JP2006076404A - Tire model, tire behavior simulation method, program, and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform the analysis of tire behavior and simulation accurately with the contacting part of a tire taken into consideration. <P>SOLUTION: As the reference the case is adopted in which a friction coefficient μ<SB>o</SB>exist at any arbitrary grounding pressure P<SB>o</SB>, sliding velocity V<SB>o</SB>, and temperature T<SB>o</SB>, and a contacting condition in another part of the tire is assumed having a grounding pressure P1, sliding velocity V1, and temperature T1. Then determination is made for the change rate Cp of the friction coefficient μ when a change takes place from P<SB>o</SB>to P1, the change rate Cv of the friction coefficient μ when a change takes place from V<SB>o</SB>to V1, and the change rate Ct of the friction coefficient μ when a change takes place from T<SB>o</SB>to T1. Multiplying together these change rates allows determination of the friction coefficient μs in any arbitrary contacting condition (μs=Cp×Cv×Ct×μ<SB>o</SB>). <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a tire model, a tire behavior simulation method, a program, and a recording medium, and a tire model, a tire behavior simulation method, a program, and a recording that are used when analyzing the performance of a pneumatic tire used in an automobile or the like. It relates to the medium.

  The analysis of tire behavior is based on the results of measuring the tires actually designed and manufactured and using the results of performance tests obtained by mounting them on automobiles. Can now be realized. As a main method for analyzing the tire behavior by simulation, a numerical analysis method such as a finite element method (FEM) is mainly used. FEM is a technique of modeling a structure with a finite number of elements and analyzing the behavior of the structure using a computer, and divides the structure into a finite number of elements from its features (hereinafter referred to as mesh division or Element division). In recent years, a physical model for modeling a tire with a large number of rigid beams has been proposed.

By the way, when analyzing the tire behavior, it is important to perform simulation with high accuracy including the contact portion of the tire. For example, if the contact state is different, the force that the tire receives from the road surface is different, which ultimately affects the steering stability of the vehicle. For this reason, in the conventional tire analysis, conditions defined by using a constant friction coefficient (for example, Coulomb friction coefficient) between the tire and the road surface are used (see, for example, Patent Document 1 or Patent Document 2). ).
Japanese Patent Laid-Open No. 11-201875 Japanese Patent Laid-Open No. 11-153520

  However, the tire contact portion is accompanied by changes due to various conditions.

  For example, rubber, which is a constituent material of tires, has very soft physical properties compared to metal materials, and the frictional force when the rubber is pulled sideways while being in contact with a flat surface is pressed against the flat surface of the rubber. Depends on pressure, pulling force and pulling speed. In addition, when rubber is pressed against an uneven surface like an actual road surface, part of the rubber is deformed according to the unevenness of the road surface and bites into the recess. The amount of bite has temperature dependence. That is, when the temperature of the rubber changes, the hardness of the rubber changes, so that the amount of biting changes, and as a result, the friction coefficient changes. It is also necessary to consider the variation of the friction coefficient due to such a change in rubber temperature.

  Therefore, if the friction coefficient is defined as a constant value, an appropriate simulation according to the tire running conditions cannot be performed.

  In consideration of the above facts, the present invention allows a tire model, a tire behavior simulation method, a program, and a recording medium capable of performing tire behavior analysis and simulation with high accuracy in consideration of a tire contact portion. Is the purpose.

  In order to achieve the above object, the present invention makes it possible to analyze the behavior of the tire contact portion in detail.

  Specifically, the invention according to claim 1 is a tire model for calculating a tire corresponding to a numerical calculation model in order to simulate the behavior of the tire in a use state, wherein the tire is in contact with the road surface. A friction coefficient having a contact pressure dependency is defined for at least one of the portion, the contact portion between the tire and the rim, and the contact portion between the tread materials separated by the sipe.

  In the present invention, when calculating the tire corresponding to the numerical calculation model, at least one of the contact portion between the tire and the road surface, the contact portion between the tire and the rim, and the contact portion between the tread materials separated by the sipe, Define the coefficient of friction with ground pressure dependency. Thus, it is possible to improve the prediction accuracy of the simulation by defining the friction coefficient having the contact pressure dependency. For example, when simulating the rubber behavior of a tread when the tire tread is in contact with the road surface, in a model that considers the contact pressure dependence, the friction coefficient of the part with a high contact pressure is set to a low value, By setting the coefficient of friction of the high part of the part to be low, the ground contact behavior close to the actual phenomenon can be predicted.

  In particular, the present invention has an effect of preventing an excessive increase in the contact pressure at the corners of the tire tread. That is, since FEM is a numerical calculation, the convergence of the calculation may be hindered if the contact pressure of an arbitrary portion is extremely high. Therefore, if the friction coefficient is defined in consideration of the ground pressure dependency, a smooth (good convergence) calculation can be performed. Further, the distribution of the ground pressure is also approximate to the actual one.

  The invention according to claim 2 is a tire model for calculating the tire corresponding to the numerical calculation model in order to analyze the behavior of the tire in a use state, the tire being in contact with the road surface, the tire A friction coefficient having a sliding speed dependency is defined for at least one of the contact portion of the rim and the contact portion between the tread materials separated by the sipe.

  In the present invention, when calculating the tire corresponding to the numerical calculation model, at least one of the contact portion between the tire and the road surface, the contact portion between the tire and the rim, and the contact portion between the tread materials separated by the sipe, Define a coefficient of friction that is dependent on the sliding speed. Thus, it is possible to improve the prediction accuracy of the simulation by defining the friction coefficient having the sliding speed dependency. For example, when the tire is brought into contact with the road surface and the slip angle is set to a predetermined angle (for example, 4 degrees), the change in the lateral force when the tire is transferred at a predetermined speed changes the friction coefficient as the speed increases. As a result, it is possible to accurately simulate the change in lateral force due to the difference in speed.

  In particular, in the present invention, the characteristics relating to the lateral force of the tire approach the actual measurement. For example, in a portion where the slip angle is low, there are few portions slipping on the ground contact surface of the tire, and the friction coefficient is high. However, when the slip angle is large (8 degrees or more), most of the ground contact surface of the tire starts to slide, resulting in a low friction coefficient. However, if a friction coefficient that does not take into account the slip dependency is set, the effect of reducing the friction coefficient due to slip cannot be incorporated into the analysis, and even when the slip angle is large, the friction coefficient remains large, resulting in a lateral force. It is highly calculated and does not match the actual measurement. In the present invention, this can be eliminated by considering the slip speed dependency.

  According to a third aspect of the present invention, the friction coefficient having the slip speed dependency has independently a slip speed dependency component in the tire circumferential direction and a slip speed dependency component in the tire width direction. Features.

  The coefficient of friction of the tire varies depending on the force acting on the tire depending on the traveling direction and the turning direction. Therefore, if the friction coefficient having the slip speed dependency has an independent component of the slip speed dependency in the tire circumferential direction and a slip speed dependency component in the tire width direction, the directionality of the slip speed is determined. Therefore, it is possible to predict the ground contact behavior close to the actual phenomenon.

  The invention according to claim 4 is a tire model for calculating the tire in correspondence with the numerical calculation model in order to analyze the behavior of the tire in use, wherein the tire is in contact with the road surface, The friction coefficient having temperature dependency is defined for at least one of the contact portion of the rim and the contact portion between the tread materials separated by the sipe.

  The rubber of an example which is a constituent material of a tire changes the hardness of the rubber when the temperature of the rubber changes, so that the amount of biting into the contacted counterpart changes, and as a result, the friction coefficient changes. Therefore, by defining a temperature-dependent friction coefficient for at least one of the contact portion between the tire and the road surface, the contact portion between the tire and the rim, and the contact portion between the tread materials separated by sipes, It is possible to improve the prediction accuracy. For example, when considering a case where the tire is applied in an automobile race under extremely severe conditions, the tire temperature varies depending on the traveling state, and the grip force varies during traveling. It works effectively on such a simulation.

  The invention according to claim 5 is a tire model for calculating a tire corresponding to a numerical calculation model in order to analyze the behavior of the tire in use, wherein the tire is in contact with the road surface, the tire For at least one of the contact part of the rim and the contact part of the tread material separated by sipe, a friction coefficient having at least two dependences of contact pressure dependence, sliding speed dependence and temperature dependence was defined. It is characterized by that.

  When analyzing the behavior of a tire, it is rare that it is a single state. Therefore, by defining a friction coefficient that has at least two dependencies: ground pressure dependency, slip speed dependency, and temperature dependency, it is possible to perform an analysis that matches the actual tire behavior considering multiple states simultaneously. it can.

  In this case, although described in claim 6, the friction coefficient having the dependency on the slip speed independently includes a component of the slip speed dependency with respect to the tire circumferential direction and a component of the slip speed dependency with respect to the tire width direction. If so, it is possible to accurately handle the direction of the sliding speed, and it is possible to predict a ground contact behavior closer to an actual phenomenon.

  By using the model, the behavior of the tire can be accurately simulated. Specifically, as described in claim 7, (a) a tire model that can be deformed by ground contact and rolling as a numerical calculation model, according to any one of claims 1 to 6. (B) a step of assigning a use condition to the tire model in order to analyze tire performance in a use state, (c) a step of performing deformation calculation of the tire model, Analyzing the behavior of a tire in a use state by a tire behavior simulation method including the step of obtaining a physical quantity generated in the tire model in step (c), and (e) predicting the performance of the tire based on the physical quantity. Can do.

  Further, when analyzing the behavior of the tire by a computer, as described in claim 8, (A) as a tire model that can be deformed by ground contact and rolling as a numerical calculation model, 6. A step of determining the tire model according to any one of 6; (B) a step of assigning a use condition to the tire model in order to analyze tire performance in a use state; and (C) a deformation calculation of the tire model. (D) calculating a physical quantity generated in the tire model in the step (C), and (E) predicting the performance of the tire based on the physical quantity. Considering this, the behavior of the tire can be analyzed with high accuracy.

  Furthermore, when analyzing the behavior of a tire with a computer, (1) as a tire model that can be deformed by ground contact and rolling as a numerical calculation model, the tire model according to any one of claims 1 to 6 A step of defining a tire model, (2) a step of assigning a use condition to the tire model in order to analyze tire performance in a use state, (3) a step of executing deformation calculation of the tire model, (4) the step A tire behavior analysis program including a step of obtaining a physical quantity generated in the tire model in (3), and a step of (5) predicting the performance of the tire based on the physical quantity is stored in a storage medium, executed, and collected. By doing so, the tire behavior analysis can be accurately predicted in consideration of the contact portion of the tire.

  As described above, according to the present invention, it is possible to provide a model capable of accurately predicting tire behavior analysis in consideration of the contact portion of the tire, and there is an effect that efficient tire development can be realized.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In the present embodiment, the present invention is applied to tire behavior analysis.

[First embodiment]
FIG. 1 shows an outline of a personal computer for carrying out the tire behavior simulation method of the present invention. The personal computer includes a keyboard 10 for inputting data and the like, a computer main body 12 that predicts tire performance according to a pre-stored processing program, and a CRT 14 that displays calculation results of the computer main body 12 and the like.

  The computer main body 12 includes a flexible disk unit (FDU) into which a flexible disk (FD) as a recording medium can be inserted and removed. Note that processing routines and the like described later can be read from and written to the flexible disk FD using the FDU. Therefore, a processing routine to be described later may be recorded in the FD in advance and the processing program recorded in the FD may be executed via the FDU. Further, a mass storage device (not shown) such as a hard disk device is connected to the computer main body 12, and the processing program recorded on the FD is stored (installed) in the mass storage device (not shown) and executed. Also good. As the recording medium, there are optical disks such as CD-ROM and DVD, and magneto-optical disks such as MD and MO. When these are used, a corresponding device may be used instead of or in addition to the FDU. In addition to a personal computer, a workstation or a super computer may be used for tire analysis.

(Behavior simulation)
FIG. 2 shows a processing routine of a tire behavior analysis program according to the present embodiment. In step 100, a design plan (tire shape, structure, material, etc.) of a tire to be subjected to behavior analysis, or the tire itself when evaluating the performance of an existing tire is determined. In the next step 102, a tire tire model for creating a tire design plan into a numerical analysis model is created. The creation of the tire model differs slightly depending on the numerical analysis method used. In this embodiment, a finite element method (FEM) is used as a numerical analysis method. Therefore, the tire model created in step 102 is divided into a plurality of elements by element division corresponding to the finite element method (FEM), for example, mesh division, and the tire is created based on a numerical / analytical method. This is a digitized input data format for computer programs. This element division refers to dividing an object such as a tire and a road surface (described later) into several small (finite) small parts. After calculating every small part and calculating all the small parts, the whole response can be obtained by adding all the small parts.

  In the creation of the tire model in step 102, a tire model creation routine shown in FIG. 3 is executed. First, in step 112, a tire radial section model (tire section model, that is, tire section data) is created. In addition, rubber in the tire cross section and supplementary teaching materials (belt, ply, etc., which is a bundle of reinforcing cords made of iron / organic fibers, etc.) are modeled according to the modeling method of the finite element method. In the next step 114, two-dimensional tire cross-section data (tire radial cross-section model) is developed for one turn (360 degrees) in the circumferential direction to create a three-dimensional (3D) model of the tire.

  FIG. 18 shows an example of a tire cross-section model, and shows a pneumatic tire 20 having a carcass 22 divided for each of a plurality of rubber members. The carcass 22 is folded back by a bead 26. The inner side of the carcass 22 is an inner liner 24, and a bead rubber 36 is disposed on the inner liner 24 so as to extend. A substantially triangular area formed by the folded carcass 22 is a bead filler 28. A belt 30 is disposed above the carcass 22, a tread rubber 32 having a groove is disposed on the outer side in the radial direction of the belt 30, and a side rubber 34 is disposed on the outer side in the axial direction of the carcass 22. Yes. In addition, although the example which divided | segmented the tire cross-section model into multiple for every rubber member was given, you may divide | segment into arbitrary shapes, such as a triangle, according to the design objective.

  Next, in step 116 of FIG. 3, the constituent material of the rubber of each part of the tire is set. In this step, a constituent material having material characteristics such as rigidity corresponding to each part of the tire is selected.

  After the tire finite element model, that is, the tire model is created as described above, the process proceeds to step 104 in FIG. 2 to create a road surface model.

  In step 105 of FIG. 2, the friction coefficient of the tire contact portion is defined. Mainly defines the state of friction between the tire tread and the road surface. This is because the friction coefficient that influences the force acting when the rubber of each part of the tire comes into contact may depend on the contact pressure, the sliding speed, and the temperature. By doing so, it is possible to perform an analysis that matches the actual tire behavior.

  Therefore, in the present embodiment, paying attention to these dependencies, the friction coefficient μ is expressed by a function f as shown in the following equation.

μ = f (p, v, t)
However, p represents the ground pressure, v represents the speed, and t represents the temperature.

  In the above formula, it is assumed that the friction coefficient has all the dependencies of the ground pressure dependency, the sliding speed dependency, and the temperature dependency. Among these dependencies, at least one of these dependencies is assumed. You may make it have dependence. In this case, the dependency terms other than the target may be deleted or not considered (described later).

  Next, the dependency of the friction coefficient will be described in detail.

・ Contact pressure dependency First, the contact pressure dependency of the friction coefficient will be described. 4A and 4B are explanatory views of the contact pressure dependence, where FIG. 4A is a verification experiment assumption diagram, and FIG. 4B is a measurement result diagram.

  As shown in FIG. 4A, in order to determine the contact pressure dependency, a case is considered in which the rubber piece 20 is moved (pulled) in a direction substantially parallel to the road surface while being pressed against the road surface 22. At this time, each force is measured by using a lateral force Fx as a force to be moved (pulled) and a pressing force Fz as a force pressing the rubber piece 20 against the road surface 22. The measurement is performed under a plurality of conditions in which the lateral force Fx is changed when the pressing force Fz is changed. In this case, the contact pressure P can be obtained by dividing the pressing force Fz by the contact area S of the rubber piece 20 (P = Fz / S). The friction coefficient μ can be obtained by dividing the lateral force Fx by the pressing force Fz (μ = Fx / Fz). From this, FIG. 4B shows the result of determining the relationship between the ground pressure P and the friction coefficient μ based on the experimental results. Therefore, the characteristic of FIG. 4B shows the dependence of the friction coefficient μ on the ground pressure P. By approximating this characteristic curve with a mathematical expression, the characteristic of the friction coefficient μ having the contact pressure dependency of the rubber piece 20 can be expressed. This characteristic is obtained in advance for an elastic material having a friction coefficient such as a plurality of rubber pieces, and the dependence on the contact pressure of the friction coefficient can be specified by creating a database.

  In the above description, the friction coefficient μ having the contact pressure dependency for the contact portion between the tire and the road surface has been described. However, the present invention is not limited to this. For example, a friction coefficient having a contact pressure dependency may be defined for a contact portion between a tire and a rim or a contact portion between tread materials separated by a sipe. In this case, in order to handle the contact between the rim and the tire, the rubber piece 20 can be produced by testing using the rubber (the rubber covering the bead) at the portion in contact with the rim of the tire. A part of rubber may be cut out, or the rubber may be placed in a mold to create a test piece of a specified size.

-Sliding speed dependence Next, the sliding speed dependence of a friction coefficient is demonstrated. FIG. 5 is an explanatory diagram of the slip pressure dependency, (A) is a verification experiment assumption diagram, and (B) to (D) are measurement result diagrams of different rubber pieces.

  As shown in FIG. 5A, in order to obtain the slip dependency, a case is considered in which the rubber piece 20 is moved (pulled) at a predetermined speed in a direction substantially parallel to the road surface while pressing the rubber piece 20 against the road surface 22. At this time, the moving (pulling) speed is measured as the speed v. In this case, it was found that the speed dependency of the friction coefficient has a somewhat different tendency depending on the type of rubber used. Therefore, as a method for measuring the speed-dependent characteristics of the friction coefficient, a test in which the rubber piece 20 is pressed uniformly with the pressing force Fz, the speed v is changed, and the rubber piece 20 is pulled sideways is repeated several times. The pressing force Fz and lateral force Fx at each speed at that time are measured, and the friction coefficient μ is obtained by (= Fx / Fz) in the same manner as described above. As a result, the relationship between the speed v and the friction coefficient is obtained. FIGS. 5B, 5C, and 5D show characteristic curves as a result of conducting the above-described experiment on different rubber pieces. By approximating this characteristic curve with a mathematical expression, the characteristic of the friction coefficient μ having the slip dependency of the rubber piece 20 can be expressed. This characteristic is obtained in advance for an elastic material having a friction coefficient, such as a plurality of rubber pieces, and the slip dependency of the friction coefficient can be specified by creating a database.

  In the above description, the friction coefficient μ having slip dependency on the contact portion between the tire and the road surface has been described. However, the present invention is not limited to this. For example, a friction coefficient having a slip dependency may be defined for a contact portion between a tire and a rim or a contact portion between tread materials separated by a sipe. Furthermore, since it may change according to the smoothness (unevenness) of the road surface, it is important to measure the road surface used in the simulation.

  Further, the friction coefficient μ having the slip dependency may define a different function depending on the direction of the acting force. For example, the friction coefficient having the slip speed dependency may be defined independently of the slip speed dependency component in the tire circumferential direction and the slip speed dependency component in the tire width direction. By defining in this way, it is possible to determine the friction coefficient in accordance with each state during straight traveling and during turning, and simulation can be performed with a friction coefficient close to an actual state.

-Temperature dependence Next, the temperature dependence of a friction coefficient is demonstrated. FIG. 6 is an explanatory diagram of temperature dependence, (A) is a verification experiment assumption diagram, and (B) is a measurement result diagram.

  As shown in FIG. 6A, in order to obtain the temperature dependence, when the rubber piece 20 is moved (pulled) in a direction substantially parallel to the road surface while pressing the rubber piece 20 against the road surface 22 as in the above-described experiment, the rubber piece 20 The temperature T is changed and measured. In this case, for one temperature, the temperature of the rubber piece 20, the temperature of the road surface 22, and the atmospheric temperature are measured at a constant temperature T, and the temperature change is measured by measuring a plurality of temperatures. . At this time, the pressing force Fz and the speed v are measured under certain conditions. The result of the experiment performed in this manner is shown in FIG. The characteristic of FIG. 6B shows the dependence of the friction coefficient μ on the temperature T. By approximating this characteristic curve with a mathematical expression, the characteristic of the friction coefficient μ having temperature dependency of the rubber piece 20 can be expressed. This characteristic is obtained in advance for an elastic material having a friction coefficient such as a plurality of rubber pieces, and the temperature dependence of the friction coefficient can be specified by creating a database.

  In the above description, the friction coefficient μ having temperature dependency for the contact portion between the tire and the road surface has been described, but the present invention is not limited to this. For example, a friction coefficient having temperature dependency may be defined for a contact portion between a tire and a rim or a contact portion between tread materials separated by a sipe.

-Complex dependency Next, the case where the said dependency is considered complex is demonstrated. FIG. 7 is an explanatory diagram of the dependence on an arbitrary rubber piece, where (A) shows the ground pressure dependence, (B) shows the speed dependence, and (C) shows the temperature dependence.

  The above-mentioned ground pressure dependency, speed dependency, and temperature dependency show the dependency when other factors (dependencies) are fixed, respectively. In an actual tire, the contact pressure differs within the contact surface of the tire that is in contact with the ground, and also varies depending on running conditions. The speed (sliding speed) also varies depending on the place where the tire is in contact with the ground, and also varies depending on the running conditions. Similarly, the temperature varies depending on the environmental temperature. These fluctuations overlap to change the actual tire friction coefficient.

  Also in the finite element model of the present embodiment, the functions of the above-described contact pressure dependency, speed dependency, and temperature dependency are defined and expressed. A superposition (multiplication) of these defined functions is a friction coefficient μ in a state to be obtained. For example, the case where each has a friction coefficient μo at an arbitrary ground pressure Po, sliding speed Vo, and temperature To is used as a reference (see FIG. 7). The friction coefficient μs in an arbitrary contact state of the tire can be obtained by considering the variation from the reference state as follows.

First, let the contact state in the different part of a tire be the contact pressure P1, the sliding speed V1, and the temperature T1. At this time, the change ratio Cp of the friction coefficient μ when the contact pressure Po changes to P1, the change ratio Cv of the friction coefficient μ when the sliding speed Vo changes to V1, and the friction when the temperature To changes to T1. Each change ratio Ct of the coefficient μ is obtained. As shown in the following equation, the coefficient of friction μs in an arbitrary contact state can be obtained by multiplying these obtained change ratios. The following equation corresponds to the equation for obtaining the friction coefficient μ by the function f described above.
μs = Cp, Cv, Ct, μo
In the above conditions, if the temperature is always constant, the friction coefficient can be obtained in consideration of the ground pressure dependency and the speed dependency. That is, the change rate Ct related to temperature may be constant (= 1). In order to simplify the mathematical formula, the term may be deleted as shown in the following formula. The same applies to either pressure dependency or slip dependency.
μs = Cp ・ Cv ・ μo
However, the temperature is always constant.

  In the above description, the dependence coefficient is defined by a function and the friction coefficient in an arbitrary state is represented by superimposing them. However, the present invention is not limited to this. For example, as another method, the dependency of the friction coefficient can be given by a matrix. An example of the matrix expression is that the ground pressure 3 levels P1, P2, P3, the sliding speed 3 levels V1, V2, V3, the temperature 3 levels T1, T2, T3 are determined in advance. The coefficient of friction is measured by this method. If this is defined as a database in the form of a matrix, the friction coefficient under an arbitrary condition can be calculated from the matrix of the database during FEM calculation. When calculating, for example, the matrix may be obtained by curve fitting.

  In this case, assuming a simulation in which the temperature is always constant at T1, the friction coefficient considers the contact pressure dependency and the sliding speed dependency. In this case, the friction coefficient can be defined as shown in the following table.

  Here, a specific method for measuring the friction coefficient of rubber will be described.

  First, as a rubber that is an elastic material used for obtaining a friction coefficient, a rubber in a tread portion of a tire is used. This is because the tire is in contact with the road surface mainly due to the tread portion. The tread part is usually made of one kind of rubber. Therefore, there are the following two examples of methods for producing the rubber piece 20 (test piece). The first example is a method of cutting rubber from an actual tire to create a rubber piece 20. In the second example, a mold in the shape of a test piece is made, unvulcanized rubber before vulcanization is pushed into the mold, and a high temperature and a high pressure are applied in the same manner as in the actual tire preparation, and the rubber piece 20 Is a way to create.

  Next, the produced rubber piece 20 is made into thin cylindrical rubber (about 500 yen coin size). The rubber piece 20 is pressed against the road surface with the pressing force Fz, and the lateral force Fx is measured when the rubber piece 20 moves left and right at the speed v. At this time, since the friction coefficient is obtained (Fx / Fz) as described above, the ground pressure dependency of the friction coefficient can be obtained by measuring the pressing force Fz. Next, the pressing coefficient Fz is constant, the moving speed v is changed, and the friction coefficient is obtained in the same manner. The speed dependence of the friction coefficient can be obtained by changing the speed v. Next, the environmental temperature of the testing machine is controlled and the temperature is changed. Here, the coefficient of friction is measured while changing from 110 degrees to 130 degrees. For example, a rubber for racing shows a high friction coefficient at 80 degrees or more, and the friction coefficient is not so high at room temperature. The coefficient of friction is defined using these experimental values.

  As described above, by creating a finite element model of a tire with a friction coefficient having a contact state characteristic considering the ground pressure dependency, the sliding speed dependency, and the temperature dependency of the friction coefficient, high accuracy is achieved. FEM analysis can be performed.

  In the above description, the tire finite element model is described as an object of the friction coefficient. However, the tire finite element model is not limited to the finite element model, and can be applied to a physical tire model such as FTire, RMOD-K, or CDTire. It is. The method of the present invention is not limited to dry road surfaces (dry: DRY), but can be applied to wet (wet: WET), ice, and snowy road surfaces.

  When the friction coefficient is set in this way, the boundary condition is set in the next step 106. The boundary conditions are necessary for analysis of the tire model, that is, for simulating the behavior of the tire, and are various conditions given to the tire model. In setting the boundary condition in step 106, first, an internal pressure is applied to the tire model, and at least one of rotational displacement and straight displacement (displacement may be force or speed) and a predetermined load load are applied to the tire model. give. With these settings, the friction coefficient μ can be determined dynamically. That is, for example, the contact pressure dependency can be taken into account by internal pressure or load load, the speed dependency can be taken into account by determining the rotation speed, and the temperature dependency is taken into account by setting the temperature such as the environmental temperature. can do. Note that the dynamic consideration of the friction coefficient μ may be processed in the next step.

  Next, a deformation calculation of the tire model as an analysis is performed based on the numerical model created or set up to step 106. That is, when the setting of the boundary condition is completed in step 106, the process proceeds to step 108, and the tire model is calculated for deformation. In this step 108, deformation calculation of the tire model is performed based on the finite element method from the tire model and the given boundary conditions. This deformation calculation repeats the tire model deformation calculation (for example, repeat the calculation within 1 msec) in order to obtain the tire rolling state (to obtain a transient state), and each time the boundary condition May be updated. The deformation calculation can employ a predetermined calculation time assuming that the tire deformation is in a steady state. In the next step 110, the calculation result is output. This calculation result uses a physical quantity at the time of tire deformation.

  The calculation result may be output by visualizing the value or distribution of the shape of the contact portion of the tire, the distribution of the contact pressure, the force acting on the center of the tire, or the like. These can be derived from the calculation result value, amount of change or rate of change, force direction (vector), and distribution, and if they are displayed together with the tire model and pattern periphery in a diagram, etc., they are presented for easy understanding. Possible visualizations can be made.

  As described above, in the present embodiment, the friction coefficient is dynamically determined for the contact portion of the tire based on the ground pressure, speed, and temperature dependence, so that the simulation according to the actual tire behavior is performed. Can do.

  When analyzing the behavior of a tire, it is important to analyze the rim and the tire as a single structure by combining the tire and the rim as an analysis target. In this case, an assembly model creation process is added to the above process (after step 102 in FIG. 2), and in the setting of the friction coefficient in step 105 in FIG. The friction coefficient is set, and the tire model deformation calculation (step 108) may be executed instead of the assembly model deformation calculation. The assembly model creation processing may be performed by modeling the rim and creating an assembly model in which the rim model is assembled to the tire model. As described above, by analyzing with an FEM using an assembly model composed of a tire model and a rim model (wheel), it is possible to easily analyze not only a tire but also a tire with a rim.

  Next, embodiments of the present invention will be described in detail.

[First embodiment]
In the present embodiment, the analysis in which the block model is brought into contact with a flat road surface is examined for the case where the ground pressure dependency is considered and the case where it is not considered. The rubber piece 20 used in this example was modeled for simulation (FEM) as described above using a rectangular rubber piece having a width of 30 mm, a depth of 20 mm, and a height of 8 mm. This modeled rubber piece is shown in FIG. This shape assumes one land portion arranged on the tread surface of the tire. Hereinafter, this one land part is called a block.

  The ground pressure distribution when this block was pressed against a flat plate was analyzed by the above simulation. The pressing force is 15 kgf. At this time, the average contact pressure is 250 kPa.

  Next, the case where the friction coefficient was made constant at 1.0 and no contact pressure dependency was considered, and the case where the friction coefficient considering the contact pressure dependency according to the above embodiment was input were examined. FIG. 8B is a plot of the ground pressure distribution on the center line of the block (for the middle abdomen) from end to end. The friction coefficient used for the ground pressure dependency is 1.0 at 200 kPa and 0.6 at 400 kPa, as shown in FIG.

  From the above analysis, when the friction coefficient was fixed at 1.0, a very high contact pressure was shown at the edge of the block. This analysis result was found to be too high at the edge portion when compared with the actual measurement value. On the other hand, in the analysis using the friction coefficient using the contact pressure dependency obtained from the experiment, the contact pressure does not rise abnormally at the edge portion and is at a reasonable level according to the actual measurement. Therefore, it can be understood that an accurate analysis was performed by inputting a friction coefficient considering the contact pressure dependency.

[Second Embodiment]
In this embodiment, a physical model is adopted as a tire model, and analysis is performed in consideration of slip dependency of a friction coefficient. Further, in this example, for a tire having a tire size of 235 / 50R16, the lateral force when the speed 100 km, the pressing force Fz with a load 4 kN, and the slip angle SA were changed was analyzed.

  9A and 9B show the relationship between the slip angle SA and the lateral force Fy. FIG. 9A shows the case where the friction speed dependence of the friction coefficient is not considered, and FIG. 9B shows the case where the friction speed dependence of the friction coefficient is considered. ing. In the figure, the dotted line indicates the characteristic of the actual measurement value, and the solid line indicates the characteristic of the predicted value by analysis.

  In the analysis by the physical model, the friction coefficient is defined in the following Table 2 and Table 3. In both analyses, the ground pressure dependence of the friction coefficient is taken into account.

  As understood from FIG. 9 and Tables 2 and 3, if the slip speed dependency is not taken into account, it is deviated from the actual measurement value especially when the slip angle SA is large, but by considering the slip speed dependency of the friction coefficient. A predicted value close to the actually measured value can be obtained, and a highly accurate analysis can be realized.

[Third embodiment]
In this embodiment, cornering analysis using a high performance PSR is performed. That is, the analysis in the case where the slip angle SA is changed while the tire model is in contact with a flat road surface is examined with and without considering the ground pressure dependency. In this example, explicit FEM was used for analysis (simulation).

  Further, in the present embodiment, the ground contact shape when the tire of tire size P225 / 55R16 turns at a speed of 100 km / h and a slip angle SA of 4 degrees is predicted. FIG. 10A shows the prediction conditions, FIG. 10B shows the ground contact portion when the slip speed dependency is taken into consideration, and FIG. 10C shows the contact portion when the slip speed dependency is not taken into consideration.

  In FIGS. 10B and 10C, the difference in ground pressure is represented by changing the hatched area. Moreover, the figure is an image of the ground contact portion of the tire as viewed from below (from the direction facing the tire). That is, it corresponds to looking up from below the road surface how the tire rolls on the transparent road surface. At this time, the load is 400 kgf and the camber angle is 0 degree. The internal pressure is 200 kPa.

  As can be understood from FIGS. 10B and 10C, when the coefficient of friction is constant (FIG. 10C), when each node of the finite element contacts the road surface, it can slip smoothly. It is not possible to get caught on the road surface. Therefore, the ground pressure distribution tends to be discontinuous and is not accurate. In particular, it is considered that the portion where the contact pressure is high is difficult to slip when the friction coefficient is constant, and the edge portion of the contacted area is easily caught on the road surface.

  On the other hand, when the contact pressure dependency and the sliding speed dependency are included in the friction coefficient, the analysis is performed smoothly. In other words, the friction coefficient of the portion where the contact pressure is high is reduced by considering the contact pressure dependency, and the friction coefficient of the portion where the sliding speed is high is also reduced by considering the dependency of the sliding speed. It was possible to perform an analysis close to.

[Fourth embodiment]
In this embodiment, a physical model is adopted as a tire model, and analysis is performed in consideration of temperature dependence of a friction coefficient. Further, in the present embodiment, as in the second embodiment, the lateral force when the speed is 100 km, the pressing force Fz with a load of 4 kN, and the slip angle SA is changed is analyzed for a tire having a tire size of 235 / 50R16. did.

  FIG. 11 shows the relationship between the slip angle SA and the lateral force Fx. FIG. 11A shows the temperature dependence of the friction coefficient when the temperature is 25 degrees, and FIG. 11B shows the temperature of the friction coefficient when the temperature is 50 degrees. The case where the dependency is considered is shown. In the figure, the dotted line indicates the characteristic of the actual measurement value at a temperature of 50 degrees, and the solid line indicates the characteristic of the predicted value obtained by analysis at each temperature.

  The coefficient of friction is defined in the following Tables 2 and 3. In both analyses, the ground pressure dependence of the friction coefficient is taken into account.

  As understood from FIG. 11 and Tables 4 and 5, the lateral force is smaller than the experimental value if the temperature dependence of the friction coefficient is not taken into consideration. On the other hand, if the coefficient of friction at a temperature of 50 degrees is specified by experiment and the coefficient of friction is correctly determined as shown in the table above, a characteristic that substantially matches the experimental value is obtained as shown in FIG. It was. Therefore, since the friction coefficient of the rubber material changes depending on the temperature, it can be understood that it is necessary to consider the temperature dependence of the friction coefficient in the simulation. As described above, by using a temperature-dependent friction coefficient, it is possible to obtain a predicted value that is close to the actual measurement value, thereby realizing a highly accurate analysis.

[Fifth embodiment]
In this embodiment, a tire for a passenger car is modeled as a tire model, and analysis is performed by changing the friction coefficient in the tire circumferential direction and the friction coefficient in the tire width direction. Further, in this example, a tire for a passenger car having a tire size of 215 / 55R15 was employed in which the pattern had only four longitudinal grooves in the circumferential direction and no lateral grooves.

  In this embodiment, the friction coefficient in the tire circumferential direction and the friction coefficient in the tire width direction are handled, the force in the tire circumferential direction is set as the longitudinal force Fx, the force in the tire width direction is set as the lateral force Fy, and both are simulated.

  FIG. 12A shows a side view of the tire model, and FIG. 12B shows the contact shape of the tire model when traveling straight along with the distribution of contact pressure. FIG. 12B shows a contact portion when pressed with a load of 400 kgf. FIG. 12B shows the distribution of ground pressure.

  FIG. 13 shows the friction coefficient used in the analysis in this example. As shown in FIG. 13, in this example, a friction coefficient considering slip speed dependency is used. When the sliding speed is 0, the coefficient of friction is 1.0, and the coefficient of friction decreases as the sliding speed increases.

  FIG. 14 shows the result of analysis using the characteristics of the friction coefficient with respect to the sliding speed shown in FIG.

  FIG. 14 (A) shows the lateral force Fy generated when the slip angle SA is changed from −10 degrees to +10 degrees while rolling the tire at a speed of 40 km / h. This is a comparison. In the figure, the dotted line indicates the characteristic based on the actual measurement value, and the solid line indicates the prediction result obtained by the analysis. As shown in FIG. 14A, the actual measurement value and the analysis result value of the lateral force are substantially the same.

  On the other hand, FIG. 14B compares the longitudinal force when the slip ratio is given in the front-rear direction between the actually measured value and the calculated value by analysis. In the figure, the dotted line indicates the characteristic based on the actual measurement value, and the solid line indicates the prediction result obtained by the analysis. In this case, the speed is 40 km / h and the load is 400 kgf. The slip ratio can be defined by giving a difference between the road surface speed and the tire speed, and% represents the difference. For example, a tire is in such a state when an automobile accelerates or decelerates.

  As shown in FIG. 14B, the actual measurement result and the analysis result do not coincide with each other and an error occurs. In the example of FIG. 14B, the characteristic based on the actually measured value (dotted line) generates a higher longitudinal force Fx.

  Accordingly, when one friction coefficient is defined by the characteristics shown in FIG. 13, the lateral force corresponds to the actual measurement value, but the longitudinal force may not match the actual measurement value.

  Here, it is natural that the predicted value obtained by the analysis and the actually measured value obtained by the experiment or the like are desired to coincide with each other. For example, when a vehicle is modeled and four tire models are attached to the vehicle and a vehicle simulation is performed, the tire model has the same lateral force characteristics and longitudinal force characteristics as the actual tire as much as possible. It is important that This necessitates the creation of a tire model having characteristics close to actual measurements. Therefore, it is clear that the setting of the friction coefficient has a large effect on the front and rear force and the lateral force. Therefore, adjusting the friction coefficient setting according to the directionality of the lateral force Fy of the predicted value based on the actual measurement and analysis and the front and rear It is most effective in adjusting the difference in force Fx.

  In the present embodiment, the lateral force Fy almost coincided, but the longitudinal force Fx did not coincide, so the friction coefficient in the lateral direction (tire width direction) and the longitudinal direction (tire circumferential direction). It is preferable to set the coefficient of friction separately. The purpose is to make both lateral force and longitudinal force predictable by FEM as in the actual measurement.

  Therefore, as shown in FIG. 16, two friction coefficients are determined in accordance with the direction handled by the tire. In the figure, the solid line represents the friction coefficient shown in FIG. 13, and this friction coefficient is used as the characteristic of the friction coefficient in the tire width direction as it is. A broken line is a characteristic of the friction coefficient obtained by increasing the friction coefficient by 20% of the solid line, and this friction coefficient is used as a characteristic of the friction coefficient with respect to the circumferential direction of the tire. That is, as shown in FIG. 17, a solid line friction characteristic is defined separately in the tire width direction, and a broken line friction coefficient is defined separately in the tire circumferential direction.

  Thus, the prediction result which analyzed the friction coefficient separately in the tire circumferential direction and the tire width direction and analyzed is shown in FIG. FIG. 15A shows the prediction result of the lateral force Fy, and FIG. 15B shows the prediction result of the longitudinal force Fx. In FIG. 15B, the solid line in FIG. 14B is shown by a thin line, and the prediction result when a separate friction coefficient is determined in the circumferential direction of the tire is shown by a thick solid line.

  As can be understood from FIG. 15, by determining two friction coefficients (the friction coefficient in the tire width direction and the friction coefficient in the tire circumferential direction) according to the direction handled by the tire, both the longitudinal force and the longitudinal force can be obtained. Almost matched. For this reason, for example, if attention is paid to the tire longitudinal force and the friction coefficient is uniformly increased (by one friction coefficient) by 20%, it is considered that the lateral force is greatly shifted even if the longitudinal force characteristics match. As in this embodiment, by defining the friction coefficients of different sizes separately for the width direction and the circumferential direction of the tire, it is possible to analyze according to the direction handled by the tire.

  This is because the force generated by the tire in the front-rear direction and the force generated by the tire in the width direction often differ in size. In this case, by defining two friction coefficients, the accuracy is high. FEM prediction can be enabled.

  In this embodiment, the two forces of the force generated by the tire in the front-rear direction and the force generated by the tire in the width direction have been described. However, the present invention is not limited to this, and is generated by tire analysis. The coefficient of friction for other directions may be defined.

1 is a schematic view of a personal computer for carrying out a tire behavior simulation method according to an embodiment of the present invention. It is a flowchart which shows the flow of a process of the tire behavior analysis program concerning embodiment of this invention. It is a flowchart which shows the flow of a tire model creation process. It is explanatory drawing of the ground pressure dependency concerning this Embodiment, (A) is a verification experiment assumption figure, (B) is a measurement result figure. It is explanatory drawing of the sliding speed dependence concerning this Embodiment, (A) is a verification experiment assumption figure, (B) is a measurement result figure by arbitrary rubber pieces, (C) is a measurement result figure by other rubber pieces. (D) is a measurement result figure by the rubber piece other than that. It is explanatory drawing of the temperature dependence concerning this Embodiment, (A) is a verification experiment assumption figure, (B) is a measurement result figure. It is explanatory drawing of the dependence regarding the arbitrary rubber | gum pieces concerning this Embodiment, (A) shows ground pressure dependence, (B) shows speed dependence, and (C) shows temperature dependence. In the first embodiment, (A) is an image view of a modeled rubber piece, (B) is a contact pressure distribution on the center line of the block (for the middle abdomen), and (C) is a relationship between the contact pressure and the friction coefficient. FIG. It is the relationship between the slip angle SA and the lateral force Fx in the second embodiment, where (A) does not consider the dependency of the friction coefficient on the sliding speed, and (B) indicates the case where the dependency of the friction coefficient on the sliding speed is considered. FIG. Regarding the third embodiment, (A) shows prediction conditions, (B) shows a ground contact portion in consideration of slip speed dependency, and (C) shows a ground contact portion in consideration of slip speed dependency. FIG. Regarding the fourth example, the relationship between the slip angle SA and the lateral force Fx is shown. (A) shows the temperature dependence of the friction coefficient when the temperature is 25 degrees, and (B) shows the friction when the temperature is 50 degrees. It is a characteristic view which shows the case where the temperature dependence of a coefficient is considered. (A) shows a side view of the tire model, (B) is a diagram showing the contact shape of the tire model when traveling straight. It is a characteristic view which shows one friction coefficient in 5th Example. FIG. 13 shows a curve showing the relationship between the slip angle and the force by the friction coefficient shown in FIG. 13, where (A) shows lateral force and (B) shows longitudinal force. As an analysis result of the fifth example, a curve indicating a relationship between a slip angle and a force is shown, (A) shows a lateral force, and (B) shows a longitudinal force. It is a characteristic view which shows two friction coefficients in 5th Example. It is explanatory drawing of the friction coefficient definition of 5th Example. It is a diagram which shows a tire cross-section model.

Explanation of symbols

10 Keyboard 12 Computer body 14 CRT
30 Tire model FD Flexible disk (recording medium)

Claims (9)

In order to simulate the behavior of the tire in use, a tire model that calculates a tire corresponding to a numerical calculation model,
A friction coefficient having a contact pressure dependency is defined for at least one of a contact portion between a tire and a road surface, a contact portion between a tire and a rim, and a contact portion between tread materials separated by a sipe. model. In order to simulate the behavior of the tire in use, a tire model that calculates a tire corresponding to a numerical calculation model,
A friction coefficient having a sliding speed dependency is defined for at least one of a contact portion between a tire and a road surface, a contact portion between a tire and a rim, and a contact portion between tread materials separated by a sipe. model.   The friction coefficient having the slip speed dependency has independently a component of the slip speed dependency with respect to the tire circumferential direction and a component of the slip speed dependency with respect to the tire width direction. Tire model. In order to simulate the behavior of the tire in use, a tire model that calculates a tire corresponding to a numerical calculation model,
A tire model having a temperature-dependent friction coefficient defined for at least one of a contact portion between a tire and a road surface, a contact portion between a tire and a rim, and a contact portion between tread materials separated by a sipe . In order to simulate the behavior of the tire in use, a tire model that calculates a tire corresponding to a numerical calculation model,
At least one of a contact portion between a tire and a road surface, a contact portion between a tire and a rim, and a contact portion between tread materials separated by a sipe is at least two of contact pressure dependency, slip speed dependency, and temperature dependency A tire model characterized by defining a coefficient of friction having dependency.   6. The friction coefficient having the slip speed dependency has independently a slip speed dependency component with respect to a tire circumferential direction and a slip speed dependency component with respect to a tire width direction. Tire model. A tire behavior simulation method including the following steps.
(A) The step which determines the tire model of any one of Claim 1 thru | or 6 as a tire model which can give a deformation | transformation by contact and rolling as a numerical calculation model.
(B) A step of assigning a use condition to the tire model in order to analyze the tire performance in the use state.
(C) A step of performing deformation calculation of the tire model.
(D) A step of obtaining a physical quantity generated in the tire model in the step (c).
(E) A step of predicting the performance of the tire based on the physical quantity. A tire behavior analysis program comprising the following steps for analyzing tire behavior by a computer.
(A) The step which determines the tire model of any one of Claim 1 thru | or 6 as a tire model which can give a deformation | transformation by contact and rolling as a numerical calculation model.
(B) A step of assigning use conditions to the tire model in order to analyze tire performance in use.
(C) A step of executing deformation calculation of the tire model.
(D) A step of obtaining a physical quantity generated in the tire model in the step (C).
(E) A step of predicting the performance of the tire based on the physical quantity. A recording medium recording a tire behavior analysis program for analyzing tire behavior by a computer, the recording medium recording a tire behavior analysis program characterized by including the following steps.
(1) A step of determining a tire model according to any one of claims 1 to 6 as a tire model capable of being deformed by ground contact and rolling as a numerical calculation model.
(2) A step of assigning use conditions to the tire model in order to analyze tire performance in use.
(3) A step of executing deformation calculation of the tire model.
(4) A step of obtaining a physical quantity generated in the tire model in the step (3).
(5) A step of predicting tire performance from the physical quantity.

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