JP4469172B2 - Tire simulation method - Google Patents

Description

  The present invention relates to a tire simulation method capable of predicting rolling resistance of a tire using a computer in a relatively simple manner.

  Regarding the fuel efficiency of a vehicle, the influence of tire rolling resistance is large, and the contribution rate is considered to be about 10%. Therefore, it is important to analyze the rolling resistance of the tire in order to improve the fuel efficiency performance of the vehicle. Conventionally, evaluation of rolling resistance of a tire has been performed by actually making a prototype of a tire and performing a test. However, these methods require a great deal of time, cost, and labor for producing prototype tires and testing prototype tires. Therefore, further improvement in development efficiency is desired. Therefore, in recent years, as described in Non-Patent Documents 1 and 2 below, tire rolling resistance is analyzed by simulation using a computer.

Japan Automobile Engineering Association Academic Workshop Preprint 852074 Yoichi Kobayashi et al. “Development of Analytical Method for Tire Rolling Resistance” Tire Science and Technology, TSTCA, Vol.27, No.1 Jan-Mar 1999 P.22 `` Tire Tempareture and Rolling Resistance Prediction with Finite Element Analysis ''

  Non-Patent Document 1 describes a static analysis in which a tire model is statically grounded to a road surface model. In this analysis, the energy loss due to viscoelasticity of the tire is calculated for the element i by the product Ui · Vi · tanδi of the strain energy density Ui, the volume Vi, and the loss tangent tanδi. Non-Patent Document 2 describes a static analysis of a tire model using FEM. In this document, in order to obtain the rolling resistance of the tire, the energy loss per unit volume is calculated by using the dynamic loss elastic modulus G ″ and the amplitude strain. The history of distortion that occurs when the tire rolls is not accurately taken into account.

  While adopting static analysis, the inventors have analyzed the tire meridian direction, the tire circumferential direction, and the tire thickness direction so that a more detailed analysis can be performed on the modeled element of the tire rubber material. It has been newly found out that the history of one rotation of a tire with six component strains including vertical strain and shear strain is calculated from the strain distribution in the circumferential direction of the grounded tire model.

  As described above, according to the present invention, for a modeled tire rubber material, one rotation of a tire having six component strains including vertical strain and shear strain in the tire meridian direction, tire circumferential direction, and tire thickness direction, respectively. It is an object of the present invention to provide a tire simulation method capable of analyzing with high accuracy by including a step of calculating the time history from the strain distribution in the circumferential direction of the grounded tire model.

The invention according to claim 1 of the present invention is a tire simulation method for simulating a tire using a computer, wherein a rubber material, a fiber composite material including a carcass and a belt, and a non-extensible bead core are provided in the tire circumference. A step of setting a tire model modeled with elements that are continuous in the same cross-sectional shape and capable of numerical analysis, and a step of grounding the tire model based on a predetermined boundary condition without rolling the tire model When, for at least a rubber material modeling elements, the tire meridian direction, the tire circumferential direction and the history of when the tire 1 rotation of the six components strain containing a vertical strain and the shear strain, respectively for the tire thickness direction, to the ground calculating from the circumferential direction of the strain distribution of the tire model, for at least one element of said rubber member And calculating energy loss of the absolute value of the distortion change amount based on the value obtained by integrating the one round of the tire model, the energy loss is characterized in that is calculated by the following equation.
W = Σπ · E · (εp / 2) ² · tan δ
(Here, Σ represents the sum for all tire coordinate systems, E is the storage elastic modulus of each element, and tan δ is the loss tangent of each element.)

The invention according to claim 2 is a tire simulation method for simulating a tire using a computer, wherein the rubber material, the fiber composite material including the carcass and the belt, and the non-extensible bead core are the same in the tire circumferential direction. Setting a tire model modeled with elements that are continuous in cross-sectional shape and capable of numerical analysis, and contacting the road surface model without rolling the tire model based on a predetermined boundary condition, and at least The tire model in which the history of one rotation of the tire with six component strains including vertical strain and shear strain in the tire meridian direction, tire circumferential direction and tire thickness direction is grounded with respect to the element modeling the rubber material. calculating the strain distribution in the circumferential direction of the at least one element of the rubber material, varying the strain And calculating energy loss of the absolute value of the amount based on the value obtained by integrating the one round of the tire model, the energy loss is characterized in that is calculated by the following equation.
W = Σ (μ · | εi + 1 -εi |)
(Where μ is the damping characteristic of each element, and the area A of the hysteresis loop of the stress-strain curve obtained from the actual viscoelastic characteristic test for the rubber material is divided by the strain amplitude εm used in the viscoelastic characteristic test. The values εi and εi + 1 are distortions of two elements adjacent in the circumferential direction, i = 1 to n, but when i = n, 1 is substituted for i + 1.)

According to a third aspect of the present invention, in the tire model, the rubber material is modeled by a solid element made of a linear elastic body or an incompressible superelastic body, and the fiber composite material has orthogonal anisotropy. The tire simulation method according to claim 1, wherein the tire simulation method is modeled by a membrane element having the tire element.

  In the invention of claim 1, since the history of strain when the tire makes one revolution can be calculated using a computer, the process of actually making and experimenting with the tire can be reduced, and the development efficiency of the tire can be reduced. Help to improve. In addition, since the tire model is set including an element modeling a rubber material and an element modeling a fiber composite material, it is useful for calculating, for example, energy loss as a composite material with high accuracy.

  In addition, at least the element modeled on the rubber material causes the history of one rotation of the tire having six component strains including vertical strain and shear strain in the tire meridian direction, the tire circumferential direction and the tire thickness direction to be grounded. Since it is calculated from the strain distribution in the circumferential direction of the tire model, a highly accurate simulation can be performed without performing dynamic analysis.

In addition, as in the first or second aspect of the invention, the energy loss of each element is calculated based on a value obtained by accumulating the absolute value of the amount of change in strain for one revolution of the tire model, Thus, a more accurate result can be obtained without being affected by the number of waveform peaks in the distortion history. Then, by comparing the energy loss, etc., it is possible to roughly evaluate the rolling resistance of the tire.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 shows a computer apparatus 1 for carrying out the rolling resistance prediction method of the present invention. The computer device 1 includes a main body 1a, a keyboard 1b as an input means, a mouse 1c, and a display device 1d as an output means. Although not shown, the main body 1a is appropriately provided with an arithmetic processing unit (CPU), a ROM, a working memory, a mass storage device such as a magnetic disk, and CD-ROM and flexible disk drives 1a1 and 1a2. The mass storage device stores a processing procedure (program) for executing a method to be described later. The computer device 1 is preferably EWS or the like.

  FIG. 2 shows an example of the processing procedure of this embodiment. In this embodiment, the process which sets the tire model 2 is first performed (step S1). FIG. 3 shows an example of the tire model 2 visualized three-dimensionally. FIG. 4 shows a tire meridian cross section including the tire rotation axis of the tire model 2. In the present embodiment, the tire model 2 having no groove on the tread surface is exemplified.

  The tire model 2 is modeled by dividing a tire to be analyzed (whether or not actually exists) into a finite number of small elements 2a, 2b, 2c. Thus, numerical data that can be handled by the computer apparatus 1 is configured. The tire model 2 is modeled so that a rubber material, a fiber composite material including a carcass and a belt, and a non-extensible bead core are continuous in the same circumferential shape in the tire circumferential direction. In the present embodiment, the rubber material includes a tread rubber disposed in the tread portion of the tire, a sidewall rubber disposed in the sidewall portion, a bead rubber disposed in the bead portion, a bead apex rubber, etc. The rubber material (for example, topping rubber) may be included. The fiber composite material can also include, for example, a band, a bead reinforcing layer, etc. in addition to the carcass and the belt.

  Each element is determined so that numerical analysis is possible. The possibility of numerical analysis means that calculation can be performed by a numerical analysis method such as a finite element method, a finite volume method, a difference method, or a boundary element method. Specifically, for each of the elements 2a, 2b, 2c..., Nodal coordinate values, shapes, material properties (for example, density, elastic modulus, loss tangent or damping coefficient) are defined. For each element 2a, 2b, 2c..., For example, a triangular or quadrangular membrane element as a two-dimensional plane, and a three-dimensional element is preferably a tetrahedral or hexahedral solid element, for example.

  The rubber material and the bead core are modeled by a three-dimensional solid element. An element modeling a rubber material is defined as an incompressible superelastic body, for example. That is, the volume does not change due to deformation, and large deformation is possible. When the load is removed, the original shape is restored. On the other hand, the bead core 5 is defined as a solid element whose surface is rigid and substantially non-deformable. Further, as shown in FIG. 5, the fiber composite material such as a carcass or a belt includes a cord array c on, for example, quadrilateral membrane elements 5a and 5b, and a topping rubber t covering the cord array c from inside and outside. It is possible to model each of the solid elements 5c to 5e as a composite shell element 5 that is 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 an orthogonal anisotropy having different rigidity in the arrangement direction (indicated by a straight line) of the cord c1 and a direction perpendicular thereto are defined. Each element has material properties defined based on the elastic modulus (longitudinal elastic modulus, transverse elastic modulus) of each rubber material, cord material, etc., complex elastic modulus such as cord or rubber, loss tangent tan δ, elastic modulus of bead core, etc. Is done. However, the method of modeling the fiber composite material is not limited to this example, and it can be modeled only by the membrane element.

  When creating the tire model 2, for example, as shown in FIG. 4, first, the tire meridian cross-sectional shape (two-dimensional cross-sectional shape) is specified using the node n. Then, as shown in FIG. 6, the nodes n... Obtained in the tire meridian cross-sectional shape are continuously copied around the tire rotation axis at every small angle pitch s. A three-dimensional tire model 2 can be easily modeled by associating adjacent nodes as two-dimensional or three-dimensional elements. Thereby, as for the tire model 2, the same cross-sectional shape will continue in a tire peripheral direction. Each element has the same length in the tire circumferential direction.

  Next, in this embodiment, a road surface model is set (step S2). As shown in FIG. 7, the road surface model 6 of the present embodiment is modeled by a flat rigid surface element. However, the road surface model 6 may have unevenness.

  Next, in the present embodiment, a process of causing the tire model 2 to contact the road surface model 6 without rolling based on a predetermined boundary condition is performed (step S3). In the present embodiment, as shown in FIG. 7, the tire model 2 is brought into contact with the road surface model 6 in a stationary state without rotating and the longitudinal load P is applied. The boundary conditions to be set include, for example, conditions such as a rim assembly condition with a mounting rim, an internal pressure of the tire model 2, the longitudinal load, or a road surface friction coefficient.

  In order to simulate the rim assembly with the tire model 2, for example, the bead core c of the tire model 2 is forcibly displaced so that the bead width BW is equal to the rim width, or the rim contact area b of the tire model 2 is set. There is a method of forcibly displacing the width BW of the bead portion of the tire model 2 equal to the rim width by restraining b to be immovable. The rim contact area b can be determined according to the dimensions 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 constant.

  Further, in order to simulate the state in which the tire model 2 is filled with the internal pressure, as shown in FIG. 7, a deformation simulation is performed by applying an equally distributed load w corresponding to the tire internal pressure to the tire cavity surface of the tire model 2. Do. Further, in order to apply the longitudinal load P to the tire model 2, conditions are given so that the load P perpendicular to the road surface acts from the tire rotation axis CL or the road surface model 6. The coefficient of friction between the tire model 2 and the road surface model 6 is defined as a value corresponding to the road surface on which the vehicle is traveling. As a result, it is possible to simulate, using the tire model 2 and the road surface model 14, a situation in which a tire that is assembled with a rim and filled with a predetermined internal pressure is in contact with the road surface with a predetermined longitudinal load. In addition, a camber angle or the like can be set if necessary.

  Next, in the present embodiment, from the elements constituting the tire model 2, specifically, from the membrane elements 5a and 5b representing the rubber elements and the solid elements representing the rubber material, the internal pressure, the longitudinal load and the road surface The distortion caused by the reaction force is calculated (step S4). For example, as shown in FIG. 3, the strain acting on each element includes vertical strains εx, εy, εz in the tensile and compression directions and shear directions in the respective directions in the entire coordinate system of the X axis, the Y axis, and the Z axis. The strains εxy, εyz, and εzx can be calculated. However, the calculation of the vertical strain in the thickness direction and the shear strain in each direction can be omitted from the shape of the membrane element. The procedure of the finite element method that gives various boundary conditions to a model composed of a finite number of elements and obtains information on the force, displacement, strain, etc. of the entire system can be performed by application software or the like according to known examples. .

  Further, in the present embodiment, the distortion is calculated based on the tire coordinate system from the distortion of the entire coordinate system of the X axis, the Y axis, and the Z axis. For example, as shown in FIG. 6, when the tire coordinate system is used as a reference, the strain acting on one solid element 2f representing a rubber material or the like is a vertical strain ε11 along the tire meridian direction and a vertical strain ε22 along the tire circumferential direction. , A vertical strain ε33 along the thickness direction perpendicular to the tire meridian direction, a shear strain ε12 that shears in the tire meridian direction, and a shear strain that shears in the tire circumferential direction as shown in FIGS. It can be calculated as a total of six components consisting of ε23 and shear strain ε31 shearing in the thickness direction.

  Further, in the present embodiment, as shown in FIG. 9, the membrane element 5a or 5b that models the fiber composite material has a total of two components, ie, a vertical strain ε11 along the tire meridian direction and a vertical strain ε22 along the tire circumferential direction. Can be converted to distortion. In the membrane element, the vertical strain ε33 along the thickness direction is substantially small and is ignored, and no shear strain occurs.

FIG. 10 shows a case where any one element 2f of the tire model 2 idles once around the tire rotation axis CL. When an internal pressure condition is applied to the tire model 2, the element 2f has, for example, a distortion a in the tire radial direction . In the global coordinate system, when the element 2f is rotated from the state (1) to the state (2), the following distortion state is obtained.
Position (1) X direction: 0, Y direction: a
Position (2) X direction: a, Y direction: 0

  Since the element 2f is merely idling, the strain in the X direction changes from 0 to a and the strain in the Y direction changes from a to 0, although there is no change in the strain. Resulting in. On the other hand, when the distortion of the tire coordinate system is used, there is no such problem. That is, the element 2f can express a state in which the vertical strain a in the tire radial direction does not change even when idling from (1) to (2).

  In the present embodiment, the distortion based on the tire coordinate system is calculated by calculating the distortion of the global coordinate system and converting it, but calculating the distortion of the global coordinate system. You can also calculate directly.

  Next, in the present embodiment, a history of strain when the tire model 2 makes one revolution is calculated from the distribution of strain in the tire circumferential direction of each element (step S5). As shown in FIGS. 11A and 11B, the history of strain will be described, for example, for one element 2f that models a rubber material. The tire model 2 rotates the road surface model 6 once (θ = 0). The change of the strain that the element 2f receives during this period is recorded continuously. FIG. 11B shows an example of a history of strain with the horizontal axis representing the rotation angle of the tire model and the vertical axis representing the magnitude of strain.

Each part of the tire moves due to rolling, generating an internal resistance and changing the apparent rigidity. 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 that actually rolls the tire model 2. However, such a method greatly increases the computation time. Therefore, in this embodiment, it is assumed that the strain that the tire model 2 receives in a state of static contact with the road surface model 6 is substantially equal to the dynamic strain that is instantaneously received when the tire is rolling. Assuming that the dynamic strain history is obtained from the static calculation results. This helps to make calculations quickly.

  As shown in FIG. 11A, when the tire model 2 is brought into static contact with the road surface model 14, for example, a certain strain acts on the element 2f. On the other hand, distortion also acts on each of the elements 2g, 2h,... Which are successively adjacent to the element 2f on one side in the tire circumferential direction. Here, in the tire model 2 of the present embodiment, elements having the same length in the tire circumferential direction are continuously arranged and the same cross-sectional shape is continuous. Therefore, for example, the strain received by the element 2g can be regarded as substantially equal to the strain received when the tire model 2 rotates by one element and the element 2f moves to the position of the element 2g. Similarly, it can be assumed that the strain received by the element 2h is substantially equal to the strain received when the tire model 2 rotates by two elements and the element 2f moves to the position of the element 2h. Accordingly, by referring to the distortion of other elements that are continuous in the tire circumferential direction from the static contact simulation result of the tire model 2, the history of distortion when the tire model 2 makes one revolution for each element is simulated. It can be calculated.

  FIG. 12 and FIG. 13 show an example of a history of distortion for the element 2f representing a part of the tread rubber obtained in this way. FIGS. 12A to 12C and FIGS. 13A to 13C show the strain history of one element of the tread rubber converted into the six components. In the graph of the figure, the vertical axis represents strain, the horizontal axis represents the tire rotation angle (0 to 360 °), and the position at 180 ° is the ground contact center. In the present embodiment, such strain history is calculated and stored by the computer device 1 for every element that appears in the tire meridian cross section of FIG.

Next, in this embodiment, energy loss is calculated for at least one element (preferably an element representing rubber) of the tire model 2 from the history of strain of each element (step S6). Since the energy loss has a correlation with the rolling resistance, it is possible to predict the rolling resistance roughly by comparing this value. Conventionally, as an example of the energy loss calculation method, the maximum amplitude εp, which is the difference between the maximum strain value εmax and the minimum value εmin, is obtained from the waveform of the strain history obtained in FIG. It is known to calculate the energy loss W per unit volume by
W = Σπ · E · (εp / 2) ² · tan δ (1)
Here, Σ means the sum of all components, E is the storage modulus of each element, and tan δ is the loss tangent of each element.

  However, such an energy loss calculation method simply focuses only on the maximum amplitude in the distortion history, and therefore there are two or more peaks in the distortion history waveform as shown in FIG. In this case, the energy loss is calculated to be smaller than the actual value, and there is a problem that, for example, the calculation accuracy of the rolling resistance is lowered. Therefore, in this embodiment, the energy loss is calculated using the strain path method. In this method, for at least one element of the tire model 2, preferably an element representing all rubber materials, the absolute value of the amount of change in strain is integrated for one revolution of the tire model, and the energy loss is calculated based on that value. Calculated.

  For example, consider a case in which a strain history as shown in FIG. 14A is obtained for one component of a tire coordinate system for a certain element. This waveform has two peaks. As shown in FIG. 14B, the first flat region a1, the first increase region b1, the first decrease region c1, the second increase region b2, The virtual area can be virtually divided into two decreasing areas c2 and a second flat area a2. Then, as shown in FIG. 14C, the first flat region a1, the first increase region b1, the second increase region b2, the first decrease region c1, the second decrease region c2, and the second If the increasing region and the decreasing region are replaced together like the flat region a2, it can be converted into a waveform having one peak. The maximum amplitude εp at this time can be calculated by a simple method shown in FIG.

FIG. 15A shows a waveform of the same distortion history as that in FIG.
Since the increment and decrement of the strain are the same amount in one rotation of the tire, the absolute value of the strain change amount (difference in strain between adjacent elements in the circumferential direction) is integrated to obtain FIG. Σ | Δε | shown in FIG. A half value of the integrated value Σ | Δε | corresponds to εp in FIG. In such a strain path method, energy loss is calculated based on the amount of change in strain. Therefore, even when there are a plurality of peaks in the distortion history waveform, energy loss can be calculated with relatively high accuracy without being affected by the number of peaks.

In the above-described strain path method, the integrated amount εp of strain is calculated by the following equation (2).
εp = {Σ | ε _{i + 1} −ε _i |} / 2 (2)
Here, i = 1 to n. However, when i = n, 1 is substituted for i + 1. Further, ε _i and ε _{i + 1} represent each distortion of two elements adjacent in the circumferential direction. And the energy loss W per unit volume of each element is computable by following formula (3).
W = Σπ · E · (εp / 2) ² · tan δ (3)
Here, Σ indicates the sum of all tire coordinate systems (6 components for solid elements, 2 components for membrane elements), E is the storage modulus of each element, and tan δ is the loss tangent of each element. .

Then, using the energy loss W, for example, the rolling resistance RR of the tire model 2 can be approximately calculated as one physical quantity representing the tire performance. The rolling resistance RR can be calculated by the following formula (4).
RR = {Σ (W · V)} / 2πR (4)
Here, V is the volume of each element, R is the load radius of the tire, and Σ is the sum of all elements with respect to the product of the energy loss W and the volume V of the element.

  Thus, in this embodiment, on the premise of static analysis, the strain history when the tire model makes one revolution is calculated from the distribution of strain in the tire circumferential direction. For this reason, it is possible to prevent the calculation amount from becoming enormous as in the case of dynamic analysis, and to greatly reduce the calculation cost and the calculation time. Further, the energy loss of each element is not calculated based on the maximum strain amplitude obtained from the waveform of the strain history, but based on a value obtained by accumulating the absolute value of the strain change amount for one round of the tire model. . Therefore, energy loss can be calculated more accurately without being influenced by the number of peaks of the waveform.

  The rolling resistance of a pneumatic tire is related to the air resistance generated when the tire rotates and travels. Although the air resistance depends on the speed, the air resistance is generally as small as 1 to 3% of the total rolling resistance. Therefore, in the present invention, such air resistance is ignored.

  16 to 17 show another embodiment for calculating the energy loss of each element of the tire model. In this embodiment, for at least one element of the tire model (preferably an element representing rubber), an energy loss is calculated based on the strain history and a damping characteristic predefined for the element.

  FIG. 16 shows each history of stress and strain. In a viscoelastic body such as rubber, part of the deformation is dissipated as heat, so that the strain has a phase difference δ with respect to the stress. FIG. 17A shows an actual viscoelasticity measurement result for a rubber material that is an object modeling target. The viscoelastic properties of the rubber material are measured using a viscoelastic spectrum tester or the like. That is, a strain amplitude having a constant frequency is given to the sample piece, and the stress generated at that time is measured. In FIG. 17A, the vertical axis represents stress σ and the horizontal axis represents strain ε. Thus, the strain history draws a hysteresis loop.

The damping characteristic is determined based on the result of the viscoelastic characteristic test, specifically based on a hysteresis loop. FIG. 17B shows an example of a damping characteristic for a certain rubber element. In this specification, the damping characteristic μ is a value obtained by dividing the area A of the hysteresis loop by the strain amplitude εm used in the viscoelasticity test. In FIG. 17B, a parallelogram graph is represented in a coordinate system in which stress σ is set on the vertical axis and strain ε is set on the horizontal axis. The area surrounded by the parallelogram is equal to the area A of the hysteresis loop. Further, the amplitude of the strain ε is equal to the strain amplitude εm. At this time, a length that is ½ of the length 2 μm of the vertical line segment of the parallelogram is defined as the attenuation characteristic μ.

In this embodiment, the energy loss W is calculated by multiplying the absolute value of the amount of change in strain of each element by the attenuation characteristic μ and integrating this value for one round of the tire model. A specific calculation formula is as shown in the following formula (5).
W = Σ (μ · | εi + 1−εi |) (5)
Here, Σ indicates the total sum for one round of the tire model, and μ is the attenuation characteristic of each element, i = 1 to n. However, when i = n, 1 is substituted for i + 1. Further, εi and εi + 1 represent respective strains of two elements adjacent in the circumferential direction. From these, the rolling resistance RR of the tire model can be calculated based on the equation (4).

Originally, a strain-stress diagram without attenuation is a single proportional line passing through the origin, and the same path is taken for tension and compression. In this embodiment, a frictional resistance (friction damping ) is applied when the elastic body is deformed, and as shown in FIG. 17B, the damping characteristic μ increases in tension and the damping characteristic μ decreases in compression, as shown in FIG. Think of it as In the parallelogram loop defining the attenuation characteristic μ of the present embodiment, the inclination angle β, which is the inclination of the hypotenuse, is set equal to the inclination angle α of the long axis of the elliptical loop of the hysteresis loop obtained from the experimental results. When the energy loss is calculated by the above equation (5) using such attenuation characteristic μ, as in the strain path method, the strain change for one tire lap is complicated and has a plurality of peaks. Even so, accurate results can be obtained.

  For pneumatic tires A to F having a tire size of 195 / 65R15, rolling resistance was calculated by a simulation method using the present invention. Each tire has different rigidity as shown in Table 1. In this experiment, a plain tire model without a tread pattern was used. The number of elements was 20000 for all. The energy loss was calculated using a strain path method (Example 1) and using an attenuation characteristic (Example 2). For comparison, the maximum amplitude value was obtained from the strain history, and the energy loss calculated using Equation (1) (Comparative Example) was also evaluated. And rolling resistance was measured with the rolling resistance tester using the actual tire of the same size and the same structure, respectively, and the correlation coefficient with this was determined. The simulation conditions were a camber angle of 0 °, a longitudinal load of 4.5 kN, and a speed of 80 km / H. Table 1 shows the test results.

As a result of the test, the rolling resistance value of the example is very close to the actually measured value, and high accuracy can be confirmed. FIG. 18 also shows the results of measuring and comparing the rolling resistance value (measured RRC) actually measured under various conditions with the rolling resistance value (calculated RRC) calculated by simulation for other tires. . As shown in the figure, it can be confirmed that the correlation is very strong (correlation coefficient: R ² = 0.9568), and the accuracy of the simulation can be confirmed.

It is a block diagram of the computer apparatus for implementing the simulation method of this invention. It is a flowchart which shows an example of the process sequence of the simulation method of this invention. It is a perspective view of the tire model used by this embodiment. FIG. It is a conceptual diagram which shows the modeling to the element of a fiber composite material. 1 is a partial perspective view of a tire model and an enlarged view of one element thereof. It is sectional drawing which illustrates the rim assembly conditions of a tire model. (A)-(C) are the perspective views of the element explaining the distortion of a solid element. It is a perspective view of the element explaining distortion of a membrane element. It is a side view which illustrates the idling state of an element. (A) is a side view of a ground contact simulation of a tire model, and (B) is a graph for explaining a history of strain. (A)-(C) are the graphs which show the history of distortion of one solid element which modeled tread rubber. (A)-(C) are the graphs which show the history of distortion of one solid element which modeled tread rubber. (A)-(B) are the graphs of the distortion explaining the distortion path | route method. (A)-(B) are the graphs of the distortion explaining the distortion path | route method. It is a graph which shows the history of stress and distortion for explaining energy loss. (A) is a graph for explaining a hysteresis loop, and (B) is a graph for explaining an attenuation characteristic. It is the graph which compared measured RRC and calculation RRC.

Explanation of symbols

2 Tire model 2a, 2b ... Element e1 Solid element 5a, 5b Membrane element

Claims (3)

A tire simulation method for simulating a tire using a computer,
Setting a tire model in which a rubber composite, a fiber composite material including a carcass and a belt, and a non-extensible bead core are modeled with elements that are continuous in the tire circumferential direction in the same cross-sectional shape and capable of numerical analysis;
Contacting the road surface model without rolling the tire model based on predetermined boundary conditions;
At least for the element modeled on the rubber material, the tire at the time of one rotation of the six-component strain including the vertical strain and the shear strain in the tire meridian direction, the tire circumferential direction, and the tire thickness direction is the grounded tire. Calculating from the circumferential strain distribution of the model;

Calculating at least one element of the rubber material an energy loss based on a value obtained by integrating the absolute value of the amount of change in strain for one revolution of the tire model,
The energy loss is calculated according to the following equation: a tire simulation method.
W = Σπ · E · (εp / 2) ² · tan δ
(Where Σ is the sum of all tire coordinate systems, E is the storage modulus of each element, εp is the absolute value of the difference in strain between adjacent elements in the circumferential direction, (Half of the integrated values integrated for minutes, tan δ is the loss tangent of each element.)
A tire simulation method for simulating a tire using a computer,
Setting a tire model in which a rubber composite, a fiber composite material including a carcass and a belt, and a non-extensible bead core are modeled with elements that are continuous in the tire circumferential direction in the same cross-sectional shape and capable of numerical analysis;
Contacting the road surface model without rolling the tire model based on predetermined boundary conditions;
At least for the element modeled on the rubber material, the tire at the time of one rotation of the six-component strain including the vertical strain and the shear strain in the tire meridian direction, the tire circumferential direction, and the tire thickness direction is the grounded tire. Calculating from the circumferential strain distribution of the model;
Calculating at least one element of the rubber material an energy loss based on a value obtained by integrating the absolute value of the amount of change in strain for one revolution of the tire model,
The energy loss is calculated according to the following equation: a tire simulation method.
W = Σ (μ · | εi + 1 -εi |)
(Where Σ is the total sum for one round of the tire model, μ is the damping characteristic of each element, and the area of the hysteresis loop of the stress-strain curve obtained from the actual viscoelastic property test for the rubber material. The value obtained by dividing A by the strain amplitude εm used in the viscoelastic property test, εi and εi + 1 are the strains of two elements adjacent in the circumferential direction, i = 1 to n, but i = n Then, 1 is substituted for i + 1.)
In the tire model, the rubber material is modeled by a solid element made of a linear elastic body or an incompressible superelastic body, and the fiber composite material is modeled by a membrane element having orthogonal anisotropy. The tire simulation method according to claim 1 or 2 .

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