JP4658580B2 - Tire behavior analysis method - Google Patents

Description

  The present invention relates to a tire behavior analysis method and relates to a tire behavior analysis method for analyzing the behavior of a tire such as a pneumatic tire used in an automobile or the like.

  Conventionally, in the development of tires such as pneumatic tires, the behavior analysis of tires involves actually designing and manufacturing tires, and actually measuring the physical quantities and their fluctuations (for example, the amount of wear) generated by running on a car. And evaluated it in consideration of the tire shape. Recently, with the development of numerical analysis methods such as the finite element method and the computer environment, it has become possible to calculate the tire shape and the like with a computer in consideration of the tire internal pressure filling state and the load state. As a result, the behavior of the tire can also be analyzed by numerical calculation.

  In particular, in tire behavior analysis, it is important to analyze the area around the road surface in contact with the tire. As an example of such tire behavior analysis, simulation is performed with liquid interposed between the tire surface and the road surface. A technique has been proposed (see, for example, Patent Document 1). In this technique, the tire behavior is simulated in consideration of minute convex portions or concave portions of 1 μm to 1 mm on the tire surface.

  However, the actual tire behavior analysis is based on the premise that the behavior of the contact portion between the road surface and the tire is taken into account. In order to accurately analyze the behavior of the contact portion between the road surface and the tire, high accuracy is required. Analysis processing is required.

By the way, when analyzing the behavior of a tire by a numerical analysis method such as a finite element method, the analysis is based on an explicit method suitable for analyzing mainly dynamic behavior such as vibration phenomenon, or calculating the energy balance of the system. Thus, there is known an implicit analysis suitable for determining the equilibrium state and analyzing the behavior. Since the implicit method requires a very long calculation time for each step, the step interval must be increased, but a highly accurate analysis result can be obtained. On the other hand, the explicit method can shorten the calculation time for each step and is suitable for analysis of inertial force that requires fine time increments (step intervals), but the accuracy of the analysis result does not reach that of the implicit method. However, since the tire behavior analysis deals with the phenomenon of tire rolling every moment, it is common to use an explicit method in consideration of calculation load and ease of handling.
JP 2004-42830 A

  However, since the explicit method can obtain only an insufficiently accurate result, it is necessary to use the implicit method when a highly accurate analysis result is required. However, since the implicit method requires a very long calculation time for each step, considering the calculation load, the time step (step interval) must be increased, and depending on the setting of the time step, the analysis result is large. Differences sometimes occurred. In particular, in order to consider the behavior of the contact portion between the road surface and the tire, it is necessary to shorten the time step and process a huge amount of calculation.

  In view of the above fact, an object of the present invention is to obtain a tire behavior analysis method capable of facilitating the behavior analysis of a tire such as a pneumatic tire used in an automobile or the like.

  In order to achieve the above object, the present invention specifies the relationship between the relative movement amount between a road surface model and a tire model and the size of an analytical element for a tire such as a pneumatic tire used in an automobile or the like. Thus, an accurate tire behavior analysis can be performed without increasing the calculation load.

Specifically, the present invention relates to a tire model formed by dividing into a plurality of elements having a predetermined element size so as to be deformable by at least one of ground contact and rolling, and at least one of the tire models. A road surface model for contacting a portion and a running condition including a friction coefficient between the tire model and the road model, and a part of the tire model is defined as the road model based on the running condition. Rolling calculation is performed in which the tire model and the road surface model are moved by a predetermined amount of movement relative to each other in a predetermined direction, and the tire is based on the friction energy obtained as a physical quantity of the calculation result of the rolling calculation. a tire behavior analysis method using the implicit method to analyze the wear performance of the tire as a behavior, a solution of at least the amount of movement smaller than the element size And performing.

  In the present invention, the behavior of the tire is analyzed using an implicit method. In order to analyze the behavior of this tire, first, the tire design plan (change of tire shape, structure, material, pattern, etc.) and the measured value of the tire shape are put into the model for numerical analysis, and the tire that can be numerically analyzed Create a model (numerical analysis model). At this time, stress or the like is applied to the tire from the road surface in contact with the tire. Therefore, by modeling the road surface and creating a model for numerical analysis, it is possible to perform numerical analysis on the behavior of the tire. Here, the tire and the road surface move relative to each other to travel. In this traveling, friction between the tire and the road surface is involved. Therefore, for numerical analysis, it is possible to simulate traveling by determining a friction coefficient and the like.

  Therefore, in the present invention, in order to analyze the behavior of the tire, a tire model formed by dividing into a plurality of elements having a predetermined element size so as to be deformable by at least one of ground contact and rolling, and a tire A road surface model for contacting at least a part of the model and a running condition including a friction coefficient between the tire model and the road surface model are determined.

  Next, based on the driving conditions, a rolling calculation is performed in which a part of the tire model is brought into contact with the road surface model and the tire model and the road surface model are moved relative to each other in a predetermined direction by a predetermined amount of movement. The tire behavior is analyzed based on the physical quantity of the calculation result of the rolling calculation.

  When analyzing the tire behavior using the implicit method in this way, the element size may be made sufficiently small in order to improve the analysis accuracy, or the time increment of the rolling calculation, that is, the movement amount may be made sufficiently short. preferable. However, the calculation load (calculation time) increases as the element size is reduced or the movement amount is reduced. In addition, improvement in accuracy cannot be expected with only one of the element size and the movement amount.

  Therefore, in the present invention, the analysis is performed with at least the movement amount smaller than the element size. This is because when a rolling calculation is performed to move the tire model and the road surface model relative to each other with a movement amount that is equal to or larger than the element size, which is the smallest unit of analysis, a state where multiple nodes simultaneously contact the road surface model is generated in the analysis. It is to do. In this state, in the analysis based on the analysis for each node, a plurality of nodes under the same condition are generated, and the accuracy in the contact portion is reduced. Note that it is preferable to determine the movement amount corresponding to the time step for each step in the calculation at the time of analysis as the movement amount equal to or larger than the element size as the minimum unit of analysis.

  Thus, by analyzing the movement amount smaller than the element size, a plurality of nodes do not simultaneously contact the road surface model at the time of analysis, and the analysis accuracy can be improved.

  The element size of the tread portion on the tire surface can be adopted as the element size of the tire model for analyzing the behavior of the tire.

  Most tire models in contact with the road surface model have a tread portion. For this reason, it is possible to perform analysis while improving accuracy only by setting the movement amount smaller than the element size of the tread portion on the tire surface.

  Specifically, the tire behavior analysis includes analysis for steering performance evaluation, analysis for tire wear performance evaluation, analysis for tire noise performance evaluation such as tire pattern noise, and stress strain analysis. At least one analysis can be employed.

  As described above, according to the present invention, since the amount of movement is made smaller than the element size and analyzed, the behavior of the tire can be analyzed accurately without causing a decrease in accuracy for the contact portion between the tire and the road surface. There is an effect.

  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 when analyzing the performance of a pneumatic tire as a tire behavior analysis. In the present embodiment, tire wear is adopted as the performance of the pneumatic tire, and the tire behavior is simulated.

  In the following description, the case where the tire wear performance is adopted as the tire behavior analysis will be described, but the present invention is not limited to this, and the analysis for maneuvering performance evaluation, pattern noise prediction, and others It can be applied to stress strain analysis and the like.

  FIG. 1 shows an outline of a personal computer for carrying out simulation of pneumatic tire wear according to 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. Recording media include recording tapes, optical disks such as CDROM and DVD, and magneto-optical disks such as MD and MO. When these are used, a read / write device corresponding to or in addition to the FDU may be used.

  FIG. 2 shows a processing routine of the tire wear simulation program of the present embodiment. In step 100, initial settings are made for the design plan of the tire to be simulated (changes in tire shape, structure, material, pattern, etc.) and various measured values of the tire. This initial setting is a process for setting various models and shapes, physical properties such as rubber, and various initial data necessary for simulating tire wear.

  Specifically, an initial setting routine shown in FIG. 3 is executed. In the initial setting routine, first, a tire model is created in order to drop the tire design proposal into a numerical analysis model. The creation of the tire model differs slightly depending on the numerical analysis method used. In this embodiment, a finite element method (FEM) based on an implicit method is used as a numerical analysis method. Therefore, the tire model to be created 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 divided into a computer program created based on a numerical / analytical method. This is a numerical value in the input data format. This element division means 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. Note that a difference method or a finite volume method may be used as a numerical analysis method.

  In creating a tire model, a pattern is modeled after a tire cross-section model is created. First, in step 200, in order to create a numericalized tire model, the minimum size h of an element to be divided into a plurality of elements by element division (for example, mesh division) corresponding to the finite element method (FEM). (Hereinafter referred to as mesh size h) is set. The size of the mesh size h is the length between nodes that are the vertices at the time of division, such as the volume, surface area, cross-sectional area, length of one piece, and longest length of the elements divided by element division (division elements) Etc. can be adopted. Here, the length between nodes will be described as a mesh size h. Further, if the mesh size h is increased, the calculation load is reduced, but the accuracy is deteriorated. On the other hand, if the mesh size h is reduced, the calculation load increases, but the accuracy improves. Therefore, the mesh size h is preferably set to a predetermined size experimentally or empirically.

  In the next step 201, a tire radial section model (tire section data) is created. The tire cross-section data is obtained by measuring the tire outer shape with a laser shape measuring instrument or the like. Also, the exact structure of the tire is taken from the design drawings and actual tire cross-section data. Rubber and supplementary teaching materials (belts, plies, etc., in which reinforcing cords made of iron and organic fibers are bundled in a sheet) are modeled according to the modeling method of the finite element method. A model of the tire radial cross section modeled in this way is shown in FIG.

  Normally, the cord angle of the belt layer is modeled with the same in the width direction (for example, 24 degrees with respect to the circumferential direction), but in this embodiment, the cord of the belt layer is set to S for improving the calculation system. It is calculated as a character (in the width direction end, a direction having a large angle with respect to the circumferential direction). This can be expected to improve accuracy.

  In the next step 202, tire cross-section data (tire radial cross-section model), which is two-dimensional data, is developed by one turn in the circumferential direction to create a three-dimensional (3D) model of the tire. In this case, it is desirable to model the rubber part with an 8-node solid element and the supplementary teaching material with an anisotropic shell element that can express an angle. In this case, a three-dimensional tire model is created based on the mesh size h set in step 200 above.

  In the next step 204, the pattern is modeled. Modeling this pattern involves modeling a part or all of the pattern separately and pasting it as a tread on the tire model, or creating a pattern when developing tire cross-section data in the circumferential direction. It is possible to adopt creating a pattern in consideration of components. FIG. 5 shows a 3D model modeled three-dimensionally in this way. In this case, pattern modeling is performed based on the mesh size h set in step 200.

  In the next step 206, a model of an object related to the tire including at least the road surface is created. In this step 206, the road surface state is input together with the creation of a road surface model obtained by dividing and modeling the road surface including a part of the tire, the ground contact surface, and the region where the tire moves and deforms. This road surface state is a road surface shape or a road surface material. The influence of friction due to this road surface condition will be described later. The fluid region interposed between the tire and the road surface may be divided and modeled.

  In the next step 208, the rubber constituent material of each part of the tire is set. As described above, structurally, the rubber in the tire and the supplementary teaching material are modeled by the finite element method, but the rubber in the tire, that is, the rubber constituent material of each part of the tire varies. Therefore, in this step 208, the rubber constituent material of each part of the tire is set. Thereby, various data constituting the tire can be defined.

  In the next step 210, various data for simulating tire wear are read. These various data are data related to tire wear, and representatively, there is a road surface friction coefficient μ. In this case, this corresponds to setting the road surface as a model and approximating the modeled road surface to the actual road surface. The road surface can be modeled by dividing the road surface shape into elements and modeling it, and selecting and setting the road surface friction coefficient μ. For example, depending on the road surface condition, there is a road friction coefficient μ corresponding to dry (DRY), wet (WET), ice, snow, unpaved, etc., so by selecting an appropriate value for the friction coefficient μ, the actual road surface Can be reproduced.

  It is known that the friction coefficient μ of a tire changes according to the contact pressure. Therefore, in the present embodiment, a characteristic (μ-P curve) obtained by an experiment or the like in advance for the relationship between the friction coefficient μ and the contact pressure P is made into a database and used.

  In this step 210, an initial temperature and a use load when using the tire for simulating tire wear can be set. Moreover, when the tire is a pneumatic tire, the filling rate of the internal pressure can be set.

  In this way, after the initial setting, the change in tire wear is grasped as follows.

  In step 102 of FIG. 2, the tire model is corrected to a tire model cut by a cutting amount Dn (n is a natural number). Note that the processing in step 102 immediately after step 100 uses the model determined in step 100 as it is for the first model correction. In the next step 104, rotational contact analysis is executed. This rotational contact analysis is a process that is necessary for grasping the possibility of wear progressing due to changes over time, by analyzing changes when the tire in contact with the road surface is rotated.

  Specifically, the processing routine shown in FIG. 6 is executed. First, in step 300, a tire model and an ideal planar road surface model are read. In the next step 301, a relative movement amount d between the tire model and the road surface model is set. The setting of the amount of movement d is a limit for maintaining the accuracy when performing a rotational contact calculation in which the tire model is brought into contact with the road surface model and rolled by the finite element method.

  The restrictions for maintaining this accuracy will be described in detail. In this embodiment, implicit FEM is adopted. There are two types of finite element methods: the implicit method and the explicit method. Generally speaking, we will observe time-varying physical phenomena (in the case of tires, the tire rolls from moment to moment), but how to deal with this time-varying effect is an implicit method. Different in explicit method.

  The implicit method is a method of calculating an energy balance in order to obtain an equilibrium state as is well known, and calculates the state at every time increment from an arbitrary time to obtain an equilibrium state. For example, this corresponds to obtaining a solution of a plurality of simultaneous equations for obtaining a solution satisfying the equilibrium in the time increment Δt from the time t where the state is known. Therefore, the time increment Δt can be increased as long as equilibrium is achieved, and the state can be obtained with high accuracy. That is, the calculation is divided from time t by time increment Δt, an equilibrium state after time increment Δt is obtained, and a new equilibrium state after new time increment Δt ′ (which may not be the same as Δt) is obtained based on this. In this way, the state is repeatedly obtained sequentially. Therefore, the implicit method can increase the time step of analysis, but the analysis time for each step becomes longer. Thus, the analysis time can be shortened by taking the analysis time increment very large.

  As is well known, the explicit method is a calculation method for finding a solution of a complex simultaneous equation of motion equation, not for convergence calculation, and for obtaining a state without balancing at every time increment Δt from an arbitrary time. It is. Generally, in order to reduce the calculation load, instead of obtaining a solution of simultaneous equations, a solution after time increment Δt (time t + Δt) is approximately obtained based on the equation of motion at time t. For example, a solution after the time increment Δt is obtained by extrapolation. However, in the explicit method, the time increment Δt must be set so as to satisfy the stability condition, and cannot be increased.

  In numerical calculations, the time is discretized and solved, but the time increments when discretized are greatly different between the two. In principle, it is preferable to use an implicit method with good accuracy, but there are the following facts at a practical level. In fact 1, in the implicit method, the calculation time per step is very long. In fact 2, since the calculation time for each step is very long, a large discretization time interval must be taken.

  On the other hand, although the accuracy of the explicit method is lower than that of the implicit method, the calculation time per step is very short (Advantage 1), and the inertial force such as centrifugal force can only be expressed in fine time increments. There is an advantage that the analysis is limited to the explicit method (Advantage 2). Therefore, the explicit method is easier to handle when high accuracy is not desired.

  However, for calculations that require a certain degree of accuracy, the implicit method must be used, and in order to complete the analysis in a realistic calculation time, a large time step must be taken. There is no theoretical value for this.

  For this reason, in order to improve accuracy, it is common to take measures such as making the mesh size finer (Improvement 1) and finer time increments (Improvement 2). Due to fact 2, it cannot be made as fine as possible. Therefore, in order to suppress the calculation load while guaranteeing high accuracy, some condition is necessary. Therefore, in the present embodiment, paying attention to the relationship between the time increment (movement amount d) and the mesh size h, the following minimum restriction condition is provided.

Restriction condition d <h
On the other hand, ignoring this condition causes an error. In the finite element method, calculation errors always occur unless the elements are made infinitely small. Therefore, when this restriction condition is not satisfied, a calculation result having two kinds of errors is obtained, and it has been known from past studies and experiments that accuracy is greatly reduced. Moreover, no matter how fine the mesh (division element) is, if the time increment is set large, the accuracy will not increase.

Here, the meaning of reducing the movement amount d is the same as making the time step finer. In other words, when trying to calculate the tire to move 1000 mm point,
(1) When calculating in 100 steps, d = 10 mm / step (2) When calculating in 1000 steps with fine time increments
d = 1mm / step (smaller)
In this case, the calculation time is 10 times. If the calculation of (1) takes 2 days, the calculation of (2) will take 20 days. Ideally, the time increment should be fine, but since it directly affects the computation time, there was a need to determine the minimum necessary fineness.

  More specifically, the tire model can obtain information such as stress, strain, slip, and the like regarding an arbitrary dividing element or node by contacting and rolling on the road surface. For example, as employed in the present embodiment, the wear energy distribution can be obtained by obtaining the wear energy from the nodal force and slip of the tire surface. As another example, the magnitude of pattern noise can be estimated from the force (contact pressure) at which the tread pattern strikes the road surface. This analytical calculation is an FEM calculation using the implicit method, and the time increment (interval of calculation steps) is very large compared to the explicit method due to the limitation of calculation time. In this embodiment, paying attention to the fact that this time step greatly affects the accuracy of the tire rolling calculation, the knowledge that the accuracy can be maintained by setting this appropriately and giving a limit has been reached. did. This is an effective limitation particularly in analysis focusing on the contact / friction state between the road surface and the tire, such as wear performance and pattern noise prediction.

  That is, in the implicit tire rolling model, the tire fixed on the wheel is basically moved in the traveling direction, and the tire rolls by friction with the road surface. The focus is on the relationship between the distance that the tire travels forward in one time step (1 step) (movement amount d) and the mesh size h of the element on the surface that contacts the road surface.

  In general, when the moving amount d is large, many points arranged in the traveling direction in one calculation step are brought into contact with the road surface. However, this is far from the actual physical phenomenon. This is because a node in front of you contacts a node, undergoes its deformation, and then contacts you. However, if the amount of movement d is set to be large, a number of nodes will be in contact at the same time in one calculation time, and the accuracy will be significantly reduced from the viewpoint of the contact state of each node (the contact state here) Is the pressure and slip amount in three directions where each node interacts with the road surface.) In addition, the node is constrained by frictional force while it is in contact with the road surface. The accuracy of the grounding state decreases until kicking.

  Therefore, the restriction condition (d <h) is set so that a plurality of nodes arranged in the direction of travel in one step do not touch at a time. Thereby, since it does not advance before the distance larger than the mesh size per step, a plurality of points are not grounded at the same time, and the accuracy is greatly improved.

  When the movement amount d is set so as to meet the above-described restriction condition, in the next step 302, the tire model and the road surface model are brought into close contact with each other. In step 302, it is assumed that the tire model is horizontally approached (flat pressed) to the road surface model. This flat pushing is controlled by a load value or a deflection amount. In addition, what is necessary is just to incline with respect to a road surface model only the camber angle which designates a tire model, when designating a camber angle. In the next step 304, the center point of the tire model is moved by the set movement amount d in the horizontal direction with respect to the road surface model. At this time, the tire model and the shaft of the tire model are constrained, and a frictional force exists between the tire model and the road surface model, so that the restraint of the tire model is released and the tire model rotates. Note that, by changing the moving direction of the center point of the tire model from the direction of the tire model, it is possible to realize in a calculation the state in which the direction is instructed by the steering angle.

  FIG. 7 shows the relationship between the tire model and the road surface model for each state when the rolling analysis is performed. 7A shows a state where the tire model and the ideal planar road surface model are separated from each other, and FIG. 7B shows a state where the tire model is horizontally approached (flat pressed) to the ideal planar road surface model. (C) has shown the state which moved the center point of the tire model to the horizontal direction with respect to the road surface model.

  FIG. 8 shows the behavior of the tire model in the vicinity of the road surface model during rolling analysis. FIG. 9 shows a state before and after the step in which the tire model and the road surface model are relatively moved by the movement amount d. As shown in FIG. 8, in the state shown in FIG. 8, the node k adjacent to the traveling direction is not in contact with the node k in contact. From this state, by moving the tire model with the movement amount d smaller than the mesh size h, only the node (k + 1) adjacent to the traveling direction comes into contact. Thereby, a plurality of nodes do not contact at the same time due to the movement of the tire model.

  In step 106 of FIG. 2, the wear energy distribution after the rotational contact analysis is obtained. The wear energy Ew corresponds to the friction work of the tire tread and can be obtained as follows. The wear energy may be referred to as friction energy.

  That is, as described in the tire wear life prediction method proposed by the present applicant (Japanese Patent Laid-Open No. 11-326144), the wear energy Ew is the frictional force (horizontal stress: tangent to the road surface received from the road surface). It can be obtained by multiplying the directional stress (T) by the slip amount S of the tire tread (Ew = T · S).

  Here, in the FEM according to the present embodiment, the stress and the displacement of the node coordinates (element distortion) can be obtained for all the nodes and elements in the model. As described above, in the tire rolling calculation, the tire model is pressed against the road surface model to move in the horizontal direction. For this reason, frictional force (horizontal stress) and vertical stress are generated in the region (tread surface) where the road surface model and the tire model are in contact. At this time, the nodes in the tread surface of the tire model in contact with the road surface model behave as follows.

(Vertical stress) x (Friction coefficient μ) ≥ (Horizontal stress)
Under the conditions, the tire model is constrained by the road surface model, the nodes in the tread do not move, and there is no displacement.

(Vertical stress) x (Friction coefficient μ) <(Horizontal stress)
Under the conditions, the tire model is not constrained by the road surface model, and the nodes in the tread move relative to the road surface model. In this case, the tire model is deformed in a direction to relax the horizontal stress, and displacement occurs.

  The displacement when the tire model mentioned above is in contact with the road surface model is defined as the slip amount. In this method, a displacement in which a node has moved in the road surface model between the time when an arbitrary node starts contact with the road surface model and the time when contact ends is obtained as a slip amount. Therefore, the wear energy can be obtained from the stress and displacement obtained by FEM.

  By the way, even if the wear energy is the same, the wear amount is different if the composition of the material (for example, rubber) constituting the tire is different. Therefore, in the present embodiment, the rubber index Gi is used to express the composition of the material (for example, rubber), that is, the difference in rubber. As described in the tire wear life prediction method proposed by the present applicant (Japanese Patent Laid-Open No. 11-326144), the rubber index Gi is a ratio of the wear depth W to the wear energy Ew (Gi). = Ew / W). Therefore, the rubber index Gi can be expressed by a ratio between the wear amount obtained from the wear depth and the above-described wear energy Ew. As the rubber index Gi, a value measured in advance with a rubber test piece is stored and used. Thereby, in step 106, the distribution of the wear energy Ew can be obtained, and the wear amount corresponding to the material (rubber) can be obtained.

  Thus, when the block is divided into a mesh shape in the circumferential direction, the length of one calculation time is shortened with respect to the time when one mesh newly enters the tread surface, so that the slip amount S can be reduced. It became possible to improve accuracy. This is one of the factors for achieving that it has become possible to replace the measurement of wear energy with FEM calculations.

  In the next step 108, the tire model is corrected to a tire model that has been cut by a minute cutting amount D. That is, the coordinates of each node are moved by a distance corresponding to the shaving amount D. The amount of cutting D is preferably set corresponding to the wear energy Ew, but the distribution of the next wear energy Ew may vary greatly depending on the amount of the amount of cutting D. When the rolling analysis is performed on a tire model with a large amount of shaving D cut, a calculation result including a lot of errors is obtained. Therefore, in step 108, in order to avoid a calculation result including a large amount of error, a predetermined fine cutting amount D (for example, a small amount of 0.01 mm or 0.01 mm or less is preferably set) is set. The tire model is corrected. The minute shaving amount D is usually set to a minute amount of 0.01 mm or less.

  In the next step 110, the rotational contact analysis is executed in the same manner as in the above step 104, and the distribution of the wear energy Ew after the rolling analysis is performed on the tire model cut by the above-mentioned cutting amount is obtained in the next step 112. From the distribution of the wear energy Ew obtained in step 112, in the next step 114, the scraping amount Dn corresponding to the wear energy Ew is determined as follows.

  As described above, it is possible to obtain a calculation result in which the error is suppressed as much as possible by repeatedly calculating with a very small amount of cutting D, but the calculation load (calculation time) becomes enormous. Therefore, in the present embodiment, in step 114, the scraping amount Dn is obtained based on the condition that suppresses the number of repeated calculations while maintaining accuracy.

  First, a wear work distribution, that is, a wear energy distribution obtained by rolling analysis with a tire model after cutting by a cutting amount D (for example, 0.01 mm) at an arbitrary position r is defined as EW (r, D). In this case, the difference dEW between the wear energy distributions of the tire model after cutting by the cutting amount D and the tire model after cutting the double cutting amount D with respect to the tire model immediately before cutting. Can be expressed by the following equations (1) and (2).

dEW (r, D) = EW (r, D) −EW (r, 0) (1)
dEW (r, 2D)) = EW (r, 2D) −EW (r, 0) (2)
However, EW (r, 0) is initial wear energy (immediately before cutting), r is a position, and D is a unit cutting amount. Using these two equations, a cutting amount Dn that satisfies the following equation (3) is obtained.

Dn << D · (4 · dEW (r, D) −dEW (r, 2D)) / (dEW (r, 2D) −dEW (r, D)) (3)
Dn is the amount of shaving required.

  In the next step 116, it is determined whether or not the number of iterations n has reached a predetermined number N (n = N?). If the result is negative, the number of iterations n is incremented by 1 in step 118. Return to step 102. On the other hand, when the result in step 116 is affirmative, the process proceeds to step 120, and the above calculation result is output. As an example of the calculation result, there is display data for displaying the finally corrected tire model. With this display data, it is possible to display an image for grasping the state of stress distribution and wear energy distribution for a tire that shifts with time. In step 142, final various data (for example, parameters such as setting conditions, wear amount, and cutting amount) may be output.

  Thus, in the present embodiment, when the rotational contact analysis is performed by relatively moving the tire model and the road surface model in contact with each other, the relationship between the time increment (movement amount d) and the mesh size h is limited. Since the condition (d <h) is set, there is no movement of a distance larger than the mesh size per step, so that a plurality of points do not touch at the same time, and the accuracy is greatly improved. Therefore, in this embodiment, it is possible to accurately simulate the wear performance of the tire while suppressing the calculation load while maintaining high accuracy.

  In the present embodiment, after obtaining the wear energy distribution after the rotational contact analysis in step 106 of FIG. 2, the wear rate distribution at each point can be obtained from the distribution. Each point here may be any predetermined point or region in the tire model, but a node is preferable in consideration of FEM calculation.

  In the present embodiment, the wear rate further obtained in step 106 represents the degree of progress of wear, and here, the wear energy Ew obtained in time series is defined by multiplying the difference by a constant as the wear rate. To do. Thus, the wear rate at each point can be obtained in each process of the iterative calculation, and the wear rate can be grasped for each point of the tire model when simulating the progress of the wear mode. Thereby, it is possible to grasp the speed of wear on the tire model as the speed.

  Further, in step 112 of FIG. 2, the wear rate may be further obtained. In this case, any wear rate in step 106 and step 112 may be used. Here, the wear rate is preferably obtained from the difference between the previous wear energy Ew and the current wear energy Ew, but is not limited to the previous wear energy Ew. For example, the wear energy Ew may be compared at regular intervals.

  The results of performing a field test on an actual tire and performing a tire wear simulation of the present embodiment using the tire data are shown below. In this example, the modeled and actually measured tire is a tire having a rectangular block pattern shape with a tire size of 195 / 65R15, and a tire having a block pattern on the tire shoulder portion. And the simulation by the calculation which calculates | requires the wear energy in the shoulder block at the time of continuing applying a fixed braking force, and the wear test using an actual test apparatus were done.

  The following two types of simulation conditions were determined in the simulation by calculation for obtaining the wear energy. The first simulation condition is to set the movement amount d to twice the mesh size h (d = 2h), and the second simulation condition is to set the movement amount d to ½ times the mesh size h (d = 0.5h).

  10 and 11 show the simulation results under the above simulation conditions. FIG. 10 shows the wear energy distribution under the first simulation condition, and FIG. 11 shows the wear energy distribution under the second simulation condition. Usually, the wear energy increases from the stepping side to the kicking side of the tire, resulting in heel and toe wear. Therefore, it is only necessary to compare the distribution of wear energy from depression to kicking. As a result, in the first simulation condition, the wear energy varies from stepping on to kicking out, but in the second simulation condition, it can be understood that it increases in a precise shape.

  In addition, FIG. 12 shows the result of measuring the distribution of the amount of wear after running 500 km as a comparative test by testing the tire with a similar braking force using an abrasion tester. The measured position is a line along the tire circumferential direction at 10 mm from the inside of the shoulder block. As can be understood from FIGS. 11 and 12, the tire wear simulation result matches the distribution obtained by actual measurement. Therefore, a simulation result commensurate with the actual test can be obtained by performing the rotational contact analysis in consideration of the above-mentioned limiting conditions.

It is the schematic of the personal computer for implementing the simulation of tire wear concerning embodiment of this invention. It is a flowchart which shows the flow of a process of a tire wear simulation program concerning this Embodiment. It is a flowchart which shows the flow of an initial setting process. It is a perspective view which shows a tire radial direction cross-section model. It is a perspective view which shows the three-dimensional model of a tire. It is a flowchart which shows the flow of a rotation contact analysis process. The relationship between the tire model and the road surface model at the time of rotational contact analysis is shown. (A) is a state where the tire and the road surface are separated from each other, (B) is a state where the tire is pushed flat on the road surface, and (C) is a center point of the tire. The state moved to the horizontal direction with respect to the road surface is shown. It is a conceptual diagram which shows the behavior in the road surface model vicinity of the tire model at the time of rolling analysis. It is an image figure which shows the state before and behind the step which moved the tire model and the road surface model by the movement amount d relatively. It is a characteristic view which shows the wear energy distribution by 1st simulation conditions. It is a characteristic view which shows the wear energy distribution by 2nd simulation conditions. It is a characteristic view which shows the wear amount distribution of the test result by an abrasion tester.

Explanation of symbols

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

Claims (3)

A tire model formed by dividing into a plurality of elements having a predetermined element size so as to be deformable by at least one of contact and rolling, and a road surface model for contacting at least a part of the tire model, And a driving condition including a friction coefficient between the tire model and the road surface model,
Based on the running condition, a part of the tire model is brought into contact with the road surface model, and a rolling calculation is performed to move the tire model and the road surface model by a predetermined amount of movement in a predetermined direction,
A tire behavior analysis method using an implicit method of analyzing tire wear performance as tire behavior based on frictional energy obtained as a physical quantity of a calculation result of the rolling calculation,
A tire behavior analysis method, wherein the analysis is performed with at least the movement amount smaller than the element size. The tire behavior analysis method according to claim 1, wherein an element size of a tire model for analyzing the behavior of the tire is an element size of a tread portion on a tire surface.   The tire behavior analysis is at least one of analysis for steering performance evaluation, analysis for tire wear performance evaluation, analysis for tire noise performance evaluation, and stress strain analysis. The tire behavior analysis method according to claim 1 or claim 2.

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