JP2003118328A - Method for predicting rolling resistance of tire - Google Patents

Abstract

PROBLEM TO BE SOLVED: To simply predict rolling resistance of a tire. SOLUTION: In this method for predicting rolling resistance performance of the tire, rolling resistance performance of the tire is predicted using a computer. This method comprises a step S1 of setting a tire model in which a rubber material, a carcass, a fiber material including a belt, and a non- expansible bead core are continuous in the same cross sectional shape in the peripheral direction of the tire and which can be handled by a finite element method, a step S2 of bringing the tire model into contact with a road surface model under the conditions determined in advance, a step S3 of calculating the history of distortion concerning each element appearing in a tire cross section of one of the tire models, and a step S4 of calculating total energy loss of the tire model from the maximum amplitude of distortion obtained from the history of distortion, material characteristics of the element, and initial volume of the element and obtaining rolling resistance by dividing total energy loss by a peripheral length of the tire model.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a tire rolling resistance predicting method capable of relatively easily predicting a tire rolling resistance by using a computer.

[0002]

2. Description of the Related Art In recent years,
In order to make effective use of global environmental resources, the fuel efficiency of vehicles is being improved. This is not an exception for tires, and various tires with low rolling resistance have been studied in the past. Conventionally, the evaluation of rolling resistance performance of tires is
This is done by actually prototyping and testing the tire. However, these methods require a great deal of time, cost, and labor to manufacture a trial tire and to test the trial tire. Therefore, further improvement in development efficiency is desired.

The present invention has been devised in view of such an actual situation, and the rolling resistance can be predicted relatively easily without actually making a trial tire, and the development of the tire can be streamlined. The purpose of the present invention is to provide a method for predicting rolling resistance of tires that is useful for.

[0004]

According to a first aspect of the present invention, there is provided a method of predicting rolling resistance of a tire using a computer, which comprises a rubber material, a carcass and a belt. A step of setting a tire model in which the fiber composite material including the non-stretchable bead core is continuous in the tire circumferential direction with the same cross-sectional shape and modeled with an element capable of numerical analysis, and based on predetermined boundary conditions Step to ground the tire model to the road surface model,
For each element that appears in one tire meridian section of the tire model, a step of calculating a strain history when the tire model makes one revolution, and for each element, a maximum amplitude of strain obtained from the strain history, Calculating the energy loss from the material properties of the element and the initial volume of the element, and obtaining the rolling resistance by dividing the total energy loss, which is the sum of the energy loss of each element, by the circumference of the tire model. It is characterized by including and.

According to a second aspect of the present invention, in the element that models the rubber material, the history of vertical strain and shear strain in the tire meridian direction, the tire circumferential direction, and the thickness direction perpendicular to the tire meridian direction is calculated. The method for predicting rolling resistance of a tire according to claim 1, wherein:

The invention according to claim 3 is characterized in that, for the element modeling the fiber composite material, the history of vertical strain in the tire meridian direction and the tire circumferential direction is calculated. Is a method for predicting rolling resistance of tires.

[0007]

BEST MODE FOR CARRYING OUT THE INVENTION An embodiment of the present invention will be described below with reference to the drawings. FIG. 1 shows a computer device 1 for implementing the rolling resistance prediction method of the present invention. The computer device 1 includes a main body 1a, a keyboard 1b and a mouse 1c as input means, and a display device 1d as output means. Although not shown in the main body 1a, a processor (CP
U), a ROM, a working memory, a mass storage device such as a magnetic disk, and a storage device such as a CD-ROM or a flexible disk drive 1a1 or 1a2. The mass storage device stores a processing procedure (program) for executing a method described later. EWS or the like is preferably used.

FIG. 2 shows an example of the processing procedure of this embodiment, which will be described below in order. First, in the present embodiment, a rubber material, a carcass, a fiber composite material including a belt,
A process of setting a tire model including non-stretchable bead cores which are continuous in the tire circumferential direction with the same cross-sectional shape and which can be numerically analyzed is performed (step S1). The numerical analysis is possible means that it can be handled by a numerical analysis method such as a finite element method, a finite volume method, a difference method, or a boundary element method. In this example, the one adopting the finite element method is exemplified.

FIG. 3 is a three-dimensional visualization of an example of the tire model 2, and FIG. 4 shows a tire meridian section including the tire rotation axis. The tire model 2 becomes numerical data that can be handled by the computer 1 by dividing the tire to be analyzed into a finite number of small elements 2a, 2b, 2c ... Specifically, the nodal coordinate values, shapes, and material properties of the respective elements 2a, 2b, 2c ... Are defined, for example, density, elastic modulus, loss tangent or damping coefficient. Each of the elements 2a, 2b, 2c ... Has a triangular or quadrangular membrane element as a two-dimensional plane, 3
As a dimensional element, it is suitable for expressing complicated shapes.
Faced solid elements are preferred. However, other than this, a pentahedral solid element, a hexahedral solid element, or the like can be used, and any element that can be processed by a computer is used.

In this example, the rubber material and the bead core which form the tire are modeled by a three-dimensional solid element e1. The element modeling the rubber material can be defined as, for example, a super viscoelastic material. On the other hand, the bead core 5 can be treated as a solid element having a rigid surface and substantially non-deformable. Further, as shown in FIG. 5, in the fiber composite material constituting the tire, for example, belt ply, carcass ply, band ply, etc., the cord array c is, for example, a quadrilateral membrane element 5a, 5b, and the cord array. The topping rubber t covering c from the inside and outside can be modeled as solid elements 5c to 5e, respectively, and can be modeled as a composite shell element 5 in which these are laminated in the thickness direction. For the membrane elements 5a and 5b, for example, a thickness equal to the diameter of the cord c1 and anisotropy of different rigidity in the arrangement direction (shown by a straight line) of the cord c1 and the direction orthogonal thereto are defined. In addition, each element has its material property defined based on the elastic modulus (longitudinal elastic modulus, transverse elastic coefficient) of each rubber or cord material, the complex elastic modulus of the cord, the rubber, the loss tangent tan δ, the elastic modulus of the bead core, and the like. .

Further, the tire model 2 of this embodiment is exemplified by the one in which the tread surface is formed as a smooth surface having no groove, but is not limited to this. In addition, in the tire model 2 as described above, in the present embodiment, first, the two-dimensional cross-sectional shape shown in FIG. 4 is specified in the tire meridian section, and as shown in FIG. It is possible to model as a three-dimensional shape relatively easily by rotating in the direction and unitizing into equal parts with a predetermined circumferential length s. As a result, in the tire model 2, the same cross-sectional shape is continuous in the tire circumferential direction.

Next, in this embodiment, the tire model 2 is brought into contact with the road surface model 14 based on a predetermined boundary condition (step S2). This is a so-called ground contact simulation, and in this example, as shown in FIG. 6, the tire model 2 is brought into contact with the road surface model 14 in a stationary state without rotating and the vertical load P is applied.

The boundary conditions to be set include various conditions based on, for example, a rim assembly condition by a mounting rim, a filled internal pressure, an axial load acting on a virtual tire rotation shaft, and a road surface friction coefficient.

The tire model 2 in the assembled state of the rim
In order to simulate with, the bead core c of the tire model 2 modeled on a rigid surface is displaced and the bead width W is adjusted to be equal to the rim width, or the rim contact areas b, b of the tire model 2 are adjusted. Can be restrained immovably, and the width W of the bead portion of the tire model 2 can be forcibly displaced so as to be equal to the rim width. The rim contact area b is determined according to the size of the rim to be mounted. At this time, the relative distance r1 between the virtual tire rotation axis CL of the tire model 2 and the rim contact area b is always kept constant.

Further, in order to simulate the state in which the tire model 2 is filled with the internal pressure, as shown in FIG. 6, an evenly distributed load w corresponding to the tire internal pressure acts on the inner surface of the tire of the tire model 2. Give the conditions. Further, in order to apply the vertical load P to the tire model 2, the vertical load P perpendicular to the road surface is calculated from the virtual tire rotation axis CL or the road surface model 14.
Conditions are given to operate. The friction coefficient between the tire model 2 and the road surface model 14 defines a value corresponding to the road surface on which the vehicle travels. As a result, it is possible to use the tire model 2 and the road surface model 14 to simulate a ground contact situation in which a tire assembled into a rim and filled with a predetermined internal pressure is pressed against the road surface with a predetermined vertical load. In addition to this,
The slip angle and camber angle can be set as required.

When the tire model 2 is grounded to the road surface model 14 due to the boundary conditions, each element constituting the tire model 2, specifically, a solid element representing a rubber material or a membrane element representing a cord material. 5a and 5b are distorted by internal pressure, vertical load, and reaction force from the road surface. The strain acting on each element is, for example, in the overall coordinate system of the x-axis, y-axis and z-axis (shown in FIGS. 3 and 4), the vertical strains εx, εy, εz in the tensile and compression directions, and The strains in the shear direction can be calculated as εxy, εyz, εzx. The calculation of each strain is performed by the computer device 1 using the finite element method. In this way, various boundary conditions are given to a model consisting of a finite number of elements, and the procedure of the finite element method for acquiring information such as force, displacement, and strain of the entire system is in accordance with a known example, and application software is used. Can be done using.

Next, in the present embodiment, for each element appearing in one tire meridian section of the tire model 2, a process of calculating a strain history when the tire model 2 makes one rotation is performed (step S3). "Each element that appears in one tire cross section of the tire model 2" means all the elements that appear in FIG. In addition, as shown in FIG. 8A, the “distortion history” means, for example, one element 2f that models a rubber material.
The tire model 2 is a road surface model 14
Is continuously recorded during one rotation (θ = 0 to 360 °) of the element 2f. Figure 8
In (B), the horizontal axis represents the rotation angle of the tire model and the vertical axis represents the magnitude of strain, and an example of the strain history is shown.

Since each part of the tire moves due to rolling, internal resistance is generated and apparent rigidity changes,
In order to more accurately simulate the rolling resistance of the tire, it is desirable to calculate the strain history by performing a rolling simulation in which the tire model 2 actually rolls, but this tends to result in a long calculation time. Therefore,
In the present embodiment, it is assumed that the strain that the tire model 2 receives in a state of statically contacting the road surface model 14 is substantially equal to the dynamic strain that the tire model receives when the tire is rolling under load. It shows that the dynamic rolling resistance can be predicted simply and quickly from such calculation results.

As shown in FIG. 8A, when the tire model 2 is statically grounded on the road surface model 14, for example, a certain strain acts on the element 2f. On the other hand, the strain also acts on the elements 2g, 2h, ... Which are sequentially adjacent to the element 2f on the one side in the tire circumferential direction. Here, the tire model 2 of the present embodiment is modeled such that elements having the same tire circumferential length are equally divided and the same cross-sectional shape is continuous. Therefore, for example, the strain received by the element 2f adjacent to the element 2f in the tire circumferential direction is considered to be substantially equal to the strain received when the tire model rotates by one element and the element 2f moves to the position of the element 2g. In addition, in the state of FIG. 8A, the strain received by the element 2g is substantially the same as the strain received when the tire model 2 rotates by two elements and the element 2f moves to the position of the element 2g. Can be considered equal. Based on such an assumption, even from the static grounding simulation of the tire model 2, the strain history of each element is pseudo-calculated by referring to the strain of other elements continuous in the tire circumferential direction. be able to. When using the faster computer device 1, the strain history can be obtained by rotating or rolling the tire model 2 at every minute angle.

Further, in this example, the strain history of each element is calculated not as the strain of the overall coordinate system of the x-axis, y-axis and z-axis but as the strain history of the tire coordinate system as a reference. For example, as shown in FIG. 7, when the tire coordinate system is used as a reference, for one solid element 2f representing a rubber material or the like, vertical strain ε11 along the tire meridian direction, vertical strain ε22 along the tire circumferential direction, tire meridian line. Vertical strain .epsilon.33 along the thickness direction perpendicular to the direction, shear strain .epsilon.12 shear deformed in the tire meridian direction, shear strain .epsilon.23 shear deformed in the tire circumferential direction as shown in FIGS. Consider the total of 6 strains including the shear strain ε31 that causes shear deformation in the vertical direction. Further, the membrane elements 5a and 5b modeling the fiber composite material.
With regard to the present embodiment, as shown in FIG. 10, in the present embodiment, the vertical strain ε33 along the tire meridian direction and the vertical strain ε22 along the tire circumferential direction are considered separately. Is considered to be negligible, and shear strain does not occur. The strain in the tire coordinate system may be obtained by first obtaining the strain in the global coordinate system and converting it, or may be calculated directly.

FIG. 11 and FIG. 12 show an example of the strain history of the element 2f representing a part of the tread rubber thus obtained. 11A to 11C, and FIG.
2 (A) to (C), the strain history of one element representing the tread rubber shown in the area a of FIG. In the graph of the figure, the vertical axis represents strain, the horizontal axis represents tire rotation angle (0 to 360 °), and the position of 180 ° is the center of contact with the ground. 13 (A) and 13 (B) show the strain history of one element of the band ply shown in the region b of FIG. Such a strain history is calculated and stored for every element that appears in the cross section of FIG.

Next, in the present embodiment, for all the elements modeling the rubber material, the strain history in each of the six directions is represented by the difference between the maximum and minimum strain values as shown in FIGS. Maximum amplitude of a strain ε11m, ε22m, ε33m, ε
Calculate 12m, ε23m and ε31m. Further, for all the film elements, as shown in FIG. 13, the strain which is the difference between the maximum value and the minimum value of the strain in two directions of the tire circumferential strain ε11 and the tire axial strain ε22 is based on the strain history. The maximum amplitudes ε11m and ε22m of are calculated respectively. These values are calculated and stored sequentially.

Next, in this embodiment, when the tire model makes one revolution from the maximum amplitude Eijm of the strain obtained from the strain history, the material characteristics of the element, and the initial volume of the element, for each element, The required energy loss is calculated (step S4). Further, a process for obtaining rolling resistance is performed by dividing the total energy loss (Le), which is the total energy loss of each element, by the circumference of the tire model 2 (step S5).

The total energy loss Le is a sum of the energy loss sum Le1 of all rubber material elements and the energy loss sum Le2 of all fiber composite materials, as shown in the following formula (1). Can be calculated. Le = Le1 + Le2 (1) Therefore, as in the following formula (2), the rolling resistance RR of the tire model 2 is obtained by dividing the total energy loss required for the tire model 2 to make one rotation by the circumference of the tire model 2. It can be calculated by RR = Le / 2πr (2) (where “r” is the initial radius of the tire model 2)

The basic concept of the energy loss calculation method can be considered based on a Voigt model having a spring B and a damper D in parallel as shown in FIG. In FIG. 15, the length of each side is a1, a2, a3.
The hexahedral solid element ex is described as an example, and it is assumed that a periodic displacement x in the z-axis direction occurs on one side a1 of the element ex. When the displacement x occurs in the element ex, an internal resistance force (internal force) proportional to the speed of this displacement occurs, and the energy loss can be calculated from this internal force.

In FIG. 14, the internal force F due to the displacement x generated in the spring B and the damper D can be expressed by the following equation (3) assuming that the strain becomes a sine curve. F = kx + η · (dx / dt) (3) Here, if the spring constant k and the viscosity coefficient η are set as follows, the internal force F can be expressed by the following equation (4). Displacement:
x = a1.epsilon.sin .omega.t Spring constant: k = a2 .a3 .G '/ a1, Viscosity coefficient: η = a2 .a3 .G "/ (a1 .ω) (where G'is the dynamic elastic modulus, G ″ is the loss elastic modulus, ε is the strain in the z-axis direction, and ω is the frequency. F = a2 · a3 · G ′ · ε · sin ωt + a2 · a3 · G ″ · ε · cos ωt… (4 )

Therefore, the total energy loss Hx caused by the strain in the z-axis direction in this element ex is obtained by integrating the above equation (4) within the range of 0 to (2π / ω) as shown in the following equation (5). Can be obtained by Hx = ∫F ・ dx = a2 ・ a3 ・ ε∫ (G'sin ωt + G "cos ωt) ・ (dx / dt) ・ dt (5) (where t = 0 to 2π / ω)

By solving the above equation (5), the following equation (6) is obtained. Hx = π · a1 · a2 · a3 · ε 2 · G "... (6) where" a1 · a2 · a3 "is nothing but the initial volume V of element ex, also the loss modulus G" and loss From the relationship tan δ = G ″ / G ′ with the tangent tan δ and the dynamic elastic modulus G ′, the equation (6) can be converted into the following equation (7). Hx = π · V · tanδ · G'ε ² ··· (7)

Here, tan δ and G ′ are both elements e
Since x is a material property specified by the modeled material, the total energy loss consumed by the element ex subjected to the strain ε is the material property (tan) of the strain ε and the element ex.
It can be seen that it can be easily calculated from δ, G ′) and the initial volume V of the element ex.

In the present embodiment, based on such a formulation, as shown in the following equation (8), the dynamic elastic modulus G ′ has a longitudinal elastic modulus E0 for vertical strain and a lateral elastic modulus G0 for shear strain. In addition to the above, the energy loss in each of the six directions is calculated for each solid element, and these are summed for all the elements to calculate the total energy loss Le1 for all the elements of the rubber material. Note that the strain ε in the above formula (7) is a single amplitude, but in the present embodiment, the maximum strain amplitude (difference between maximum and minimum) is used, so the whole is divided by 4.
Further, since the tire model 2 of this example is equally divided in the tire circumferential direction, the energy loss Le1 can be calculated by summing this energy loss if all the energy losses of the solid elements appearing in one tire meridian section can be calculated. It can be easily calculated by multiplying by the number of divisions.

[Equation 1]

Similarly, for each of all the membrane elements, the maximum strain amplitudes ε11m and ε22m are expressed by the following equation (9).
It is possible to calculate the sum Le2 of the energy losses of all the membrane elements occurring during one rotation of the tire model 2 by multiplying each of the above by the elastic coefficient and the loss tangent and summing them. The energy loss Le2 can be easily calculated by multiplying this sum by the number of divisions in the tire circumferential direction, if all the energy losses of the film elements appearing in one tire meridian section can be calculated.

[Equation 2]

In the equation (9), the converted Young's modulus is used as E1 and E2. As shown in FIG. 16 (A),
In the material coordinate system, the membrane element 5a (or 5) has anisotropy with different elastic moduli in the direction m of the cord material and the direction n along the membrane element and perpendicular thereto. The longitudinal elastic modulus Em of m and the longitudinal elastic modulus En of the direction n are determined according to the compound rule. As shown in FIG. 16B, the volume fraction of the cord material c1 in the ply of the membrane element 5a before modeling is φ, and the longitudinal elastic modulus of the cord material c1 is E.
If f and the longitudinal elastic modulus of the topping rubber t are Er, the longitudinal elastic moduli Em and En in the respective directions m and n are given by the compound rule.
It can be calculated by the following equations (10) and (11). Em = Ef · φ + Er (1-φ) (10) En = (Ef · Er) / {Ef (1-φ) + Erφ} (11)

In this embodiment, the longitudinal elastic moduli Em and En are converted into the meridian direction and the circumferential direction of the tire coordinate system and used as the converted Young's moduli E ₁ and E ₂ .

As described above, in the rolling resistance predicting method of this embodiment, since the rolling resistance of the tire can be predicted relatively easily by using the computer device 1, an attempt is made to analyze the tire without actually manufacturing it. Approximate rolling resistance of tires can be predicted. Further, since the strain history is calculated in a pseudo manner from a static grounding simulation, the calculation processing time of the computer can be significantly shortened without significantly lowering the accuracy.

Further, the cord material c1 may have a characteristic that the modulus differs between compression and tension, that is, bimodulus. In this case, the sum Le2 of the energy losses of all the membrane elements is expressed by the following formula (1) instead of the above formula (9).
2) can also be used. In this case, it is useful for further improving the prediction accuracy. The symbol "A" in the equation (12) represents the compression ratio (rigidity in the tensile direction / rigidity in the compression direction).

[Equation 3]

Conventionally, for example, as shown in FIGS. 17 (A) and 17 (B), total strain energies in the x- and y-axis directions of the overall coordinate system of the tire model are obtained, and these are added and added to the same figure (C). )
It is also proposed to try to calculate the rolling resistance from the sum of energy as shown in. However, in this method, the sum of distortions (dWx
When + dWy) is taken, they are canceled by each other and the amplitude dWt at the sum of strain energy becomes small. On the other hand, in the present embodiment, the strain is considered separately for each of the above six components or two components related to the tire seat surface system, and the energy loss is calculated for each element using the maximum amplitude of the strain. Since they are summed, more accurate calculation can be performed.

Further, as shown in FIG. 18, a tire model 2
When the internal pressure is filled in, for example, an initial stress σ1
Occurs. When the stress changes to σ2 due to running or load, the energy loss caused by running or load is the triangular portion A1 shown by hatching, but if the energy loss is simply calculated from the strain energy difference,
The energy loss of the trapezoidal portion including the rectangular portion A2 is estimated, which is not preferable. In the present embodiment, the above problem can be corrected by using the parameter of the maximum amplitude of distortion.

The rolling resistance of a pneumatic tire includes the air resistance generated as the tire rotates and progresses,
The frictional resistance generated at the ground contact portion between the tire and the road surface and the resistance due to the hysteresis loss of the tire constituent members, that is, the rubber and the cord reinforcing material are related. Although the air resistance depends on the speed, it is generally as small as 1 to 3% of the total rolling resistance, and thus the air resistance is ignored in the present invention.

[0039]

EXAMPLE The rolling resistance of pneumatic tires A to E having a tire size of 225 / 65R16 was predicted using the present invention. In this example, an experiment was conducted using a plain tire model in which no tread pattern was formed. For comparison, rolling resistance was measured using an actual tire (comparative example). FIG. 19 shows these results.
A good correlation was found between the example and the comparative example.

[0040]

As described above, according to the first aspect of the present invention, by predicting the rolling resistance of a tire using a computer, it is possible to reduce the number of steps for actually making a tire and making an experiment. Helps improve development efficiency. Further, since the tire model is set to include the rubber element that models the rubber and the code element that models the cord material, the energy loss as the composite material can be accurately calculated and is sufficiently effective as an index. Can predict rolling resistance. Further, since the energy loss is calculated from the maximum amplitude of strain for each element and these are summed up, the strains are not offset in each direction, and the energy loss of the rubber can be calculated accurately.

[Brief description of drawings]

FIG. 1 is a configuration diagram of a computer device for implementing a simulation method of the present invention.

FIG. 2 is a flowchart showing an example of a processing procedure of a simulation method of the present invention.

FIG. 3 is a perspective view of a tire model used in this embodiment.

FIG. 4 is a sectional view thereof.

FIG. 5 is a conceptual diagram showing modeling of a fiber composite material into elements.

FIG. 6 is a cross-sectional view illustrating a rim assembly condition of a tire model.

FIG. 7 is a partial perspective view of a tire model and an enlarged view of one element thereof.

FIG. 8A is a side view of a tire model grounding simulation, and FIG. 8B is a graph illustrating strain history.

FIG. 9 is a perspective view of an element for explaining distortion of a solid element.

FIG. 10 is a perspective view of an element explaining the distortion of the membrane element.

11 (A) to (C) are graphs showing strain histories of one solid element that models a tread rubber.

12A to 12C are graphs showing strain histories of one solid element that models a tread rubber.

13 (A) to (B) are graphs showing strain histories of one membrane element modeling a band ply.

FIG. 14 is a conceptual diagram of a Voigt model.

FIG. 15 is a perspective view of a solid element for explaining energy loss.

16 (A) is a perspective view for explaining the reduced Young's modulus of the membrane element, and FIG. 16 (B) is an enlarged sectional view thereof.

17 (A) to (C) are graphs showing strain energy.

FIG. 18 is a graph showing the relationship between stress and strain.

FIG. 19 is a graph showing an example of the present invention.

[Explanation of symbols]

2 tire model 2a, 2b ... elements e1 Solid element 5a, 5b Membrane element

Claims (3)

[Claims] 1. A method of predicting rolling resistance of a tire using a computer, comprising: a rubber material; a fiber composite material including a carcass and a belt; and a non-stretchable bead core. A step of setting a tire model that is continuous with the same cross-sectional shape and is modeled with elements that can be numerically analyzed, a step of grounding the tire model to a road surface model based on a predetermined boundary condition, and the tire model For each element appearing in one tire meridian section, a step of calculating a strain history when the tire model makes one revolution, a maximum strain amplitude obtained from the strain history for each element, and a material of the element The step of calculating the energy loss from the characteristics and the initial volume of the element, and the total energy loss which is the sum of the energy loss of each element Rolling method of predicting tire characterized by comprising the steps of obtaining a rolling resistance by dividing the circumferential length of the tire model. 2. A history of vertical strain and shear strain in the tire meridian direction, the tire circumferential direction, and the thickness direction perpendicular to the tire meridian direction is calculated for the element modeling the rubber material. The method for predicting rolling resistance of a tire according to claim 1. 3. The method for predicting rolling resistance of a tire according to claim 1, wherein a history of vertical strain in a tire meridian direction and a tire circumferential direction is calculated for the element modeling the fiber composite material. .