JP7346784B2 - Tire simulation method - Google Patents

Description

The present invention relates to a tire simulation method.

For example, as described in Patent Document 1 and Patent Document 2, simulations using the finite element method for phenomena involving tire deformation have been conventionally performed. Such simulations are usually performed using explicit methods that are suitable for handling phenomena that occur over a short period of time.

It is known that in a simulation using an explicit method, the time required for the simulation becomes long when the element length of the finite element model is short or when the Young's modulus set in the finite element model is large.

Patent No. 5151040 Patent No. 3650342

By the way, the bead cores on both sides of the tire in the width direction are made of metal and have a large Young's modulus. Therefore, when an explicit method is used in a simulation using a finite element model of a tire, there is a problem in that the time required for the simulation becomes long. In particular, when performing simulations that focus on the displacement of the bead core of a tire, it is preferable to shorten the element length of the bead core in the finite element model, but shortening the element length also increases the time required for simulation. There was a problem.

Therefore, an object of the present invention is to provide a method that can perform tire simulation in a short time using an explicit method.

The tire simulation method of the embodiment includes the steps of preparing a finite element model that reproduces a tire with a metal bead core, setting material property values including Young's modulus to the finite element model, and using an explicit method. A tire simulation method comprising the step of performing a simulation involving displacement of a bead core of the finite element model, wherein in the simulation, a time when the bead core begins to be displaced or a predetermined time before the bead core begins to be displaced is set as a reference time; The Young's modulus of the bead core before the reference time is made smaller than the Young's modulus of the bead core after the reference time.

In this embodiment, the Young's modulus of the bead core before the reference time is made smaller than the Young's modulus of the bead core after the reference time, so tire simulation using an explicit method can be performed in a short time.

FIG. 1 is a block diagram of a simulation device according to an embodiment. FIG. 3 is a diagram showing a tire cross-sectional model and a rim cross-sectional model separated from each other. A perspective view of a three-dimensional tire model with a rim. FIG. 3 is a cross-sectional view in the width direction of a three-dimensional tire model with a rim. FIG. 3 is a diagram showing a slope road surface model placed next to a tire model. The figure which shows the bead part of a tire model about to come off from a rim model. A cross-sectional view of a groove in a tread rubber portion. (a) is a diagram when the slope road surface model is not in contact with the tire model. (b) is a diagram when the tire model is hit by the slope road model and the tire model is greatly deformed. A cross-sectional view in the width direction of a tire model. This is a diagram when the tire model is greatly deformed and its inner surfaces come into contact with each other. FIG. 3 is a diagram showing a state in which a tire model and a slope road surface model are brought into contact. 1 is a flowchart of a simulation method according to an embodiment.

Embodiments will be described based on the drawings. Note that the embodiment described below is merely an example, and any modifications made as appropriate without departing from the spirit of the present invention are included within the scope of the present invention.

First, the structures of the pneumatic tires (hereinafter referred to as "tires") and rims that are the targets of simulation will be explained. First, let's talk about tires. Bead cores are provided on both sides of the tire in the tire width direction, and are formed by winding a metal (for example, steel) bead wire in an annular shape a plurality of times. A bead filler is provided on the outer diameter side of the bead core.

Further, the carcass ply is folded back from the inner side to the outer side in the tire width direction to wrap the bead core and bead filler, and forms the frame of the pneumatic tire. A belt is provided on the outside of the carcass ply in the tire radial direction, and tread rubber having a contact surface is provided on the outside of the belt in the tire radial direction. Further, a rim strip and sidewall rubber are provided on both sides of the carcass ply in the tire width direction. The rim strip is provided outside the bead core and bead filler in the tire width direction. The sidewall rubber is located between the tread rubber and the rim strip. An inner liner is provided inside the carcass ply.

Note that the bead core and its vicinity (a portion including the radially inner end of the tire) in a tire are referred to as a bead portion. Further, the inner diameter surface of the bead portion is referred to as the bead bottom surface.

Next, the rim will be explained. The rim is provided with a bead seat, which is a surface with which the bottom surface of the bead of the tire comes into contact when the tire is fitted onto the rim. A flange that extends outward in the radial direction of the bead seat is provided on one side (outside in the tire width direction) of the bead seat. Further, on the other side of the bead seat (on the inner side in the tire width direction), a hump having an arcuate cross section and projecting outward in the radial direction of the bead seat is provided. This rim and disc are integrated into a wheel.

Next, an example of the simulation apparatus 10 used in the simulation of the embodiment will be described. As shown in FIG. 1, the simulation device 10 of the embodiment includes an input section 12, a two-dimensional model creation section 14, an inflation analysis section 16, a three-dimensional model creation section 18, a slope surface setting section 20, and a contact definition setting section 22. , a friction coefficient setting section 24, a rim detachment analysis section 26, and an output section 28.

This simulation device 10 can be realized by using a general-purpose computer as basic hardware. That is, the input section 12, the two-dimensional model creation section 14, the inflation analysis section 16, the three-dimensional model creation section 18, the slope surface setting section 20, the contact definition setting section 22, the friction coefficient setting section 24, and the rim separation analysis section. 26 and the output unit 28 can be realized by causing a processor installed in the computer described above to execute a program. The above program may be stored in the storage device of the above computer, or may be stored in a device other than the above computer (for example, a database server) and can be accessed by the above computer via communication. good.

Each part of the simulation device 10 will be explained in [1] to [9] below. It is assumed that the simulation by this simulation device 10 is performed using the finite element method.

[1] Input section 12
The input unit 12 acquires data on tires and rims to be simulated. Tire data includes the shape and dimensions of the entire tire, as well as the shape and arrangement of each component that makes up the tire (e.g. bead core, bead filler, carcass ply, belt, tread rubber, sidewall rubber, rim strip, inner liner, etc.) and material physical property values. Furthermore, the rim data includes the shape of the rim and the dimensions of each part (specifically, the rim diameter, rim width, etc.). These inputs are performed via a keyboard, a recording medium such as a CD-ROM, or a network.

[2] Two-dimensional model creation section 14
The two-dimensional model creation unit 14 creates a two-dimensional tire model with a rim, which includes a tire cross-section model 30 and a rim cross-section model 40, based on the data acquired by the input unit 12.

First, the two-dimensional model creation unit 14 creates a tire cross-sectional model 30 that reproduces the cross-section of the tire in the width direction. The tire cross-sectional model 30 is a two-dimensional model. As shown in FIG. 2, the tire cross-section model 30 is a finite element model in which the tire cross-section is divided into a finite number of elements.

As shown in FIG. 2, the tire cross-section model 30 includes a bead core part 31 and a bead filler part that reproduce the tire's bead core, bead filler, carcass ply, belt, tread rubber, sidewall rubber, rim strip, inner liner, etc. 32, a carcass ply part 33, a belt part 34, a tread rubber part 35, a sidewall rubber part 36, a rim strip part 37, an inner liner part 38, and the like. Element numbers, node numbers, node coordinates, material property values (for example, density, Young's modulus, Poisson's ratio, etc.), etc. are set for each element of the tire cross-sectional model 30 having these parts.

Further, the tread rubber portion 35 is formed with a groove portion 39 that reproduces the groove formed in the tread rubber. The groove portion 39 in this embodiment is the deepest groove among a plurality of grooves formed in the tread rubber of the tire, and reproduces a main groove that is a groove extending in the circumferential direction of the tire.

The element length of the finite element model is preferably 5 mm or less. However, in this embodiment, an attempt is made to reproduce the phenomenon in which the bead portion of a tire comes off the rim, and attention is paid to the movement of the bead portion in the tire cross-sectional model 30. Therefore, regarding the bead core portion 31 and its surrounding area (for example, the portion of the bead core portion 31 that is radially inner than the outer end of the tire and includes a portion of the rim strip portion 37 and the carcass ply portion 33), It is preferable that the length of the element is smaller than the other parts, for example, 2 to 4 mm. By making the element length of the portion including the bead core portion 31 smaller than other portions, the movement of the tire bead portion can be precisely reproduced.

Furthermore, the two-dimensional model creation unit 14 creates a rim cross-sectional model 40 that reproduces the cross-section of the rim in the width direction. The rim cross-sectional model 40 is a two-dimensional model. The rim cross-sectional model 40 is a finite element model in which the rim is divided into a finite number of elements. As shown in FIG. 2, the rim cross-sectional model 40 is provided with a bead seat portion 41, a flange portion 42, and a hump portion 43 that reproduce the bead seat, flange, and hump of the rim, respectively. Element numbers, node numbers, node coordinates, material property values (for example, density, Young's modulus, Poisson's ratio, etc.), etc. are set for each element of the rim cross-sectional model 40 having these parts. Note that the rim cross-sectional model 40 may be modeled as a deformable body, or may be modeled as a rigid body.

Note that in this embodiment, it is sufficient to model only the left and right rims of the wheel, but the entire wheel including the disk portion may be modeled.

Further, the two-dimensional model creation unit 14 fits the bead portion (near the bead core portion 31) of the tire cross-sectional model 30 into the bead seat portion 41 of the rim cross-sectional model 40. Various known methods can be applied as specific methods for fitting. For example, first, the bead portion of the tire cross-sectional model 30 is deformed inward in the tire width direction and placed between the hump portions 43 on both sides of the rim cross-sectional model 40 in the width direction, and then the bead portion of the tire cross-sectional model 30 is returned to its original shape. It is made to fit into the bead seat part 41 by restoring it.

In a state where the tire cross-sectional model 30 is fitted to the rim cross-sectional model 40, the bead bottom surface 52 contacts the bead seat portion 41, and at least a portion of the bead portion outer surface 53 contacts the flange portion 42. Further, a hump portion 43 is present on the inner side in the tire width direction than the bead tow 50 (the inner end in the tire width direction and the inner end in the tire radial direction of the bead portion).

Furthermore, the two-dimensional model creation unit 14 defines contact between the tire cross-sectional model 30 and the rim cross-sectional model 40 so that the tire cross-sectional model 30 does not bite into the rim cross-sectional model 40. The specific method of contact definition is not limited, and for example, Lagrange's undetermined multiplier method or penalty method, which will be described later, is applied.

In the tire cross-sectional model 30, the range in which contact is defined is the bead bottom surface 52 and the bead portion outer surface 53. The bead bottom surface 52 is the inner surface of the bead portion in the tire radial direction, and one end thereof is the bead tow 50. The bead outer surface 53 is a surface extending outward in the tire radial direction from the bead bottom surface 52 to the boundary 54 on the tire outer surface between the rim strip section 37 and the sidewall rubber section 36 along the outer surface of the tire cross-sectional model 30. be. Therefore, in the tire cross-sectional model 30, contact is defined in the range from the bead toe 50 to the boundary 54 on the tire outer surface between the rim strip portion 37 and the sidewall rubber portion 36.

In addition, the range in which contact is defined in the rim cross-sectional model 40 is the surface of the bead seat portion 41 and the flange portion 42 that comes into contact with the tire cross-sectional model 30.

Further, the two-dimensional model creation unit 14 sets a coefficient of friction between the tire cross-sectional model 30 and the rim cross-sectional model 40. The portions where the friction coefficient is set are the contact portion between the bead bottom surface 52 and the bead seat portion 41 and the contact portion between the bead portion outer surface 53 and the flange portion 42. The friction coefficient to be set is, for example, a value between 0.1 and 1.5, but preferably a value between 0.7 and 1.0. Which value to use may be determined by considering past experimental results, ease of calculation, etc.

Note that it is also possible to conduct an experiment in advance to determine the friction coefficient using a rubber sample made of the same rubber as that of the tire to be simulated and a metal sample made of the same metal as that of the rim to be simulated. . The obtained friction coefficient may be set as the friction coefficient between the tire cross-sectional model 30 and the rim cross-sectional model 40.

[3] Inflate analysis section 16
The inflation analysis section 16 executes an inflation analysis of the two-dimensional rim-equipped tire model created by the two-dimensional model creation section 14. Specifically, the inflation analysis unit 16 calculates the deformation of the tire cross-sectional model 30 while applying internal pressure to the inner liner portion 38 of the tire cross-sectional model 30 in the two-dimensional rimmed tire model. The magnitude of the internal pressure applied at this time is appropriately set.

[4] Three-dimensional model creation section 18
The three-dimensional model creation unit 18 creates a three-dimensional rim-equipped tire model 66 by copying and expanding the two-dimensional rim-equipped tire model in the tire circumferential direction around the tire rotation axis. As a result, each node of the two-dimensional rimmed tire model is copied and expanded in small angle increments in the tire circumferential direction, and a three-dimensional finite element model is completed. As shown in FIGS. 3 and 4, the three-dimensional rim-equipped tire model 66 includes a three-dimensional tire model 60 and a three-dimensional rim model 62. The number of elements of the three-dimensional tire model 60 is, for example, 100,000 to 200,000 elements.

In the following description, the names and codes of each part in the two-dimensional tire cross-sectional model 30 and the two-dimensional rim cross-sectional model 40 will be used as they are as the names and codes of each part in the three-dimensional tire model 60 and the three-dimensional rim model 62. .

[5] Slope surface setting section 20
The slope road surface setting unit 20 sets a slope road surface model 64 that is inclined with respect to the width direction of the tire model 60 (left-right direction in FIG. 5) as shown in FIG. The slope road surface model 64 is set, for example, as a rigid plane. The angle of inclination (θ in FIG. 5) of the inclined road surface model 64 with respect to the width direction of the tire model 60 is preferably 1 to 20 degrees. Calculations tend to converge when the tilt angle is 20° or less.

The slope road surface setting unit 20 arranges the slope road surface model 64 at a location on one side of the tire model 60 in the width direction. With this arrangement, when the tire model 60 or the slope road surface model 64 is moved in the width direction of the tire model 60 (however, in the direction in which the tire model 60 and the slope road surface model 64 approach each other), the tire model 60 moves to the slope road surface model 64. This will be the case.

Further, the slope road surface setting unit 20 defines a contact between the tire model 60 and the slope road surface model 64 so that the tire model 60 can come into contact with the slope road surface model 64. The specific method of contact definition here is not limited, and for example, Lagrange's undetermined multiplier method or penalty method, which will be described later, is applied. Further, the slope road surface setting unit 20 sets the coefficient of friction between the tire model 60 and the slope road surface model 64. The value of the friction coefficient is appropriately determined based on experimental results.

[6] Contact definition setting section 22
The contact definition setting section 22 performs a plurality of contact definitions. First, the contact definition setting unit 22 connects the bead portion inner surface 51 extending outward in the tire radial direction from the bead toe 50 on the inner surface of the tire model 60 (that is, the surface to which internal pressure is applied, the surface of the inner liner portion 38), and the hump of the rim model 62. Contact definition with the section 43 is performed. The length of the inner surface 51 of the bead portion, where the contact is defined, is preferably 1.0 to 1.2 times the length of the arc of the hump portion 43. The length of the bead inner surface 51 is the length along the inner surface of the tire model 60 from the bead tow 50 toward the outside in the tire radial direction. Further, the length of the arc of the hump portion 43 is the length along the shape of the hump portion 43 on the rim cross-sectional model 40.

The contact definition between the bead inner surface 51 and the hump portion 43 is performed when the bead portion of the tire model 60 comes off the rim model 62, as shown in FIG. This is because it is necessary to contact the portion 43 so that the bead portion can overcome the hump portion 43, and it is necessary to prevent the inner surface 51 of the bead portion from penetrating the hump portion 43.

Further, the contact definition setting unit 22 defines contact between the inner walls of the groove portions 39 of the tread rubber portion 35. The range in which the contact is defined may be only the left and right side walls 39a of the groove 39 (see FIGS. 2 and 7(a)), or the range in which the contact is defined is the left and right side walls 39a and the bottom surface 39b of the groove 39 (see FIGS. 2 and 7(a)). (see) is also fine. This contact definition is performed by bringing the inner walls of the grooves 39 into contact with each other when the tire model 60 is significantly deformed as shown in FIG. This is because it is necessary to prevent it from being put away.

Note that there is also a method of preventing one inner wall of the groove 39 from penetrating the other inner wall without defining contact between the inner walls of the groove 39. Specifically, virtual elements are added along the inner wall of the groove portion 39. Then, physical property values such as a Young's modulus of 1/1000 to 1/10000 of the tire material and a Poisson's ratio of 0 are set for this virtual element. If this virtual element exists in the groove 39, even if the inner walls of the groove 39 try to contact each other, the virtual element will only be compressed, and the inner walls of the groove 39 will not come into contact with each other, and one inner wall of the groove 39 will not touch the other. It will not penetrate the inner wall of the

Further, the contact definition setting unit 22 defines contact between the inner surfaces of the tire model 60 (the surfaces of the inner liner portions 38). The range in which the contact is defined is, for example, the entire inner surface of the tire model 60. This contact definition is performed by bringing the inner surfaces of the tire models 60 into contact with each other when the tire model 60 is significantly deformed as shown in FIG. This is because it is necessary to prevent a portion of the material from penetrating.

The contact definition setting unit 22 preferably uses the Lagrangian undetermined multiplier method or the penalty method as the contact definition method described above. Simply put, Lagrange's undetermined multiplier method is a method that adds contact surface force to the contact surface. Moreover, the penalty method is, simply put, a method in which a spring is stretched between contact surfaces to maintain balance.

[7] Friction coefficient setting section 24
The friction coefficient setting unit 24 defines each contact portion for which the contact definition setting unit 22 defines contact, that is, the contact portion between the inner surface of the bead portion 51 and the hump portion 43, the contact portion between the inner walls of the groove portion 39, and the contact portion between the inner surfaces of the tire model 60. Set the coefficient of friction at the contact area.

The method of setting the friction coefficient by the friction coefficient setting section 24 is not limited. For example, a function (specifically, a quadratic function, a higher order function, an exponential function, a logarithmic function, etc.) with pressure or sliding speed as an independent variable and friction coefficient as a dependent variable is set in advance in the simulation device 10, Based on that function, the coefficient of friction may be varied during the simulation in response to changes in pressure or sliding speed. Such a function can be determined in advance based on experiments or the like. Further, as an alternative to such a function, a table showing the relationship between pressure or sliding speed and friction coefficient may be set in the simulation device 10.

Further, if a function in which pressure is an independent variable and a friction coefficient is a dependent variable is known in advance, the friction coefficient can be set using another method. For example, first, the coefficient of friction at each contact portion is set to an appropriate value, and then a preliminary simulation is performed using the method shown in FIG. 10, which will be described later, to determine the average contact pressure or maximum contact pressure generated at each contact portion. Then, the coefficient of friction at each contact portion is set from the above-mentioned function known in advance and the average contact pressure or maximum contact pressure found through preliminary simulation.

[8] Rim detachment analysis section 26
The finite element method includes an explicit method and an implicit method, and the rim removal analysis unit 26 executes the simulation using the explicit method.

The rim detachment analysis unit 26 sets two types of Young's modulus as the Young's modulus of the bead core portion 31 before executing the simulation. One is the Young's modulus of the material of the bead core of an actual tire or a Young's modulus close to it (these are collectively referred to as the "actual Young's modulus"). Incidentally, the Young's modulus of the material of the bead core of an actual tire is, for example, 180 to 220 GPa, which is particularly high among the materials constituting the tire. The other is a Young's modulus (referred to as "initial Young's modulus") whose value is smaller than the actual Young's modulus. The initial Young's modulus value is, for example, 1/100 or less of the actual Young's modulus value. The rim detachment analysis unit 26 sets the Young's modulus of the bead core portion 31 as the initial Young's modulus at the start of the simulation.

After setting the two types of Young's modulus, the rim detachment analysis unit 26 analyzes at least one of the tire model 66 with rim and the slope road surface model 64 in the width direction of the tire model 60, and the tire model 66 with rim and the slope road surface. The model 64 is moved in the direction in which it is pressed. For this movement, the rim separation analysis unit 26 sets a moving speed for the model to be moved. The moving speed is, for example, 150 to 250 mm/sec. The rim separation analysis unit 26 continues to maintain the tire model 60 in a non-rolling state while moving the model.

As a result of this movement, the tire model 60 and the slope road surface model 64 first come into contact as shown in FIG. The rim detachment analysis unit 26 continues to move the model in the same direction even after the tire model 60 and the slope road surface model 64 come into contact. After the tire model 60 and the slope road surface model 64 come into contact, a force is generated between the tire model 60 and the rim model 62.

If the model continues to be moved even after the tire model 60 and the slope road surface model 64 come into contact, the tire model 60 gradually deforms. Specifically, first the tread rubber portion 35 deforms, then the sidewall rubber portion 36 begins to deform, then the tire maximum width position on the surface of the sidewall rubber portion 36 begins to displace, and then the rim The boundary 54 (see FIG. 2) on the outer surface of the tire between the strip portion 37 and the sidewall rubber portion 36 begins to shift. As the deformation of the tire model 60 further progresses, the bead core portion 31 of the tire model 60 begins to displace at a certain point. Then, at some point thereafter, the bead portion of the tire model 60 climbs over the hump portion 43 of the rim model 62 and the bead portion of the tire model 60 comes off from the rim model 62. When the rim detachment analysis unit 26 detects that the bead portion of the tire model 60 has detached from the rim model 62, it ends the movement of the model.

Note that even if the model continues to be moved after the tire model 60 and the slope road surface model 64 come into contact, the bead portion of the tire model 60 may not come off from the rim model 62. In that case, the force generated between the bead part of the tire model 60 and the rim model 62 increases without the bead part of the tire model 60 coming off the rim model 62, and the force exceeds a predetermined value. When the rim detachment analysis unit 26 detects this, the rim detachment analysis unit 26 ends the movement of the model without waiting for the tire model 60 to detach from the rim model 62.

The rim detachment analysis unit 26 monitors the force generated between the tire model 60 and the rim model 62 while moving at least one of the rim-equipped tire model 66 and the slope road surface model 64 in this manner. The force to be monitored is, for example, contact pressure or shear stress.

The range in which the force is monitored is the range in which the contact between the tire model 60 and the rim model 62 is defined on the width direction cross section of the tire model 66 with a rim. That is, the range to be monitored is the bead inner surface 51, bead bottom surface 52, and bead outer surface 53 for the tire model 60, and the bead seat portion 41, flange portion 42, and hump portion 43 for the rim model 62. Only the range of one of the tire model 60 and the rim model 62 may be monitored, or the range of both the tire model 60 and the rim model 62 may be monitored.

However, when the bead portion of the tire model 60 comes off the rim model 62, it is assumed that the bead toe 50 of the tire model 60 and the hump portion 43 of the rim model 62 are in contact to the end. Therefore, the range to be monitored may be one or both of the bead tow 50 and the hump portion 43.

Further, the range to be monitored may be the entire circumferential direction of the rim-equipped tire model 66 with respect to the circumferential direction of the rim-equipped tire model 66. However, it is assumed that when the bead portion of the tire model 60 begins to come off the rim model 62, it begins to come off at the bottom of the rim-attached tire model 66 in the circumferential direction (that is, at the part closest to the contact part with the slope road surface model 64). Ru. Therefore, the range to be monitored may be limited to the lowest circumferential portion of the rimmed tire model 66 (that is, the portion closest to the contact portion with the slope road surface model 64).

In this way, the force generated between the tire model 60 and the rim model 62 is monitored, and the time when the monitored force disappears (for example, when it becomes 0) is determined as the time when the tire model 60 comes off the rim model 62. Detect.

Further, while moving at least one of the tire model 66 with rim and the slope road surface model 64, the rim detachment analysis unit 26 changes the Young's modulus of the bead core part 31 from the initial Young's modulus having a small value to the actual Young's modulus. Change to rate. Specifically, the rim detachment analysis section 26 sets the Young's modulus of the bead core section 31 to the initial Young's modulus when starting the movement of the model. Then, the rim detachment analysis unit 26 maintains the Young's modulus of the bead core portion 31 before a predetermined reference time as the initial Young's modulus, and converts the Young's modulus of the bead core portion 31 after the reference time into the actual Young's modulus. shall be. Note that the Young's modulus at the reference time may be an initial Young's modulus or an actual Young's modulus.

Here, the reference time is a time when the deformation of the tire model 60 has progressed to a certain extent and the bead core portion 31 begins to be displaced, or a predetermined time before the bead core portion 31 begins to be displaced. The predetermined time before the bead core part 31 starts to displace is, for example, when the tire maximum width position on the surface of the sidewall rubber part 36 starts to displace, or when the position between the rim strip part 37 and the sidewall rubber part 36 starts to displace. This is when the boundary 54 (see FIG. 2) on the outer surface of the tire begins to displace. Here, the time when the bead core portion 31, the tire maximum width position, and the boundary 54 begin to displace is the time when the nodes at these parts and positions begin to displace.

The reason why the Young's modulus is changed before and after the reference time in this way will be explained. First, the Courant conditions in the explicit method will be explained.

When simulating a dynamic phenomenon that occurs over a short period of time using an explicit method, the entire simulation time is divided into small pieces and the state at each time is sequentially calculated. In such a simulation, the force input to the model is calculated as a wave (stress wave) that is transmitted through the model, but the wave is calculated per unit time (time increment Δt) divided as above. If the distance traveled exceeds elements, it is not possible to correctly calculate how the waves travel.

What is therefore required is the Courant condition expressed by the following formula (I).

Here Δt _CR is the critical time increment. As can be seen from equation (I), the Courant condition limits the time increment Δt from exceeding the critical time increment Δt _CR .

The critical time increment Δt _CR is expressed by the following equation (II) using the minimum edge length Lmin of the element of the finite element model and the propagation speed C of the stress wave.

Further, the propagation velocity C of the stress wave is expressed by the following equation (III) using the Young's modulus E and the density ρ of the material.

From equations (I) to (III), it can be seen that when the minimum edge length Lmin of the element is short or when the Young's modulus E is large, the critical time increment Δt _CR becomes small. If the critical time increment Δt _CR is small, the time required for simulation becomes longer because the time increment Δt must be made smaller.

Therefore, if the Young's modulus of the bead core portion 31 in this embodiment is set to the actual Young's modulus, which has a large value, the time required for simulation becomes long. Here, while the bead core portion 31 is displaced, it is necessary to set the Young's modulus of the bead core portion 31 to the actual Young's modulus in order to perform accurate simulation. However, before the bead core portion 31 starts to be displaced, even if the Young's modulus of the bead core portion 31 is set to the actual Young's modulus, the time required for the simulation will only increase, and the accuracy of the simulation will not be affected.

Therefore, at a stage before the above-mentioned reference time, the Young's modulus of the bead core portion 31 is set to an initial Young's modulus with a small value, thereby making it possible to perform a simulation until the bead core portion 31 starts to displace in a short time. Then, at a stage after the above-mentioned reference time, the Young's modulus of the bead core portion 31 is set to the actual Young's modulus, which has a large value, so that accurate simulation can be performed.

[9] Output section 28
The output unit 28 outputs at least whether the tire model 60 has separated from the rim model 62 as a result of the simulation performed by the rim separation analysis unit 26. Further, the output unit 28 may output physical quantities (for example, displacement and stress) of each node when the rim detachment analysis unit 26 is moving the model or when the tire model 60 is detached from the rim model 62. Further, the output unit 28 may output the progress of the simulation performed by the rim detachment analysis unit 26 one by one. Examples of output methods include displaying on a display device and saving in a storage device.

A simulation method using the simulation apparatus 10 having the above configuration will be explained based on FIG. 10.

First, in step S1, the input unit 12 acquires data on tires and rims to be simulated.

Next, in step S2, the two-dimensional model creation unit 14 creates a tire cross-sectional model 30 and a rim cross-sectional model 40 based on the data acquired by the input unit 12. Then, the two-dimensional model creation unit 14 fits the tire cross-sectional model 30 to the rim cross-sectional model 40 to create a two-dimensional tire model with a rim. The two-dimensional model creation unit 14 also defines contact between the portion from the bead bottom surface 52 to the bead outer surface 53 in the tire cross-sectional model 30 and the portion from the bead seat portion 41 to the flange portion 42 in the rim cross-sectional model 40. , also sets the friction coefficient of the defined contact area. Note that since the simulation for fitting the tire cross-sectional model 30 to the rim cross-sectional model 40 is performed by an implicit method, the actual Young's modulus is used as the Young's modulus of the bead core portion 31 at this time.

Next, in step S3, the inflation analysis unit 16 performs an inflation analysis of the two-dimensional rim-equipped tire model. At this time, the inflation analysis section 16 applies a predetermined internal pressure to the tire cross-sectional model 30. Since the inflation analysis is performed by an implicit method, the actual Young's modulus is used as the Young's modulus of the bead core portion 31 at this time.

Next, in step S4, the three-dimensional model creation unit 18 copies and develops the two-dimensional rimmed tire model in the tire circumferential direction to create a three-dimensional model consisting of the three-dimensional tire model 60 and the three-dimensional rim model 62. A tire model 66 with a rim is created.

Next, in step S5, the slope road surface setting unit 20 places the slope road surface model 64 that is sloped with respect to the width direction of the tire model 60 at a location on one side of the tire model 60 in the width direction. Here, the slope road surface setting unit 20 also defines the contact between the tire model 60 and the slope road surface model 64 and sets the friction coefficient between the tire model 60 and the slope road surface model 64.

Next, in step S6, the contact definition setting unit 22 performs a plurality of contact definitions. The contact definitions performed here include a contact definition between the bead inner surface 51 of the tire model 60 and the hump portion 43 of the rim model 62, a contact definition between the inner walls of the groove portion 39 of the tread rubber portion 35 of the tire model 60, and a contact definition between the tire model 60 and the hump portion 43 of the rim model 62. This is the definition of contact between the inner surfaces of .

Next, in step S7, the friction coefficient setting unit 24 determines the friction at each of the contact portion between the bead inner surface 51 and the hump portion 43, the contact portion between the inner walls of the groove portion 39, and the contact portion between the inner surfaces of the tire model 60. Set the coefficient.

Next, in step S8, the rim detachment analysis unit 26 performs a simulation using an explicit method. Specifically, the rim detachment analysis unit 26 brings the tire model 66 with a rim into contact with the slope road surface model 64 while maintaining the tire model 60 in a non-rolling state. at least one of them is moved in the width direction of the tire model 60 and in the direction of pressing the rim-equipped tire model 66 and the slope road surface model 64. Then, the rim detachment analysis unit 26 monitors the force generated between the tire model 60 and the rim model 62, and detects the point in time when the force disappears as the point in time when the tire model 60 detaches from the rim model 62. Further, when the rim detachment analysis unit 26 detects that the force generated between the tire model 60 and the rim model 62 increases and exceeds a predetermined value without the tire model 60 detaching from the rim model 62, the tire model 60 The movement of the model is finished without waiting for it to come off the rim model 62.

In this step S8, the rim detachment analysis section 26 initially sets the Young's modulus of the bead core section 31 to a small initial Young's modulus. The Young's modulus of the bead core part 31 is maintained at the initial Young's modulus before the above reference time (when the bead core part 31 starts to displace or at a predetermined time before the bead core part 31 starts to displace), and the Young's modulus of the bead core part 31 is maintained at the initial Young's modulus, and After that time, the Young's modulus of the bead core portion 31 is set as the actual Young's modulus.

Next, in step S9, the output unit 28 outputs the simulation result by the rim detachment analysis unit 26.

If the above steps S1 to S9 are executed and it is found in step S9 that the tire model 60 has not come off the rim model 62, the internal pressure applied to the tire cross-section model 30 is lowered in step S3, and then steps S4 to S9 are performed again. may be executed. By repeating steps S3 to S9 while lowering the internal pressure until the tire model 60 comes off the rim model 62, the internal pressure at which the tire model 60 comes off the rim model 62 is determined. Repeating steps S3 to S9 in this way is reproducing the above-mentioned rim detachment performance test.

Note that the order of steps S1 to S9 may be changed as appropriate. For example, the inflation analysis may be performed after the three-dimensional rim-equipped tire model 66 is created by replacing steps S3 and S4 described above.

The effects of the above embodiment will be explained. As described above, in this embodiment, the steps include preparing a finite element model that reproduces a tire with a metal bead core, setting material property values including Young's modulus in the finite element model, and setting the bead core of the finite element model. A tire simulation including a step of performing a simulation involving displacement of the portion 31 using an explicit method is executed. In this simulation, the time when the bead core part 31 starts to be displaced or a predetermined time before the bead core part 31 starts to be displaced is set as the reference time, and the Young's modulus of the bead core part 31 before the reference time is calculated as the Young's modulus of the bead core part 31 after the reference time. The Young's modulus is set to be smaller than the Young's modulus of the bead core portion 31.

By setting the Young's modulus of the bead core portion 31 before the reference time to be smaller than the actual Young's modulus in this way, a simulation before the bead core portion 31 starts to be displaced can be performed in a short time. Therefore, according to this embodiment, tire simulation using an explicit method can be performed in a short time.

Furthermore, since the simulation of this embodiment is a simulation that reproduces the phenomenon in which the tire comes off the rim, and focuses on the displacement of the bead core portion 31 of the tire model 60, it is preferable to shorten the element length of the bead core portion 31. . If the element length of the bead core portion 31 is shortened, the time required for simulation becomes longer; however, in this embodiment, the Young's modulus of the bead core portion 31 before the reference time is made smaller than the actual Young's modulus, so the time required for simulation is reduced. You can prevent it from becoming too long.

Here, by setting the Young's modulus (initial Young's modulus) of the bead core portion 31 before the reference time to 1/100 or less of the Young's modulus (actual Young's modulus) of the bead core portion 31 after the reference time, The time required for simulation can be effectively shortened.

Various changes can be made to the above embodiments. For example, although the embodiments described above are simulations of a tire coming off a rim, the present invention can be applied to simulations of various phenomena involving displacement of a bead core. Thereby, tire simulation using an explicit method can be performed in a short time.

Further, simulations similar to those in the above embodiment can also be performed using other analysis methods such as the boundary element method and the finite difference method.

Further, at least one of the tire cross-sectional model 30 and the rim cross-sectional model 40, a two-dimensional tire model with a rim, or a three-dimensional tire model with a rim 66 is created in advance, and the previously created model is inputted into the input section. 12 may be acquired and used for simulation.

DESCRIPTION OF SYMBOLS 10... Simulation device, 12... Input unit, 14... Two-dimensional model creation part, 16... Inflate analysis part, 18... Three-dimensional model creation part, 20... Ramp surface setting part, 22... Contact definition setting part, 24... Friction Coefficient setting section, 26... Rim detachment analysis section, 28... Output section, 30... Tire cross section model, 31... Bead core section, 32... Bead filler section, 33... Carcass ply section, 34... Belt section, 35... Tread rubber section, 36...Sidewall rubber part, 37...Rim strip part, 38...Inner liner part, 39...Groove part, 39a...Side wall, 39b...Bottom surface, 40...Rim cross section model, 41...Bead seat part, 42...Flange part, 43... Hump part, 50... Bead toe, 51... Bead part inner surface, 52... Bead bottom surface, 53... Bead part outer surface, 54... Boundary, 60... Tire model, 62... Rim model, 64... Sloped road surface model, 66... Tire model with rim

Claims (3)

A step of preparing a finite element model that reproduces a tire with a metal bead core, a step of setting material property values including Young's modulus in the finite element model, and a step of calculating the displacement of the bead core of the finite element model using an explicit method. In a tire simulation method, the tire simulation method includes a step of performing an accompanying simulation,
In the simulation, the time when the bead core starts to displace or a predetermined time before the bead core starts to displace is set as the reference time, and the Young's modulus of the bead core before the reference time is the Young's modulus of the bead core after the reference time. A tire simulation method characterized by making tires smaller. 2. The tire simulation method according to claim 1, wherein a finite element model in which the tire is fitted to a rim is prepared, and the simulation simulates that the tire comes off from the rim. The simulation method according to claim 1 or 2, wherein the Young's modulus of the bead core before the reference time is set to 1/100 or less of the Young's modulus of the bead core after the reference time.

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