat generation amount obtained by the integration by a distance traveled by the tire model during one rotation, thereby calculating a rolling resistance of the tire model.

5. 2. The simulation method according to claim 1, wherein the heat transfer conditions applied to the outer surface of the tire model in the heat conduction analysis in the fifth step are values ​​calculated using one or more physical quantities among a function of a distance from a tire rotation axis to each element of the outer surface of the tire model, a curvature of the tire model surface, a groove width of the tire model, a groove depth of the tire model, a groove volume of the tire model, a contact length of the tire model, a contact width of the tire model, and a surface roughness of the outer surface of the tire model.

6. The method of claim 1 , wherein the tire model is axisymmetric.

7. 2. The simulation method according to claim 1, wherein the heat conduction analysis in the fifth step is performed for a preset time interval, and the time interval is in a range of 1 to 300 seconds.

8. The simulation method according to claim 1 , wherein the heat conduction analysis in the fifth step is a steady-state heat conduction analysis.

9. 2. The simulation method according to claim 1, further comprising the steps of: calculating tire characteristics using a modified tire model in which elasticity or viscoelasticity is modified for each element of the tire model, using a temperature distribution of the tire model obtained by repeatedly performing the fourth step, the fifth step, and the sixth step until the preset condition is reached.

10. 2. The simulation method according to claim 1, further comprising, prior to the first step, a step of creating the tire model, which represents the tire and is constituted by elements that can be numerically analyzed by a computer, and the road surface model, which represents the road surface and is constituted by elements that can be numerically analyzed by a computer.

11. an analysis unit that performs a contact analysis between a tire model that represents a tire and is configured with elements that can be numerically analyzed by a computer, and a road surface model that represents a road surface and is configured with the elements that can be numerically analyzed by a computer; Obtaining stress and strain waveforms in the tire circumferential direction in each element of the meridian section of the tire model; a calculation unit that performs a Fourier transform on the obtained stress and strain waveforms in the tire circumferential direction in each element of the tire meridian cross section, and obtains a stress and strain spectrum for each element of the tire meridian cross section, the calculation unit calculates a heat generation amount in each element of a meridian section of the tire model by using a stress amplitude, a stress phase difference, a strain amplitude, a strain phase difference, and a phase lag based on the acquired stress and strain spectra, and an element volume, a Fourier order, and a deformation mode of the tire model, and calculates a temperature of each element of the tire model by a heat conduction analysis using a heat conduction equation; correcting the stress amplitude and the phase lag of each element of a meridian section of the tire model using the calculated temperature of the tire model; a simulation device that repeatedly calculates the amount of heat generated in each element of a meridian cross section of the tire model, calculates the temperature of each element of the tire model, and corrects the stress amplitude and the phase lag of each element of the meridian cross section of the tire model until a preset condition is reached.

12. The simulation apparatus according to claim 11 , wherein the stress amplitude and the phase lag to be corrected are corrected using a function of temperature or a mathematical table relative to temperature.

13. The simulation device according to claim 12 , wherein the stress amplitude to be corrected is corrected using a value normalized by a value of a complex elastic modulus when the complex elastic modulus becomes a constant value in the function of temperature or in the numerical table.

14. 12. The simulation device according to claim 11, wherein the calculation unit calculates the rolling resistance of the tire model by integrating the calculated heat generation amount in each element of a meridian cross section of the tire model over the entire tire model and dividing a total heat generation amount obtained by the integration by a distance traveled by the tire model during one rotation.

15. 12. The simulation device according to claim 11, wherein the heat transfer conditions applied to the outer surface of the tire model in the heat conduction analysis use values ​​calculated using one or more physical quantities among a function of a distance from a tire rotation axis to each element of the outer surface of the tire model, a curvature of the tire model surface, a groove width of the tire model, a groove depth of the tire model, a groove volume of the tire model, a contact length of the tire model, a contact width of the tire model, and a physical quantity of a surface roughness of the outer surface of the tire model.

16. The simulation device according to claim 11 , wherein the heat conduction analysis uses an axisymmetric tire model.

17. 12. The simulation device according to claim 11, wherein the heat conduction analysis is performed at a preset time interval, and the time interval is in a range of 1 to 300 seconds.

18. The simulation device according to claim 11 , wherein the heat conduction analysis is a steady-state heat conduction analysis.

19. 12. The simulation device according to claim 11, wherein the calculation unit calculates tire characteristics using a modified tire model in which elasticity or viscoelasticity is modified for each element of the tire model, using a temperature distribution of the tire model after the preset condition is reached.

20. 12. The simulation device according to claim 11, further comprising a model creation unit that creates the tire model, which represents the tire and is constituted by elements that can be numerically analyzed by the computer, and the road surface model, which represents the road surface and is constituted by elements that can be numerically analyzed by the computer.

21. A program for causing a computer to execute the steps of the simulation method according to any one of claims 1 to 10 as a procedure.

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