JP5533277B2 - Evaluation method of tire inclusion jumping characteristic, tire inclusion jumping characteristic evaluation apparatus and program - Google Patents

Description

  The present invention relates to a method and an apparatus for evaluating the inclusion jumping characteristic of a tire when the tire passes over an inclusion provided on a road surface, and a program for executing the method.

In recent years, various methods for predicting the wet performance of a pneumatic tire (hereinafter simply referred to as a tire) mounted on a vehicle by using a finite element method or a finite volume method have been proposed along with an improvement in computer processing speed. Yes.
The wet performance of a tire means that tire characteristics are deteriorated due to water intervening between the tire and a road surface, for example, as represented by a hydroplaning phenomenon. Therefore, good wet performance of the tire means that water does not intervene between the tire and the road surface, even if water intervenes, the interposition is suppressed as much as possible, and the influence of this water interposition Is small.

  On the other hand, when the tire passes through the water film formed on the road surface, a part of the water film may jump from the road surface and the water may be scattered. Such water splashes are caused when the vehicle passes on a wet road surface, and may hinder traffic on the side of the road. Alternatively, a vehicle traveling on a lane adjacent to a truck or bus traveling on a highway may be subject to traveling obstacles due to the water splash of the truck or bus.

  Under such circumstances, when predicting and evaluating the tire characteristics according to the road surface condition such as the wet performance of the tire, it is not an enormous model, and it is possible to obtain and evaluate a calculation result with higher accuracy than the conventional model. A tire characteristic prediction method is known (Patent Document 1).

Japanese Patent No. 4152109

In Document 1, a tire model and a road surface model of a finite element model, and a road surface state reproduction model in which a plurality of particle models are arranged on at least a part of the road surface model are created. When this tire model steps into the area on the road surface model where the particle model is placed, the tire model and the particle surface model are calculated while calculating the interaction between the tire model and the particle model at each time step when the tire model and the road surface state reproduction model are calculated. Deformation calculation of model and road surface state reproduction model is performed. From this calculation result, a predetermined characteristic physical quantity of the tire model or the road surface state reproduction model is calculated to predict and evaluate the tire characteristics.
In the document 1, as the characteristic physical quantity, the lift force that the road surface state reproduction model acts on the tire model, the road surface reaction force that the road surface model acts on the tire model, and the movement position and flow velocity of the particle model in the road surface state reproduction model can be calculated. The water splash characteristics of a tire cannot be evaluated.

  In general, it is possible to evaluate water splash characteristics of a tire by performing actual water splash using a vehicle equipped with a tire, but quantitative evaluation is difficult. Moreover, the complicated work which produces an actual tire and performs the test by a vehicle is required. For this reason, the water splash characteristic of a tire cannot be evaluated efficiently and quantitatively. Such a problem is not limited to water splashing, but also occurs for snow, sand, mud, gravel and the like.

  Accordingly, the present invention provides a method for evaluating inclusion jumping characteristics of a tire, a tire that can efficiently and quantitatively evaluate the inclusion jumping characteristics of a tire when the tire passes over inclusions provided on a road surface. An object of the present invention is to provide an evaluation device and program for the jumping property of inclusions.

One aspect of the present invention is a method for evaluating the jumping characteristics of tire inclusions when the tire passes over inclusions provided on a road surface,
Creating a tire model that reproduces a tire, a road surface model that reproduces a road surface, and an inclusion model that reproduces inclusions provided on the road surface and includes a plurality of minute models that are separable from each other;
Scattering the micro model by rolling the tire model on the road surface model provided with the inclusion model;
Projecting the scattered micro model on a plane perpendicular to the plane of the road surface model at set time intervals ;
Using the time-series projection image of the micro model projected on the plane, an envelope of the projection image of the micro model scattered is obtained for each projection image, and the envelope obtained for each projection image And the step of evaluating the jumping characteristics of the inclusions of the tire using the envelope having the largest shape of the envelope .

Another aspect of the present invention is an apparatus for evaluating the jumping characteristics of tire inclusions when the tire passes over inclusions provided on a road surface,
A model creation unit that creates a tire model that reproduces a tire, a road surface model that reproduces a road surface, and an inclusion model that reproduces inclusions provided on the road surface and includes a plurality of minute models that are separable from each other; ,
A simulation calculation unit that scatters the minute model by rolling the tire model on the road surface model provided with the inclusion model;
A simulation result processing unit that projects the scattered micro model on a plane perpendicular to the plane of the road surface model for each set time interval ;
Using the time-series projection image of the micro model projected on the plane, an envelope of the projection image of the micro model scattered is obtained for each projection image, and the envelope obtained for each projection image And an evaluation unit that evaluates the jumping characteristic of the inclusions of the tire using the envelope having the largest shape of the envelope .

Yet another aspect of the present invention is a program that causes a computer to evaluate inclusion jumping characteristics of a tire when the tire passes over inclusions provided on a road surface.
A procedure for a computer to create a tire model that reproduces a tire, a road surface model that reproduces a road surface, and an inclusion model that reproduces inclusions provided on the road surface and includes a plurality of minute models that can be separated from each other. ,
A step of causing the computer to scatter the minute model of the inclusion model by rolling the tire model on the road surface model provided with the inclusion model;
The computer projects the scattered micro model on a plane perpendicular to the plane of the road surface model at set time intervals , and
Using the time-series projection image of the micro model projected on the plane, an envelope of the projection image of the micro model scattered is obtained for each projection image, and the envelope obtained for each projection image The computer has a procedure for evaluating the jumping characteristics of the inclusions of the tire using the envelope having the largest shape of the envelope .

  The method for evaluating the inclusion jumping characteristic of the tire, the apparatus for evaluating the inclusion jumping characteristic of the tire, and the program efficiently and quantitatively determine the inclusion jumping characteristic of the tire when the tire passes over the inclusion provided on the road surface. Can be evaluated.

It is a figure which shows the structure of the outline of the evaluation apparatus which evaluates the water splash characteristic of the tire of this embodiment. (A) is a figure explaining rolling simulation of a tire model, (b) is a figure explaining a water film model used for rolling simulation. It is a figure explaining the plane which projects the particle model for evaluating the water splash characteristic of the tire of this embodiment. (A)-(c) is a figure explaining the state of water splash using a tire model and a particle model, and an evaluation method. It is a figure which shows the example of the various envelopes obtained by FIG.4 (c). It is a flowchart which shows the flow of the evaluation method of this embodiment. (A)-(c) is a figure explaining the difference in a finite element model and the particle model used for this embodiment. (A), (b) is a figure explaining a particle model. It is a flowchart which shows the process flow of the principal part of the rolling simulation used with the evaluation method of this embodiment. (A)-(c) is a figure explaining the interaction of the tire model in a rolling simulation used with the evaluation method of this embodiment, and a particle model.

  Hereinafter, the evaluation method of the inclusion jumping characteristic of the tire, the evaluation device for the inclusion jumping characteristic of the tire, and the program according to the present invention will be described in detail.

(Tire evaluation device)
FIG. 1 is a diagram illustrating a schematic configuration of an evaluation apparatus 10 that evaluates the water splash characteristics of a tire according to the present embodiment. Evaluation of water splash characteristics refers to evaluation of reach distance and reach height, or water splash density when water splashes around the tire when the tire passes a water film on the road surface.

The evaluation device 10 evaluates the water splash characteristics of the tire using a rolling simulation using a tire model. The evaluation apparatus 10 performs a rolling simulation in which the created tire model is rolled on a road surface model provided with a separately created water film model. The water film model includes a plurality of particle models so as to be separable from each other. When the tire model passes through the water film model, since the particle models in the water film model are separated from each other and scattered, the evaluation apparatus 10 projects the scattering state of the particle model onto one plane to generate particles. The model's projected image is used to evaluate the water splash characteristics of the tire.
The tire for which the evaluation device 10 evaluates the water splash characteristic includes, for example, a passenger car tire or a heavy load (bus or truck) tire, and is not limited to the tire size.

  The evaluation apparatus 10 includes a computer that mainly includes a CPU 12, a bus 14, a memory 16, and an input / output interface unit 18. The evaluation device 10 is connected to an input operation system 20 such as a mouse and a keyboard and an output device 22 such as a display and a printer through an input / output interface unit 18. The evaluation device 10 calls a program stored in the memory 16 and executes the program, thereby forming a model creation unit 24, a simulation calculation unit 26, a simulation result processing unit 28, and an evaluation unit 30, and a processing module group. 36 is formed.

  The model creation unit 24 creates a tire model that reproduces a tire by a plurality of elements, a road surface model that reproduces a road surface on which the tire contacts the ground, and a water film model that reproduces a water film provided on the road surface. The water film model includes a plurality of particle models in a separable manner. Although this embodiment uses water as inclusions, snow, sand, mud, gravel, or the like may be reproduced instead of water. In this embodiment, water, that is, a water film is used as a representative inclusion. As described later, a plurality of particle models modeled using the particle method are used as the water film model. The plurality of particle models have weak binding forces that can be separated from each other by an external force received from the tire model.

FIG. 2A is a diagram showing a tire model T _M , a road surface model R _M, and a water film model S _M.
The created tire model T _M is a tire model based on the finite element method having a three-dimensional shape as shown in FIG. In the tire model T _M shown in FIG. 2, the mesh for element division is not displayed.
The road surface model R _M is a rigid road surface model R _M as shown in FIG. 2A or a finite element model composed of a plurality of elements.
As shown in FIG. 2A, the water film model S _M is formed in a part of the traveling portion of the tire model T _M of the road surface model R _M.

FIG. 2B illustrates the water film model _SM in detail.
The water film model S _M provided in a part on the road surface model R _M is a model in which a plurality of particle models P _M are arranged at a constant interval. When creating the water film model S _M , specifically, the model creation unit 24 converts a plurality of particle models P _M in the X direction and Y as a fluid model reproducing the water film, as shown in FIG. Isotropically arranged at regular intervals in the Z direction. For example, the model creation unit 24 sets the interval between the particle models P _M to 2.5 mm and the total number N of the particle models N to several tens of thousands, and is regular in an isotropic manner so that the mass of each particle model P _M becomes the same. For example, a water film model S _M having a lateral width of 400 mm, a thickness of 10 mm, and a length of 120 mm is created.
The particle method applied to the particle model P _M of the water film model S _M will be described later.

Simulation unit 26 by the water film model S _M is to roll the tire model Le T _M on the road Moderuru R _M provided, to scatter the particles Moderuru P _M of the water film Moderuru S _M. The interaction between the particle model P _M and the tire model particle model T _M will be described in the description of the particle method described later.

Simulation result processing section 28, during the simulation, scattered particles Moderuru P _M, performs a process of projecting the plane perpendicular to the plane of the road surface model R _M.
Specifically, the simulation result processing section 28, the tire model T _M is a predetermined time range to the passage end from passing the start of the water film model S _M every predetermined time interval, the particle model scattering P _M Are projected onto the plane. The plane used for the projection is a plane perpendicular to the plane of the road surface model R _M passing through the center of the tire model T _M. Since the rolling tire model T _M moves with respect to the road surface model R _M , the plane is provided every set time, and the scattered particle model P _M is projected onto the plane. The plane is normal to the direction of this plane is provided such that the moving direction of the tire model T _M. In addition, as shown in FIG. 3, if the plane is a plane perpendicular to the plane of the road surface model R _M , the inclination angle θ in any direction with respect to the moving direction of the tire model T _M May be provided with an inclination. FIG. 3 is a view of the tire model T _M as viewed from above the road surface model R _M.
Simulation result processing section 28, a process of projecting the particles Moderuru P _M that scattered plane, performed every time the set interval, acquires the projected image of the particle Moderuru P _M in a time series.

Evaluation unit 30 uses the projection image of the projected particles Moderuru P _M in the plane, to evaluate the water splash property of the tire.
Figure 4, (a) ~ (c) is a diagram showing the flow of the evaluation of water splash with projected image of the particle model P _M. In the figure, Y-direction, as shown in FIG. 1, corresponds to the tire width direction orthogonal to the moving direction of the tire model T _M, is a direction parallel to the rotation axis of the tire model T _M. Z direction is a direction perpendicular to the plane of the road surface model R _M.
First, as shown in FIG. 4 (a), the evaluation unit 30, for each projection image of the particle Moderuru P _M at the time set, Z direction of the particle Moderuru P _M at predetermined respective positions in the Y-direction Plot the highest position of.
Next, as shown in FIG. 4B, the evaluation unit 30 performs curve fitting using a curve using the plotted points. That is, the evaluation unit 30 creates an envelope shape of the projection image of the particle model P _M. The envelope is preferably a curve represented by a polynomial, for example, and the polynomial is a · (x−x ₀ ) ^b + c (a, b, c, x ₀ are constants, and b is a natural number). Preferably there is. The polynomial a · (x−x ₀ ) ^b + c can curve-fit each plotted point of the projection image of the particle model P _M with high accuracy.
Next, the evaluation unit 30, as shown in FIG. 4 (c), the envelope is created, the maximum height H from the surface of the road surface model R _M, to the surface of the road surface model R _M of the envelope intersection L, and calculates the output angle Φ from the tire model T _M envelope. The calculated maximum height H, intersection position L, and emission angle Φ are stored in the memory 16.

Evaluation unit 30, for each projection image of the particle Moderuru P _M of the time series, performs the processing shown in FIG. 4 (a) ~ (c) , using the largest envelope, to evaluate the water splash property.
The evaluation unit 30 uses the maximum height H, the intersection position L, and the emission angle Φ of the largest envelope to compare with the corresponding maximum height H, intersection position L, and emission angle Φ in other tires, Evaluate the ranking of tires with respect to water splash characteristics. Further, the evaluation unit 30 outputs the envelope shape obtained by curve fitting to an output device 22 such as a display or a printer.
The evaluation unit 30 calculates and uses the maximum height H, the intersection position L, and the exit angle Φ for evaluation, but calculates at least one of the maximum height H, the intersection position L, and the exit angle Φ. It can also be used for evaluation.

  FIG. 5 is a diagram illustrating an example of an envelope obtained by curve fitting in the evaluation unit 30. FIG. 5 shows the envelopes of the tires A and B at two traveling speeds where the rolling speed is 40 km / hour and 60 km / hour. The tires A and B have different tire shapes. It can be seen that the maximum height H of the tire B is lower than that of the tire A at any travel speed. Thus, the water splash characteristic can be efficiently and quantitatively evaluated using the envelope obtained by curve fitting.

The evaluation device 10, since use particles model P _M, the evaluation of water splash characteristics, using the density distribution of the particle model P _M at the position where the plurality of particles model P _M falls into the plane of the road model R _M It may be done. For example, determine the density distribution of the particle model P _M falling on the road surface model R _M at each position in the Y direction, it is also possible to evaluate the water splash property by the density distribution. For example, the Y direction position where the density exceeds a predetermined value is used as the evaluation index.

The evaluation device 10 is a device that exhibits the above functions by causing a computer to execute. The following program is stored in the memory 16 of such a computer, and this program is called as needed to function as the evaluation device 10.
That is, the memory 16 stores a program that causes the computer to evaluate the inclusion jumping characteristic of the tire when the tire passes over the inclusion such as a water film provided on the road surface. This program
A tire model T _M that reproduces a tire, a road surface model R _M that reproduces a road surface, and a water film model S _M that includes a plurality of particle models P _M that reproduce a water film provided on the road surface in a separable manner. The steps the computer creates,
A procedure for causing the computer to scatter the particle model P _M by rolling the tire model T _M on the road surface model R _M provided with the water film model S _M ;
A procedure in which the computer projects the scattered particle model P _M onto a plane perpendicular to the plane of the road surface model R _M ;
The computer has a procedure for evaluating the water splash characteristics of the tire using the projection image of the particle model P _M projected on the plane.

(Evaluation method for water splash characteristics of tires)
FIG. 6 is a flowchart illustrating an example of a flow of a method for evaluating the water splash characteristics of a tire.
First, an input is received from an operator through an input operation system 20, and various conditions including conditions for creating each model and running conditions for tire rolling simulation are set based on this input. The set condition is stored in the memory 16.

Next, the model creation unit 24 sets the water film model S in which the tire model T _M , the road surface model R _M , and the particle model P _M are arranged at regular intervals according to the model creation conditions called from the memory 16. _M is created (step S10).
The tire model _TM is, for example, a three-dimensional finite element model, and a material constant is given to each element.
The road surface model _RM is a rigid body model or a finite element model made of finite elements. A material constant is given to this finite element model.
In the water film model S _M, the particle model P _M is formed in layers as shown in FIG. The water film model S _M preferably has at least two particle models P _M from the viewpoint of obtaining an accurate evaluation of water splash characteristics. In addition, by changing the value of a parameter in a formula that will be described later that governs the behavior of the particle model P _M, the inclusion includes any one of snow, sand, mud, and gravel instead of water. The thing can be reproduced.

Next, the simulation calculation unit 26 sets traveling conditions for the tire model T _M , executes a tire rolling simulation, and scatters the particle model P _M (step S20).
The traveling conditions include air pressure, load load, rolling speed, lateral force, camber angle, braking / driving force. These conditions are stored in advance in the memory 16 and are called from the simulation calculation unit 26 and set.
The rolling simulation of the tire model T _M, tire inflation process to the tire model T _M, grounding, and the rolling process is performed.
Pneumatic filling process, each node of the inner peripheral surface facing the tire cavity region of the tire model T _M, given the force corresponding to the set pressure.

In grounding, the tire model T _M is the road surface model R _M, is brought close at a certain interval, the presence or absence of contact between the road surface model R _M is determined. Furthermore, each node receives the force of the tire model T _M from the road surface model R _M when the contact is calculated, until the sum of the calculated force is set applied load, the tire model T _M is the road surface model R Can approach _M.

In the rolling process, by gradually speed up the rolling speed set by the rolling speed 0 to the tire model T _M is applied, creating a tire model T _M rolling at a rolling speed which is set. In this case, each node of the tire model T _M, is rotated by applying forced displacement determined by the predetermined time step size and the rolling speed, the rolling condition is reproduced rolling on the road surface model R _M . In rolling process, the friction coefficient between the road model R _M is applied to each node of the tire model T _M, adhesion to the road surface model R _M of the tire model T _M, the state of slip is reproduced.
Incidentally, when the tire model T _M passes over the water film model S _M, the interaction between the particle model P _M and the tire model T _M will be described later. The particle model P _M is scattered by the interaction between the particle model P _M and the tire model T _M.

Next, the simulation result processing unit 28 projects the scattered particle model P _M on a plane perpendicular to the plane of the road surface model R _M for each set time interval (step S30). The plane through the center of the tire model T _M, it is a plane parallel to the tire width direction is preferable in terms of accurately evaluating the water splash property.

Next, the evaluation unit 30 from the projection image on the plane of the particle model P _M scattered, as shown in FIG. 4 (a), (b) , to form the envelope of the projection image of the particle model P _M (Step S40). Specifically, the evaluation unit 30, as shown in FIG. 4 (a), by plotting the highest position of the projected image of the particle model P _M at each position in the Y direction, using the point that the plot, FIG. 4 (b), a curve fit by a curve represented by a polynomial, for example, a · (x−x ₀ ) ^b + c (a, b, c, x ₀ are constants and b is a natural number) is performed. Do. Thus, the evaluation unit 30 creates an envelope of the projection image of the particle model P _M. In addition, since the projected image on the plane of the scattering particle model P _M is obtained in time series for each set time interval, the evaluation unit 30 is the largest of the envelopes of the projected image of the particle model P _M. An envelope is selected for evaluation of water splash characteristics.

Next, the evaluation unit 30 extracts at least one of the selected envelope parameters, that is, the maximum height H, the intersection position L, and the emission angle Φ as an evaluation parameter for water splash characteristics (step S50). ).
The evaluation of water splash characteristics is performed by using superiority or inferiority or ranking between tire models having different specifications, using the extracted envelope parameter values. Alternatively, the evaluation of the water splash characteristic may be performed by determining whether or not the value of the extracted envelope parameter is included in the predetermined allowable range of the evaluation parameter.

When creating the tire model T _M , the road surface model R _M, and the water film model S _M , the evaluation apparatus 10 creates a vehicle model that reproduces at least the wheel house of the vehicle on which the tire is mounted, and generates the particle model P _M. when to scatter, it is also possible to attach a tire model T _M on the vehicle model. In this case, scattered particles model P _M is also possible to examine the state of collision to the vehicle model.

In order to evaluate the water splash characteristics of the tire model T _M accurately, efficiently, and quantitatively, it is preferable to use the following particle model P _M.
Hereinafter, the particle model P _M and the interaction between the particle model P _M and the tire model T _M will be described.

(Particle model)
In general, a model created by the finite element method represents the distribution of physical quantities such as stress and strain of a finite element using physical quantities of nodes constituting the finite element, as shown in FIG. On the other hand, as shown in FIG. 7 (b), the fluid element (the hatched portion in FIG. 7 (b)) is moved in the space lattice fixed in the space, and the physical quantity in the region partitioned by the space lattice is used. There is also a way to express a water film model. However, as shown in FIG. 7C, the water film model S _M of the present embodiment is composed of a plurality of particle models P _M , and the particle models P _M are arranged in an isotropic manner at regular intervals. From this, the particle model P _M is moved under the movement regulation condition described later, and is expressed using the speed, density, and total energy amount of the particle model P _M. Therefore, unlike the conventional method, no spatial grid or finite element is provided. Moreover, since the particle model P _M moves freely under the particle model movement regulation conditions, even if the behavior accompanied by large movement and scattering is expressed based on Lagrangian described in the coordinate system fixed to the fluid, numerical calculation You can get the appropriate solution above.

The calculation and prediction of physical behavior using such a particle model P _M is generally known as the SPH (Smoothed Particle Hydrodynamics) method in the numerical analysis method of compressible flow in the field of astronomy (Monaghan, JJ, Smoothed Particle Hydrodynamics, Annu. Rev. Astron. Astrophys. Vol. 30, 1992, pp 543-574). In the present embodiment, the interaction between the tire model T _M and the particle model P _M is calculated using a water film model S _M composed of a plurality of particle models P _M arranged in an isotropic manner at regular intervals. The movement including the scattering of the particle model P _M is calculated.

Table behavior of fluids expressed using a particle model P _M, using as known, continuity equation of fluid represented by the following formula (1) to (3), as the governing equation of the equations of the motion equation and the energy equation Is done.



Here, ρ is the density of the fluid, U is the velocity of the fluid, σ is the stress tensor of the fluid, the quantity is in the relationship between the pressure p of the fluid and σ = −pI (I is the unit tensor), e is per unit volume The total amount of energy.

On the other hand, the distribution f (x) of the physical quantity of interest such as the velocity (flow velocity) of the fluid (where x represents the three-dimensional position coordinate of the space) is a predetermined position coordinate x ′ as shown in the following equation (4). It can be approximated by the distribution <f (x)> of the approximate physical quantity obtained using the physical quantity of interest f (x ′) and the kernel function W (| x−x ′ |, h) (h is a parameter).

Therefore, the 'attention physical quantity f (x in') coordinates x of the particle model P _M at this time, the target physical quantity f _j (j having particle model P _j with one or more N a natural number less than or equal, N is the particle model P and the total number) and can be represented by discrete as the following equation (5) using the density [rho _j particle model P _M, and a mass m _j particle model P _M. For example, the fluid velocity U (x) can be expressed by the following equation (6).

Similarly, the fluid density ρ (x) and the total energy amount e (x) can also be expressed using the physical quantity f (x) of interest in the above equation (5). That is, the fluid velocity U, density ρ, and total energy amount e in the above formulas (1) to (3) are approximated using the velocity U _j and density ρ _j of the particle model P _M <U (x)>. , Approximate density <ρ (x)>, approximate total energy <e (x)>. Therefore, substituting approximate velocity <U (x)>, approximate density <ρ (x)>, and approximate total energy <e (x)> into U, ρ, and e in the above equations (1) to (3). The following formulas (7) to (9) can be obtained. i indicates the number of the particle model of interest among the plurality of particle models P _M. Hereinafter, the particle model to be noted is P _i .



Here, ▽ W _ij represents the following formula (10).

In addition, ▽ represents spatial differentiation. In addition, π _ij represents artificial viscosity, suppresses the generation of numerical vibration solutions in the deformation calculation described later, and does not slip through each other when different particle models P _M collide with each other. Are set in advance.

Thus, the equations (7) to (9) defined by approximating the distribution f (x) of the physical quantity of interest such as the velocity U, the density ρ, and the total energy amount e using the physical quantity f _j of the particle model P. ) Is created. In the present embodiment, the particle model P _M does not have to include all of the equations (7) to (9), and the equation (9) is included as a particle model movement defining condition that defines the movement of the particle model P _M. it is in the water film model S _M may be. In the following, description will be made based on a water film model S _M provided with Equation (8) as a particle model movement regulation condition.

Here, the kernel function W (| x−x ′ |, h) is not particularly limited. However, as | x−x ′ | / h = ν, for example, as shown in the following formula (11), a cubic function A B-spline function may be used.

When the cubic B-spline function shown in Expression (11) is used as the kernel function W (| x−x ′ |, h), when ν is 2 or more, the kernel function W (| x−x ′ |, h ) Becomes 0 and becomes a positive value when ν is less than 2, as shown in equations (7) to (9), the behavior of the particle model P _i of interest is located within the range where ν is less than 2. It depends on the particle model P _j to be used. That is, as shown in FIG. 8 (a), the particle model P included in a range of a sphere having a radius 2h centered on the particle model P _i (this range is referred to as a neighboring region R _i corresponding to the particle model P _i ). _j defines the movement of the particle model P _i . This radius 2h is also called a smoothing length. Further, the water film model S _M, as shown in FIG. 8 (b), so as to cover the entire area of the water film model S _M, particle model P region near around each of the _i R _i particle model P _i It is determined corresponding to each of. Moreover, it determined by approximating with attention physical quantity of speed U _j or the like having a distribution of attention physical quantity of speed U and the like of the neighboring region R _i particle model P _j included in the neighboring region R _i, particles Equations (Expressions (7) to (9)) relating to the speed U _{i and the} like that define the movement of the model P _i are provided. A water film is reproduced by such a water film model S _M composed of a plurality of particle models P _M.

(Calculation of interaction between tire model and particle model)
Next, the calculation of the interaction between the tire model T _M and the plurality of particle models P _M will be described.
Specifically, the deformation calculation of the tire model T _M and the movement calculation of the plurality of particle models P _M are performed in consideration of the interaction between the models. These calculations, that is, the deformation calculation of the tire model T _M , the deformation calculation of the particle model P _M , and the calculation of the interaction between the tire model T _M and the plurality of particle models P are performed at each time step at predetermined time intervals. It is performed sequentially. Specifically, the physical quantity such as stress or speed and acceleration of each element of the tire model T _M immediately before the tire model T _M starts passing over the water film model S _M is taken out, the physical quantity as an initial condition, A speed is given to the particle model P _M.

FIG. 8 is a flowchart showing a processing flow of a main part of the rolling simulation.
First, in the time step of time T ⁽ⁿ⁾ when the position of each particle model P _M is in a known state, the setting of the smoothing length of each particle model P _M , that is, the range of the sphere having the radius 2h (neighboring region) R _i ) is set for each of the particle models P _i (step S100), and the adjacent particle models P _j included in the neighboring region R _i are searched for (step S102). Thereafter, to calculate the density [rho _i in the particle model P _i on the basis of the number of particles model P _j adjacent, is calculated by using the position and velocity of the strain and strain rate of particles model P _j in the neighboring region R _i (Step S104). Thereafter, determining the pressure applied to the particle model P _i by using the condition of the state equation and the isothermal change governing the water from the density [rho _i in the particle model P _i. Specifically, the pressure applied to the particle model P _i is calculated in proportion to the density. Further, the kinetic energy and strain energy of each of the particle models P _i are calculated (step S106). If the pressure in the calculated particle model P _i is p, there is a relationship between σ _i in equation (8) and σ _i = −pI (I is a unit tensor), and a particle model P _{M to be} described later using this relationship. Used in the calculation of movement. Furthermore, when considering the viscosity in the calculation of the movement of the particles model P _M, viscosity stress is obtained from the strain rate in the neighboring region R _i in the particle model P _i, is added to the sigma _i in equation (8). Thereby, the behavior of inclusions of snow, sand, mud, and gravel can be reproduced. Note that when the neighboring region R _i does not include the particle model P _j at all, m _j in the equation (8) is 0 and the right side is 0.

On the other hand, the strain in each finite element of the tire model T _{M at} the same time T ⁽ⁿ⁾ as the particle model P _M is calculated (step S108), and further the stress, kinetic energy and strain energy in each finite element of the tire model T _M. Is calculated (step S110). Next, it is determined whether or not the time T ⁽ⁿ⁾ has passed a predetermined elapsed time (step S112). If it is determined that the predetermined elapsed time has not elapsed, the time T ^{(n) ) At} time T ^{(n + 1)} , the calculation of the interaction between the tire model T _M and the particle model P _M (step S114) and the movement of the particle model P _M (deformation calculation of the water film model S _M ) ( and step S116), deformation calculation of the tire model T _M (step S118) is performed. If the time T ⁽ⁿ⁾ has passed a predetermined elapsed time in step S112, the calculation of the interaction ends. In this way, steps S100 to 110 and steps S114 to 118 are repeated until a predetermined elapsed time.

10A to 10C, the particle model P _M included in the neighboring region R _i in the particle model P ₂ is the particle models P ₁ and P ₃ , and the particle model P ₂ is in contact with the tire model T _M. Thus, an example of moving at a speed U ₂ is shown. Explaining along this example, from the state (FIG. 10A) immediately before the tire model T _M that moves at a speed u at the time step of time T ⁽¹⁾ contacts the particle model P ₂ , the time At a time step of T ⁽²⁾ , the particle model P ₂ is temporarily changed to a state (FIG. 10B) positioned inside the tire model T _M , and further, at a time step of time T ⁽³⁾ , the particle model P _{2 is changed.} so it changed to a state (FIG. 10 (c)) which moves in a position outside the tire model T _M, the calculation of the interaction (step S114), the mobile computing particle model P (step S116), the tire Model deformation calculation (step S118) is performed.

First, steps S100 to S106 are performed on the particle model P _{M at} the time step of time T ⁽²⁾ , and steps S108 and S110 are performed on the tire model T _M. If the time T ⁽²⁾ is determined in step S112 When it is time has not yet passed a predetermined time elapsed, when shifting from the state of the time steps in the time T ⁽²⁾ to the time step of the state at time T ⁽³⁾ The interaction between the tire model T _M and the particle model P _M is calculated (step S114). In the calculation of the interaction, first, whether the particle model P _M has entered the inside of the tire model T _M is determined for each particle model P _M. If the particle model P ₂ is determined to have entered the inside of the tire model T _M, so as to be positioned outside of the tire model T _M at time step of the particle model P ₂ in this state the time T ^(3), 10 As shown in (b), an interaction energy term corresponding to the amount of the particle model P ₂ entering the tire model T _M is calculated, and this term is added to the equation (8) relating to the particle model P ₂ .

Thereafter, Expression (8) relating to the particle model P ₂ to which the interaction energy term is added and Expression (8) relating to the particle models P ₁ and P ₃ to which the interaction energy term is not added are used by a differential scheme described later. Solve, find the acceleration of the particle models P _{1 to} P ₃ , and calculate the velocity and position. Thereby, the movement of the particle model P at the time step at time T ⁽²⁾ is calculated (step S116), and the movement state of the particle model P _M at the time step at time T ⁽³⁾ is calculated. On the other hand, since an interaction energy term is given to the tire model T _M as a reaction of the interaction energy term given to the particle model P ₂ , the time T ⁽²⁾ at which this interaction energy term was given. The deformation calculation of the tire model T _M at the time step is performed (step S118), and the deformation state of the tire model T _M at the time step of time T ⁽³⁾ is calculated. The interaction energy term is the collision pressure that the particle model P ₂ applies to the tire model T _M. After the processing in steps S100 to S106 is performed on the particle model P _{M at} the time step of time T ⁽³⁾ calculated in this way, and the processing in steps S108 and S110 is performed on the tire model T _M. In step 112, a determination is made. In this manner, the calculation of the interaction between the tire model T _M and the particle model P _M , the calculation of the movement of the particle model P _M , and the deformation calculation of the tire model T _M are performed for each time step until a predetermined elapsed time elapses. Repeatedly, when the determination result in step S112 is affirmative, the calculation of the interaction ends.
In the present embodiment, since calculating the behavior of scattering of particles model P _M, even after the calculation of the interaction is completed, the calculation of the movement of the particles model P _M is continued.

Note that the time differential equation in equation (8) is solved using a solution using a time integration scheme based on the center difference, and the velocity U _i is calculated. That is, a differential scheme such as the following equation (12) is taken, and the following equation (13) is obtained from U _i ^{n + 1/2} (an intermediate speed between the n-th time step and the (n + 1) -th time step). Using this, the displacement amount d _i ^{n + 1} of the particle model P _i at the (n + 1) th time step is obtained. Further, the displacement d _i ^{n + 1} is added to the position coordinates x _i ⁰ in the initial state using the following equation (14), and the position coordinates x _i ^{n + 1} of the particle model P _i in the (n + 1) th time step. Is required. Δt ⁿ is a time interval of time steps in the nth time step. When the time steps are steps at regular time intervals, Δt ⁿ is all constant regardless of n. Thus, the position coordinates of each particle model P _M is obtained.

Incidentally, giving to determine whether particles model P _i that enters the tire model T _M at the next time step is present, the interaction energy terms against ingress particles model P _i in equation (8), in addition to the above-described method of moving the tire model T _M outside the particle model P _i in the next time step, as entry into the tire model T _M of the particle model P _i does not occur, the movement of the particle model P _i when calculating, adding the surface shape of the tire model T _M as a constraint condition in undetermined constant method of Lagrange, it may be used a method of determining the undetermined constants. In this case, the undetermined constant obtained as a numerical value is the collision pressure of the particle model P _M that prevents the particle model P _i from entering the tire model T _M.

As described above, the deformation calculation of the tire model T _M and the movement of the particle model P _M are calculated. In the present embodiment, it is given a rotational speed corresponding to the translational velocity and the translational speed of the tire model T _M, the tire model T _M will not slip relative to the road surface model R _M (the slip ratio 0) tumbling condition Although the calculation is performed, a state where the slip rate of the tire model T _M is not 0 may be calculated.

In addition to the SPH method, the particle method includes an RKPM method (Reproducing Kernel Particle Method), a finite particle method (Finite Particle Method), and an EFGM (Element Free Galerkin Method) method.
Alternatively, instead of using the particle model by particle method, a fluid such as granules or water modeled by a plurality of particles model P _M, and coupling between a plurality of particles model P _M simple spring and dashpot or the like or particles A method (DEM: Discrete Element Method) that expresses contact between the models P _M using frictional force can also be applied to the particle model P _M.

Thus, in the evaluation device 10 and the evaluation method of this embodiment, a tire model T _M when a to scatter the particles model P _M reproduces the water, road model R _M particle model P in a plane perpendicular to the plane of the _{Since M} is projected and the projected image of the projected particle model P _M is used, the water splash characteristics of the tire can be evaluated efficiently and quantitatively.

  As described above, the method for evaluating the inclusion jumping characteristic of the tire, the evaluation device for the inclusion jumping characteristic of the tire, and the program according to the present invention have been described in detail. Of course, various improvements and changes may be made within the range not to be performed.

10 Evaluation device 12 CPU
14 Bus 16 Memory 18 Input / output interface unit 20 Input operation system 22 Output device 24 Model creation unit 26 Simulation operation unit 28 Simulation result processing unit 30 Evaluation unit 36 Processing module group

Claims (9)

A method for evaluating the jumping characteristics of a tire inclusion when the tire passes over an inclusion provided on a road surface,
Creating a tire model that reproduces a tire, a road surface model that reproduces a road surface, and an inclusion model that reproduces inclusions provided on the road surface and includes a plurality of minute models that are separable from each other;
Scattering the micro model by rolling the tire model on the road surface model provided with the inclusion model;
Projecting the scattered micro model on a plane perpendicular to the plane of the road surface model at set time intervals ;
Using the time-series projection image of the micro model projected on the plane, an envelope of the projection image of the micro model scattered is obtained for each projection image, and the envelope obtained for each projection image A method for evaluating the jumping characteristic of a tire inclusion using the envelope having the largest shape of the envelope , and the step of evaluating the jumping characteristic of the tire inclusion. The envelope is a curve represented by a polynomial, and the polynomial is a · (x−x ₀ ) ^b + c (a, b, c, x ₀ are constants, and b is a natural number), Item 2. The evaluation method according to Item 1 . The evaluation of the inclusion using the projection image is performed by measuring the maximum height of the envelope from the plane of the road model, the intersection position of the envelope with the plane of the road model, and the tire of the envelope The evaluation method according to claim 1, wherein the evaluation method is performed using at least one of emission angles from the model. The micro model includes a plurality of particles model using particle method, the evaluation method according to any one of claims 1-3. The evaluation method according to claim 4 , wherein the evaluation of the jump property of the inclusion using the projection image is performed using a density distribution of the particle model at a position where a plurality of particle models fall on the surface of the road surface model. . Furthermore, when creating the tire model, the road surface model and the inclusion model, create a vehicle model that reproduces at least the wheel house of the vehicle on which the tire is mounted,
Time of scattering the said micro model, by mounting the tire model on the vehicle model, is scattered the micro model, the evaluation method according to any one of claims 1-5. The evaluation method according to any one of claims 1 to 6 , wherein the inclusion includes any one of water, snow, sand, mud, and gravel. An apparatus for evaluating the jumping characteristics of tire inclusions when the tire passes over inclusions provided on a road surface,
A model creation unit that creates a tire model that reproduces a tire, a road surface model that reproduces a road surface, and an inclusion model that reproduces inclusions provided on the road surface and includes a plurality of minute models that are separable from each other; ,
A simulation calculation unit that scatters the minute model by rolling the tire model on the road surface model provided with the inclusion model;
A simulation result processing unit that projects the scattered micro model on a plane perpendicular to the plane of the road surface model for each set time interval ;
Using the time-series projection image of the micro model projected on the plane, an envelope of the projection image of the micro model scattered is obtained for each projection image, and the envelope obtained for each projection image And an evaluation unit that evaluates the jumping characteristics of the inclusions of the tire using the envelope having the largest shape of the envelope . A program for causing a computer to evaluate the inclusion jumping characteristic of a tire when the tire passes over inclusions provided on a road surface,
A procedure for a computer to create a tire model that reproduces a tire, a road surface model that reproduces a road surface, and an inclusion model that reproduces inclusions provided on the road surface and includes a plurality of minute models that can be separated from each other. ,
A step of causing the computer to scatter the minute model of the inclusion model by rolling the tire model on the road surface model provided with the inclusion model;
The computer projects the scattered micro model on a plane perpendicular to the plane of the road surface model at set time intervals , and
Using the time-series projection image of the micro model projected on the plane, an envelope of the projection image of the micro model scattered is obtained for each projection image, and the envelope obtained for each projection image The computer has a procedure for evaluating the jump characteristics of the inclusions of the tire using the envelope having the largest shape of the envelope .