JP2007131206A - Method and model for analyzing assembly of tire and wheel - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for analyzing the assembly of a tire and a wheel, which assembly is nearly equal to the assembly of an actual tire on an actual wheel, and further to provide a model to be used in the analysis of the assembly of the tire and the wheel. <P>SOLUTION: A model 10M of the assembly of the tire and the wheel is composed of a wheel model 11M and a tire model 12M. A bead portion 12k of the tire model 12M is moved inside the wheel model 11M in the direction of the width so as not to come into contact with the wheel model 11M by giving boundary conditions to the bead portion 12k. After that, the bead portion 12k is moved in the reverse direction so as to come into contact with the wheel model and is held at rest, and also the tire model is assembled on the wheel model by making the tire model 12M deform by applying the internal pressure. In this analysis, a large coefficient of static friction is given between elements corresponding to the contacting portions of the bead portion 12k with the wheel model 11M, and a small coefficient of dynamic friction is given to moving portions. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a method for analyzing an assembled state of a tire and a wheel using a finite element method, and a numerical analysis model used for this analysis.

Conventionally, as a method for simulating tire performance, the tire to be evaluated is approximated by a tire finite element model obtained by dividing a tire into a finite number of elements, and characteristics such as density and elastic modulus are given to each finite element. A finite element method (Finite Element Method) is often used in which boundary conditions such as internal pressure and load are given to a model to calculate the deformation state of each of the above elements and simulate the deformation and motion state of the tire.
By the way, as a method for simulating various characteristics such as rolling resistance of a tire, a virtual road surface 52 having a flat quadrilateral rigid surface is provided as a tire model 51 having the finite element model 50 of the tire mounted on a virtual rim as shown in FIG. A method of running on a predetermined traveling condition by grounding to the ground is performed (for example, see Patent Document 1). The tire model 51 is a model in which a tire is divided into a finite number of elements. The tire rim contact area R is constrained and the tire axial distance w of the bead portion 51a is forcibly displaced to a rim width of a virtual rim (not shown). Thus, the tire model 51 is connected and fixed to the virtual rim so that the relative distance r between the rotation axis CL and the restraint region R is always constant, and the tire model 51 is in contact with the virtual road surface 52. A condition such as applying a load to the tread portion 51b is set to simulate the rolling state of the tire.

In addition, in order to improve the simulation accuracy, a tire model and a wheel model in which the tire and the wheel are divided into a finite number of elements are set before the tire rolling simulation, and the tire model and the wheel model are fitted. There has also been proposed a method for performing a simulation (see, for example, Patent Document 2). Specifically, as shown in FIG. 14A, a tire model in which an axial force F directed inward in the tire axial direction is applied to the left and right bead portions 61a and 61a to deform the bead width to be smaller than the rim width. After 61 is mounted on the wheel model 62, the axial force F is returned to 0 and the deformation calculation is performed again to fit the tire model 61 to the wheel model 62. Then, as shown in FIG. The tire model 61 is deformed and assembled to the wheel model 62 by setting an internal pressure condition. The tire model 61 is deformed until the internal pressure becomes a predetermined value even after fitting.
At this time, in the tire deformation calculation, by setting a friction coefficient between the tire model 61 and the wheel model 62, the assembled state of the tire and the wheel can be accurately obtained. That is, before the fitting, a dynamic friction having a friction coefficient μ = 0.1 corresponding to the value of the friction coefficient when the lubricant is applied between the wheel and the bead seat when the rim of the actual tire is assembled is applied after the fitting. 11 is obtained by performing deformation calculation by applying a dynamic friction with a general friction coefficient μ = 0.3 corresponding to the value of the friction coefficient between the surface of the general wheel and the bead portion. Compared with the case where the width of the portion 51a is forcibly displaced to the rim width of the virtual rim, the state of the tire can be accurately obtained.
Japanese Patent Laid-Open No. 11-153520 Japanese Patent No. 3650342

  However, in the above conventional fitting simulation method, although the friction coefficient is changed in two stages, since the effect of changing the amount of lubricant due to the tire slipping on the wheel surface during assembly is not considered, The friction coefficient is different from that when the tire is assembled to the wheel. As a result, the tire / wheel assembly model obtained by the above-mentioned fitting simulation differs from the actual tire assembly state, and therefore, there is a problem that various characteristics of the tire cannot be simulated accurately. there were.

  The present invention has been made in view of the conventional problems, and provides a tire and wheel assembly analysis method close to the actual tire assembly state, and a tire and wheel assembly analysis model used for the analysis. Objective.

As a result of detailed examination of the contact state between the tire and the wheel at the time of assembly, the present inventor confirmed that the bead portions on the left and right sides of the tire are in contact with the wheel and are stationary before filling with the internal pressure, and the tire slides on the wheel. Since the lubricant applied at the time of assembly is pushed out, the frictional force acting between the bead portion and the wheel is increased at the portion that is in contact with the wheel, and the bead portion slips. Sometimes, it was found that the higher the sliding speed, the smaller the dynamic friction coefficient. Therefore, by creating a model that takes into account the influence of the frictional force change between the bead part and the wheel as described above, analysis results that are close to the actual tire assembly state can be obtained. The present invention has been reached.
That is, the invention according to claim 1 of the present application is a method of numerically analyzing an assembled state of a tire and a wheel,
A first step of creating a tire model in which a tire is divided into a finite number of elements and a wheel model in which a wheel is divided into a finite number of elements;
A second step of creating a tire / wheel assembly model in which the tire model and the wheel model are combined with each other being allowed to overlap;
After moving the left and right bead portions inward in the width direction to a position where they do not contact the wheels of the tire / wheel assembly model by applying boundary conditions to the right and left bead portions of the tire / wheel assembly model of the tire / wheel assembly model , A third step of moving to the opposite side and bringing the left and right bead portions into contact with the wheel to make them stationary;
A fourth step of deforming the tire of the tire / wheel assembly model by filling the tire / wheel assembly model with the bead portion stationary to deform the tire of the tire / wheel assembly model, and assembling the tire to the wheel of the tire / wheel assembly model;
And at the time of deformation analysis of the tire in the fourth step, the friction of the portion stationary on the wheel between the lower part of the bead part and the surface of the wheel in contact with the lower part of the bead part. The friction coefficient is set such that the static friction coefficient, which is a coefficient, is larger than the dynamic friction coefficient, which is the friction coefficient of the portion sliding on the wheel.

The invention according to claim 2 is a method for numerically analyzing an assembled state of a tire and a wheel,
A first step of creating a tire model in which a tire is divided into a finite number of elements and a wheel model in which a wheel is divided into a finite number of elements;
A second step of creating a tire / wheel assembly model in which the tire model and the wheel model are combined with each other being allowed to overlap;
The wheel of the tire / wheel assembly model is divided into two in the width direction, and the wheel is moved outward in the width direction to a position where it does not contact the left and right bead portions of the tire / wheel assembly model. A third step of moving the wheel to the opposite side to the wheel width and bringing the wheel into contact with the left and right bead portions to be stationary;
A fourth step of deforming the tire of the tire / wheel assembly model by internally filling the tire / wheel assembly model with the wheel stationary, and assembling the tire on the wheel of the tire / wheel assembly model;
And at the time of deformation analysis of the tire in the fourth step, the friction of the portion stationary on the wheel between the lower part of the bead part and the surface of the wheel in contact with the lower part of the bead part. The friction coefficient is set such that the static friction coefficient, which is a coefficient, is larger than the dynamic friction coefficient, which is the friction coefficient of the portion sliding on the wheel.

The invention according to claim 3 is the tire / wheel assembly analysis method according to claim 1 or 2, wherein the outer shape of the bead portion of the tire model is the inner shape of the bead portion of the tire vulcanization mold. It is characterized by being the same.
According to a fourth aspect of the present invention, in the tire and wheel assembly analysis method according to any one of the first to third aspects, the dynamic friction coefficient can be changed by a relative slip speed between the tire and the wheel. The dynamic friction coefficient is set so that the dynamic friction coefficient decreases when the relative slip speed increases.

The invention according to claim 5 is a numerical analysis model for performing assembly analysis of a tire and a wheel, and is set when a tire model formed by dividing the tire into finite elements is deformed. As the coefficient of friction between the lower part of the bead part of the tire model and the surface that contacts the lower part of the bead part of the wheel model obtained by dividing the wheel into a finite number of elements, the surface that the lower part of the bead part makes contact with The static friction coefficient is given to the part that is stationary above, the dynamic friction coefficient is given to the part where the lower part of the bead slides on the contact surface, and the static friction coefficient is set to be larger than the dynamic friction coefficient. It is what.
According to a sixth aspect of the present invention, in the tire / wheel assembly analysis model according to the fifth aspect, the dynamic friction coefficient can be changed by a relative slip speed between the tire and the wheel, and the relative slip speed is increased. In this case, the dynamic friction coefficient is set so that the dynamic friction coefficient becomes small.
The invention according to claim 7 is the tire / wheel assembly analysis model according to claim 5 or 6, wherein the outer shape of the bead portion of the tire model is the inner shape of the bead portion of the tire vulcanization mold. Are the same.
According to an eighth aspect of the present invention, in the tire / wheel assembly analysis model according to any one of the fifth to seventh aspects, a width of a contact surface between at least the bead portion of the tire model of the wheel model is set to a width. Divided into two in the direction.

According to the present invention, an assembly analysis of a tire and a wheel is performed using a tire / wheel assembly model created by combining a tire model and a wheel model obtained by dividing a tire and a wheel into finite elements. When performing, by giving boundary conditions to the right and left bead portions of the tire of the assembly model, the left and right bead portions are moved inward in the width direction to positions where they do not contact the wheels of the tire and wheel assembly model. After that, the left and right bead portions are brought into contact with the wheel to be stationary, and the lower portion of the tire bead portion and the bead set when the tire model is deformed by filling the assembly model with internal pressure As the coefficient of friction between the wheel and the surface of the wheel that is in contact with the wheel, a dynamic friction coefficient is given to the part sliding on the wheel. The in which part seals since to give a static friction coefficient with a value greater than the dynamic friction coefficient, it is possible to perform the actual tire and assembly analysis of the wheel near the assembled state of the tire.
At this time, if the value of the dynamic friction coefficient is set so that the value of the dynamic friction coefficient decreases when the relative slip speed increases, the analysis accuracy can be further improved.
Also, if the outer shape of the bead part of the tire model is the same shape as the inner shape of the bead part of the tire vulcanization mold, the model is equivalent to the case where the model is created by collecting the geometric shape from the actual tire Can be created efficiently.
Further, in place of the step of applying boundary conditions to the left and right bead portions of the tire of the assembly model to bring the left and right bead portions into contact with the wheels and stopping the wheels, the wheel of the tire / wheel assembly model is set to 2 in the width direction. And after moving the wheel outward in the width direction to a position where it does not come into contact with the right and left bead portions of the tire / wheel assembly model of the tire and wheel assembly model, and then moving the wheel to the opposite side to the normal wheel width. The same effect can be obtained even if a step of bringing the bead portion into contact with the bead portion and making it stand still is analyzed.
Furthermore, if a model in which at least the contact surface of the wheel model with the bead portion of the tire model is divided into two in the width direction is generated and analyzed, the force of the bead portion and the flange portion can be easily analyzed. .

Hereinafter, the best mode of the present invention will be described with reference to the drawings.
Embodiment 1 FIG.
FIG. 1 is a cross-sectional view of a main part of a tire / wheel assembly model 10M for performing assembly analysis of a tire and a wheel according to the best mode 1. The tire / wheel assembly model 10M is shown in FIG. And a tire model 12M and a tire model 12M obtained by dividing a tire 12 as shown in FIG. 2B into a finite number of elements.
The wheel model 11M is generally modeled as a whole wheel with solid elements. In this example, as shown in FIG. 1, the rim part 11A is modeled with a shell element, and the disk part 11B is modeled with a solid element. Yes. The shape of the wheel model 11M can be obtained from a CAD drawing, a die drawing, or an actual wheel shape, but when obtaining from the die shape, the shape change due to thermal shrinkage or residual stress should be considered. Is desirable. In addition, as the material physical properties, the physical properties of the raw material of the wheel, the physical properties measured by cutting a test piece from the product wheel, or the physical properties of the product specification can be used.
In the tire model 12M, rubber members such as the tread 12a, the side 12b, and the internal rubber 12c are modeled by solid elements, and reinforcing members such as the belt 12p and the carcass ply 12q are modeled by shell elements, membrane elements, and river elements. To do. The bead wire 12r is modeled by a solid element. As a material model of the above rubber member, we modeled a superelastic body such as Mooney-Rivln material and Ogdcn material, a viscoelastic body considering viscosity, and the viscosity is a model using wire diameter viscoelasticity and Prony series. Can be used. On the other hand, as the material model of the reinforcing member, an anisotropic material model can be used and modeled as a linear elastic body, but the reinforcing member is rigid on the tension side and the compression side. Since it is known that these are different, it is preferable to model this as a non-linear elastic body in order to improve accuracy.
Further, the tire shape used for the tire model 12M can be obtained from a CAD drawing, a mold shape, or an actual tire shape. However, in the case of obtaining from the mold shape, similarly to the wheel model 11M. It is desirable to consider the shape change due to heat shrinkage and residual stress.

By the way, it was found from experiments that the contact pressure between the two when the wheel 11 and the tire 12 are assembled becomes a high pressure of 2 MPa or more. This is because when the rubber sandwiched between the rigid bead wire and the rigid wheel is crushed, there is no escape, and the pressure is generated by the incompressibility of the rubber. . In order to accurately obtain such a high pressure by analysis, it is necessary to increase the number of elements in the bead portion and analyze the shape change. That is, when the number of elements in the bead portion is small, the volume of the rubber is different from the actual volume, so that the incompressibility cannot be expressed accurately and the contact pressure cannot be expressed accurately. . Therefore, in this example, the initial shape of the tire model 12M is set to the actual product tire shape. In particular, for the bead portion 12k, the geometric shape of the bead portion is accurately sampled from the actual tire, and this sample is collected. The tire model 12M is created using the geometric shape of the bead portion as a model.
In this example, as the tire model 12M, a model of a tire having only circumferential grooves in which the same elements are arranged in the rotational direction as shown in FIG. 3 is used.

Next, a method of analyzing the assembled state of the wheel 11 and the tire 12 using the tire / wheel assembly model 10M will be described with reference to the flowchart of FIG.
First, a tire model 12M in which a tire is divided into a finite number of elements and a wheel model 11M in which a wheel is divided into a finite number of elements are respectively created (step S11). As described above, the initial shape of the tire model 12M was created using the actual product tire shape as a model, and the wheel model 11M was also created using the actual wheel shape as a model.
Next, as shown in FIG. 5, an initial tire shape, that is, a tire model 12M obtained by modeling a tire in which no stress is applied is matched with the wheel model 11M (step S12). In this state, since the tire and the wheel overlap each other and are physically wrong, contact between the tire and the wheel, which should occur in this state, cannot be considered.
Therefore, as shown in FIG. 6, boundary conditions of force, displacement, speed, and acceleration are given to the bead portion 12k of the tire model 12M, and the tires are arranged inside the left and right flange portions 11a and 11b of the wheel model 11M. The left and right bead portions 12k, 12k are moved inward in the width direction to a position where they do not contact with each other (step S13), and then moved to the opposite side, and the left and right bead portions 12k, 12k as shown in FIG. When the model 11M comes into contact, the left and right bead portions 12k, 12k are stopped (step S14). When the left and right bead portions 12k and 12k are moved, the contact between the tire and the wheel should not be considered. When the left and right bead portions 12k and 12k move and come into contact with the wheel model 11M, the left and right bead portions 12k and 12k are not affected. The movement of the bead parts 12k, 12k is stopped. At this time, the boundary condition can be given to the surface of the bead portion 12k, the entire bead portion 12k, and the bead wire 12r.
This state corresponds to a state in which when the tire is mounted on the wheel, the bead portion is bent inward to make the bead width smaller than the rim width and then mounted on the tire. In FIG. 6, the tire model 12M is not completely in contact with the wheel model 11M. However, the analysis is possible even in a state where one surface element of the bead portion 12k overlaps the wheel.

By the way, when assembling a tire to a wheel, a lubricant is generally used, and the lubricant is applied only to the tire side, only to the wheel side, or to both the tire and the wheel. Then, the lubricant was apply | coated to the tire side and the state (before internal pressure filling) which set the tire bead part inside the wheel flange was observed in detail from the experiment. FIG. 7 is a diagram in which the result is superimposed on the analysis model, and the thick line in the figure indicates the lubricant 13. From this detailed experiment, it was found that the lubricant applied to the tire side disappeared in the portion where the tire and the wheel indicated by the arrow P in FIG. As shown in FIG. 8, it is considered that the lubricant is pushed out when the bead portion 12 k contacts the wheel 11. Such a phenomenon is the same even when the lubricant is applied only to the wheel side or to both the tire and the wheel.
Therefore, as shown in FIG. 9, when the tire is deformed and the bead portion 12k is combined with the flange 11b (or the flange 11a), the tire 11 and the wheel 12 are in contact with each other. Since there is almost no lubricant, when the bead portion 12k is stationary on the wheel 12 in this state, the friction coefficient of both is large.
When an experiment in which the internal pressure is filled from this state is performed, the bead portion moves to the flange portion side while sliding on the wheel surface. Where the bead part is moving, it rides on the lubricant film applied to the surface, but at the part where the tire is in contact with the wheel, the lubricant that was between the tire and the wheel is pushed out by the contact pressure, As shown in FIG. 8, it was found from experiments that almost no lubricant remained after sliding. This indicates, on the other hand, that the lubricant is pushed out while the bead portion is moving, so that the effect of the lubricant is further increased, and the friction coefficient is further reduced.

Therefore, when the assembly analysis of the tire and wheel is performed, in order to model the result found in the above experiment, the contact of the bead portion with the wheel is not performed before filling with the internal pressure and after the tire and the wheel are assembled. A large friction coefficient may be given to an element corresponding to the portion, and a small friction coefficient may be given to a moving portion.
Therefore, after moving the left and right bead parts 12k, 12k to be stationary, the tire / wheel assembly model 10M is filled with internal pressure to deform the tire model 12M, and the lower part of the bead parts 12k, 12k The static friction coefficient, which is the friction coefficient of the portion that is stationary on the wheel, between the contact surface of the wheel model 11M that is in contact with the bead portions 12k and 12k is the friction coefficient of the portion that is sliding on the wheel. If a friction coefficient that is larger than the dynamic friction coefficient is set and the tire model 12M is deformed to analyze the assembly of the tire and the wheel (step S15), the same phenomenon as the actual assembly is accurately reproduced. Can improve the simulation accuracy of the tire and wheel assembly state
Each of the above friction coefficients depends on the type of lubricant, the rubber material and surface roughness of the tire bead portion, the surface roughness of the wheel, and the like. Therefore, when the friction coefficient was experimentally obtained by combining a plurality of lubricants, wheels, and tires, the static friction coefficient was in the range of 0.3 to 0.6, and the dynamic friction coefficient was 0.05 to 0.2. I found it in the range. Therefore, in the analysis, if each friction coefficient is in the above range, an actual phenomenon can be accurately reproduced.
FIG. 10 is a view showing an analysis result of the assembled state of the tire and the wheel after the internal pressure filling. From this figure, the distance W between the center of the bead wire 12k and the rim reference surface 11z, the bead portion 12k and the flange portion 11b When the area of the space between them (the area of the gap) S was calculated, the values were almost the same as the actual measurements.

  Thus, according to the best mode 1, the actual product tire shape is used as a shape model, the tire model 12M is divided into a finite number of elements, and the shape of the product wheel is used as a shape model. A tire / wheel assembly model 10M is created from the wheel model 11M divided into the following elements, a boundary condition is given to the bead portion 12k of the tire model 12M, and the tire / wheel assembly model does not contact the wheel. The left and right bead portions 12k, 12k are respectively moved inward in the width direction and then moved to the opposite side, the left and right bead portions are brought into contact with the wheel to be stationary, and the tire is filled with an internal pressure so that the tire When analyzing the model by deforming the model and assembling the tire and the wheel, the wheel of the beads 12k, 12k is used. Since a large static friction coefficient is given between the elements corresponding to the contact part with the Dell 11M, and a small dynamic friction coefficient is given to the moving part, the same phenomenon as the actual assembly is accurately reproduced. It is possible to improve the simulation accuracy of the assembled state of the tire and the wheel.

In the best mode 1, the tire model 12M employs a model in which the same elements are arranged in the tire rotation direction. However, the tire model 12M may be modeled in consideration of a tread pattern or may be a member that is in a real tire. By modeling small overlaps, changes in thickness, and changes in rigidity to create a model that is non-uniform in the direction of rotation, the accuracy of the analysis can be further improved.
In the above example, the initial shape of the tire model 12M is the actual geometric shape of the product tire. However, the initial shape of the bead portion having a large number of elements may be the geometric shape of the bead portion of the tire vulcanization mold. Good. In other words, the vulcanization mold is manufactured in a shape that accurately matches the CAD model, and the bead portion occupies a large volume of the bead wire having a small heat shrinkage, and the volume of the rubber or the reinforcing material having the large heat shrinkage is small. The shape of the bead portion before and after vulcanization is almost unchanged. Therefore, even if an approximate model is created in which the outer surface shape of the bead portion 12k of the tire model 11M is the same as the inner surface shape of the bead portion of the vulcanization mold, the accuracy of the tire model 12M is sufficient. It is. As a result, it is possible to save the trouble of accurately collecting the geometric shape of the tire bead portion from the actual tire and creating a model, and thus the tire model 12M can be efficiently manufactured.
In the above example, the bead wire 12r is modeled as a collective element, but a plurality of steel cords can also be modeled. Alternatively, the bead wire alone may be subjected to rigidity analysis in advance, and modeled as an anisotropic elastic body based on the obtained rigidity. It is also possible to model the bead wire as an elasto-plastic body.

In the above example, the static friction coefficient between the tire bead portion and the wheel is set to a constant value within a range of 0.3 to 0.6, and the dynamic friction coefficient is set to a constant value within a range of 0.05 to 0.2. Although each was set, as a result of examining in detail the phenomenon of assembling the actual tire on the wheel, when the tire bead slips on the wheel surface, it is stick slip, so the value of the dynamic friction coefficient is changed depending on the slip speed By doing so, the analysis accuracy can be further improved.
That is, it is known that the stick slip has a sliding dependency of the dynamic friction coefficient, and the friction coefficient decreases as the sliding speed increases. Therefore, in order to reproduce this phenomenon, for example, as shown in the following equation (1), if the dynamic friction coefficient μ of the analysis model is set to be small when the sliding speed v _d is large, the analysis can be performed. The accuracy can be further improved.
μ = μ _d + (μ _s −μ _d ) · exp (−0.4 · v _d ) (1)
μ _d : friction coefficient when the sliding speed v _d → ∞ (for example, μ _d = 0.05)
μ _s : coefficient of friction when sliding speed v _d = 0 (for example, μ _d = 0.4)
Note that if v _d = 0 in the above equation (1), μ becomes a static friction coefficient, and therefore, the static friction coefficient and the dynamic friction coefficient are set simultaneously by this equation (1).

Embodiment 2. FIG.
In the above best mode 1, the tire was deformed and assembled to the wheel. As shown in FIG. 11, the rim portion 11A was divided into two parts, and the rim portion was wider than the actual one. After the wheel model 11N that does not contact the wheel is created, the wheel model 11N is moved to the opposite side to the normal wheel width so that the wheel model 11N contacts the left and right bead portions 12k and 12k as shown in FIG. The same effect can be obtained even if the analysis is performed after the tire model 12M is deformed by filling the inner model with the internal pressure after being in a stationary state.
In this case, the rim portions 11P and 11Q need to be restrained by, for example, a joint J so as not to be separated from each other. Moreover, you may fix each rim | limb part 11P and 11Q on space.
In this case, it is preferable that the analysis is performed in a state where the wheel model 11N and the tire model 12M are in contact with each other, or one element on the surface of the bead portion 12k overlaps with the wheel model 11N or is separated by about one element on the surface of the model. . This is because when the models 11N and 12M are separated from each other, there is a problem that the moving distance of the wheel model 11N increases and the analysis time becomes long. This is because it deforms strongly against the wheel, resulting in a contact pressure different from the actual phenomenon.

By the way, when the assembly state of the tire on the wheel is experimentally observed, it is found that the assembly state by the internal pressure filling is different between the two bead portions separated in the width direction. As shown in FIG. 12, when the internal pressure is filled, the entire bead portion 121k fits the flange 111a in one bead portion 121k, but the other bead portion 122k is in partial contact. The whole thing is in a state where it does not fit the flange 111b.
In order to analyze such a state and analyze the force of each of the bead portions 121k and 122k and the flange portions 111a and 111b, the wheel model 11N having the rim portion divided into two as described above is suitable. That is, in the wheel model 11N, since the rim portion is divided into two, there is an advantage that the force acting on each portion can be analyzed only by obtaining the sum of the forces applied to the respective members.
Further, when it is desired to obtain the contact force, the same effect can be obtained by defining the wheel model itself by dividing the contact surface into two parts.

表１から明らかなように、摩擦係数を０、もしくは、０．１に固定した従来モデル１，２での解析結果は、いずれもワイヤ位置の値が小さく、かつ、隙間の面積も小さくなっていることから、ビード部が実測値よりもフランジ側によってしまっていることが分かる。
これに対して、内圧充填前にはタイヤは静止しているとし、かつ、タイヤ変形解析時の摩擦係数を、ホイール上で静止している部分では静摩擦係数（μ_s＝０．４）、ホイール上を滑っている部分では動摩擦係数（μ_d＝０．０５）に設定した新モデル１では、ワイヤ位置も隙間の面積もほぼ実測値と一致しており、実際の組み立てと同じ現象を精度よく再現することができることが確認された。
また、ビード部形状をタイヤ製造金型形状と一致させた新モデル２は、上記新モデルよりは若干精度は落ちるものの、実際の組み立て状態をほぼ再現できることが確認された。
一方、ホイールの初期モデルを、フランジ部を広げたモデルとした新モデル３においても、ワイヤ位置も隙間の面積もほぼ実測値と一致しており、タイヤとホイールの組み付け解析を精度よく行うことができることが分かった。
また、新モデル４では、ワイヤ位置、隙間の面積ともに実測値と一致しており、滑り速度により動摩擦係数を変更することで、解析精度を更に向上させることができることが確認された。 Create a wheel model that models a wheel with a rim size of 7JJ × 17 and a tire model that models a tire with a tire size of PSR215 / 45R17. Table 1 below shows the results of comparison and comparison of the state after incorporation with the actual state.
In Table 1, as shown in FIG. 10, in the tire / wheel assembly, the wire position is the center of the bead wire and the rim reference plane (the plane in which the rim flange is parallel to the wheel center plane on the radially outer side). The distance W is compared between the actual measurement and the analysis, and the area of the gap is the comparison of the space area S between the bead portion and the flange portion between the actual measurement and the analysis. It was shown as an index.
Conventional model 1: Analysis was performed with the tire product shape as the initial shape and the friction coefficient as 0.
Conventional model 2: Analysis was performed with the tire bead portion entering the inside of the flange and not contacting the wheel as an initial shape and a friction coefficient of 0.1.
New model 1: A model with a tire product shape including a bead portion as an initial shape is used, and the tire is stationary before filling with internal pressure, and the static friction coefficient when the tire is deformed is 0.4, and the dynamic friction coefficient is Analysis as 0.05.
New model 2: The portion other than the bead portion was analyzed by assuming that the tire product shape was the initial shape, the bead portion shape was matched with the tire manufacturing mold shape, the static friction coefficient was 0.4, and the dynamic friction coefficient was 0.05.
New model 3: The tire product shape including the bead portion was set as the initial shape, the wheel flange portion shape was set to 8JJ, the static friction coefficient was set to 0.4, and the dynamic friction coefficient was set to 0.05.
New model 4: The tire product shape including the bead portion is an initial shape, the friction coefficient at a sliding speed of 0 is μ _s = 0.4, the dynamic friction coefficient at a sliding speed ∞ is μ _d = 0.05, and is given by the following equation: The friction coefficient when the sliding speed is v _d was analyzed as μ.
μ = μ _d + (μ _s −μ _d ) ・ exp (−0.4 ・ v _d )

As is apparent from Table 1, the analysis results of the conventional models 1 and 2 in which the friction coefficient is fixed to 0 or 0.1 are both small in the value of the wire position and the area of the gap. From this, it can be seen that the bead portion is located closer to the flange side than the actually measured value.
On the other hand, it is assumed that the tire is stationary before filling with the internal pressure, and the friction coefficient at the time of tire deformation analysis is the static friction coefficient (μ _s = 0.4) in the portion stationary on the wheel. In the new model 1 where the coefficient of dynamic friction (μ _d = 0.05) is set on the sliding part, the wire position and the gap area are almost the same as the measured values, and the same phenomenon as the actual assembly is accurately performed. It was confirmed that it can be reproduced.
In addition, it was confirmed that the new model 2 in which the bead portion shape is matched with the tire manufacturing mold shape can substantially reproduce the actual assembled state, although the accuracy is slightly lower than that of the new model.
On the other hand, in the new model 3 where the initial model of the wheel is a model in which the flange portion is widened, the wire position and the gap area almost coincide with the measured values, and the assembly analysis of the tire and the wheel can be accurately performed. I understood that I could do it.
Further, in the new model 4, both the wire position and the gap area coincide with the measured values, and it was confirmed that the analysis accuracy can be further improved by changing the dynamic friction coefficient according to the sliding speed.

  Thus, according to the present invention, since the assembly analysis of the tire and the wheel close to the actual assembly state of the tire can be performed, the state of the tire assembled on the wheel can be accurately predicted. In addition, if this tire / wheel assembly is used for rolling analysis, etc., it will be possible to accurately analyze the deformation and motion state of the tire during running, thus improving tire design and development efficiency. be able to.

It is principal part sectional drawing of the assembly | attachment analysis model of the tire and wheel which concerns on the best form 1 of this invention. It is a schematic diagram of the wheel and tire which concern on this best form 1. FIG. 1 is a schematic diagram showing a tire model according to the best mode 1. FIG. It is a flowchart which shows the method of analyzing the assembly | attachment state of the tire which concerns on this best form 1, and a wheel. It is a figure which shows the initial state of the analysis model which concerns on this best form 1. FIG. It is a figure which shows the analysis model which moved the bead part to the flange side. It is a figure which shows the analysis model of the state which apply | coated the lubricant to the tire side and has set the tire bead part inside the wheel flange. It is a figure which shows the state which the bead part is sliding on the wheel. It is a figure which shows the state which the bead part has contact | connected the flange part. It is a figure which shows the analysis result of the assembly | attachment state of the tire and wheel after internal pressure filling. It is a figure which shows the assembly | attachment analysis method of the tire and wheel which concerns on the best form 2 of this invention. It is a figure which shows the assembly | attachment analysis method of the tire and wheel by this invention. It is a figure which shows the conventional tire model. It is a figure which shows the assembly | attachment analysis method of the conventional tire and wheel.

Explanation of symbols

10M tire and wheel assembly analysis model, 11 wheel, 11A rim part, 11a, 11b flange part, 11B disk part, 11M wheel model,
12 tires, 12M tire model, 12a tread, 12b side,
12c rubber inside, 12k bead, 12p belt, 12q carcass ply,
12r bead wire, 13 lubricant.

Claims (8)

A first step of creating a tire model in which a tire is divided into a finite number of elements and a wheel model in which a wheel is divided into a finite number of elements;
A second step of creating a tire / wheel assembly model in which the tire model and the wheel model are combined with each other being allowed to overlap;
After moving the left and right bead portions inward in the width direction to a position where they do not contact the wheels of the tire / wheel assembly model by applying boundary conditions to the right and left bead portions of the tire / wheel assembly model of the tire / wheel assembly model , A third step of moving to the opposite side and bringing the left and right bead portions into contact with the wheel to make them stationary;
A fourth step of deforming the tire of the tire / wheel assembly model by filling the tire / wheel assembly model with the bead portion stationary to deform the tire of the tire / wheel assembly model, and assembling the tire to the wheel of the tire / wheel assembly model;
And at the time of deformation analysis of the tire in the fourth step, the friction of the portion stationary on the wheel between the lower part of the bead part and the surface of the wheel in contact with the lower part of the bead part. A tire and wheel assembly analysis method characterized by setting a friction coefficient such that a static friction coefficient that is a coefficient is larger than a dynamic friction coefficient that is a friction coefficient of a portion sliding on the wheel. A first step of creating a tire model in which a tire is divided into a finite number of elements and a wheel model in which a wheel is divided into a finite number of elements;
A second step of creating a tire / wheel assembly model in which the tire model and the wheel model are combined with each other being allowed to overlap;
The wheel of the tire / wheel assembly model is divided into two in the width direction, and the wheel is moved outward in the width direction to a position where it does not contact the left and right bead portions of the tire / wheel assembly model. A third step of moving the wheel to the opposite side to the wheel width and bringing the wheel into contact with the left and right bead portions to be stationary;
A fourth step of deforming the tire of the tire / wheel assembly model by internally filling the tire / wheel assembly model with the wheel stationary, and assembling the tire on the wheel of the tire / wheel assembly model;
And at the time of deformation analysis of the tire in the fourth step, the friction of the portion stationary on the wheel between the lower part of the bead part and the surface of the wheel in contact with the lower part of the bead part. A tire and wheel assembly analysis method characterized by setting a friction coefficient such that a static friction coefficient that is a coefficient is larger than a dynamic friction coefficient that is a friction coefficient of a portion sliding on the wheel.   The tire / wheel assembly analysis method according to claim 1 or 2, wherein the outer surface shape of the bead portion of the tire model is the same as the inner surface shape of the bead portion of the tire vulcanization mold.   The dynamic friction coefficient can be changed by the relative sliding speed between the tire and the wheel, and when the relative sliding speed increases, the dynamic friction coefficient is set so that the dynamic friction coefficient decreases. The tire and wheel assembly analysis method according to any one of claims 1 to 3.   A model for assembly analysis of a tire and a wheel, which is set when a tire model formed by dividing a tire into a finite number of elements is deformed. As a coefficient of friction between the lower surface of the bead portion and the surface in contact with the lower portion of the wheel model divided into individual elements, a static friction coefficient is given in a portion where the lower portion of the bead portion is stationary on the contact surface, An assembly analysis model for a tire and a wheel, wherein a dynamic friction coefficient is given to a portion where the lower part of the bead portion slides on the contacting surface, and the static friction coefficient is set larger than the dynamic friction coefficient.   The dynamic friction coefficient can be changed by the relative sliding speed between the tire and the wheel, and when the relative sliding speed increases, the dynamic friction coefficient is set so that the dynamic friction coefficient decreases. The tire and wheel assembly analysis model according to claim 5, wherein   The tire / wheel assembly analysis model according to claim 5 or 6, wherein the outer surface shape of the bead portion of the tire model is the same as the inner surface shape of the bead portion of the tire vulcanization mold. The tire / wheel assembly analysis model according to any one of claims 5 to 7, wherein a contact surface of at least the bead portion of the tire model of the wheel model is divided into two in the width direction.

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