JP2016045798A - Simulation method of tire - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide the simulation method of a tire capable of accurately evaluating transient cornering characteristics of the tire.SOLUTION: A simulation method of a tire for evaluating transient cornering characteristics of the tire using a computer includes: a tire model setting step #1 for setting a tire model in which the tire is subjected to modeling with a finite number of elements capable of numerical analysis; a rolling motion step #3 for making the tire model perform rolling motion on a virtual road surface based on a prescribed boundary condition; a lateral force calculation step #5 for calculating a lateral force that the tire model generates at each slip angle while the slip angle of the tire model is gradually increased or gradually decreased; and a time constant calculation step #7 for calculating the time constant of a delay transfer function based on the lateral force.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a tire simulation method for evaluating transient characteristics of a tire using a computer.

  Conventionally, various techniques for evaluating tire characteristics by simulation using a computer have been proposed.

  For example, in Patent Document 1 below, a tire model obtained by modeling a tire with a finite number of elements capable of numerical analysis is set, and the tire model is rolled on a virtual road surface based on predetermined boundary conditions. A technique for calculating a physical quantity of a tire model is disclosed.

JP2013-216167A

  By the way, as an index indicating a steady cornering characteristic of a tire, there is a lateral force generated per unit slip angle. On the other hand, in order to evaluate the transient cornering characteristics of a tire, it has been proposed to use a time constant that is a delay from when a slip angle is applied to the tire until a lateral force is generated as an index.

  However, the technology for calculating the time constant by simulation has not been sufficiently developed at present, and establishment of a new simulation method is required.

  The present invention has been devised in view of the above circumstances, and a main object of the present invention is to provide a tire simulation method capable of accurately evaluating the transient cornering characteristics of a tire in a short time.

  A first invention of the present invention is a tire simulation method for evaluating transient characteristics of a tire using a computer, and a step of setting a tire model in which a tire is modeled by a finite number of elements that can be numerically analyzed Rolling the tire model on a virtual road surface based on a predetermined boundary condition, and generating the tire model at each attitude angle while gradually increasing or decreasing the attitude angle of the tire model. And calculating a time constant of a delay transfer function based on the lateral force.

  In the simulation method according to the first aspect of the invention, it is preferable that the posture angle is gradually decreased or gradually increased by a predetermined constant value.

  In the simulation method according to the first aspect of the invention, it is desirable that the posture angle includes a slip angle.

  In the simulation method according to the first aspect of the present invention, it is desirable that the posture angle includes a camber angle.

  A second invention of the present invention is a tire simulation method for evaluating transient characteristics of a tire using a computer, and a step of setting a tire model in which a tire is modeled by a finite number of elements capable of numerical analysis And rolling the tire model on a virtual road surface while fixing the tire model at a predetermined slip angle and camber angle based on a predetermined boundary condition, and gradually increasing the axial load of the tire model. Alternatively, the method includes a step of calculating a lateral force generated by the tire model at each axial load while gradually decreasing, and a step of calculating a time constant of delay based on the lateral force.

  In the simulation method according to the first aspect of the invention, it is preferable that the axial load is gradually decreased or gradually increased at a predetermined constant value.

  In the simulation methods according to the first and second aspects of the present invention, it is preferable that the transfer function includes a time constant of a first-order lag transfer function.

  In the simulation method according to the first and second aspects of the invention, it is preferable that the transfer function includes a second-order lag transfer function.

  A simulation method according to a first aspect of the present invention includes a step of setting a tire model obtained by modeling a tire with a finite number of elements that can be numerically analyzed, and a tire model on a virtual road surface based on a predetermined boundary condition. Rolling. As a result, a steady rolling state of the tire model is obtained.

  Furthermore, the simulation method of the first invention includes a step of calculating a lateral force generated by the tire model at each posture angle while gradually increasing or decreasing the posture angle of the tire model. Thereby, the change in the attitude angle input to the tire model becomes quasi-static, and no torsional vibration that affects the calculation occurs between the tread portion and the bead portion of the tire model. Therefore, the noise component included in the calculated lateral force is reduced, and the time constant can be obtained accurately and uniquely.

  Further, the simulation method of the first invention includes a step of calculating a time constant of the delay transfer function based on the lateral force calculated for each posture angle. As a result, when the change rate of the posture angle and the change rate of the lateral force are considered to be equal, the time constant can be calculated, and the time constant can be obtained easily and in a short time.

  In the simulation method of the second invention of the present invention, a tire model is determined in advance based on a step of setting a tire model obtained by modeling a tire with a finite number of elements that can be numerically analyzed, and a predetermined boundary condition. Rolling on a virtual road surface while fixing at the determined slip angle and camber angle. As a result, a steady rolling state of the tire model is obtained.

  Further, the simulation method of the second invention includes a step of calculating a lateral force generated by the tire model at each axial load while gradually increasing or decreasing the axial load of the tire model. Thereby, the change of the axial load input to the tire model becomes quasi-static, and no torsional vibration that affects the calculation occurs between the tread portion and the bead portion of the tire model. Therefore, the noise component included in the calculated lateral force is reduced, and the time constant can be obtained accurately and uniquely.

  Further, the simulation method of the second invention includes a step of calculating a time constant of the delay transfer function based on the lateral force calculated for each axial load. As a result, when the change rate of the axial load and the change rate of the lateral force are considered to be equal, the time constant can be calculated, and the time constant can be obtained easily and in a short time.

It is a perspective view which shows an example of the computer used by this embodiment. It is a flowchart which shows the process sequence of embodiment of 1st invention of this invention. It is a perspective view which visualizes and shows a tire model. It is a graph which shows transition of the slip angle input into a tire model, and the lateral force calculated with a tire model. It is a flowchart which shows the process sequence of another embodiment of 1st invention of this invention. It is a flowchart which shows the process sequence of embodiment of 2nd invention of this invention. It is a graph which shows the correlation with the relaxation length of the tire model calculated through the simulation method of 1st invention of this invention, and the relaxation length of the tire obtained from measurement.

  FIG. 1 shows a computer 1 for carrying out the simulation method of the present invention. The computer 1 includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with an arithmetic processing unit (CPU), a ROM, a working memory, a mass storage device such as a magnetic disk (all not shown), and drive devices 1a1, 1a2 such as a CD-ROM. The large-capacity storage device stores a processing procedure (program) necessary for executing a simulation method described later.

  FIG. 2 shows an embodiment of the processing procedure of the simulation method of the first invention of the present invention performed using the computer 1. First, in the present embodiment, a tire model setting step (# 1) for setting a tire model in which a tire is modeled with a finite number of elements that can be numerically analyzed is performed. Here, that numerical analysis is possible means that it can be handled by a numerical analysis method such as a finite element method, a finite volume method, a difference method or a boundary element method. In this example, the finite element method and the finite volume method are used. Adopted.

  In FIG. 3, an example of the tire model 2 created using the computer 1 is visualized and represented in three dimensions. The tire model 2 is modeled by representing a tire to be analyzed using a finite number of small elements 2a, 2b, 2c. Such an entity of the tire model 2 is numerical data that can be handled by the computer 1. Specifically, node coordinate values, element numbers, node numbers, and the like of each element 2a, 2b, 2c... Are defined. In the tire model 2 of the present embodiment, a carcass, a belt layer, a bead core, and the like are modeled in addition to various rubbers such as a tread rubber, a side wall rubber, and a bead apex rubber constituting the tire.

  As each of the elements 2a, 2b, 2c..., For example, a tetrahedral solid element suitable for expressing a complex shape is preferable, but a pentahedral or hexahedral solid element may be used in addition to this.

  Each element 2a, 2b, 2c... Is defined with numerical data such as an element number, a node number, a node coordinate value, and material properties (for example, density, Young's modulus and / or attenuation coefficient, etc.) and stored in the computer 1. The

  As shown in FIG. 2, in the boundary condition setting step (# 2), conditions necessary for performing the steps described later are defined. The set conditions include, for example, the rim on which the tire model 2 is mounted, the internal pressure, the friction coefficient between the virtual road surface and the tire model 2, the initial slip angle, the initial camber angle, the rolling speed, and the tire model of the tire model 2. Conditions such as the initial time increment at the time of deformation calculation 2 and the initial position of the tire model 2 are included. In the present embodiment, the initial slip angle and the initial camber angle of the tire model 2 are both zero, but may be set to predetermined angles.

  The virtual road surface is a model of a road surface on which a tire travels. In the present embodiment, the virtual road surface is modeled by plane rigid elements arranged horizontally.

  Next, a rolling step (# 3) for rolling the tire model 2 on the virtual road surface is executed based on the boundary condition. In this rolling step (# 3), the computer 1 calculates a state in which the tire model 2 rolls on the virtual road surface based on predetermined conditions of traveling speed, internal pressure and load (hereinafter referred to as “rolling calculation”). ").

  In the rolling calculation, deformation calculation of the tire model 2 is mainly performed. In this deformation calculation, the mass matrix, stiffness matrix and damping matrix of each element are created based on the shape and material properties of each element, and the matrix of the entire system is created by combining these matrices. .

  Then, equations of motion are created by applying the above various conditions, and these are sequentially calculated and stored in the computer 1 in increments of minute time increments Δt (for example, 1 μsec). Thereby, physical quantities such as coordinate values, stress, and strain of each element of the rolling tire model 2 can be calculated in time series.

  The above-mentioned rolling calculation can be performed using, for example, engineering analysis application software using a finite element method (for example, LS-DYNA developed and improved by Livermore Software Technology, USA).

  A steady rolling state of the tire model 2 is obtained on the computer 1 by the rolling calculation executed in the rolling step (# 3). Thereafter, the slip angle of the rolling tire model 2 is input, and the time constant of the delay is calculated.

  As examples of slip angle input, for example, a method using a function represented by a sine wave, or a method using step input that discretely fluctuates in one step up to a target value of the slip angle with an infinite increase angle of the slip angle. Can be considered. However, in the method using a function represented by a sin wave, the calculation time until the time constant is calculated becomes very long, and it is difficult to perform simulation for a large number of tire models. On the other hand, in the method using step input, a torsional vibration occurs between the tread portion and the bead portion of the tire model, and the calculated lateral force includes a large noise component. It is difficult to find the correct and accurate.

  Therefore, in the present embodiment, the slip angle ramp input step (# 4) for gradually increasing or decreasing in steps is performed so that the slip angle of the tire model 2 reaches the target value in a predetermined time, and further, A lateral force calculation step (# 5) for calculating the lateral force generated by the tire model 2 at each slip angle is executed.

  When the slip angle of the tire model 2 is gradually increased, it is desirable that the increment ΔSA of the slip angle input in the slip angle ramp input step (# 4) is small, but the calculation capacity and storage capacity of the computer 1 are taken into consideration. Is set. By setting the increment value ΔSA of the slip angle to be sufficiently small, the change of the slip angle input to the tire model 2 becomes quasi-static, and between the tread portion and the bead portion of the tire model 2, There is no torsional vibration that affects the calculation. Accordingly, the noise component included in the lateral force calculated in the lateral force calculating step (# 5) is reduced, and the time constant can be accurately and uniquely determined in the time constant calculating step (# 7) described later. Become. The same applies to the case where the slip angle of the tire model 2 is gradually reduced.

  The slip angle ramp input step (# 4) and the lateral force calculation step (# 5) are repeatedly executed until it is determined in the time determination step (# 6) described later that a preset time has arrived ( NO in # 6).

  FIG. 4 shows the transition between the slip angle SA input in the slip angle ramp input step (# 4) and the lateral force Fy calculated in the lateral force calculation step (# 5). In FIG. 4, the horizontal axis indicates the rolling calculation time (different from the actual time) with the time when the slip angle is zero as the initial time T0, and the vertical axis indicates the slip angle SA of the tire model 2. And lateral force Fy is represented. The slip angle SA of the tire model 2 is indicated by a broken line, and the lateral force Fy is indicated by a solid line.

  In the present embodiment, the slip angle SA is gradually input at a predetermined constant value and increases linearly. That is, the slope dSA / dt of the slip angle SA is constant and is represented by a straight line in FIG. The slope dSA / dt of the slip angle SA is preferably 6 ° / second or less, for example.

  On the other hand, due to the transient characteristics of the tire, the lateral force Fy rises with a delay, and its slope dFy / dt gradually increases. Soon, the inclination dFy / dt of the lateral force Fy becomes equal to the inclination dSA / dt of the slip angle SA after time T1. Thereafter, the inclination dFy / dt is kept constant within the range of the calculation error, and the lateral force Fy increases with a time constant T delayed from the slip angle SA.

  FIG. 4 shows a case where the slip angle SA is input with a predetermined constant value gradually increased, but the same applies when the slip angle SA is input with a predetermined constant value gradually decreased. .

  As shown in FIG. 2, in the time determination step (# 6), it is determined whether or not a preset time T2 has arrived. This time T2 is sufficiently later than the time T1, and as a result of repeatedly executing the slip angle ramp input step (# 4) and the lateral force calculation step (# 5), the slope dSA / slip of the slip angle SA. The time is sufficient for dt and the inclination dFy / dt of the lateral force Fy to be regarded as equivalent. The time T2 can be determined empirically by calculating the lateral force Fy by ramp-inputting the slip angle SA in various tire models 2.

  If it is determined in time determination step (# 6) that time T2 has not arrived (NO in # 6), the process returns to the slip angle ramp input step (# 4) and the ramp input of slip angle SA is continued. The On the other hand, when it is determined that time T2 has arrived (YES in # 6), the process proceeds to the time constant calculation step (# 7).

  In the time constant calculating step (# 7), the time constant T of the delay transfer function is calculated based on the lateral force Fy.

  In FIG. 4, the lateral force Fy can be approximated to a cornering force generated by the tire model 2 in a region where the slip angle SA is small. In this case, the cornering power CP can be approximated by the ratio dFy / dSA of the slope dFy / dt of the lateral force Fy to the slope dSA / dt of the slip angle SA.

  The time constant T of the delay transfer function calculated in the time constant calculation step (# 7) shown in FIG. 2 includes, for example, the time constant τ of the first-order delay transfer function G (s). The time constant τ of the first-order lag transfer function G (s) is expressed by the following equations (1) to (3).

  The time constant τ of the first-order lag transfer function G (s) can be obtained by fitting. In the fitting, for example, a method such as a least square method can be applied.

  The time constant T of the delay transfer function may further include the time constant ωn of the second order delay transfer function G (s). The time constant ωn of the second-order lag transfer function G (s) is expressed by the following equations (4) to (8).

  Similar to the time constant τ of the first-order lag transfer function G (s), the time constant ωn of the second-order lag transfer function G (s) can be obtained by fitting. In the fitting, for example, a method such as a least square method can be applied.

  In the first invention, transient characteristics when the slip angle SA of the tire changes during straight traveling or cornering can be evaluated.

  As already described, in this embodiment, no torsional vibration that affects the calculation occurs between the tread portion and the bead portion of the tire model 2, so that the lateral constants used for calculating the time constants τ, ωn, etc. The noise component included in the force Fy is small. Accordingly, the time constants τ and ωn can be obtained accurately and uniquely.

  Further, when it is determined that time T2 has arrived (YES in # 6), the process proceeds to the time constant calculation step (# 7), and the time constants τ and ωn of the delay transfer function based on the lateral force Fy are set. Calculated. Accordingly, the time constants τ and ωn can be obtained easily and in a short time.

  Instead of the time determination step (# 6), a step of comparing the slope dSA / dt of the slip angle SA and the slope dFy / dt of the lateral force Fy may be executed. In this case, when the slope dSA / dt of the slip angle SA and the slope dFy / dt of the lateral force Fy are regarded as equivalent, that is, the rate of change of the slip angle SA and the rate of change of the lateral force Fy are regarded as equivalent. At this point, it is possible to move to the time constant calculation step (# 7) and calculate the time constants τ, ωn, etc., and to obtain the time constants τ, ωn, etc. more easily and in a short time. Become.

  In the present embodiment, the calculation of the lateral force Fy is executed in the lateral force calculation step (# 5) while the slip angle SA is linearly increased or decreased gradually in the slip angle ramp input step (# 4). In the ramp input step (# 4), the slip angle SA input to the tire model 2 may be nonlinearly gradually increased or gradually decreased.

  Further, the increment value or the decrement value of the slip angle SA input in the slip angle ramp input step (# 4) is not limited to a constant value, and affects the calculation between the tread portion and the bead portion of the tire model 2. A variable value may be used as long as no torsional vibration is exerted.

  FIG. 5 shows another embodiment of the processing procedure of the simulation method of the first invention of the present invention. This embodiment is shown in FIG. 2 in that, instead of the slip angle ramp input step (# 4) shown in FIG. 2, a camber angle ramp input step (# 14) for ramp input of the camber angle is executed. Different from the embodiment. In the camber angle ramp input step (# 14), the camber angle of the tire model 2 is gradually increased or decreased, and further, the lateral force calculation step (# 15) for calculating the lateral force generated by the tire model 2 at each camber angle. ) Is executed.

  With the above change, when the slip angle of the tire model 2 set in the boundary condition setting step (# 12) is zero, the lateral force due to the camber thrust is calculated in the lateral force calculation step (# 15). When a slip angle is given to the tire model 2, the resultant force of the cornering force and the camber thrust is calculated. For other explanations, the embodiment shown in FIG. 2 can be applied mutatis mutandis.

  In the present embodiment, transient characteristics when the camber angle of the tire changes during straight traveling or cornering can be evaluated.

  FIG. 6 shows an embodiment of the processing procedure of the simulation method of the second invention of the present invention. The second invention differs from the first invention in that an axial load ramp input step (# 24) for ramp-inputting an axial load is executed instead of the slip angle ramp input step (# 4) of FIG. In the second invention, from the rolling step (# 23) to the time constant calculation step (# 27), the slip angle and camber angle set in the tire model 2 are fixed at predetermined angles.

  In the axial load ramp input step (# 24), the axial load of the tire model 2 is gradually increased or decreased, and further, the lateral force calculating step (# 25) for calculating the lateral force generated by the tire model 2 at each axial load. ) Is executed. For other explanations, the first invention can be applied mutatis mutandis.

  In the second invention, transient characteristics when the axial load of the tire changes during straight traveling or cornering can be evaluated.

  Although the tire simulation method of the present invention has been described in detail above, the present invention is not limited to the above-described specific embodiment, and can be implemented in various forms.

  For example, the ramp-input parameter may be any two of slip angle, camber angle or axial load, or all of the slip angle, camber angle and axial load. In this case, the parameters can be gradually increased or decreased while being related, and the transient characteristics of the tire can be evaluated under conditions closer to actual driving.

   Four types of tire models with different structures were created with the size 195 / 65R15 shown in FIG. Each tire model has boundary conditions of an internal pressure of 230 kppa, an axial load of 4.1 kN, and a speed of 50 km / h. As an example, a time constant is calculated for each tire model by the simulation method of the first invention shown in FIG. The relaxation length σc was calculated. The relaxation length σc is calculated by the product of the time constant and the speed. The slope dSA / dt of the slip angle SA is 1.5 ° / second. As a comparative example, the slip angle was step-inputted to each tire model, and the relaxation length σc was calculated from the time required for the lateral force to reach 63.2% of the saturation value at the steady state.

  On the other hand, tires of each structure were prototyped, and the cornering power was measured by the flat belt type testing machine at the internal pressure, axial load and speed, and the relaxation length σm was calculated. The relaxation length σm is calculated by dividing the cornering power by the transverse spring constant.

  The relaxation length σc of the tire model calculated through the simulation method of the example and the comparative example was compared with the relaxation length σm obtained from the actual measurement of the tire, and their correlation was verified.

  FIG. 7 shows the relationship between the relaxation length σc of the tire model calculated through the simulation method and the relaxation length σm of the tire obtained from actual measurement. The examples are represented by black circle plots and solid lines, and the comparative examples are represented by square plots and broken lines.

As is clear from FIG. 7, the coefficient of determination R ² is 0.98 between the relaxation length σc of the tire model calculated through the simulation method of the first invention and the relaxation length σm of the tire obtained from actual measurement. It was confirmed that a very strong correlation was obtained. On the other hand, between the relaxation length σm of the tire obtained from actual measurement and mitigation length σc calculated from the method of Comparative Example, the coefficient of determination R ² is remained weak correlations 0.54.

1 Computer 2 Tire model SA Slip angle Fy Lateral force τ Time constant ωn Time constant

Claims (8)

A tire simulation method for evaluating the transient characteristics of a tire using a computer,
Setting a tire model that models a tire with a finite number of elements that can be numerically analyzed;
Rolling the tire model on a virtual road surface based on predetermined boundary conditions;
Calculating the lateral force generated by the tire model at each posture angle while gradually increasing or decreasing the posture angle of the tire model;
Calculating a time constant of a delay transfer function based on the lateral force.   The tire simulation method according to claim 1, wherein the posture angle is gradually decreased or gradually increased by a predetermined constant value.   The tire simulation method according to claim 1, wherein the posture angle includes a slip angle.   4. The tire simulation method according to claim 1, wherein the posture angle includes a camber angle. A tire simulation method for evaluating the transient characteristics of a tire using a computer,
Setting a tire model that models a tire with a finite number of elements that can be numerically analyzed;
Rolling the tire model on a virtual road surface while fixing the tire model at a predetermined slip angle and camber angle based on a predetermined boundary condition;
Calculating the lateral force generated by the tire model at each axial load while gradually increasing or decreasing the axial load of the tire model;
Calculating a delay time constant based on the lateral force, and a tire simulation method.   The tire simulation method according to claim 5, wherein the axial load is gradually reduced or gradually increased at a predetermined constant value.   The tire simulation method according to claim 1, wherein the transfer function includes a time constant of a first-order lag transfer function.   The tire simulation method according to claim 7, wherein the transfer function includes a second-order lag transfer function.

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