JP2006007913A - Tire model, tire behavior simulation method, tire behavior analyzing program, and record medium recording tire behavior analyzing program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To minimize vibrations generated under calculation in analyzing a tire by a numerical analyzing manner such as a finite element method (FEM) and the like. <P>SOLUTION: This tire model calculates a tire corresponding to a numerical calculation model to analyze behaviors of the tire under a used condition in a simulation manner. In this tire model, one tire periphery is divided into 120 or more and 360 or less elements. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a tire model, a tire behavior simulation method, a tire behavior analysis program, and a recording medium on which a tire behavior analysis program is recorded, and is used when analyzing the performance of a pneumatic tire used in an automobile or the like. The present invention relates to a tire model, a tire behavior simulation method using the tire model, a tire behavior analysis program, and a recording medium on which a tire behavior analysis program is recorded.

  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 partitioning, or Element division) is required (see, for example, Patent Document 1).

Therefore, when the tire is analyzed by FEM, it is necessary to divide the tire into elements. However, since the tire has an annular shape, two-dimensional element division is performed on the cross section of the tire, and this is made into an annular shape. It is usual to develop 360 degrees to make a three-dimensional model. Here, assuming that the tire rolling direction is the circumferential direction of the tire, generally, elements of about 60 divisions are generally arranged in the circumferential direction of the tire. Also, in the modeling in which the tire case portion (including the Sidewall portion, the carcass portion and the bead portion under the tread) and the tire tread portion are combined, the annular shape of the case portion is usually divided in the circumferential direction. For example, even in the FEM tire model disclosed in Patent Document 1, since the case portion and the tread portion are created separately, the case portion is equally divided into 60 in the circumferential direction.
Japanese Patent Laid-Open No. 11-153520

  When a rotating contact analysis is performed on a tire model divided in the circumferential direction, assuming that the moving body is traveling, the polygonal object rolls on the road surface geometrically, so the reaction force that the tire receives from the road surface is Vibrate. This vibration occurs when the polygon vertex touches the road surface and when the line segment connecting the vertex and the vertex touches the road surface due to the difference in the tire model radius and the rigidity of the part. Yes. This vibration also occurs when the tire tread is affixed to the case as in Patent Document 1. The cause is assumed to be the shape modeled by the polygon of the tire case portion. That is, even if the pattern to be applied to the case part is divided into fine elements, if the case part element (MESH) is not modeled sufficiently finely in the circumferential direction, the tire rolls while vibrating up and down. Become. In this way, when the tire axial force (the force received by the tire rotation center axis, which is the same as the reaction force of the normal road surface) is vibrating, the entire tire is analyzed with unexpected vibration. Therefore, there are cases where an appropriate analysis result cannot be obtained.

  In consideration of the above facts, the present invention can minimize the vibration generated in the calculation in the tire analysis by the numerical analysis method such as the finite element method (FEM). It is an object to obtain a recording medium recording a behavior simulation method, a tire behavior analysis program, and a tire behavior analysis program.

  In order to achieve the above object, the present invention makes it possible to analyze the behavior of a tire while minimizing the vibration generated in the calculation.

  Specifically, the invention described in claim 1 is a tire model that calculates a tire corresponding to a numerical calculation model in order to analyze the behavior of the tire in a use state. The circumference is divided into 120 or more and 360 or less elements.

  In the present invention, basically, the division in the circumferential direction of the tire is 120 or more. Also, the number of divisions is 360 or less. In this case, it is preferable to divide the case portion of the tire.

  That is, when a tire is modeled by FEM, conventionally, the circumferential division of the tire case portion is about 60, and at this time, the tire is divided every 6 degrees in the circumferential direction. Here, when the tire model is rotated and analyzed, a large vibration force is received from the road surface. This is because the deformation is different between the case where the vertex of the FEM tire model is in contact with the road surface and the case where a line segment tangling the vertex and the vertex of the FEM tire model is in contact with the road surface.

  Therefore, in the present invention, the circumferential division of the tire (particularly the case portion) is set to 120 or more. In this division, it is particularly preferable to divide the case part into element divisions of 120 or more, and the pattern to be pasted on the case may have the same number of divisions as the case or even more divisions. good. In other words, what is important is that the case part determines the deformation that is very dominant with respect to the side deformation of the tire, and even if the tread part is divided into fine elements, the case part must be sufficiently divided so that the analysis is highly accurate. Is a point that cannot be realized. For this reason, attention was paid to the division of the case portion.

  When the tire case is divided into 120 parts, the tire is divided every 3.0 degrees. By dividing the tire into 120 parts in this way, the tires are polygonal but approach a circular shape compared to about 60 parts. If the tire model is increased in the number of divisions in the circumferential direction by 180 divisions, further 360 divisions, vibration can be suppressed accordingly.

  On the other hand, if it is divided into 60 divisions and 72 divisions in the circumferential direction as in the prior art, large vibrations are generated. The inventor of the present invention has obtained knowledge that vibrations can be greatly reduced between 100 to 120 divisions from various experiments and examinations. That is, the 120 divisions is the minimum number of circumferential divisions necessary for performing accurate calculation by placing the tire in the rolling analysis using the FEM model.

  Therefore, in the tire circumferential direction, vibration can be suppressed as the number of divisions of the tire (case portion thereof) is increased to 120 divisions or more. However, as it is subdivided into 180 divisions, 360 divisions, and more, the calculation time of analysis increases in a quadratic curve. For example, when 180 divisions are compared with 360 divisions, vibrations due to the polygonal nature of the tire are often less changed. Further, in the 720 division and the 360 division, there is almost no change in the vibration level. For this reason, even if a tire divided into 360 or more elements is analyzed, the analysis accuracy does not change from the case of 360 divisions, but there is a disadvantage that the calculation time increases significantly. For this reason, in the present invention, the upper limit of the number of divisions is set to 360 divisions.

  The invention according to claim 2 is a tire model in which the tire is calculated in correspondence with the numerical calculation model in order to analyze the behavior of the tire in use, and the tire contact surface is 10 in the tire circumferential direction. It is characterized by being divided into no less than 30 elements.

  In an ordinary tire, in an FEM tire model divided into 120 in the circumferential direction, there are 10 or more elements in the circumferential direction on the ground contact surface (that is, the portion where the tire is in contact with the road surface) when analyzed. Accordingly, it is preferable that at least 10 elements are continuously arranged in the circumferential direction on the ground plane.

  When performing tire rolling analysis by the finite element method, the polygonal one rotates. With about 60 divisions in the circumferential direction, there are only about 6 elements in the circumferential direction in the ground contact surface of the tire. That is, when the tire rolls, at a certain moment, the number of elements that are in contact with the ground changes depending on the rotation angle, from 6 elements to 5 elements and back to 6 elements. This change in the number of elements greatly affects the vibration. If there are 10 or more elements in the circumferential direction of the ground plane, even if the number of elements in contact with the rotation angle of the tire changes, 10 becomes 9 and 9 becomes 10, The change is much smaller compared to conventional modeling where 6 elements become 5 elements. As a result of various studies, the present inventor has obtained knowledge that vibration can be greatly suppressed when about 10 elements are in contact with each other. Further, in the case of a general tire divided into 120 in the circumferential direction, the number of divisions is about the same as when 10 elements are arranged in the ground contact area. For this reason, the division corresponding to the upper limit of 360 is when 30 elements are arranged in the ground plane.

  If the number of divisions increases to 180 divisions, 360 degree divisions, and 720 degree divisions, the vibration when the tire rotates becomes very small. However, the vibration level does not change much between 360 divisions and 720 divisions. However, there is a large difference between 60 divisions and 120 divisions, and it has been concluded that 120 divisions are the minimum level that can be used industrially, which can balance both efficiency in tire development and analysis accuracy. In other words, when considering development efficiency, the minimum threshold value is that 120 elements or more or 10 or more elements are arranged in the circumferential direction of the contact surface.

  There are many types of tires, from inexpensive to high performance, from large to small, automobile, truck and bus, and aircraft. Since these tires have different members, different tread widths, and different shapes, there are various shapes of portions where the tire contacts the road surface (referred to as contact shapes). For example, in general passenger car tires, the higher the performance, the smaller the flatness, and the ground contact shape is wider in the width direction and shorter in the circumferential direction. For this reason, even in the FEM tire model, if the number of divisions in the circumferential direction is increased in a flat system and more than 10 elements are arranged in the circumferential direction within the ground plane, the tire rotation must be performed. When the dynamic analysis is performed, the tire easily vibrates.

  According to a third aspect of the present invention, there is provided a tire model for calculating a tire corresponding to a numerical calculation model in order to analyze the behavior of the tire in a use state, and for performing vibration analysis as the analysis. The element division number is set in the tire circumferential direction so that the vibration frequency generated by the elements divided in the tire circumferential direction becomes a vibration frequency excluding the resonance frequency of the rim to which the tire is assembled.

  Invention of Claim 4 is a tire model of Claim 3, Comprising: The vibration frequency which generate | occur | produces in the element divided | segmented into the tire circumferential direction by the vibration frequency except the resonance frequency of the rim | limb which mounts the said tire is 500 Hz. It is the above.

  Next, the number of divisions in the circumferential direction of the tire is considered from the viewpoint of the natural frequency of the tire and the natural frequency of the wheel combined with the tire. Since the tire is a structural body, it has a natural frequency, and generally has a natural frequency in the front-rear direction near 50 Hz and a natural frequency in the vertical direction near 100 Hz. In general, there is a donut-shaped space filled with air inside the tire in the vicinity of 200 Hz, and a cavity resonance frequency generated by the air therein. Also important is the natural frequency of the foil. A typical passenger car wheel has a vibration frequency in the vicinity of 400 Hz to 450 Hz. When performing tire rolling analysis using a combination of tires and foils, high-accuracy analysis will occur if vibrations at specific frequencies resulting from the number of divisional elements in the tire circumferential direction of the tire model resonate with the eigenvalues of these tires and foils. I can't hope. That is, unless these natural frequencies are emphasized depending on the case element (MESH) division, a highly accurate analysis cannot be expected.

  For example, consider an analysis that rotates a tire and a wheel at 50 km / h. The outer circumference of a typical tire for a passenger car is about 2 m. When rolling at a speed of 50 km / h, the tire rotates about 7 times per second. When the tire model is divided into 60 in the circumferential direction as in the conventional case, 7 rotations / second · 60 division = 420 Hz, and the frequency at which the polygonality of the element division occurs is about 420 Hz. This coincides with the natural frequency of the foil, and there is a high possibility that a resonance phenomenon that should not be present will occur in the analysis. In this case, for example, if the tire is divided into 120 elements, the frequency at which the polygonality of the element division occurs becomes a high frequency of 840 Hz, and resonance can be avoided. In general, the resonance of a moving body (for example, an automobile) due to the characteristic value of a tire is often considered in a so-called low speed region where the speed is about 30 km and in a high speed region where the speed is 80 km or more. For example, when the speed is 30 km / h, the tire rotates 4.2 times per second, and in order to avoid resonance with the foil, the analysis results from the polygonal nature of the case part element (MESH) Considering that the vibration is 500 Hz or more, it is necessary to make 500 Hz / 4.2 = 119 divisions or more. In a region where the speed is further slower than this, it is necessary to control the number of elements (MESH) in the case portion according to the speed. At a speed of 20 km, the element division number needs to be 180 divisions or more in order to avoid resonance with the foil. That is, in the assembly structure of the tire and the foil, the resonance frequency with the foil is a relatively high vibration frequency among the main natural frequencies, and attention is required at the time of analysis. Since the natural frequency of the foil is generally 400 Hz to 450 Hz, resonance can be avoided if the frequency resulting from the element division is set to 500 Hz or higher, which is larger than this.

Further verification shows that when the tire diameter is 2R (m), the outer periphery of the tire is 2Rπ (m). , Tire model in 1 second,
(V / 3.6) / (2Rπ) (1)
Will only rotate. Since the circumference of the tire is divided into N parts, the vibration component generated in the analysis by the element division is
N · (V / 3.6) / (2Rπ) Hz (2)
It becomes. In the present invention, this frequency is determined to be 500 Hz or higher, which is larger than the natural frequency of the foil.
N · (V / 3.6) / (2Rπ)> 500 Hz (3)
In particular, the problem is analysis at a low speed of about 30 km / h. In this case, V = 30 (km / h), R = 0.3 ( Substituting m), N of 113 divisions or more is necessary to make the frequency generated in the analysis 500 Hz or more.

  If the speed is even slower, it is necessary to divide further. However, since the speed used in normal analysis is rarely 30 (km) or less, it is practical if the number of element divisions is 120 or more. It is enough. Of course, when an analysis at a lower speed, such as 20 (km) per hour, is performed, a finer division may be performed.

  By using the tire model described above, it is possible to simulate the behavior of the tire while minimizing the vibration generated in the calculation. Specifically, (a) a step of determining the tire model described above as a tire model that can be deformed by ground contact and rolling as a numerical calculation model, (b) in order to analyze the tire performance in the use state, (C) executing a deformation calculation of the tire model, (d) obtaining a physical quantity generated in the tire model in the step (c), and (e) a tire based on the physical quantity. By the tire behavior simulation method including the step of predicting the behavior of the tire, the behavior of the tire can be analyzed in a simulated manner in the use state.

  Further, when the behavior of the tire is analyzed by a computer, (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 4. A step of defining a tire model, (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 executing deformation calculation of the tire model, (D) the step A tire behavior analysis program including a step of obtaining a physical quantity generated in a tire model in (C) and a step of (E) predicting the behavior of the tire based on the physical quantity. The behavior can be analyzed.

  Furthermore, when the behavior of the tire is analyzed by a computer, (1) 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 4. 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 behavior of the tire based on the physical quantity is stored in a storage medium, executed, and collected. By doing so, it is possible to analyze the behavior of the tire while minimizing the vibration generated in the calculation.

  As described above, according to the present invention, it is possible to provide a tire model capable of accurately analyzing the behavior of a tire while minimizing the vibration generated in the calculation, and to achieve efficient tire development. There is.

  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 is determined. In the next step 102, a tire model of a tire (for example, a smooth tire having no pattern or a tire having a pattern) 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 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 this embodiment, an allowable range is set in this embodiment, as will be described in detail later.

  In the creation of the tire model in step 102, a tire model creation routine shown in FIG. 3 is executed. First, in step 140, the number of element divisions corresponding to the finite element method (FEM) is set. Although details will be described later, the number of divisions is set between 120 and 360 with an allowable range of dividing one round into 120 or more and 360 or less elements in the tire circumferential direction. In the next step 142, a tire radial section model (ie, tire section data) is created. As the tire cross-section data, a value obtained by measuring the tire outer shape with a laser shape measuring instrument or the like can be used. In addition, an accurate value such as a design drawing and actual tire cross-section data can be used for the structure inside the tire. 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 144, tire cross-section data (tire radial cross-section model), which is two-dimensional data, is developed in one cycle (360 degrees) in the circumferential direction to create a three-dimensional (3D) model of the tire. When developing one round (360 degrees) in this circumferential direction, the number of divisions set in step 140 is reflected. That is, one round in the tire circumferential direction is developed to be 120 or more and 360 or less elements. FIG. 4 shows a state in which the tire model created as described above is placed on the road surface. FIG. 4A shows an example of 72 divisions, and FIG. 4B shows an example of 144 divisions.

  After the tire model is created as described above, the process proceeds to step 104 in FIG. 2, and the road surface state is input together with the road surface setting, that is, the road surface model creation. In this step 104, the road surface is modeled and input for setting the modeled road surface to an actual road surface state. The road surface is modeled by dividing the road surface shape into elements and selecting the road surface friction coefficient μ and inputting the road surface state. For example, depending on the road surface condition, there is a road friction coefficient μ corresponding to dry (DRY), wet (WET), on ice, snow, unpaved, etc., so by selecting an appropriate value for the friction coefficient μ, The road surface condition can be reproduced.

  A fluid model may be created and provided between the road surface and the tire model. The fluid model divides and models a part (or all) of a tire, a ground surface, and a fluid region including a region where the tire moves and deforms, and the tire model and the fluid model are defined by overlapping each other. It is preferable.

  In this way, when the road surface condition is input, 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, the boundary condition setting routine shown in FIG. 5 is executed. First, in step 152, an internal pressure is applied to the tire model, and in the next step 154, at least one of rotational displacement and linear displacement (displacement may be force or speed) and a predetermined load are applied to the tire model. In addition, when considering friction with the road surface, only one of rotational displacement (or force or speed) or straight displacement (or force or speed) may be used.

  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. Specifically, the vibration (kgf) of the force acting on the tire center is derived.

  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 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.

(Division number)
The allowable range for dividing the tire model will be described based on the tire behavior simulation. The inventor has conducted various experiments and studies, and has come to the knowledge that it is preferable to divide one turn into 120 or more and 360 or less elements in the tire circumferential direction.

  First, FIG. 6 shows a tire model when the tire is divided into 60 parts, (A) is an area of the contact surface, and (B) is a side view of the tire model. Similarly, FIG. 7 shows a tire model when the tire is divided into 120 parts, and FIG. 8 shows a tire model when the tire is divided into 180 parts.

  As can be understood from each drawing, the number of elements arranged in the circumferential direction increases as the number of divisions increases. That is, the tire model in which the tire is divided into 60 has 4 to 5 elements arranged in the circumferential direction on the contact surface, and the tire model in which the tire is divided into 120 has 9 to 10 elements arranged in the circumferential direction on the contact surface and 360 divided tires. In the model, 13 to 14 elements are arranged in the circumferential direction on the ground plane.

  Next, a simulation was performed on the tire axial force when the tire was rolled while being in contact with the road surface. Specifically, for a tire of tire size 215 / 55R15, the load is 400 kg, the speed is 50 km / h, the slip angle is 0 degree, the friction coefficient with the road surface is 1.0, and the tire filling internal pressure is 1.8 (SI unit). In the system, the tire behavior simulation (rotational contact analysis) was performed under the condition of 0.18 Mpa). The calculation results (analysis results by FEM) are shown in FIGS. 9 shows the analysis result when the tire is divided into 72 parts, FIG. 10 shows the analysis result when the tire is divided into 120 parts, FIG. 11 shows the analysis result when the tire is divided into 180 parts, and FIG. Shows the analysis results when the tire is divided into 360 parts. The calculation result is a characteristic in which the rolling distance of the tire is set on the horizontal axis and the vertical vibration of the tire is set on the vertical axis. The vertical vibration of the tire is a vibration of a force acting on the tire center. In this analysis, the tire contact shape at 400 kgf is almost the same as that in FIG. 6 for the tire model in which the tire is divided into 72, the tire model in which the 120 is divided is FIG. 7, and the tire model that is divided into 180 is FIG. .

  FIG. 13 shows the result of determining the relationship between the number of divisions of the tire model and the vibration amplitude with respect to the tire axial force when the tire is rolled while being in contact with the road surface.

  As understood from FIG. 13, there is a large difference between 60 divisions (72 divisions) and 120 divisions of the tire model. Further, in the division of 120 divisions or more, there is vibration inherent to the tire, so that it is assumed that the vibration amplitude decreases gently without the axial force becoming zero. Further, when the tire model is divided into 120 parts, the vibration amplitude is 10 kgf, which is 2.5% with respect to the applying force of 400 kgf, which is a practical level.

  Furthermore, in FIG. 14, the result of having calculated | required the relationship between the number of division | segmentation of a tire model (tire circumferential direction) and calculation time was shown. The calculation time required for the analysis increases exponentially as the number of divisions of the tire model increases. In this figure, it tends to increase in a quadratic function curve. That is, the calculation time for 60 divisions is shown as an index with 1 being used, and if 360 divisions are exceeded, it is not a realistic division number.

  From these figures, it can be understood that the 120 division significantly suppresses vibration compared to the 60 division (72 division) of the tire model. Also, from these figures, it can be determined that the accuracy is sufficient for use at the site of tire development at a level of 120 divisions.

  That is, it can be sufficiently obtained from the results obtained in FIGS. 9 to 12 (horizontal axis: number of tires in the circumferential direction, vertical axis: vibration amplitude of vertical axial force). As in the prior art, if the tire is divided into 60 parts, an axial force vibration of 33 kgf is generated only by rolling the tire model by FEM against a vertical load of 400 kgf. 33 kgf with respect to 400 kgf is a large error. On the other hand, with 120 divisions, the axial force vibration is 10 kgf. Thus, the error (vibration amplitude) is dramatically reduced. Further, additional experiments have shown that this vibration is hardly reduced even when the number of divisions is increased to 180 or more. That is, there is a marked improvement in changing the tire model division from 60 to 120 divisions.

  The vibration amplitude is generated based on the principle that the polygon generated by the division rotates as long as the finite element method is used. Therefore, if the number of divisions is increased, the vibration as an error can be reduced, but 120 divisions are possible. Sufficient to be used for industrial site design.

  Therefore, when FEM analysis using a tire model is performed, the number of divisions into elements is preferably greater than or equal to 120 (120 divisions or more) considering the vibration amplitude. In view of (calculation time), it is concluded that it is practically preferable to set the number of divisions to 360 or less (360 divisions or less).

  As described above, in this embodiment, when FEM analysis using a tire model is performed, the number of divisions into elements is set to 120 divisions or more and 360 divisions or less, so that vibrations generated in calculation are minimized. It is possible to provide a tire model that can be analyzed while reducing the calculation load while limiting to the limit.

  In addition, you may make it obtain | require the pattern (for example, groove | channel) and shape of a tread part from the said calculation result. The tire model can be reconstructed by developing the derived pattern in the tire circumferential direction and creating a tire model with a pattern.

[Second Embodiment]
Since this embodiment has the same configuration as that of the above-described embodiment, the same portions are denoted by the same reference numerals and detailed description thereof is omitted. In this embodiment, lateral force is adopted as an analysis target. That is, in the above embodiment, an example of vibration (kgf) of a force acting on the tire center as a physical quantity at the time of tire deformation has been described, but a lateral force is employed in this embodiment.

  Specifically, in the present embodiment, the slip angle (SA) is changed by 0 to 12 degrees (deg), the analysis is executed, and the lateral force at that time is output as the calculation result. The tires and their states targeted in the present embodiment are the same as those in the above-described embodiments of the tire size 215 / 55R15, the load is 400 kgf, the speed is 50 km / h, and the friction coefficient with the road surface is 1.3. A behavior simulation (rotational contact analysis) was performed when the slip angle (SA) was changed by 0 to 12 degrees under the condition that the tire filling internal pressure was 1.8 (0.18 MPa in the SI unit system). The calculation results (analysis results by FEM) are shown in FIGS. 15 and 16.

  FIG. 15 shows an analysis result of obtaining the maximum value (Fy-max) of the lateral force when the slip angle is changed, and is a characteristic diagram in which the slip angle is set on the horizontal axis and the maximum value of the lateral force is set on the vertical axis. As shown. FIG. 16 shows the result of obtaining the relationship between the number of divisions and the maximum value of the lateral force for the analysis results when the tire model is divided into 60 divisions, 120 divisions, 180 divisions, and 360 divisions.

  From these figures, when the number of divisions of the tire model is small (coarse elements), the maximum value of the lateral force becomes small. For example, in the case of 60 divisions, it is 475 kgf, which is understood to be smaller than 120 divisions. This is considered to be because if the element division is rough and the number of divisions is small, such as 60 divisions, the tire model vibrates up and down, the contact state of the tire model deteriorates, and sufficient frictional force cannot be obtained. On the other hand, in 120 divisions or more, the maximum value of the lateral force is 495 to 499 kgf, and it is considered that the influence of vibration is suppressed. Therefore, even when the lateral force is taken into consideration at a level of 120 divisions or more, it can be determined that there is sufficient accuracy to be used at the site of tire development.

  As described above, in the present embodiment, when FEM analysis using a tire model is performed, the number of divisions to be divided into elements is set to 120 divisions or more and 360 divisions or less, so that vibration is taken into account while considering lateral force. Therefore, it is possible to provide a tire model that can perform analysis while reducing the calculation load while minimizing.

[Third Embodiment]
Since this embodiment has the same configuration as that of the above-described embodiment, the same portions are denoted by the same reference numerals and detailed description thereof is omitted. In this embodiment, lateral force is adopted as an analysis target. That is, in the above embodiment, an example of vibration (kgf) of a force acting on the tire center as a physical quantity at the time of tire deformation has been described, but a lateral force is employed in this embodiment.

  There are various types of tires depending on the use form (running state and type of moving body to be mounted). For example, since the flatness is different or the structure is different, the contact length (the length in the circumferential direction of the grounded portion) is different even for tires of the same size. Therefore, the strict part (corresponding to each tire) may be insufficient only by defining the number of divisions in the tire circumferential direction as in the above embodiment. Therefore, in the present embodiment, a contact surface is defined for the tire model. The insufficiency of the above-mentioned strict portion means that in a tire with a short contact length, the number of elements that fall within the contact surface is reduced even if the tire is divided into 120 parts, and in some cases, vibration is likely to occur. For example, when 10 elements are arranged in the circumferential direction in the ground contact portion, when the tire rotates, the elements in the circumferential direction change to 11 or 9 at a certain moment. For one increase / decrease for ten, one increase / decrease for six has a large variation, resulting in a large vibration. For this reason, in this embodiment, it is specified that there are 10 or more elements in the ground plane.

  The tires targeted in this embodiment and their states are the conditions of a high-performance tire having a tire size of 245 / 50R17, a load of 400 km, a speed of 50 km / h, and a tire filling internal pressure of 2.0 (200 kPa). Thus, a behavior simulation (rotational contact analysis) similar to that in the above embodiment was performed. The calculation results (analysis results by FEM) are shown in FIGS.

  FIG. 17 shows the contact surface of the tire model for the analysis result when the tire model is divided into 60 parts. Similarly, FIG. 18 shows the contact surface of the tire model for the analysis result when the tire model is divided into 120 parts, and FIG. 19 shows the contact surface of the tire model for the analysis result when the tire model is divided into 180 parts. .

  In the high-performance tire employed in the present embodiment, the shape of the ground contact surface is short in the circumferential direction and long in the width direction. Further, when the load is light, the ground contact area is reduced and the ground contact length is shortened. In the case of 60 divisions shown in FIG. 17, since only about 4 elements are present on the ground plane, the vibration becomes extremely large. On the other hand, even in the example of FIG. 18 divided into 120 as in the above embodiment, only 6 to 7 elements exist on the ground plane. For this reason, the vibration was output stronger.

  Therefore, as shown in FIG. 19, when 180 divisions were made, about 10 elements existed on the ground plane, and vibration was suppressed. That is, by dividing the tire model 180 in the circumferential direction, 10 elements are arranged in the circumferential direction within the ground contact surface. Therefore, in addition to the number of divisions for the entire tire (case part), it is effective to set the number of divisions that defines the number of elements in the ground plane, or to set only the number of divisions that defines the number of elements in the ground plane It may become.

  Accordingly, there are tire models in which 10 elements are arranged in the ground plane by dividing 120 in the circumferential direction. On the other hand, in tire models having less than that, for example, only 7 elements, the number of divisions is increased to 10 in the ground plane. Make sure that the elements are lined up. In consideration of the calculation load, if it exceeds 30, it takes a calculation time and is not preferable. Therefore, it is preferable to divide into 30 or less elements in the ground plane.

  For these reasons, it is necessary to define the number of divisions to divide the tire model so that 10 or more and 30 or less elements are arranged in the ground plane. However, it can be judged that there is sufficient accuracy for the tire development site.

  As described above, in the present embodiment, when FEM analysis using a tire model is performed, the number of divisions into elements should be 10 or more and 30 or less in the ground plane. Accordingly, it is possible to provide a tire model that can perform analysis while reducing calculation load while minimizing vibration without depending on the type of tire.

[Fourth embodiment]
Since this embodiment has the same configuration as that of the above-described embodiment, the same portions are denoted by the same reference numerals and detailed description thereof is omitted. Further, in the present embodiment, a combination of a tire and a rim is adopted as an analysis target.

  First, the frequency considered in this embodiment will be described. Tire vibrations are closely related to the ride comfort that the driver feels when driving on a road or riding on a road. Therefore, knowing the vibration mode and resonance frequency of the tire is very important in the field of tire development. When considering using the tire in combination with various rims (wheels), it is important to perform vibration analysis using the rim and the tire as a single structure. The problem here is the vibration mode of the rim, and the resonance point (resonance frequency) of the rim alone is in the vicinity of 400 Hz to 450 Hz. This is a general rim, but is applicable to almost all rims.

  On the other hand, the tire resonance point has a plurality of vibration modes (that is, a plurality of vibration modes), and is mostly around 200 Hz or less. That is, in an actual tire, when a tire and a rim are combined, vibrations of 200 Hz or less are mainly vibrations caused by the tire, and vibrations in the vicinity of 400 to 450 Hz are considered to be vibrations by the rim.

  Therefore, also in the tire behavior simulation, both the rim and the tire are modeled by FEM (the rims may be combined in step 102 in FIG. 2), and these are combined and analyzed. In this analysis, the same result as that in which the tire caused vibrations of 200 Hz or less and the rim caused vibrations in the vicinity of 400 to 450 Hz was obtained.

  However, when the behavior simulation is performed on the vibration at the time of rolling of the tire, when the tire model rotates, the tire model is not a circle but a polygon, so that vibration is generated only by rolling (only rotating). This vibration is a vibration inherent to analysis that is not found in an actual tire. That is, vibrations that do not actually occur are caused by the polygonal tire model modeled for analysis.

Therefore, for example, considering an analysis of rotating a tire and a wheel at a speed of 50 km / h, the outer circumference of a general passenger car tire is about 2 m, and if it rolls at 50 ports per hour, the tires per second Rotates about 7 times. When the tire model is divided into 60 in the circumferential direction as in the conventional case, 7 rotations / second · 60 division = 420 Hz, and the frequency at which the polygonality of the element division occurs is about 420 Hz. This coincides with the natural frequency of the foil, and there is a high possibility that a resonance phenomenon will occur in the analysis. In this case, since it is 50 km / h, this corresponds to 13.89 m / s. Since the outer circumference of the tire is about 2 m, it rotates 7 times at 13.89 m / 2 m. That is, a tire traveling at 50 km / h rotates 7 times per second. Next, when the tire case portion is divided into 60 parts, the vertex of the polygon of the model is in contact with the 60 circuit surface during one rotation of the tire, so that 60 vibrations occur when the tire makes one rotation. Therefore, (a tire with a speed of 50 km / h rotates 7 times per second) + (the tire model has a geometric characteristic that vibrates 60 times when it rotates once) = (7 in a behavior simulation that runs at 50 km / h) -Generates “extra-vibration due to the geometrical shape of the model in the analysis that cannot actually occur” of 60 = 420 Hz),
It will be.

  Here, the relationship with the foil (rim) will be described. The actual rim has a resonance frequency of 400-450 Hz. When this frequency and vibration that can only occur in the tire behavior simulation overlap, the vibration is amplified and greatly generated. That is, in the simulation, since the vibration of the tire just matches the resonance point of the rim, the vibration near 420 Hz is exaggerated and output as an analysis result.

  Therefore, if the tire model is divided into 120 parts, the frequency at which the polygonality of the element division occurs becomes a high frequency of 840 Hz, and resonance can be avoided. In general, when considering the resonance of a vehicle due to an eigenvalue of a tire, there are many cases of a so-called low speed region where the speed is about 30 km and a high speed region where the speed is 80 km or more. For example, when the speed is 30 km / h, the tire is rotating 4.2 times per second, and in order to avoid resonance with the foil, it is derived from the polygonal nature of the case element (MESH). Considering that the vibration in analysis is 500 Hz or more, it is necessary to make 500 Hz / 4.2 = 119 divisions or more. Furthermore, in the region where the speed is low, it is necessary to control the number of elements (MESH) in the case portion according to the speed. At a speed of 20 km, the element division number needs to be 180 divisions or more in order to avoid resonance with the foil. That is, when considering an assembly structure of a tire and a foil, the resonance frequency with the foil is a relatively high vibration frequency among the main natural frequencies, and attention must be paid during analysis. Since the natural frequency of the foil is generally 400 Hz to 450 Hz, resonance can be avoided if the frequency resulting from element division is set to 500 Hz or higher, which is higher than this.

  That is, in the present embodiment, when considering vibration analysis of the tire, the number of divisions of the tire FEM model is set so as not to cause a resonance phenomenon with the rim that should not be present (step 140 in FIG. 3). .

  In order to prevent the geometrical factor vibration caused by the polygonal shape of the tire model from overlapping the resonance point of the rim 400 to 450 Hz, This specifies the minimum required number of element divisions in the circumferential direction.

  Thus, in this embodiment, when performing analysis by FEM using a tire model, by setting the number of divisions into elements so that the frequency generated from the divided elements is 500 Hz or more, An assembly combining a tire and a rim can be analyzed with a reduced calculation load while minimizing vibration.

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 1st Embodiment of this invention. It is a flowchart which shows the flow of a tire model creation process. It is a perspective view which shows a tire model and a road surface. It is a flowchart which shows the flow of a boundary condition setting process. The tire model when the tire is divided into 60 parts is shown, (A) is the area of the contact surface, and (B) is a side view of the tire model. A tire model when a tire is divided into 120 parts is shown, (A) is an area of a contact surface, and (B) is a side view of the tire model. A tire model when a tire is divided into 180 parts is shown, (A) is an area of a contact surface, and (B) is a side view of the tire model. It is a characteristic view which shows the analysis result of the tire model divided into 72. It is a characteristic view which shows the analysis result of the tire model divided into 120. It is a characteristic view which shows the analysis result of the tire model divided into 180. It is a characteristic view which shows the analysis result of the 360 divided tire model. FIG. 6 is a characteristic diagram showing a relationship between the number of divisions of a tire model and vibration amplitude. It is a characteristic view which shows the relationship between the division | segmentation number of a tire model, and calculation time. It is a characteristic view which shows the relationship of the maximum value of lateral force when it concerns on 2nd Embodiment and a slip angle is changed. FIG. 10 is a characteristic diagram showing the relationship between the number of divisions of the tire model and the maximum value of lateral force according to the second embodiment. It is a diagram which shows a contact surface when it concerns on 3rd Embodiment and a tire model is divided into 60 parts. It is a diagram which shows 3rd Embodiment and shows the contact surface when a tire model is divided into 120 parts. It is a diagram which shows 3rd Embodiment and shows the contact surface when a tire model is divided into 180 parts.

Explanation of symbols

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

Claims (7)

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 in which one round of a tire case is divided into 120 or more and 360 or less elements in the tire circumferential direction. In order to simulate the behavior of the tire in use, a tire model that calculates a tire corresponding to a numerical calculation model,
The tire contact surface is divided into 10 or more and 30 or less elements in the tire circumferential direction. In order to simulate the behavior of the tire in use, a tire model that calculates a tire corresponding to a numerical calculation model,
In order to perform vibration analysis as the analysis, the number of element divisions is set in the tire circumferential direction so that the vibration frequency generated by the elements divided in the tire circumferential direction becomes the vibration frequency excluding the resonance frequency of the rim to which the tire is assembled. A tire model characterized by   The tire model according to claim 3, wherein a vibration frequency generated by an element divided into elements in the tire circumferential direction at a vibration frequency excluding a resonance frequency of a rim to which the tire is assembled is 500 Hz or more. 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 4 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) Predicting the behavior 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 4 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 behavior 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 4 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 the behavior of the tire based on the physical quantity.

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