JP2010287042A - Simulation method, device and program for rotating body - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a simulation method, device, program and recording medium for a rotating body, capable of analyzing a deformation behavior of a microstructure, such as a tire compound, of a rotating body from time (or rotation angle) history information on macro model deformation including a dynamic rolling condition of the rotating body, such as a tire. <P>SOLUTION: A rotating body model for simulating a rotating body using a plurality of finite elements is generated; one of the elements located on a meridional cross section of the rotating body is selected as a target element; a simulation for deformation analysis is performed using a finite element method, with a preset simulation condition given; change information on a first physical quantity affecting the finite element is calculated and converted into time change information on the first physical quantity; a micro model for simulating a microstructure of the rotating body is generated; time history information on a second physical quantity generated in the micro model is calculated by performing a time-dependent analysis simulation on the micro model, with the time change information on the first physical quantity given, as a boundary condition, to the micro model; and time change information on a third physical quantity is calculated, or displayed, from the time history information. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention is a rotating body simulation method, apparatus and program for analyzing the behavior of a rotating body modeled by elements capable of numerical analysis, and its micro model, and a recording medium in which the program is described. The present invention relates to a simulation method, an apparatus and a program for efficiently analyzing a micro behavior generated in a compound of a tire or a compound rubber (heterogeneous material) when rolling, and a recording medium on which the program is described.

  A compound in which granular fillers such as carbon black and silica and various elastomers (rubber components) are inhomogeneously blended, such as compound rubber (hereinafter referred to as a compound) of tire treads, which are tire components, is reinforced with granular fillers. In order to efficiently analyze the behavior of the rubber, a simulation using a discretized model is used as an effective means.

  In the simulation using the conventional discretized model, the physical property value of the tire constituent member is based on the physical property values of a plurality of material phases arranged on the tire constituent member using a microscale model reproducing the representative region of the tire constituent member. And predicting and calculating the behavior of the tire under a predetermined condition based on the predicted physical property value of the tire constituent member using a macro scale model reproducing the tire. Conversely, the load conditions and road surface contact conditions acting on the tires are determined from the reproduction conditions that reproduce the tire behavior, and the load conditions and road surface contact conditions are assigned to the macroscale model to predict and calculate the tire behavior, Based on the prediction calculation result, a physical quantity acting on the tire constituent member is predicted and calculated using a microscale model (see, for example, Patent Document 1).

  In addition, a simulation calculation is performed using a discretized model (macroscale model) of a structure containing a heterogeneous material, and the microstructure is calculated from the result of the strain or strain rate of the representative point of the arrangement portion of the heterogeneous material. In some cases, the displacement or displacement speed of the boundary region in the discretized model (microscale model) of the inhomogeneous material that reproduces the above is determined, and this displacement or displacement speed is given as the boundary condition of the microscale model for microscale simulation. Yes (see, for example, Patent Document 2).

  Furthermore, uniaxial tensile deformation is applied in two directions of the micro constitutive model, and a two-scale coupled analysis is performed using the macro constitutive model as a single element. A single-scale macro analysis is performed using a macro constitutive model with identified parameters, and a single-scale micro analysis is performed using the resulting macro deformation state history at each evaluation point as input data. There are some (see, for example, Non-Patent Document 1).

JP 2006-18454 A Japanese Patent No. 4093994

Watanabe, et al., “Micro-macro disjoint approximate solution of two-variable boundary value problem in nonlinear homogenization theory”, Applied Mechanics, Japan Society of Civil Engineers, August 2005, Vol. 8, p. 277-285

  However, in the multi-scale simulation of the tire using the discretized model disclosed in Patent Documents 1 and 2, the result of the simulation by the macro-scale model that reproduces the tire is used, and the micro-scale model that reproduces the tire microstructure is used. Simulations are used to calculate physical quantities acting on microstructured tire components and heterogeneous materials. In the simulation using a macro scale model, load conditions, road surface contact conditions such as friction coefficient or rolling speed are used. The vehicle's running simulation is used to determine the tire behavior, but the deformation time history (tire rolling state, especially dynamic rolling state) in the tire macroscale model is not applied to the microscale model. So the micro structure of the tire compound It deformation behavior that can not be simulated, there is a problem that can not be analyzed micro behavior of tire compounds.

  Further, as described above, Non-Patent Document 1 discloses a procedure for non-coupled bidirectional multi-scale simulation, and discloses a method for performing a micro analysis by applying an analysis result of a macro configuration model to a micro configuration model. However, there has been a problem that it is impossible to analyze the micro model when the rotating body rotates by inputting the deformation history in the circumferential direction of the rotating body such as a tire.

  An object of the present invention is to solve the above-mentioned problems of the prior art, and from a time history (or rotational angle history) of a macro model including a dynamic rolling state of a rotating body such as a tire, to a micro of a rotating body such as a tire compound. A simulation method, apparatus, and program for a rotating body capable of simulating the deformation behavior of a structure, particularly a microstructure of a heterogeneous material, and capable of efficiently analyzing the micro-deformation behavior, and a recording medium describing the program are provided. There is.

  In the specification of Japanese Patent Application No. 2008-114037 filed earlier, the present inventor creates a rotating body model and a representative model that reproduce a rotating body such as a tire and a part thereof using a finite element, The rotating body rotates using the first physical information based on the deformation of the element of interest, which is one finite element on the circumference of the rotating body model obtained by performing simulation of the stationary state of the rotating body using static analysis. Is converted into time change information of the displacement gradient, and after performing a dynamic analysis simulation using the time change information obtained by this conversion, the time of the second physical quantity such as viscoelastic loss energy acting on the element of interest We propose a method of simulating a rotating body that repeatedly calculates history information while changing the element of interest, and accumulates time history information of the second physical quantity of each element. This method is capable of efficiently computing the rolling resistance of the rolling state of the tire from the circumferential deformation history of the tire contact analysis.

  However, the method described in this specification of the prior application uses the time history or rotational angle history (including the tire rolling state) of the deformation of the macro model as a representative model for obtaining the second physical quantity such as viscoelastic loss energy. It is applied to calculate the time history and calculate rolling resistance of tires etc., but analysis of rotating bodies such as tires is only static grounding, and representative models also rotate tires etc. Since it is not a micro model that reproduces the microstructure of the body itself, it is not possible to analyze the deformation behavior of the microstructure by applying the time history or rotation angle history of the deformation of the macro model to the micro model, especially tire compounds, etc. Since it is not a micro model that reproduces the microstructure of the heterogeneous material, the deformation behavior of the microstructure cannot be analyzed.

  Therefore, in order to solve the above problems and achieve the above object, the present inventor uses a finite element method to analyze the micro behavior of a microstructure such as a compound in a rolling state of a rotating body such as a tire. In order to provide a method, in a rotating body such as a tire, a rotating body model such as a tire model and a micro model of the microstructure, particularly a micro model such as a tire compound (heterogeneous material) are prepared. By extracting the finite element deformation history from the ground contact analysis and rolling analysis of the rotating body model, converting the deformation history into a time history (rotation angle history) and analyzing the micro model as a micro model boundary condition, the tire Dynamic change process of micro strain and stress generated in the microstructure such as compound during rolling of rotating body such as compound, etc. Simulating the micro behavior of black structures, and found that it is possible to efficiently analyze, and have reached the present invention.

  That is, the rotating body simulation method according to the first aspect of the present invention is a rotating body simulation method for analyzing the behavior of a rotating body modeled by elements capable of numerical analysis and the micro model thereof, The first step of creating a rotating body model that reproduces using a plurality of finite elements, and the meridian of the rotating body model cut at a plane including the rotation axis of the rotating body model created in the first step A second step of selecting one of the finite elements located on the cross section as the element of interest and a preset simulation condition are applied to at least a part of the circumference of the rotating body model, and the finite element method is used. A third step of simulating deformation analysis of the rotating body and calculating change information of a first physical quantity acting on a finite element of the rotating body model; The change information of the first physical quantity calculated by the third step that acts on the element of interest of the rotating body model selected in the second step is the time or rotation angle of the first physical quantity. A fourth step of extracting by converting to change information, a fifth step of creating a micro model that reproduces the microstructure that is a part of the rotating body using a plurality of finite elements, and the fourth step. The time of the first physical quantity or the rotation angle change information extracted in step 5 is applied to the micro model created in the fifth step as a boundary condition, and the time using the finite element method is applied to the micro model. A sixth step of calculating time or rotation angle history information of the second physical quantity generated in the micro model by performing a simulation of dependence analysis; and the sixth step Calculating, displaying or calculating the time or rotation angle change information of the third physical quantity of the micro model from the time or rotation angle history information of the second physical quantity of the micro model calculated by And a seventh step of displaying.

Here, in the fourth step, it is preferable that the change information of the first physical quantity to be extracted is created from the rotating body circumferential direction information of the finite element along the trajectory when the rotating body makes one round. .
The boundary condition given to the micro model in the simulation of the time-dependent analysis performed on the micro model in the sixth step is preferably a periodic boundary condition that allows relative displacement.
In the simulation of the time-dependent analysis performed on the micro model in the sixth step, it is preferable that a material property parameter given to the micro model depends on at least one of time, deformation, and field.

The micro model is preferably a micro structure of a heterogeneous material in which a plurality of material phases having different material properties are dispersedly arranged using the plurality of finite elements.
The micro model is preferably a model of a compound rubber which is a heterogeneous composite material in which a polymer material is filled with at least a reinforcing agent.
The micro model is preferably a model of a rubber-based composite material including a reinforcing material.
In the simulation of deformation analysis of the rotating body performed on the rotating body model in the third step, the material property parameter given to the rotating body model is the micro model when the micro model is deformed. Is preferably obtained from the second physical quantity of deformation occurring in

The rotating body is a tire, and the simulation of the deformation analysis of the rotating body performed on the rotating body model in the third step preferably includes a state in which at least the tire and the road surface are in contact with each other. .
Further, the simulation method of the rotating body further includes an eighth step of defining a circumferential path in which the element of interest of the rotating body model makes one round in the circumferential direction of the rotating body model,
The third step calculates change information of the first physical quantity along the circumferential path that acts on the finite element of the rotating body model, and the fourth step acts on the element of interest. The change information of the first physical quantity along the circumferential path is converted into time or rotation angle change information of the first physical quantity in accordance with a rotation period when the rotating body rotates, In the step 6, it is preferable to calculate time or rotation angle history information of a second physical quantity generated in the micro model when the element of interest makes a round along the circumferential path.

  The second physical quantity of the micro model for which the time or rotation angle history information is calculated in the sixth step is at least one of a strain, a displacement gradient, and a deformation gradient. In the seventh step, The third physical quantity of the micro model for which the time or rotation angle history information is calculated includes strain energy, viscoelastic energy loss, strain amplitude value, stress amplitude value, and physical quantity of these physical quantities generated in the micro model. Preferably, at least one of each statistic and each histogram of these physical quantities.

In order to achieve the above object, a rotating body simulation apparatus according to a second aspect of the present invention includes a rotating body modeled with a finite element capable of numerical analysis and a rotating body for analyzing the behavior of the micro model. A simulation apparatus, comprising: a rotating body model creating means for creating a rotating body model that reproduces the rotating body using a plurality of finite elements; and a rotation axis of the rotating body model created in the first step. Attention element selection means for selecting one of the finite elements located on the meridional section of the rotating body model cut along a plane as an attention element, and at least a part of the circumference of the rotating body model with preset simulation conditions And performing a simulation of deformation analysis of the rotating body using the finite element method, and changing the first physical quantity acting on the finite element of the rotating body model. A rotating body model simulation means for calculating information,
The change information of the first physical quantity calculated by the third step that acts on the element of interest of the rotating body model selected in the second step is the time or rotation angle of the first physical quantity. In the fourth step, a time conversion unit that converts and extracts change information, a micro model generation unit that generates a micro model that reproduces a microstructure that is a part of the rotating body using a plurality of finite elements, and the fourth step The extracted time or rotation angle information of the first physical quantity is given as a boundary condition to the micro model created in the fifth step, and the micro model is time-dependent using a finite element method. The simulation of the micro model simulation for calculating the time or rotation angle history information of the second physical quantity generated in the micro model by performing the simulation of the analysis of And calculating or displaying the time or rotation angle change information of the third physical quantity of the micro model from the time or rotation angle history information of the second physical quantity of the micro model calculated by the sixth step. Or a micro behavior analysis means for calculating and displaying.

In order to achieve the above object, a third aspect of the present invention provides a rotating body simulation program for causing a computer to execute each step of the rotating body simulation method of the first aspect of the present invention. To do.
Furthermore, in order to achieve the above object, according to a fourth aspect of the present invention, there is provided a program for causing a computer to execute each step of the simulation method for a rotating body according to the first aspect of the present invention, that is, the first aspect of the present invention. The present invention provides a computer-readable recording medium in which a rotating body simulation program according to the third aspect is described.

According to the simulation method, apparatus and program for a rotating body of the present invention and the recording medium in which the program is described, a simulation is performed on a rotating body model (macro model) created so as to reproduce a rotating body such as a tire. The change information of the first physical quantity of one finite element which is the calculated element of interest on the circumference, for example, the change information in the circumferential direction of the physical quantity of deformation such as strain, displacement gradient, deformation gradient, etc. The time-dependent analysis simulation is performed for the micro model created to reproduce the microstructure of the rotating body by using the physical condition of 1 as the time or rotation angle change information and extracting it. Time or rotation angle change information of a second physical quantity that occurs when the circle makes a round, for example, a physical quantity such as strain, stress, strain energy, etc. By calculating the time or rotation angle change information of the second physical quantity obtained, the time or rotation angle change information of the third physical quantity, for example, strain energy, viscoelastic energy loss, strain or stress generated in the micro model. Since it is possible to calculate and display information such as amplitude values, statistical values such as the average value and standard deviation of these physical quantities, and histograms of these physical quantities, the micro area of the rotating body ( It is possible to simulate temporal changes (rotational angle changes) in the deformation state occurring in the microstructure), calculate time or rotational angle changes of various physical quantities in the micro region, and efficiently analyze the microstructure micro behavior. .
Thus, according to the present invention, it is possible to analyze the temporal change of the deformation state of the micro area of the rotating body. That is, according to the present invention, from the time history (or rotational angle history) of the deformation of the macro model including the dynamic rolling state of the rotating body such as the tire, the microstructure of the rotating body such as the tire compound, particularly the heterogeneous material. The dynamic change process of the micro strain and stress generated in the micro structure, that is, the micro behavior of the micro structure of the compound or the like can be simulated and analyzed efficiently.

It is a block diagram which shows functionally the structure of one Embodiment of the simulation apparatus which implements the simulation method of the rotary body of this invention. It is a flowchart explaining an example of the flow of the simulation method of the rotary body of this invention. (A) is sectional drawing of an example of the two-dimensional tire model created so that the tire used for this invention may be reproduced, (b) is a 1-round rotation with respect to the rotating shaft of the two-dimensional model of (a). It is a perspective view which illustrates an example of the rigid road surface model created to reproduce the 3D tire model created by making it reproduce and a road surface. (A) and (b) are examples of a micro model created to reproduce the microstructure of the tire, respectively used in the present invention, and in the micro region of the tread rubber compound of the tire modeled in this micro model. It is a perspective view which shows an example of filler distribution. FIG. 4 is a perspective view including an example of a tire model grounded on a rigid road surface model illustrated in FIG. 3B and including a cross section cut along a plane including a rotation axis thereof. FIG. 4 is a perspective view showing an example of a circumferential path along the circumferential direction of the tire when the element of interest in the tread center portion makes one rotation in the circumferential direction of the tire model shown in FIG. It is a graph which shows an example of the time change log | history information of the displacement gradient of the attention element of the tread center part of the tire model shown to Fig.3 (a) and (b). It is a perspective view which shows an example of the predetermined time change process of the dynamic behavior of the micro model which reproduced a part of tread center part of the tire to which the time change history information of the displacement gradient shown in Drawing 7 was given as a boundary condition. It is explanatory drawing which shows an example of the time change log | history of the deformation | transformation state of the micro model which performed the time-dependent simulation when the attention element of the tire model shown to Fig.3 (a) goes around. (A) is a perspective view of an example of the micro model which shows the position of the element which calculates | requires the result of having performed time-dependent simulation, (b) is the time of 11 components of the distortion which generate | occur | produces in the element shown to (a). It is a graph which shows an example of change history information. (A) is a perspective view of an example of a micro model before deformation before performing a simulation of uniaxial extension, and (b) is a perspective view of an example of a micro model after deformation after performing a simulation of uniaxial extension. . This is an SS curve obtained by simulating uniaxial stretching for a micro model.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A rotating body simulation method, apparatus and program according to the present invention and a recording medium on which the program is described will be described in detail below based on preferred embodiments shown in the accompanying drawings.
FIG. 1 is a block diagram functionally showing the configuration of a rotating body simulation apparatus according to the present invention that implements the rotating body simulation method of the present invention. Hereinafter, a tire will be described as a representative example of a rotating body. However, the present invention is not limited to this, and any rotating body using a polymer material such as a rubber material may be used. Of course, the present invention can also be applied to a belt conveyor or the like.

The simulation apparatus 10 shown in the figure uses a tire as a rotating body and performs the tire simulation method of the present invention shown in FIG. 2 to analyze the micro behavior of the rubber compound (heterogeneous material) in the rolling state of the tire. And a simulation calculation processing device (hereinafter referred to as a processing device) 12, an input operation device 14, and an output device including a display 16 and a printer 18.
The processing device 12 is a computer including a CPU 20, a memory 22, an I / O port 24, and a ROM 26 as a hardware configuration, reads application software stored in the memory 22 or the ROM 26, and sets a condition setting unit 30, a tire model. Each of the creation unit 32, the deformation analysis calculation unit 34, the time conversion unit 36, the micro model creation unit 38, the boundary condition setting unit 40, the micro model analysis calculation unit 42, and the micro behavior analysis unit 44 is created and configured. By executing application software including these subroutines on the CPU 20, a tire model and a micro model, which are finite element models, which will be described later, are created, and simulation operations are performed by deformation analysis and micro model analysis using the finite element method. Tires go Analyzing the microscopic behavior of the compound (heterogeneous material).

  The processing device 12 is connected to an input operation system 14 such as a mouse / keyboard and an output device such as a display 16 and a printer 18 through the I / O port 24. Information necessary for the finite element model, conditions necessary for the simulation calculation, and the like are input to the processing device 12 by the input operation system 14 while the operator views the input screen displayed on the display 16. The simulation calculation result by the processing device 12 is displayed as a soft copy on the display 16 or output as a hard copy to the printer 18 by a numerical value, a graph, or a figure. Further, a data supply system such as CAD / CAM (not shown) is connected to the processing device 12 through an I / O port 24.

Hereinafter, each component of the processing device 12 will be described. First, an outline for each component will be described, and various steps of the simulation method performed in each component will be described later by a simulation performed by the simulation device 10. This will be described in detail when explaining the method.
The condition setting unit 30 sets various conditions for tire simulation based on the operator's input while looking at the input screen displayed on the display 16. These conditions include information on the structure and material of a tire model, which is a finite element model created by the tire model creation unit 32, and information on simulation conditions for deformation analysis in the tire model. Further, information on the structure of the micro model and information on the material, which are necessary in advance for use in the micro model creation unit 38 described later, are included. Various conditions set by the condition setting unit 30 are stored in the memory 22. Here, a pneumatic tire is described as a tire, and internal pressure conditions are used as various conditions of the tire. However, the present invention is not limited to this, and is applicable to a ring-shaped tire that is not pneumatic. Of course.

  The tire model creation unit 32 is a part that creates and sets a tire model, which is a finite element model reproducing a tire, as a macro model using various information called from the memory 22. Here, it is preferable that the various conditions set by the condition setting unit 30 are temporarily stored in the memory 22 and then recalled from the memory 22 for use, but may be used directly for tire model creation. The tire model is composed of hexahedral elements, tetrahedral elements, pentahedral elements, and the like. Although the details will be described later, the tire is a rotating body, and the two-dimensional section cut by the meridional plane including the rotation axis is symmetrical with respect to the rotation axis in any section. 3 (a) and 3 (b), a tire model two-dimensional cross section (hereinafter referred to as a two-dimensional tire model) 52 indicated by a meridional section of a tire cut along a meridional plane including a rotation axis of the tire is used as a tire. An example is a tire model 50 that is a three-dimensional finite element model developed by one rotation in the circumferential direction.

Further, the tire model creation unit 32 is based on the information on the attention element set by the condition setting unit 30, and is the target of deformation analysis among the plurality of finite elements of the tire model 52 shown in FIG. Element 54 is selected. Here, the element of interest 54 is an element to be analyzed for the deformation of the tire. The tire model creating unit 32 further includes an element located on the meridional section of the tire model 50 selected as the element of interest 54 (in the illustrated example, near the tread center of the two-dimensional tire model 52) in the circumferential direction of the tire model. It is preferable to define a circumferential path along the circumferential direction of the tire when rotating.
In addition to the tire model 50 that reproduces the tire, the tire model creation unit 32 also creates and sets a rigid road surface model 56 that reproduces the road surface on which the tire contacts and rolls.
In the illustrated example, the condition setting unit 30 and the tire model creation unit 32 are provided separately, but the present invention is not limited to this, and may be an integrated unit.

  The deformation analysis calculation unit 34 is a part that performs deformation analysis such as contact analysis and rolling analysis on the created tire model 50, which will be described in detail later. This is a part for performing a grounding process for grounding the vehicle on the rigid road surface model 56 and a rolling process for rolling on the rigid road surface model 56. That is, using the tire model 50, a simulation is performed that reproduces rolling on the rigid road surface model 56 in a grounded state or a rolling state of the tire, and a physical quantity of deformation that acts on a plurality of finite elements of the tire model 50. Change information (first physical quantity) change information (geometric circumferential change information), for example, change information such as strain / displacement gradient and deformation gradient is calculated. In this way, the deformation analysis calculation unit 34 calculates change information of the physical quantity of deformation along the set circumferential direction path that acts on the target element 54 of the tire model 52 selected by the tire model creation unit 32. Simulation results, such as change information of deformation physical quantities calculated by the deformation analysis calculation unit 34, are stored in the memory 22.

  The time conversion unit 36 calls the simulation result from the memory 22 and acts on the target element 54 of the tire model 52 for which the deformation analysis calculation unit 34 performed the simulation of the deformation analysis. This is a part that converts change information of a physical quantity of deformation such as a deformation gradient along the direction path into time change history information or rotation angle change history information of the physical quantity of deformation such as a displacement gradient. The time of the physical quantity of deformation or the rotation angle change history information is information converted in accordance with the rotation cycle (time or rotation angle) when the tire rotates at a set constant rolling speed. The attention element 54 is an element set as a condition by the tire model creation unit 32. The time (or rotation angle) change history information of the physical quantity of deformation for one rotation of the tire created by the conversion in the time conversion unit 36 is stored in the memory 22. The time conversion unit 36 may determine a circumferential path along the tire circumferential direction when the element of interest 54 makes one rotation in the circumferential direction of the tire model before the time conversion.

The micro model creation unit 38 is a part that creates and sets a micro model that reproduces the microstructure of the tire using a plurality of hexahedral shapes, for example, cubic shaped finite elements.
The micro model created by the micro model creation unit 38 will be described in detail later, but a rubber compound (inhomogeneous) in which a plurality of different material phases such as a microstructure of a predetermined part of a tire, for example, material property parameters are dispersedly arranged. The material is preferably a model that reproduces the microstructure of the material using a plurality of finite elements. For example, the micro model is, for example, the same rectangular parallelepiped modeled in the micro region of the tread rubber compound having the filler distribution shown in FIG. 4B, like the micro model 60 shown in FIG. A cube-shaped finite element model in which a large number of hexahedral) voxels (unit cells) are arranged as finite elements can be given.
In the illustrated example, the tire model creation unit 32 and the micro model creation unit 38 are provided separately, but the present invention is not limited to this, and may be a model setting unit in which both are integrated, Furthermore, the condition setting unit 30 may be integrated with the model setting unit.

  The boundary condition setting unit 40 is a part for setting a boundary condition, preferably a periodic boundary condition, used when a time-dependent simulation in the micro model 60 is performed by the micro model analysis calculation unit 42 described later. Specifically, using the time (rotation angle) change history information of the physical quantity of deformation such as the displacement gradient called from the memory 22, a cyclic symmetry condition that allows relative displacement of the nodes is set as a periodic boundary condition. That is, in order to reproduce a state in which the micro model 60 is continuously arranged infinitely, in each of the three directions of the micro model 60, the micro model 60 is at the same relative position on the boundary surface facing the node on one boundary surface. Define a relational expression that relates the behavior between nodes. Such a periodic boundary condition setting method can be performed in the same manner as the periodic boundary condition setting in the micro model disclosed in Japanese Patent Application Laid-Open No. 2007-265382. In the present invention, it is not essential that the boundary condition setting unit 40 sets the periodic boundary condition.

  The micro model analysis calculation unit 42 performs a time-dependent behavior analysis simulation on the micro model 60 using the boundary conditions set by the boundary condition setting unit 40, preferably the periodic boundary conditions, and is generated in the micro model. This is a part that acquires time (rotation angle) change history information of physical quantities (second physical quantities) such as strain, stress, and strain energy. Note that the micro model analysis calculation unit 42 directly assigns a physical quantity of deformation called from the memory 22, for example, time change history information of the displacement gradient, as a boundary condition to the micro model 60, and viscoelastic behavior in the micro model. You may perform the simulation of the behavioral analysis of the mechanical deformation which reproduces microbehaviours. Since the time (rotation angle) history information of the physical quantity of deformation used in the micro model analysis calculation unit 42 is time (rotation angle) history information for one rotation of the tire, this time-dependent behavior analysis simulation is also performed for one rotation of the tire. Done about. The result of this simulation is stored in the memory 22. The details of the simulation of the time-dependent behavior analysis performed on the micro model 60 by the micro model analysis calculation unit 42 will be described later.

  The micro behavior analysis unit 44 is a part that calculates and / or displays in order to output an analysis result for analyzing the dynamic micro behavior of the micro model 60. Specifically, the second physical quantity time (rotation angle) history information of the micro model 60 calculated by the micro model analysis calculation unit 42 is used to change the third physical quantity time (rotation angle) history information of the micro model 60, for example, The processing unit 12 calculates strain energy, viscoelastic energy loss, strain amplitude value, stress amplitude value, statistical values of these physical quantities, histograms of these physical quantities, and the like generated in the micro model 60. Processing for outputting the result of the simulation operation to the display 16 or the printer 18 via the I / O port 24 is performed. In this way, the simulation calculation result by the processing device 12 is displayed as a soft copy on the display 16 or output as a hard copy to the printer 18 in accordance with a numerical value, a graph or a figure.

  The rotating body simulation apparatus according to the present invention is basically configured as described above. The operation of the rotating body according to the present invention performed by the simulation apparatus will be described below by explaining the operation thereof. A tire will be used as a representative example to explain in detail below.

FIG. 2 is a diagram for explaining the flow of the tire simulation method of the present invention.
First, in step S100 shown in FIG. 2, in the simulation apparatus 10 shown in FIG. 1, various conditions necessary for simulation of the tire model 50 and the micro model 60 shown in FIGS. Is input and set by an operator or the like using the input operation system 14. These conditions include, for example, information on the structure (mesh, nodal point and element shape) of the tire model 50 and the micro model 60, information on material property parameters (material constants, etc.), and simulation of deformation analysis in the tire model 50. Information on tire pressure conditions, load conditions, rolling speed conditions, slip angle conditions, camber angle conditions, etc., as well as information on simulation conditions for applying contact processing to the tire model, and if necessary, micro Information necessary for micro behavior analysis such as time-dependent simulation of models is also included.

  In the present invention, the condition setting unit 30 sets the material property parameters (superelastic potential parameter etc.) of the tire model 50 that is a macro model using the material property parameters input in advance by an operator or the like. However, the present invention is not limited to this, and a material property parameter of the tire model 50 that is a macro model is changed to a predetermined deformation in the micro model 60 by using a homogenization method from a micro model to a macro model in multi-scale simulation. If given, it may be acquired from the physical quantity of deformation that occurs in the micro model 60 and set. Details of this method will be described later.

Next, in step S102, the tire model creation unit 32 sets, for example, mesh conditions (nodes and element shapes) based on the tire model structure information for simulation of deformation analysis set by the condition setting unit 30. And the tire model 50 shown in FIG. 3 is created.
Here, tire models 52 and 50 shown in FIGS. 3A and 3B are finite element models created by reproducing a tire having a tire size 205 / 65R15 as an example. The tire model 50 is developed so that the two-dimensional model 52 having a meridional cross section shown in FIG. 3A is developed one turn in the tire circumferential direction, and the developed two-dimensional model 52 is divided into elements at a constant angle in the circumferential direction. It is a delimited 3D finite element model. In this three-dimensional finite element model, a rubber member such as a tread member, a side member, and a bead filler member, a reinforcing layer of a carcass member and a belt member, and the like are configured by a hexahedral element, a tetrahedral element, a pentahedral element, or the like.
The tire model setting performed in step S102 may include mesh creation, material property parameter input, and boundary condition setting performed in step S100.

In step S102, the tire model creation unit 32 also creates a rigid road surface model 56 created so as to reproduce the road surface, as shown in FIG. 3B. FIG. 5 is a perspective view including a cross section of the tire model 50 grounded to the rigid road surface model 56 cut along a plane including the rotation axis. In the present invention, the tire deformation analysis by the tire model 50 and the rigid road surface model 56 with which it contacts the ground includes at least a state in which the tire and the road surface are in contact with each other. It is possible to analyze the deformation state of the micro region of the tire.
In the present invention, the road surface model is not limited to the rigid road surface model 56 in the illustrated example, and may be a model of a plane including irregularities or a model of a curved surface like a drum of a drum testing machine.
Next, in step S103, the tire model creation unit 32 further selects a deformation analysis target from a plurality of finite elements of the tire model 50 (52) as shown in FIGS. 3 (a) and 3 (b). While the attention element 54 is selected, as shown in FIG. 6, a circumferential path 58 is set along the circumferential direction of the tire when the attention element 54 makes one rotation in the circumferential direction of the tire model 50.

Here, the element of interest 54 is an element to be analyzed for the deformation of the tire. Information on which element is the target element is input by the operator in the condition setting in step S100. Since all elements of the two-dimensional tire model 52 shown in FIG. 3A can be targeted as the attention elements, the operator may input the order of the attention elements in the condition setting. The elements of interest may be automatically determined in a predetermined order without inputting the order.
Further, the circumferential path 58 of the attention element 54 shown in FIG. 6 is the attention element 54 in the tread center portion of the tire model 50 when an element near the tread center shown in FIG. Corresponds to the trajectory when is rotated once. This trajectory is a path in the deformed shape of the tire deformed by the deformation analysis process described later.

  Next, in step S <b> 103, the deformation analysis calculation unit 34 executes a deformation analysis simulation for the created tire model 50. Deformation analysis performed here includes, for example, contact analysis (static analysis), rolling analysis (dynamic rolling analysis (dynamic analysis), steady transportation analysis (general nonlinear finite element analysis program Abaqus (Simulia product name)) In this case, the created tire model 50 is subjected to an internal pressure filling process that reproduces the process of filling the tires assembled in the rim with the internal pressure, and then touches the road surface. In order to reproduce a tire that has been subjected to rolling or rolling on the road surface, a grounding process in which the tire model 50 subjected to the internal pressure filling process is grounded under a load condition set in the rigid road surface model 56 that models the road surface, Then, a rolling process is performed in which the rigid road surface model 56 is grounded and rolled.

First, only a static contact analysis is performed as a tire deformation analysis, and when the tire model 50 is not rolled, the ground contact is made as a method for extracting change information of a physical quantity of deformation such as a displacement gradient when the tire model 50 rotates from the result. The tire model 50 can be artificially rotated by taking a history of predetermined elements in the circumferential direction of the tire model 50. For example, by obtaining change information of physical quantities of deformation such as displacement gradients of all elements on the circumferential path 58 of the element 54 of interest in the tread center portion of the tire model 50, and taking deformation information of all these elements, Deformation information (history) for one round of the tire of the element of interest 54 can be obtained.
For example, static contact analysis as tire deformation analysis can be performed as follows.
In the deformation analysis by the static contact analysis of the tire, first, an internal pressure filling process is performed on the created tire model 50. The internal pressure filling process is a process of applying a predetermined force to a node that contacts the hollow region of the tire model 50. Next, with respect to the rigid road surface model 56 that reproduces the road surface, a grounding process for grounding the tire model 50 that has been subjected to the internal pressure filling process under a set load condition is performed based on the simulation conditions. When a static analysis simulation is performed as the deformation analysis, the material properties of the tire model 50 may be any material that reproduces the elastic properties, and for example, those represented by a neo-Hookean elastic model may be used. The result of the grounding process is stored in the memory 22.

Next, the circumferential path of the element of interest 54 in the meridional section (two-dimensional tire model 52) of the tire model 50 selected in advance when the tire model 50 makes one rotation is set as shown in FIG. Therefore, the displacement gradient of each element along the circumferential path of the element of interest 54 is extracted from the result of the grounding process stored in the memory 22. The tire model 50 after the grounding process is deformed by the grounding process, and each element is displaced in the tire circumferential direction. The circumferential distribution of the displacement gradient is displaced based on the position of each element after the deformation. Created as gradient change information. It should be noted that each element along the circumferential path 58 that is a trajectory when the tire model 50 shown in FIG. 6 makes one rotation (one turn) may not be continuous in the circumferential direction. That is, the displacement gradient extracted along the circumferential path 58 of the element of interest 54 does not have to be extracted from continuous elements.
In this way, the tire model 50 is used to perform a simulation that reproduces the ground contact in a stationary state of the tire, and to perform a simulation that reproduces the rolling of the tire model 50 on the rigid road surface model 56, The displacement gradient of each element along the direction path is extracted, and the displacement gradient change information (circumferential direction) as the change information (geometric circumferential change information) of the deformation that acts on the target element 54 of the tire model 50 is extracted. Distribution (distribution with respect to rotation angle information)) is calculated.

Of course, in step S106, as the deformation analysis, a macro-scale simulation for performing a rolling analysis for dynamically rolling the tire model 50 may be directly performed.
In the macroscale simulation, the tire model 50 is used to simulate the behavior of the tire in a rolling state of the tire under a predetermined condition. The predetermined conditions are, for example, conditions such as an internal pressure when applying an internal pressure to a tire, a load applied to a road surface, a tire rolling speed, a tire slip angle, and a tire camber angle. That is, in the macroscale simulation, a rim model that reproduces a separately created rim is mounted on the tire model 50, and an internal pressure is applied to the inner peripheral surface of the tire model 50 that faces a hollow region surrounded by the tire model 50 and the rim model. After the filling process is performed, a load is applied by contacting the rigid road surface model 56 of the road surface, and the tire model 50 is rolled by applying a predetermined rolling speed. At that time, the tire model 50 is given a slip angle, a tire camber angle, a rotational torque, or the like. In the rolling analysis as well, steady transportation is obtained by analyzing only the material inside without rolling the mesh of the tire model 50 to obtain a pseudo effect as if the mesh was rolled. Analysis may be performed.
Next, change information such as strain / displacement gradient and deformation gradient is calculated from the calculation results obtained by this simulation.

In this way, in this deformation analysis step S106, the tire model 50 is used to perform a simulation that reproduces the rolling on the rigid road surface model 56 in the ground contact state and the rolling state of the tire in a stationary state. Geometric circumferential direction change information of a physical quantity of deformation acting on a plurality of finite elements is calculated.
Thus, in this deformation analysis step S106, the deformation analysis calculation unit 34 changes the physical quantity of deformation along the set circumferential path that acts on the target element 54 of the tire model 52 selected by the tire model creation unit 32. Information is calculated. The simulation result of the change information of the physical quantity of deformation calculated here is stored in the memory 22.

Next, in step S108, the change information of the deformation physical quantity such as the circumferential distribution of the displacement gradient (distribution with respect to the rotation angle) is converted into the time of the deformation physical quantity such as the displacement gradient time change history information or the like in the time conversion unit 28. It is converted into rotation angle change history information and extracted. In the following, the time change history information of the physical quantity of deformation will be described. However, since the tire is a rotating body, rotation angle change history information using the rotation angle as a parameter instead of time change history information using the time as a parameter. Of course, may be used. Note that the time converted by the time conversion unit 28 in step S108 may be a virtual time in the static analysis of the numerical analysis instead of the real time.
Here, FIG. 7 shows the time change of the displacement gradient extracted as the time change history information of the physical quantity of the deformation of the element of interest 54 in the tread center portion of the tire model 50 (52) shown in FIGS. 3 (a) and 3 (b). An example of history information is shown. FIG. 7 shows a finite element using the tire model 50 when the internal pressure applied to the tire model 50 is 200 [kPa], the load is 4.0 [kN], and the rolling speed is 80 [km / h]. It is the result of a rolling analysis by a method (FEM).

  Here, since the time change history information of the displacement gradient is represented by a three-dimensional second-order asymmetric tensor, in FIG. 7, there are nine components (components 11, 22, 33, 12, 13, 21, 23, 31, 32). ). In the time conversion of the displacement gradient, if the period of one rotation of the tire is T, and the rotation angle that determines the position of the displacement gradient in the tire circumferential direction is θ (degrees) (0 to 360 degrees), the displacement gradient at the rotation angle θ is The value is converted into a displacement gradient value at a time represented by T × θ / 360. The period T of one rotation is obtained by dividing the length of the circumferential path of the tire by the rolling speed of the tire. Therefore, the time width of the displacement gradient time change history information is substantially the same as the period T of one rotation. Note that the position in the tire circumferential direction of the element of interest representing the rotation angle θ is the position after each element of the tire model is displaced in the tire circumferential direction due to deformation of the tire model, as described above. Time change information can be obtained. The obtained time change history information of the displacement gradient is stored in the memory 22. Here, since the tire is a rotating body, the rotation angle change history information of the displacement gradient may be used instead of the time change history information of the displacement gradient.

In the present invention, in the tire model 50 shown in FIG. 6, the elements along the circumferential path 58 of the tire model 50 when the tire makes one turn are continuous, but in the present invention, they are not necessarily continuous. You don't have to. In such a case or when the information of the division points on the circumference of the element division is too coarse, the movement of the micro model 60 does not become smooth and does not become a part of the macro behavior of the tire model 50. It is desirable to interpolate between the pieces of information when the time change history information of the physical quantity is created. For example, in interpolating information between elements, use of element shape functions, linear interpolation between information points, and quadratic interpolation can be cited. Further, when creating the time change history information of the physical quantity of deformation, it is preferable to convert the deformation information of the element into a value in the rotating coordinate system of the rotating body.
Further, as described above, in the present invention, the time course history information of the physical quantity of the deformation of the element of interest extracted in this step S108 is the circumferential path 58 of the tire model 50 that is a trajectory when the tire makes one round. Can be created from the tire circumferential direction information of the tire model 50 of the element along the tire, so even in the analysis in which the mesh of the tire model 50 does not move (contacting analysis or steady transportation analysis), the time of the deformation state of the micro region of the tire Changes can be analyzed.

Next, in step S110, the micro model creating unit 38 creates and sets a micro model that reproduces the tire microstructure using a plurality of hexahedral shapes, for example, cubic shaped finite elements. Such a micro model includes information on the structure of the micro model for performing time-dependent simulation using the time change history information of the physical quantity of deformation of the target element 54 of the macro model 50 obtained in the time conversion step S108. For example, a micro model divided into meshes based on mesh conditions (nodes and element shapes) can be mentioned.
The micro model used in the present invention may be a model of any micro region as long as it reproduces the microstructure of a predetermined part of the tire. Preferably, the model is a model in which a microstructure of a rubber compound (heterogeneous material) in which the material phases are dispersedly arranged is reproduced using a plurality of finite elements.
For example, a micro model 60 shown in FIG. 4A can be given as an example of a micro model suitably used in the present invention.

Here, the micro model 60 shown in FIG. 4 (a) has the same hexahedral voxel modeled on the micro region of the tread rubber compound of the tire having the filler distribution shown in FIG. 4 (b) as a finite element. It is a cube-shaped finite element model that is adjacently arranged along three orthogonal directions and is continuously arranged.
The micro model 60 shown in FIG. 4A includes a polymer material (rubber) 62, a reinforcing agent (filler), for example, carbon black (CB) 64 indicated by a dark color and silica 66 indicated by a light color. This is a model of a heterogeneous composite filled with different types of fillers. In the illustrated example, these two kinds of fillers are each a plurality of particles in the polymer material (rubber) 62 in the micro region of the tread rubber compound modeled as a micro model 60, as shown in FIG. For this modeling, for example, a finite element (FE) model mesh is created, and each mesh is included in these particles using the center coordinates and radius of each filler particle. If it is included, the mesh is made up of the filler particles. If not, the mesh is made up of a polymer (rubber). It is only necessary to input the physical properties of the material or the physical properties of the polymer (rubber) material.

Thus, by using the micro model 60 that models the rubber compound that is a heterogeneous composite material in which the polymer material 62 is filled with at least the reinforcing agent (64, 66), the micro deformation of the rubber compound of the rolling tire is achieved. Can be analyzed. For example, by analyzing the micro strain distribution when the filler (carbon black 64 and / or silica 66) is filled, it is possible to predict the failure of the rubber compound during rolling of the tire. In this case, when the rubber compound is micro-modeled, it is preferable to input different material properties to the polymer phase composed of the polymer material 62 and the phase composed of the carbon black 64 and the silica 66.
For example, in the example shown in FIG. 4A, as a micro region of the tread rubber compound, a region of 0.1 μm × 0.1 μm × 0.1 μm is a micro model 60 composed of voxel elements composed of 30 × 30 × 30. The modeled element composed of the polymer (rubber phase) material 62 has an elastic modulus E of 1.0 [MPa], and the element composed of carbon black 64 and silica 66 has an elastic modulus E of 10,000. [MPa] is given.

In the example shown in FIG. 4A, the micro model 60 is a model of a rubber compound that is a heterogeneous composite material in which at least a reinforcing agent (64, 66) is filled in a polymer material 62. The invention is not limited to this, and a rubber-based composite material including a reinforcing material may be modeled.
Here, the reinforcing material is an organic fiber reinforcing material such as a carcass or a belt carver, a metal material such as a belt or a bead, a steel cord wire, or the like. As a micro model, the reinforcing material to be modeled may be a single wire or a stranded wire composed of a plurality of wires.
In this way, by using a micro model that models a rubber-based composite material including a reinforcing material, it is possible to analyze micro deformation near the reinforcing material of the rolling tire. For example, it is possible to analyze strain generated in a rubber compound sandwiched between stranded wires such as tire belts.

In step S110, a tire rubber compound micromodel can be created as described above. However, the present invention is not limited to this, and various other models of the tire constituting the tire are also included. Can be created. Note that the methods described in Patent Documents 1 and 2 may be used when creating a micro model.
The micro model setting performed in step S110 may include mesh creation, material property parameter input, and boundary condition setting performed in step S100.
The setting of the micro model performed in step S110 is performed before the execution of the time-dependent simulation using the micro model 60 in the subsequent step S114, preferably before the boundary condition setting of the micro model 60 in the next step S112. Anytime, anywhere.

Next, in step S112, the boundary condition setting unit 40 sets boundary conditions used when the micro model analysis calculation unit 42 performs time-dependent simulation in the micro model 60. At this time, in order to set a boundary condition to be given to the micro model 60, time change history information of a physical quantity of deformation such as a displacement gradient is called from the memory 22, and a period applied to the micro model 60 from this time change history information. Boundary conditions (periodic symmetry conditions that allow relative displacement of nodes) are preferably set.
That is, as a periodic boundary condition, in order to reproduce a state in which the micro model 60 is continuously arranged infinitely, each of the three directions of the micro model 60 that is a hexahedral element is opposed to a node on one boundary surface. It is better to define a relational expression that relates the behavior between the nodes at the same relative position on the boundary surface. This relational expression is used as a constraint condition in the simulation described later.
Thus, by setting a periodic boundary condition that allows relative displacement as the boundary condition, it is possible to apply a homogenization method, and it is possible to analyze the micro model 60 as a part of the micro region of the tire. That is, a multi-scale analysis between both regions of the tire model 50 that is a macro scale model and the micro model 60 that is a micro scale model can be performed.

Next, in step S114, the micro model analysis calculation unit 42 calls the time change history information of the physical quantity of the deformation such as the displacement gradient stored in the memory 22 from the memory 22, and the time dependence of the deformation using the micro model. An analysis simulation is performed. That is, in this step S114, a simulation of time-dependent behavior analysis is performed on the micro model 60 using the boundary conditions set in step S112, and physical quantities such as strain, stress, strain energy, etc. generated in the micro model. The time change history information of is acquired. Specifically, time variation information of the displacement gradient and periodic boundary conditions are given, and a deformation simulation is performed using the rotation period of the tire model 50 as an analysis time by a constant time step using the micro model 60. Is called.
For example, with respect to the micro model 60 of the tire tread rubber compound shown in FIG. 4A, the extraction shown in FIG. 7 extracted as time change history information of the physical quantity of deformation of the tire tread center portion in step S108. The time change history information of the displacement gradient is read from the memory 22, given as the boundary condition set in step S112, and micro model deformation analysis is executed for each time change, for example, simulation of stress and strain analysis is performed. Thus, for each time change, a deformation generated in the micro model, for example, a deformation like the micro model 60A shown in FIG. 8 is obtained. Here, FIG. 8 shows a predetermined time-varying process of the dynamic behavior of the micro model reproducing the tread center portion of the rolling tire that is in contact with the ground, for example, the attention element 54 or a part of the tread rubber compound thereof. It is a perspective view which shows an example, and has shown the micro model 60A of the state deform | transformed for grounding.

Here, the time-dependent simulation performed on the micro model 60 and the dynamic change process of the deformation of the micro model 60 will be described with reference to FIG.
FIG. 9 is a micro model that reproduces a finite element of the tread center portion when the tire model 50 makes one rotation, for example, each position of the attention element 54 and the attention element 54 corresponding to each position or a part of the tread rubber compound. It is explanatory drawing which shows the time change log | history of the state of 60 deformation | transformation. Here, the tire model 50 is shown by a cross-sectional view cut along an equator plane orthogonal to the rotation axis, and includes eight micro models 60a to 60h showing the state of deformation in each time-varying process subjected to time-dependent simulation. Show.
In FIG. 9, the tire model 50 is, for example, divided into 36 meshes every 10 degrees in the circumferential direction, and within a range of ± 25 degrees with respect to the meridional section on the rigid road surface model 56 side (lower side) of the tire model 50. Is finely divided into meshes every 2.5 degrees. In this way, attention is paid to one finite element (the attention element 54) of the tire model 50 divided into meshes, and the displacement gradient acting on the micro model 60 that reproduces all or part of the tread rubber compound is affected. FIG. 9 shows a result of performing time-dependent simulation by giving time change history information as a boundary condition. Such a simulation result is stored in the memory 22. In addition, in the element division shown in FIG. 9, when the obtained information is too rough with the number of division points on the circumference, the movement of the micro model is not smooth and does not become a part of the macro behavior of the tire, Since accurate micro behavior cannot be analyzed, it is preferable to interpolate between the division points. As the interpolation method, the various interpolation methods described above can be used.

As shown in FIG. 9, the element (target element 54) on the opposite side (upper side) of the rigid road surface model 56 of the tire model 50 has no deformation and no distortion as shown by the micro model 60a. It is the same as the micro model shown in (a), and even when the tire model 50 is rotated 90 degrees clockwise, for example, there is no deformation and no distortion as in the micro model 60b. Immediately before (for example, an element rotated by 150 degrees), the micro model 60c is slightly deformed and slightly strained. In a slightly grounded state (for example, an element rotated by 160 degrees), the micro model is considerably deformed and considerably strained. At the center of contact (the element on the rigid road surface model 56 side (lower side) of the tire model 50), 60e, the tire model 50 further rotates, and the element further moves in the circumferential direction (for example, 200 degrees, 210 degrees, and 270 degrees rotation), conversely, the micro models 60f, 60g, and 60h are gradually deformed. When the element is reduced and the occurrence of distortion is reduced and the element is further rotated to return to the original position (position of 0 degree rotation), the micro model 60a returns to the initial state without deformation.
Here, since the rotation angle and the rotation time when the tire model 50 makes one rotation are mutually converted by solving the rotation speed, the rotation angle change history of the deformation of the micro model obtained as the micro models 60a to 60h is Can be obtained as a time change history.

Thus, from the deformation state of the micro model in each time change process (each rotation angle) of the micro model of the tire rubber compound when the tire makes one revolution, the desired micro model in each time change process (each rotation angle), respectively. By obtaining a physical quantity of deformation of a finite element, for example, strain, stress, strain energy, etc., it is possible to acquire time change history information of the physical quantity of deformation such as strain, stress, strain energy, etc. of the micro model element.
FIG. 10B shows a graph of the time change history information of the physical quantity of the deformation of the element E indicated by a circle in the micro model 60 of FIG. Here, FIG. 10A shows that the element E that is the polymer material (rubber) 62 indicated by a circle in the drawing of the micro model 60 is an element for calculating the time-dependent simulation result, and FIG. ) Shows a graph of the time change history information of the strain component 11 calculated for the element E.
In this way, it is possible to analyze the micro behavior (deformation behavior in the micro region) of the rubber compound at the time of rolling of the tire, that is, the dynamic change process such as micro strain, stress, strain energy, etc. generated in the rubber compound.

By the way, in the simulation of the time-dependent analysis performed on the micro model in step S114, the material property parameter given to the micro model may depend on at least one of time, deformation, and field. For example, examples of material property parameters that depend on time include viscosity properties, and examples of material property parameters that depend on deformation include elastic properties (superelastic properties, etc.) in which the relationship between strain and stress is nonlinear. Examples of the material property parameter depending on the field include a temperature field and an electromagnetic field, and examples of the material property parameter depending on the viscosity include a viscous property and an elastic property.
Thus, by making the material physical property parameter given to the micro model depend on at least one of time, deformation, and field, a physical quantity that depends on at least one of time, deformation, and field generated in the micro model can be calculated. .

Next, in step S116, the micro behavior analysis unit 44 calls the time change history information of the physical quantity of the deformation of the micro model stored in the memory 22 from the memory 22, and analyzes the dynamic micro behavior of the micro model 60. The calculation, conversion and display for outputting the analysis result is performed. That is, in this step S116, the micro behavior of the micro model 60 is analyzed from the time (rotation angle) change history information of the physical quantity (second physical quantity) of the deformation of the micro model 60 such as strain, stress, and strain energy. Time (rotation angle) change information of the third physical quantity of the micro model 60 is calculated.
Here, examples of the time change information of the third physical quantity include strain energy, viscoelastic energy loss, strain amplitude value, and stress amplitude value generated in the micro model 60. Also, since the micro model models inhomogeneous compounds, the strain and stress generated in the micro model are locally different. Therefore, as the time change information of the third physical quantity, It is also possible to obtain statistical values such as the average value and standard deviation of the strains and stresses, that is, the statistical values of the above-mentioned physical quantities. Furthermore, the above-mentioned histograms of physical quantities such as a strain histogram and a stress histogram representing the number of elements having values in a predetermined range as strain values and stress values in the micro model can be listed.

Thus, the time variation information of the third physical quantity obtained in step S116 is displayed as a soft copy on the display 16 via the I / O port 24 as a simulation calculation result by the processing device 12, and as a hard copy on the printer 18. Is output.
Thus, in the rotating body simulation method of the present invention, a tire model and its micro model, particularly a micro model in which a rubber compound (heterogeneous material) is modeled, are prepared. The change history information of the deformation of the finite element is extracted from the dynamic analysis, and the change history information of the deformation is converted into time (rotation angle) change history information such as a displacement gradient shown in FIG. Since the micro model can be analyzed as a boundary condition, the dynamic change process of the physical quantity of deformation such as micro strain and stress generated in the compound during rolling of the tire as shown in FIG. 8 is analyzed. be able to. That is, in the present invention, the time history (rotation angle history) of the macro deformation (including the dynamic rolling state) of the tire can be input to the compound micro model to simulate the micro deformation behavior of the compound.
The rotating body simulation method of the present invention is basically configured as described above.

In the above-described rotating body simulation method, the material physical property parameter input by the operator or the like is used in advance as the material physical property parameter to be given to the tire model. In addition, when a predetermined deformation is given to the micro model, it may be obtained from a physical quantity of the deformation that occurs in the micro model. Here, examples of the deformation applied to the micro model include uniaxial stretching, uniform biaxial stretching, and pure shear. Examples of physical quantities of deformation that occur in the micro model include stress, strain, and loss tangent (tan δ) of viscoelasticity. Furthermore, examples of the material property parameter of the rubber of the tire provided to the tire model include an elastic constant, a superelastic potential parameter, a viscoelastic parameter, and the like.
Thus, also in the present invention, a homogenization technique from a micro model to a macro model in multi-scale simulation can be used. As a result, the material properties of the tire model (macro model) can be determined using the micro model.

Thus, a method for determining the material property parameter of the tire model using the micro model will be specifically described.
FIG. 11A shows a micro model 70 of a rubber compound (heterogeneous material) of a tread center of a tire created in the same manner as the micro model 60 shown in FIG. 4A.
Here, first, a uniaxial extension analysis is performed on the micro model 70 shown in FIG. That is, a predetermined material phase (for example, polymer material, carbon black particle, silica particle) and a predetermined boundary condition are given to the micro model 70 shown in FIG. Under the conditions, a uniaxial extension process is performed in the direction of the arrow in the figure, the micro model 70 is deformed, the deformation state of the micro model 70a as shown in FIG. 11B is obtained, and the stress-strain relationship (stress-strain curve) (SS curve)) is performed to calculate a stress distribution or strain distribution in the micro model 70, for example, an SS curve shown in FIG. Further, when the calculated stress distribution or strain distribution does not satisfy the predetermined condition, the boundary condition given to the microscale model is corrected so that the stress distribution or strain distribution satisfies the predetermined condition.

Using the calculation result of the microscale simulation (SS curve shown in FIG. 12) obtained in this way, the superelastic potential when the heterogeneous microstructure of the rubber compound (heterogeneous material) is made a homogeneous structure. And material constant parameters based on this potential can be identified.
For example, an Arruda-Boyce superelastic potential function U as shown in the following formula (1) is exemplified as a function for obtaining the material property parameter of the compound rubber. Using this potential function, the material property parameters μ and λ _m can be obtained from the SS curve shown in FIG. 12 by the nonlinear least square method. Specifically, by repeatedly changing the values of the material physical property parameters μ and λ _m and calculating the material physical property parameter that minimizes the error function shown in the following equation (2), for example, the tire tread center portion As a material property parameter of the rubber compound, μ = 0.52 and λ _m = 1.16 can be identified.
As described above, the material property parameters of the tire model (macro model) can be determined and input using the micro model. For this method, specifically, the method disclosed in Patent Document 2 can be used.

Note that the above-described method of simulating a rotating body can be processed on a computer by executing a program.
For example, the rotating body simulation program of the present invention has a procedure for causing a computer, specifically, the CPU 20 (see FIG. 1) to perform each step of the above-described rotating body simulation method. The program composed of these procedures may be configured as one or a plurality of program modules.
The rotating body simulation program comprising the procedures executed by these computers may be stored in the memory (storage device) of the computer or server, or may be stored in a recording medium. At the time of execution, the program is read from the memory or the recording medium and executed by the computer (CPU 20) or another computer. Therefore, the present invention may be a computer-readable memory or recording medium storing a rotating body simulation program for causing a computer to execute the rotating body simulation method of the first aspect.

  As described above, the simulation method, apparatus, and program of the rotating body of the present invention and the recording medium on which the program is described have been described in detail. However, the present invention is not limited to the above-described embodiment, and the scope of the present invention is not deviated. Of course, various improvements and changes may be made.

10 simulation device 12 simulation calculation processing device (processing device)
14 Input operation system 16 Display 18 Printer 20 CPU
22 Memory 24 I / O port 26 ROM
DESCRIPTION OF SYMBOLS 30 Condition setting part 32 Tire model creation part 34 Deformation analysis calculation part 36 Time conversion part 38 Micro model creation part 40 Boundary condition setting part 42 Micro model analysis calculation part 44 Micro behavior analysis part 50, 52 Tire model 54 Target element 56 Rigid road surface Model 60, 60A, 60a, 60b, 60c, 60d, 60e, 60f, 60g, 60h, 70, 70a Micro model 62 Polymer (rubber) material 62
64 carbon black 66 silica

Claims (14)

A rotating body simulation method for analyzing the behavior of a rotating body modeled with elements capable of numerical analysis and its micro model,
A first step of creating a rotating body model that reproduces the rotating body using a plurality of finite elements;
A second step of selecting, as an element of interest, one of the finite elements located on the meridional section of the rotating body model cut by a plane including the rotation axis of the rotating body model created in the first step;
A simulation condition set in advance is applied to at least a part of the circumference of the rotating body model, a deformation analysis of the rotating body is performed using a finite element method, and a simulation is applied to the finite element of the rotating body model. A third step of calculating change information of one physical quantity;
The change information of the first physical quantity calculated by the third step, which acts on the element of interest of the rotating body model selected in the second step, is the time or angle change of the first physical quantity. A fourth step of converting to information and extracting;
A fifth step of creating a micro model that reproduces the microstructure that is part of the rotating body using a plurality of finite elements;
The time or angle change information of the first physical quantity extracted in the fourth step is given as a boundary condition to the micro model created in the fifth step, and the finite element method is applied to the micro model. A sixth step of calculating time or angle history information of the second physical quantity generated in the micro model by performing a time-dependent analysis simulation using
The time or angle change information of the third physical quantity of the micro model is calculated, displayed, or calculated from the time or angle history information of the second physical quantity of the micro model calculated by the sixth step. And a seventh step of displaying. Furthermore, the element of interest of the rotating body model has an eighth step of defining a circumferential path that makes one round in the circumferential direction of the rotating body model,
The third step calculates change information of the first physical quantity along the circumferential path acting on the finite element of the rotating body model,
In the fourth step, the change information of the first physical quantity acting on the element of interest along the circumferential path is matched with the rotation period when the rotating body rotates, so that the first physical quantity is changed. Into time or angle change information
2. The sixth step of calculating time or angle history information of a second physical quantity generated in the micro model when the element of interest makes a round along the circumferential path. The rotating body simulation method described.   In the fourth step, the change information of the first physical quantity to be extracted is created from rotating body circumferential direction information of a finite element along a trajectory when the rotating body makes one round. Item 3. The rotating body simulation method according to Item 1 or 2.   The boundary condition given to the micro model in the simulation of the time-dependent analysis performed on the micro model in the sixth step is a periodic boundary condition that allows relative displacement. The method of simulating a rotating body according to any one of the above.   The material property parameter given to the micro model in the simulation of the time-dependent analysis performed on the micro model in the sixth step depends on at least one of time, deformation, and field. Item 5. The rotating body simulation method according to any one of Items 1 to 4.   6. The micro model is obtained by reproducing a microstructure of a heterogeneous material in which a plurality of material phases having different material properties are dispersedly arranged by using the plurality of finite elements. The method of simulating a rotating body according to any one of the above.   The rotating body according to any one of claims 1 to 6, wherein the micro model is a model of a rubber compound that is a heterogeneous composite material in which a polymer material is filled with at least a reinforcing agent. Simulation method.   The method of simulating a rotating body according to claim 1, wherein the micro model is a model of a rubber-based composite material including a reinforcing material.   In the simulation of deformation analysis of the rotating body performed on the rotating body model in the third step, material property parameters given to the rotating body model are generated in the micro model when the micro model is deformed. The method according to claim 1, wherein the method is obtained from the second physical quantity of deformation. The rotating body is a tire,
The simulation of deformation analysis of the rotating body performed on the rotating body model in the third step includes at least a state in which a tire and a road surface are in contact with each other. The method for simulating a rotating body according to item. The second physical quantity of the micro model for which the time or angle history information is calculated in the sixth step is at least one of strain, displacement gradient, and deformation gradient,
The third physical quantity of the micro model for which the time or angle history information is calculated in the seventh step includes strain energy, viscoelastic energy loss, strain amplitude value, and stress amplitude value generated in the micro model. 11. The method of simulating a rotating body according to claim 1, wherein at least one of a statistical value of each of these physical quantities and a histogram of each of these physical quantities. A rotating body simulation device for analyzing the behavior of a rotating body modeled by a finite element capable of numerical analysis and its micro model,
A rotating body model creating means for creating a rotating body model for reproducing the rotating body using a plurality of finite elements;
Attention element selection means for selecting, as an attention element, one of the finite elements located on the meridional section of the rotating body model cut at a plane including the rotation axis of the rotating body model created at the first step;
A simulation condition set in advance is applied to at least a part of the circumference of the rotating body model, a deformation analysis of the rotating body is performed using a finite element method, and a simulation is applied to the finite element of the rotating body model. A rotating body model simulation means for calculating change information of one physical quantity;
The change information of the first physical quantity calculated by the third step, which acts on the element of interest of the rotating body model selected in the second step, is the time or angle change of the first physical quantity. Time conversion means for converting to information and extracting;
A micro model creating means for creating a micro model that reproduces a microstructure that is a part of the rotating body using a plurality of finite elements;
The time or angle change information of the first physical quantity extracted in the fourth step is given as a boundary condition to the micro model created in the fifth step, and the finite element method is applied to the micro model. Micro model simulation means for calculating time or angle history information of the second physical quantity generated in the micro model by performing time-dependent analysis simulation using
The time or angle change information of the third physical quantity of the micro model is calculated, displayed, or calculated from the time or angle history information of the second physical quantity of the micro model calculated by the sixth step. And a micro-behavior analysis means for displaying the rotating body.   The program for making a computer perform each step of the simulation method of the rotary body of any one of Claims 1-11.   The computer-readable recording medium which described the program for making a computer perform each step of the simulation method of the rotary body of any one of Claims 1-11.