JP2012030702A - Method and computer program for simulating tire - Google Patents

Abstract

PROBLEM TO BE SOLVED: To suppress a deterioration in calculation accuracy while suppressing an increase in calculation time in the analysis of a tire using a computer.SOLUTION: A method for simulating the tire includes: a model creation step (step S101) of creating a response analysis model for obtaining a dynamic response of the tire; a power history setting step (step S102) of setting a history of the power acting on the response analysis model in a ground-contact region of the response analysis model; a displacement history setting step (step S103) of obtaining a history of the displacement of the response analysis model in the ground-contact region on the basis of the history of the power; a forced displacement input setting step (step S104) of setting an input of the forced displacement to be input in the response analysis model on the basis of the history of the displacement; and a response calculation step (step S105) of obtaining a dynamic response of the response analysis model by giving the set input of the forced displacement to the ground-contact region.

Description

  The present invention relates to a technique for analyzing a tire using a computer.

  Predicting various performances of tires or physical quantities related thereto by numerical analysis such as a finite element method by analysis using a computer is useful for improving performance and improving development efficiency. Among these, the simulation of the dynamic response of the tire caused by the input generated between the tire and the road surface due to the road surface unevenness and the tire tread pattern is important for the transient response and the vibration / noise performance. For example, Patent Document 1 describes a method in which a road surface and a tread pattern are modeled in detail and a rolling calculation is directly performed on a non-flat road. Further, Patent Document 2 obtains a road surface model that is an aggregate of a plurality of protrusions arranged in a planar shape, obtains at least one of vibration and noise when a tire passes over a single protrusion, and based on the road surface model. A method for synthesizing at least one of noise and vibration is described.

Japanese Patent Laid-Open No. 11-201874 JP 2000-241308 A

  However, in the method of Patent Document 1, it is necessary to execute a travel analysis with a large model and a large calculation load in order to ensure accuracy, and a travel analysis is necessary again to calculate responses at different speeds. Therefore, there is a problem that calculation time increases. In addition, the method of Patent Document 2 has a problem in that the accuracy of analysis is lowered because input by a tread pattern is not considered. For this reason, it has been desired to analyze the dynamic response of the tire accurately and efficiently by using the road surface unevenness and the tread pattern as input.

  The present invention has been made in view of the above, and an object of the present invention is to suppress a decrease in calculation accuracy while suppressing an increase in calculation time in a tire simulation using a computer.

  Means for solving the above-mentioned problems are: a model creation procedure in which a computer creates a response analysis model for obtaining a dynamic response of the tire based on a tire to be analyzed; and the computer A force history setting procedure for setting a history of force acting on the response analysis model in the region of the response analysis model corresponding to the ground contact region, and the computer based on the force history A displacement history setting procedure for obtaining a displacement history of a response analysis model; a forced displacement input setting procedure for setting an input of a forced displacement input to the response analysis model based on the displacement history by the computer; and A computer gives a response input of the set forced displacement to the region and obtains a dynamic response of the response analysis model. When a simulation method of tire, which comprises a.

  As means for solving the problem, in the force history setting procedure, the computer quasi-statically analyzes a tire model that can analyze a history of force acting on the ground contact area by a computer created based on the tire. In the forced displacement input setting procedure, the forced displacement history or force history is changed to the fluctuation in the rolling speed set in the dynamic response analysis in the response calculation procedure. It is preferable to use after conversion.

  As a means for solving the problem, the computer preferably uses a transformation matrix linearized in a prescribed state in the displacement history setting procedure.

  As a means for solving the problem, the computer preferably uses a stiffness matrix of the response analysis model as the transformation matrix.

  As a means for solving the problem, in the force history setting procedure, the computer uses a quasi-static tire model that can analyze a history of force acting on the ground contact area and a computer created based on the tire. It is preferable that the response analysis model is obtained from the result of rolling to the above, and the element division of the region is coarser than that of the tire model.

  As a means for solving the problem, in the forced displacement input setting procedure, the computer uses the rolling speed set in the analysis of dynamic response in the response calculation procedure in the forced displacement history or the force history. It is preferable to use it after converting it to the fluctuation of.

  As a means for solving the problem, the response analysis model is preferably a model converted into a modal model by a constraint mode method with at least the nodes of the region where the input of the forced displacement is set as a degree of freedom of holding. .

  Means for solving the above-described problem is a computer program for tire simulation, which causes a computer to execute the tire simulation method.

  The present invention can suppress a decrease in calculation accuracy while suppressing an increase in calculation time in a tire simulation using a computer in tire analysis using a computer.

FIG. 1 is a meridional sectional view of a tire. FIG. 2 is an explanatory diagram illustrating an analysis apparatus that executes the tire simulation method according to the present embodiment. FIG. 3 is a flowchart showing the procedure of the tire simulation method according to the present embodiment. FIG. 4 is a partial perspective view showing an example of a response analysis model. FIG. 5 is a schematic diagram illustrating a state in which the response analysis model is in contact with the road surface model. FIG. 6 is a plan view of the response analysis model ground contact area. FIG. 7 is a conceptual diagram showing a state in which the response analysis model ground contact area moves on a road surface model having protrusions. FIG. 8 is an explanatory diagram of the force history of the response analysis model ground contact region. FIG. 9 is a diagram illustrating an example of the direction of force. FIG. 10 is a partial perspective view showing an example of a tire model used when obtaining a force history. FIG. 11 is a perspective view showing an example of a road surface model. FIG. 12 is an explanatory diagram showing a ground contact rolling analysis. FIG. 13 is an explanatory diagram of a state in which a static load is applied to the tire model to perform ground contact analysis. FIG. 14 is a plan view showing a tread surface of a tire model. FIG. 15A is a schematic diagram illustrating an example of a displacement history. FIG. 15B is a schematic diagram illustrating an example of processing the displacement history to obtain a forced displacement input. FIG. 16 is a plan view of the response analysis model. FIG. 17 is a side view of the response analysis model. FIG. 18 is a schematic diagram showing a state in which a dynamic response is obtained by applying a forced displacement input to the response analysis model ground contact area. FIG. 19 is a schematic diagram of an example in which a force obtained from a tire model is transferred to a response analysis model using a response analysis model in which element division is coarser than that of a tire model used for ground contact analysis. FIG. 20 is a diagram illustrating the relationship between the rolling speed and the vertical axial force. FIG. 21 is a diagram showing the relationship between the rolling speed and the longitudinal axial force.

  DESCRIPTION OF EMBODIMENTS Hereinafter, modes (embodiments) for carrying out the present invention will be described in detail with reference to the drawings. In addition, this invention is not limited by the content described in the following embodiment. The constituent elements described below include those that can be easily assumed by those skilled in the art and those that are substantially the same. Furthermore, the constituent elements described in the following embodiments can be appropriately combined.

  FIG. 1 is a meridional sectional view of a tire. The tire 1 is an annular structure that rotates about a rotation axis (Y axis), and a meridional section having a similar shape is developed around the rotation axis in the circumferential direction. As shown in FIG. 1, a carcass 2, a belt 3, a belt cover 4, and a bead core 5 appear on the meridional section of the tire 1. The tire 1 is a composite material structure in which rubber as a base material is reinforced by a reinforcing cord such as a carcass 2, a belt 3 or a belt cover 4 as a reinforcing material. A layer of a reinforcing cord made of a cord material such as a metal fiber or an organic fiber, such as the carcass 2, the belt 3, and the belt cover 4, is referred to as a cord layer.

  The carcass 2 is a strength member that serves as a pressure vessel when the tire 1 is filled with air. The carcass 2 supports a load by its internal pressure and withstands a dynamic load during traveling. The belt 3 is a layer of reinforcing cords in which rubberized cords arranged between the cap tread 6 and the carcass 2 are bundled. In the radial tire, the belt 3 plays an important role as a shape retention and strength member.

  A belt cover 4 is disposed on the tread surface G side of the belt 3. The belt cover 4 serves as a protective layer for the belt 3 and serves as a reinforcing layer for the belt 3. The bead core 5 is a bundle of steel wires that supports the cord tension generated in the carcass 2 by internal pressure. The bead core 5 becomes a strength member of the tire 1 together with the carcass 2, the belt 3, the belt cover 4, and the tread. A groove 7 is formed on the tread surface G side of the cap tread 6. This improves drainage during rainy weather. The side portion of the tire 1 is called a sidewall 8 and connects between the bead core 5 and the cap tread 6. Further, a shoulder portion Sh is provided between the cap tread 6 and the sidewall 8. Next, an apparatus for executing the tire simulation method according to the present embodiment will be described.

  FIG. 2 is an explanatory diagram illustrating an analysis apparatus that executes the tire simulation method according to the present embodiment. The tire simulation method according to the present embodiment can be realized by the analysis device 50 shown in FIG. The analysis device 50 is a computer and includes a processing unit 52 and a storage unit 54 as shown in FIG. In addition, an input / output device 51 is electrically connected to the analysis device 50. The input / output device 51 has input means 53. This input means 53 inputs the physical property value of the rubber constituting the tire, the physical property value of the reinforcing cord, or boundary conditions used for grounding analysis, rolling analysis, vibration analysis, and the like to the processing unit 52 and the storage unit 54.

  An input device such as a keyboard and a mouse can be used for the input means 53. The storage unit 54 stores a computer program including tire analysis (ground contact analysis, rolling analysis, vibration analysis, etc.) and a tire simulation method according to the present embodiment. The storage unit 54 is a hard disk device, a magneto-optical disk device, a non-volatile memory such as a flash memory (a storage medium that can be read only such as a CD-ROM), or a volatile memory such as a RAM (Random Access Memory). The memory can be configured by a combination of these, or a combination thereof.

  The computer program may be capable of realizing the ground contact analysis, the rolling analysis, or the tire simulation method according to the present embodiment, in combination with a computer program already recorded in the computer system. The “computer system” here includes hardware such as an OS (Operating System) and peripheral devices.

  The processing unit 52 includes a model creation unit 52a, an analysis unit 52b, a history setting unit 52c, and a displacement input setting unit 52d. The model creation unit 52 a divides the tire to be analyzed into a plurality of elements having a plurality of nodes, creates a response analysis model for analysis, and stores the response analysis model in the storage unit 54. The analysis unit 52b reads the response analysis model created by the model creation unit 52a from the storage unit 54, and executes vibration analysis under a predetermined condition.

  In the vibration analysis, as described later, the analysis unit 52b reads the input of the forced displacement set by the displacement input setting unit 52d from the storage unit 54, and the response analysis model corresponding to the contact area with the road surface of the tire. To the area (response analysis model grounding area). More specifically, the analysis unit 52b inputs a history of displacement corresponding to a plurality of nodes existing in the response analysis model ground contact area as forced displacement. And the analysis part 52b calculates | requires the dynamic response of the said response analysis model by performing a vibration analysis with respect to the said response analysis model. Thereafter, the analysis unit 52 b stores the obtained dynamic response of the response analysis model in a predetermined area of the storage unit 54. The model creation unit 52a obtains a history of forces acting on the response analysis model ground contact region using the analysis model of the tire to be analyzed, the response analysis model, and the like, and stores the history of the force in the predetermined region of the storage unit 54.

  The history setting unit 52 c sets a history of forces acting on the response analysis model grounding region of the response analysis model, and stores it in a predetermined region of the storage unit 54. Further, the history setting unit 52 c obtains the history of displacement of the response analysis model in the response analysis model ground contact region based on the force history read from the storage unit 54 and stores it in a predetermined region of the storage unit 54. The displacement input setting unit 52 d sets an input of forced displacement input to the response analysis model based on the displacement history read from the storage unit 54, and stores it in a predetermined area of the storage unit 54. The input of the forced displacement may be, for example, the displacement history itself or a value obtained by converting the displacement history into a frequency.

  The processing unit 52 includes, for example, a memory and a CPU (Central Processing Unit). At the time of analysis, based on the analysis model created by the model creation unit 52a, input data, and the like, the processing unit 52 reads the program into a memory incorporated in the processing unit 52 and performs computation. At that time, the processing unit 52 appropriately stores a numerical value in the middle of the calculation in the storage unit 54, and extracts the numerical value stored in the storage unit 54 and advances the calculation. The processing unit 52 may realize the function by dedicated hardware instead of the computer program.

  The display means 55 is a display device such as a liquid crystal display device. The storage unit 54 may be in another device (for example, a database server). For example, the analysis device 50 may access the processing unit 52 and the storage unit 54 by communication from a terminal device including the input / output device 51. Next, a tire simulation method according to this embodiment will be described. The tire simulation method according to this embodiment can be realized by the analysis device 50 described above.

  FIG. 3 is a flowchart showing the procedure of the tire simulation method according to the present embodiment. FIG. 4 is a partial perspective view showing an example of a response analysis model. In executing the tire simulation method according to the present embodiment, in step S101, the model creation unit 52a of the analysis apparatus 50 shown in FIG. 2 creates a tire model (analysis model) to be analyzed (model creation procedure). ). The analysis model is a model used by a computer to perform vibration analysis or ground contact analysis using a numerical analysis method such as a finite element method (FEM) or a finite difference method (FDM). It can be analyzed with a computer. The analysis model includes a mathematical model and a mathematical discretization model. The analysis model created in step S101 is the response analysis model 10 shown in FIG. The response analysis model 10 is subjected to vibration analysis in step S105 described later to obtain a dynamic response or the like. In this embodiment, since the finite element method is used for the analysis of the response analysis model 10, the response analysis model 10 is created based on the finite element method.

  An analysis method applicable to the analysis according to the present embodiment is not limited to the finite element method, and an analysis method such as a finite difference method or a boundary element method (BEM) can also be used. Further, the most appropriate analysis method can be selected according to the boundary condition or the like, or a plurality of analysis methods can be used in combination. The finite element method is an analysis method suitable for structural analysis, and is particularly suitable for a structure such as a tire.

  For example, the model creation unit 52a creates the response analysis model 10 from CAD (Computer Aided Design) data of the tire to be analyzed. When the response analysis model 10 is created based on the finite element method, the model creation unit 52a divides the tire specified by the CAD data into a plurality of finite elements 11 as shown in FIG. A response analysis model 10 is created. In the present embodiment, the response analysis model 10 is an analysis model having a three-dimensional shape as shown in FIG.

  For example, in the three-dimensional analysis model, the element 11 included in the response analysis model 10 is a solid element such as a tetrahedral solid element, a pentahedral solid element, or a hexahedral solid element, a shell element such as a triangular shell element, a rectangular shell element, or a plane element. It is desirable to use elements that can be handled by a computer. In the process of analysis, the elements divided in this way are identified one by one using three-dimensional coordinates and cylindrical coordinates in a three-dimensional analysis model. When the response analysis model 10 is created, the processing unit 52 executes the process of step S102.

  FIG. 5 is a schematic diagram illustrating a state in which the response analysis model is in contact with the road surface model. FIG. 6 is a plan view of the response analysis model ground contact area. FIG. 6 shows a state in which the response analysis model ground contact region 12 is viewed from the outside in the radial direction of the response analysis model 10. FIG. 7 is a conceptual diagram showing a state in which the response analysis model ground contact area moves on a road surface model having protrusions. FIG. 8 is an explanatory diagram of the force history of the response analysis model ground contact region. FIG. 9 is a diagram illustrating an example of the direction of force.

  In step S102, the history setting unit 52c of the analysis device 50 illustrated in FIG. 2 sets a history of forces acting on the response analysis model 10 in the response analysis model ground region 12 of the response analysis model 10 illustrated in FIGS. (Force history setting procedure). That is, the history setting unit 52 c sets a history of forces acting on the response analysis model ground contact area 12 and stores it in a predetermined area of the storage unit 54. The response analysis model contact area 12 is an area of the response analysis model 10 corresponding to the contact area with the road surface of the tire to be analyzed, as described above. For example, as illustrated in FIG. 5, the response analysis model ground contact region 12 includes the response analysis model 10 and the road surface model 30 when it is assumed that the response analysis model 10 contacts the road surface analysis model (road surface model) 30. Of the contacted regions, the region can be the region on the response analysis model 10 side.

  As shown in FIG. 6, the response analysis model ground area 12 is divided into a ground area and a non-ground area by a ground boundary 13. The response analysis model ground contact region 12 has a plurality of nodes N1, N2, N3, N4,... Nn existing on the surface of the response analysis model 10 inside the ground contact boundary 13. In step S102, force history is set for each of the nodes N1, N2, N3, N4,. Next, the force history will be described.

  In general, when a tire rolls on a road surface, a force caused by a tread pattern of the tire, road surface unevenness (including protrusions), or a force caused by a vehicle such as steering acts on a ground contact region of the tire. When the analysis device 50 obtains a dynamic response when the tire rolls on the road surface using the response analysis model 10, it is necessary to apply a force acting on the contact area of the tire to the response analysis model contact area 12 in some form. There is. For this reason, in step S102, a history of forces acting on the response analysis model ground contact region 12 is set.

  Consider a case where the response analysis model 10 shown in FIGS. 5 and 6 rolls on a road surface model with protrusions while rolling in the direction of arrow R. In this case, as shown in FIG. 7, the response analysis model ground contact region 12 causes the surface of the road model 30 to be tangential to the rolling direction and parallel to the surface of the road model 30 as the response analysis model 10 rolls. It moves in the direction (direction shown by arrow R1 in FIG. 7). In this process, the response analysis model ground contact region 12 gets over the protrusion 31 on the surface of the road surface model 30. Since the response analysis model ground contact area 12 receives a force from the protrusion 31, the nodes N1, N2, N3, and N4 included in the response analysis model ground contact area 12 are time t (or center angle θ) as shown in FIG. In response to this, the input F1 caused by the protrusion 31 is received in order.

  The nodes N1, N2, N3, and N4 are nodes that exist at the same position in the response analysis model ground region 12 and in the circumferential direction of the response analysis model 10. 8 is the position (center angle) of the ground contact boundary 13 in the rolling direction of the response analysis model 10. As shown in FIG. 5, Δθ represents the range of the response analysis model ground contact region 12 in the circumferential direction of the response analysis model 10 as a central angle around the rotation axis (Y axis) of the response analysis model 10. Value. Δt shown in FIG. 5 is a time required for the response analysis model 10 to roll in the range of the response analysis model ground contact region 12 in the circumferential direction of the response analysis model 10. If the angular velocity when the response analysis model 10 rolls is ω, Δt = Δθ / ω.

  The force history is a history of changes with respect to time of the forces received by the respective nodes N1, N2, N3, N4,... Nn included in the response analysis model ground contact region 12. When an element composed of a plurality of nodes is a solid element, the solid element has three translational degrees of freedom. In this case, the force history is set for each of the nodes N1, N2, N3, N4,... Nn in three translational components, ie, three components Fx, Fy, and Fz as shown in FIG. Is done. Fx is a component of force in the circumferential direction, Fy is a component of force in a direction parallel to the rotation axis, and Fz is a component of force in the radial direction.

  The force history may be obtained by experiment or may be obtained by computer simulation using a tire model. When obtaining a force history by experiment, it is preferable to obtain the force history on the contact surface with the road surface of the tire by rolling the tire to be analyzed quasi-statically. The quasi-static means that the tire rolls at a low rotational angular velocity that is not affected by the inertial force due to the mass. For example, when obtaining a dynamic response in step S105 described later, so as to satisfy a condition that the fluctuation frequency of the input to the response analysis model 10 is ¼ or less of the natural frequency of the tire to be analyzed. It is preferable to set the angular velocity of the tire. For example, when the tire tread pattern is obtained by connecting m sections of the same tread pattern in the circumferential direction, the rotational angular velocity ω is set as follows. That is, ω ≦ 2 × f0 × π / m. Here, f0 is the natural frequency of the tire to be analyzed.

  When the force history is obtained by computer simulation, the response analysis model 10 is not necessarily used, and a tire model suitable for the analysis for obtaining the force history can be used. For example, as a tire model used in computer simulation for obtaining a force history, there are an elastic ring model for mechanism analysis, a tire model obtained by modeling a tire including a detailed tread pattern based on a finite element method, and the like. . Next, an example of a method for obtaining a force history by computer simulation using a tire model based on the finite element method will be described.

  FIG. 10 is a partial perspective view showing an example of a tire model used when obtaining a force history. FIG. 11 is a perspective view showing an example of a road surface model. FIG. 12 is an explanatory diagram showing a ground contact rolling analysis, and FIG. 13 is an explanatory diagram of a state in which a static load is applied to the tire model to perform the ground contact analysis. In obtaining the force history, a tire model (analysis model) used for computer simulation is first created. For example, the model creation unit 52a of the analysis device 50 illustrated in FIG. 2 creates a tire model and an analysis model of a road surface on which the tire model contacts the ground.

  In the present embodiment, the model creation unit 52 a creates the tire model 20 shown in FIG. 10 and the road surface model 41 shown in FIG. 11 based on the tire to be analyzed, and stores it in a predetermined area of the storage unit 54. The road surface model 41 is, for example, an analysis model of a road surface on which an analysis target tire comes into contact, and may be configured by a two-dimensional analysis model (surface) such as a planar analysis model. Elements constituting the two-dimensional analysis model include, for example, a triangle element and a quadrilateral element. Elements constituting the two-dimensional analysis model are identified one by one using the two-dimensional coordinates in the analysis process. The tire model 20 contacts the surface 41P of the road surface model 41. The tire model 20 and the road surface model 41 are both analytical models that can be analyzed by a computer.

  When the tire model 20 and the road surface model 41 are created, the analysis unit 52b of the analysis device 50 illustrated in FIG. 2 reads the tire model 20 and the road surface model 41 from the storage unit 54. Then, the analysis unit 52 b performs a ground contact analysis on the tire model 20 and stores the analysis results (such as coordinates of each node and physical quantities) in a predetermined area of the storage unit 54. The ground contact analysis is to analyze at least the deformation, strain, or stress state of the tire model 20 in a dynamic or static contact state between the tire model 20 and a plane or curved surface. In this embodiment, as shown in FIGS. 12 and 13, the tire model 20 is in contact with an object to be grounded (in this example, the road surface model 41), and the deformation, strain, or stress state of the tire model 20 is analyzed. To do. The ground contact analysis may be performed in a state where the tire model 20 is loaded with the load P or the internal pressure.

  FIG. 12 shows an example in which a dynamic contact state between the tire model 20 and the road surface model 41 is analyzed. In this example, the tire model 20 is grounded to the surface 41P of the road surface model 41, the load P is applied to the rotation axis (Y axis) of the tire model 20, and the tire model 20 is rotated at an angular velocity around the rotation axis (Y axis). The grounding rolling analysis that rolls at ω is shown. The ground rolling analysis includes dynamic rolling analysis and steady transportation analysis. In the example shown in FIG. 13, a load (static load) P is applied to the rotation axis (Y axis) of the tire model 20 to ground the tire model 20 on the surface 41 </ b> P of the road surface model 41. An example of executing analysis is shown.

  In executing the contact analysis, analysis conditions (such as the rotational angular velocity ω of the tire model 20 and the load P applied to the tire model 20) are set. The analysis conditions are input through the input unit 53 of the analysis device 50 shown in FIG. 2 and temporarily stored in the storage unit 54, for example. When the analysis condition is set, the analysis unit 52b executes the ground contact analysis of the tire model 20 while acquiring the analysis condition from the storage unit 54. When the grounding analysis is completed, the analysis unit 52b stores the analysis result in a predetermined area of the storage unit 54. The analysis result includes at least a change history (force time history) with respect to time of force acting on the tire model 20 at the contact portion 42 with the road surface model 41 of the tire model 20. The force may be a pressure. In this case, the pressure is converted into force by multiplying the pressure by the area.

  In step S102 described above, the history setting unit 52c reads the time history of the force from the analysis result stored in the storage unit 54. Then, the history setting unit 52 c sets the read time history of the force as a history of force acting on the response analysis model 10 in the response analysis model ground contact region 12. When the time history of the force is obtained by the contact rolling analysis, the force time history is a change with respect to time of the force acting on each node existing in the contact portion 42 of the tire model 20.

  When the time history of the force is obtained by performing a static contact analysis of the tire model 20, the force time history itself of each node (referred to as a surface node) existing in the contact portion 42 cannot be obtained. In this case, the surface node force is obtained by static contact analysis, and the forces received by the respective surface nodes existing at the same position in the circumferential direction of the tire model 20 are arranged in the circumferential direction of the ground contact portion 42. Then, the force arranged in this way is treated as a time history of the force.

  In the ground contact analysis, the analysis unit 52b preferably acquires the time history of the force acting on the ground contact portion 42 by rolling the tire model 20 semi-statically. As described above, quasi-static means rolling the tire model 20 at a low rotational angular velocity that is not affected by the inertial force due to mass. For example, when the tread pattern of the tire model 20 is obtained by connecting m sections of the same tread pattern in the circumferential direction, the rotational angular velocity ω in the ground contact analysis is ω ≦ 2 × f0 × π / m. It is set (f0 is the natural frequency of the tire to be analyzed). In addition, when using computer simulation, you may perform what is called a static analysis.

  FIG. 14 is a plan view showing a tread surface of a tire model. The force history obtained by experiments or computer simulation may be a combination of a plurality of forces. For example, the tread of the tire model 20 used for the ground contact analysis includes a shoulder portion Sh that exists on both sides in the width direction of the tire model 20 and a center portion C that is scattered between both shoulder portions Sh, as in an actual tire. Have. In this case, the force history set in step S102 may be a combination of the force history in the center portion C and the force history in the shoulder portion Sh. That is, the force history in the center portion C and the force history in the shoulder portion Sh may be obtained separately, and the obtained results may be combined to form the force history set in step S102. In this way, for example, when it is desired to change and evaluate only the tread pattern of the center portion C, the force history of only the center portion C may be obtained and combined with the force history of the shoulder portion Sh. So it can be evaluated efficiently.

  Also, force history obtained by grounding a tire model without a tread pattern on a road model with protrusions and grounding analysis, and grounding analysis by grounding a tire model with a tread pattern on a road model without protrusions The force history set in step S102 may be combined with the force history obtained in step S102. In this way, when it is desired to change the tread pattern and roll the road surface with protrusions, the tire model without the tread pattern is grounded to the road surface model with protrusions, and the ground contact analysis is performed. The force history set in step S102 may be combined with the force history obtained from different tread patterns. Therefore, it is not necessary to roll a road surface model having protrusions for all tread patterns, so that the influence of the tread pattern can be evaluated efficiently. Note that the force obtained by the tire model 20 or experiment may be converted into speed or acceleration, and these changes with time may be used instead of the force history set in step S102. When the force history is set in step S102, the process proceeds to step S103.

  FIG. 15A is a schematic diagram illustrating an example of a displacement history. In step S103, the displacement history of the response analysis model 10 in the response analysis model ground contact region 12 is obtained based on the force history set in step S102 (displacement history setting procedure). The history setting unit 52c reads a force history from the storage unit 54 and obtains a displacement history. The displacement is obtained by executing a calculation for applying a force to the response analysis model 10. Accordingly, the history setting unit 52c calculates the displacement at each time by executing a calculation for applying the force at each time of the set force history to the response analysis model 10, and FIG. The displacement history is as shown. The horizontal axis in FIG. 15A represents time (t), and the vertical axis represents displacement amplitude (u). That is, the displacement history is a history of changes of the response analysis model 10 in the response analysis model ground contact region 12 with respect to time.

  The history setting unit 52 c stores the obtained displacement in a predetermined area of the storage unit 54. The history of displacement is set for each force component for all nodes existing in the response analysis model ground contact region 12. When a change in velocity or acceleration with respect to time is used instead of force history, a value obtained by integrating velocity once in time or a value obtained by integrating acceleration twice in time is the displacement. Therefore, the displacement history is obtained by using the displacement thus obtained. If a displacement history is obtained in step S103, the process proceeds to step S104.

  In step S104, the displacement input setting unit 52d of the analysis apparatus 50 shown in FIG. 2 responds to the response analysis model 10 based on the displacement history obtained in step S103 (or the force history obtained in step S102). A forced displacement input (forced displacement input) input to the analysis model ground contact area 12 is set (forced displacement input setting procedure). For example, the displacement input setting unit 52d sets the displacement history obtained by the history setting unit 52c in step S103 as the forced displacement input as it is and stores it in a predetermined area of the storage unit 54. Thus, in step S104, the displacement history may be used as the forced displacement input that is directly input to the response analysis model ground contact area 12. However, in addition to this, the displacement history amplitude and time axis were changed, the displacement history time axis was converted to the frequency axis, and the displacement history was filtered. A history of later displacement may be set as a forced displacement input and given to the response analysis model ground contact area 12.

  FIG. 15B is a schematic diagram illustrating an example of processing the displacement history to obtain a forced displacement input. In the example shown in FIG. 15B, the time axis of the displacement history is converted to the frequency axis by Fourier transform. The horizontal axis of FIG. 15-2 represents the frequency (f), and the vertical axis represents the amplitude (u) of the displacement history after the Fourier transform. The forced displacement input set in step S104 may be obtained by converting the time axis of the displacement history to the frequency axis as described above. Further, the displacement input setting unit 52d may set information obtained by filtering the displacement history obtained in step S103 as a forced displacement input and give the information to the response analysis model grounding region 12. For example, the displacement input setting unit 52d performs a low-pass filter process on the displacement history, thereby setting the displacement history after removing a component higher than a predetermined frequency as the forced displacement input, so that the response analysis model ground area 12 can be given. Generally, in tire response analysis, high-frequency vibrations do not matter, and relatively low-frequency vibrations are targeted. For this reason, in the step S105, the dynamic response can be obtained only for the frequency component necessary for the evaluation by the above-described method, so that the calculation amount when obtaining the dynamic response can be reduced. For this reason, the efficiency of evaluation improves.

  Further, the time axis of the displacement history may be changed according to the rolling condition when obtaining the dynamic response in step S105. For example, consider a case where the response analysis model 10 is rolling with a rotational angular velocity of ω1 as a rolling condition when obtaining a dynamic response. When the rotational angular velocity of the tire or tire model 20 when the force history is set in step S102 is ω0, the displacement input setting unit 52d changes the time axis by multiplying ω0 / ω1 by the time of the displacement history. . Further, the displacement input setting unit 52d may change the magnitude of the amplitude (u) of the displacement history in accordance with the conditions for obtaining the dynamic response in step S105. For this reason, even if the conditions for obtaining the dynamic response are changed, it is possible to easily cope with it, so that the efficiency of evaluation is improved.

  In step S104, it is preferable to convert the displacement history into a change in rolling speed set when obtaining a dynamic response in step S105. In the conversion to the fluctuation in the rolling speed, the conversion may be performed based on the rotation of the response analysis model 10 or the movement of the road surface model 30 (see FIG. 7). For example, when the dynamic response is obtained, it is assumed that the response analysis model 10 rolls at the rotational angular velocity ω1, and the rotational angular velocity of the tire or the tire model 20 when the force history is set in step S102. Assume that ω0. In this case, by multiplying one cycle of the displacement history by ω0 / ω1, the displacement history is converted into fluctuations at the rolling speed set when the dynamic response is obtained.

  Thus, it is preferable to convert and use the displacement history so as to correspond to the rolling conditions for performing the response analysis, that is, the speed V and the rotational angular velocity ω1 of the response analysis model 10. At this time, when the response analysis model 10 is rolling at a low speed (rotational angular velocity is ω_L), the displacement history has data with respect to time. For this reason, when the response analysis model 10 is rolled at a low speed, the fluctuation of the time calendar can be expressed by changing the time axis by t ′ = t × ω0 / ω1. Moreover, what is converted to the frequency axis may be converted by f ′ = f × ω1 / ω0.

  On the other hand, when the displacement history is acquired by static analysis, since there is no time scale, data is obtained with respect to the rotation angle θ of the response analysis model 10 or the relative road surface movement distance x between the response analysis model 10 and the road surface model 30. Have. When the displacement history is obtained by static analysis, the displacement history can be converted at t = θ / ω1 for the rotation angle θ and t = x / V for the relative road surface movement distance x. Once the time calendar at a certain speed is obtained, the displacement history can be converted to the time calendar at another speed in the same manner as when the response analysis model 10 is rolled at a low speed.

  In addition, the Fourier transform in this case is, for example, an order in which one rotation of the response analysis model 10 is the first order, so the nth order component is converted to the frequency axis by f = ω1 × n / (2 × π). Is done. In this case as well, the displacement history can be converted to a different speed in the same manner as described above. In addition, when the fluctuation is repeated at a cycle of 1 / M lap of the tire (for example, when the pattern arrangement has such regularity in the analysis of fluctuation due to the tread pattern), the waveform is repeatedly connected M times. A waveform corresponding to one rotation of the response analysis model 10 may be created and the above conversion may be performed. Alternatively, the displacement history may be converted into the frequency axis using f = ω1 × n / (2 × π) for the order component k Fourier-transformed based on the period.

  It is more preferable that the response analysis model 10 used when obtaining the dynamic response considers the effect of the set rolling speed. Examples of the rolling effect include an effect based on centrifugal force or Coriolis force. For example, there is software that can consider the effect of rolling by performing a steady transport analysis. As described above, when an input is obtained by computer simulation, it is possible to eliminate the need for dynamic analysis that requires calculation time, so that there is an advantage that calculation time can be reduced. Further, even when a plurality of calculations are executed at different rolling speeds, only a simple conversion is required, so that there is an advantage that the calculation cost can be reduced.

  In step S103, when obtaining the displacement history of the response analysis model 10 in the response analysis model ground contact region 12 based on the force history, it is preferable to use a transformation matrix linearized in a prescribed state. The prescribed state is a state in which air pressure and preload are applied to the response analysis model 10, and a set input is not applied from the road surface model. In general, tires have geometric non-linear deformation caused by deflection due to air pressure and preload, and non-linear deformation caused by material. For this reason, it is preferable to remove in advance at least the steady deformation component due to the preload from the above-described force history.

  In general, when analyzing a dynamic response in a computer simulation, a vibrational response having the prescribed state as a median value is acquired. For this reason, the deformation of the response analysis model 10 can be linearized in the vicinity of the prescribed state. By doing so, the problem in converting the force history into the displacement history can be replaced with a linear problem that requires less calculation time from a nonlinear problem that requires calculation time. As a result, the calculation time for converting to a displacement history can be shortened, so that the evaluation can be made more efficient.

By solving equation (1) for {u}, the force history can be converted to a displacement history. In equation (1), [K] is a transformation matrix, {F} represents a force (vector), and {u} represents a displacement (vector). It is preferable to use the stiffness matrix of the response analysis model 10 as the transformation matrix [K]. In the conversion to the displacement history, the stiffness matrix of the response analysis model 10 is used to match the input from the road surface model when the dynamic response analysis is executed with the axial reaction force of the response analysis model 10. (For example, the input from the road surface model and the axial reaction force are balanced by a low-frequency response). As shown in Expression (1), since the expression to be solved is simple, the displacement history can be calculated at high speed.
{F} = [K] {u} (1)

In converting the force history to the displacement history, only the degree of freedom of the response analysis model ground contact region 12 is required. For this reason, it is more preferable that the degree of freedom of the transformation matrix [K] is reduced by Guyan's static reduction and used for conversion to a displacement history. As a result, the scale of the transformation matrix is reduced, so that calculation can be performed at higher speed. Next, Guyan's static reduction will be briefly described. Equation (2) is an equation of motion. [M] is a mass matrix, [K] is a stiffness matrix, {u} is a displacement vector, and {f} is a force vector. When the equation (2) is divided into the holding degree of freedom and the others (no external force), the displacement vector {u} is as in equation (3) and the force vector {f} is as in equation (4). The stiffness matrix [K] is as in equation (5), and the mass matrix [M] is as in equation (6). u _α is a displacement of a node existing at the boundary (corresponding to the response analysis model ground contact region 12), and u _β is a displacement of a node existing outside the boundary. Considering only the static term (stiffness matrix), the equation of motion of Equation (2) is as shown in Equation (7). When this is rewritten, equation (8) is obtained. When Expression (8) is described using the transformation matrix [T], Expression (9) is obtained. From equation (9), the equation of motion shown in equation (2) is rewritten as shown in equation (10) and reduced to only the degree of holding freedom. Here, [M ′] is represented by Expression (11), and [K ′] is represented by Expression (12). When the rotational angular velocity ω = 0, the expression (10) becomes as shown in the expression (13). If the degree of freedom of the equation of motion is reduced by Guyan's static reduction, the reduced equation of motion (Equation (10)) can be approximated in the dynamic analysis, but static analysis (ω = 0, that is, the mass is If there is no influence, an exact solution is obtained in equation (13)).

  FIG. 16 is a plan view of the response analysis model. FIG. 17 is a side view of the response analysis model. When the displacement history is used as the forced displacement input, the displacement history may be processed by repeatedly connecting or setting a constant displacement without variation. When the response analysis model 10 has a tread pattern on the tread, as shown in FIG. 16, the section S having the same tread pattern, which is partitioned by adjacent lug grooves L2, may be created so as to be repeated in the circumferential direction. Many. That is, as shown in FIG. 17, in the section S, the range of the central angle θs around the rotation axis (Y axis) is set as one unit of repetition. The response analysis model 10 has 2 × π / θs one section S in the circumferential direction.

  The displacement history may be a forced input displacement by repeatedly connecting the history of the response analysis model 10 for one turn with the section S as one unit. By doing in this way, it is not necessary to analyze the tire model and one round of the tire when the force history is obtained in the previous stage of obtaining the displacement history, so that the calculation amount or the number of experiments can be reduced. The forced input displacement is equivalent to the response analysis model ground contact region 12 while the displacement S does not vary, that is, the section S having a constant displacement is repeatedly connected for one turn in the circumferential direction of the response analysis model 10. The sections S may be connected to each other. By doing in this way, it is not necessary to analyze the tire model or one round of the tire, so the amount of calculation or the number of experiments can be reduced.

  FIG. 18 is a schematic diagram showing a state in which a dynamic response is obtained by applying a forced displacement input to the response analysis model ground contact area. When the forced displacement input is set in step S104, the process proceeds to step S105. In step S105, the analysis unit 52b of the analysis apparatus 50 gives the forced displacement input uc set in step S104 to the response analysis model ground region 12 as shown in FIG. Obtain (response calculation procedure). The dynamic response calculation includes a transient response analysis calculated on the time axis and a frequency response analysis calculated on the frequency axis. In the present embodiment, the response analysis model 10 used for calculating the dynamic response is smaller than the detailed ground contact analysis model, so that the calculation efficiency is improved. The calculation result of the dynamic response can also be used for acoustic analysis (for example, analysis of tire radiated sound).

  Since the response analysis model ground contact area 12 is in contact with the road surface model 30, the movement of the response analysis model ground contact area 12 is restricted by the road surface model 30. Here, when the action between the response analysis model 10 and the road surface model 30, that is, the action on the response analysis model ground contact area 12 is set by force, a boundary condition is established in which the response analysis model ground contact area 12 can freely move. This is because the force cannot be input to the response analysis model ground contact area 12 unless this is done. For this reason, if the action on the response analysis model grounding region 12 is set by force, an actual response that behaves as if the response analysis model grounding region 12 is constrained cannot be reproduced. As in the present embodiment, by making the input to the response analysis model ground contact area 12 as a forced displacement input, it is possible to reproduce the response under the boundary condition in which the response analysis model ground contact area 12 is constrained. Further, in this embodiment, after the input is extracted, it can be converted into a displacement and input to the response analysis model ground contact area 12. That is, if only the input to the response analysis model ground contact area 12 is obtained, the influence of changing the structure can be analyzed efficiently without performing repeated rolling calculations. As described above, according to the present embodiment, when analyzing a combination of a plurality of inputs and a plurality of structures, an effect that the efficiency of analysis can be improved is obtained.

  The response analysis model 10 used for the analysis in step S105 uses an analysis model converted into a modal model by the restraint mode method with at least the nodes existing in the response analysis model ground contact region 12 for setting the forced displacement input as the holding freedom. Is preferred. That is, it is preferable to use the restraint mode method (Craig-Bampton method) when applying the forced displacement to the response analysis model ground contact region 12. The constraint mode method is a method of reducing unknown quantities to be solved by omitting higher order modes. For this reason, since the freedom degree at the time of calculating a dynamic response can be reduced by converting the response analysis model 10 into a modal model, the calculation time can be further shortened. In addition, it is more preferable that the rotation axis (Y axis) of the response analysis model 10 has a degree of freedom of holding because the resonance of the wheel can be considered.

(Modification)
In this modification, a history of forces acting on the response analysis model contact area 12 is obtained using the tire model 20 shown in FIG. 10, and the response in which the element division of the response analysis model contact area 12 is rougher than the contact area of the tire model 20. The analysis model 10 is given in the form of a displacement history or a force history. The tire model 20 preferably takes into account the tread pattern, and the response analysis model 10 may omit at least a part of the tread pattern. Examples of such a response analysis model 10 include those having only the main groove and those not having the groove itself. In this manner, by omitting the tread pattern of the response analysis model 10, the scale of the response analysis model 10 can be reduced, so that calculation efficiency can be improved. Since static analysis is appropriate for the tire model 20, when a wheel model is combined with the tire model 20, it is preferable that the wheel model be an analytical model as a rigid body. In this case, it is not necessary to model the air in the tire model 20. As a result, the amount of calculation can be reduced, and the time required for ground contact analysis using the tire model 20 can be shortened.

  When the response analysis model 10 is combined with a wheel model in order to improve the accuracy of the calculation result of the dynamic response, it is preferable to use a wheel model modeled as an elastic body. In this case, it is preferable to model the air in the response analysis model 10 as well. Thereby, the influence of the wheel and air (about 200 Hz or more) can be taken into account, and the accuracy of the dynamic response calculation result can be improved. It is preferable that the dimension of the element in the response analysis model ground contact area 12 is not less than 2 times and not more than 10 times the dimension of the element in the ground contact area of the tire model 20. Further, in the response analysis model 10, it is preferable to divide the response analysis model ground contact region 12 in the circumferential direction from 5 divisions to 50 divisions. Accordingly, it is possible to suppress an increase in calculation time in the dynamic response while appropriately expressing the input distribution of the response analysis model ground contact region 12. Next, a method for giving a displacement history or a force history to the response analysis model ground contact region 12 will be described. In the following description, it is assumed that the displacement history is transferred to the response analysis model ground contact area 12.

  FIG. 19 is a schematic diagram of an example in which a force obtained from a tire model is transferred to a response analysis model using a response analysis model in which element division is coarser than that of a tire model used for ground contact analysis. FIG. 19 shows the relationship between the nodes 25a, 25b, 25c, and 25d of the tire model used in the ground contact analysis and the node 15 of the response analysis model. In step S104, the displacement input setting unit 52d reads the displacement history from the storage unit 54, and gives the displacement history to the response analysis model ground contact region 12 as a forced displacement input. At this time, since the element division of the response analysis model ground contact area 12 is coarser than the element division in the ground contact area of the tire model 20, the displacement history in the ground contact area of the tire model 20 is obtained by the following method. To grant.

  The displacement input setting unit 52d has positional information of a predetermined node (second node) 15 of the response analysis model 10 shown in FIG. 19 and nodes (first nodes) 25a of the tire model 20 existing around the second node 15. , 25b, 25c, 25d, the displacement history of the first nodes 25a, 25b, 25c, 25d is given to the second node 15. In this manner, the displacement history of the first nodes 25a, 25b, 25c, and 25d is given to the second node 15 in relation to the relative positions of the first nodes 25a, 25b, 25c, and 25d and the second node 15. Thus, the distribution of the history of displacement of the tire model 20 can be given to the response analysis model 10.

  For example, the displacement input setting unit 52d detects the displacement of the first nodes 25a, 25b, 25c, and 25d existing around the second node 15 shown in FIG. 19 whose distance from the second node 15 is within a predetermined range. The value obtained by adding the histories is used as the displacement history of the second node 15. Further, for example, the displacement input setting unit 52d assigns a weight based on the magnitude of the relative distance between the second node 15 and the first nodes 25a, 25b, 25c, and 25d existing around the second node 15. A value obtained by adding the displacement history after the weight is given to the displacement history of the node 15 may be used as the displacement history of the second nodes 25a, 25b, 25c, and 25d. Thereby, the displacement history included in the region 16 (see FIG. 19) that the second node 15 is responsible for can be represented by the sum of the displacement history of the first nodes 25a, 25b, 25c, and 25d. Note that the method of applying the displacement history to the response analysis model ground contact region 12 is an example, and is not limited to the above.

(Evaluation example)
The tire simulation method according to the present embodiment was executed using a response analysis model having a size of 215 / 55R17. The response analysis model is an analysis model whose accuracy of the natural frequency has been confirmed. In order to confirm the usefulness of inputting displacement in the response analysis model ground contact area, the frequency response when force is applied to the entire area of the response analysis model ground contact area and when input is applied by forced displacement The frequency response was calculated, and the resonance frequency was extracted from the peak. And it compared with the protrusion response peak frequency obtained from the experiment which calculates | requires a frequency response. The peak response frequency of the protrusion by experiment is 79 Hz, the resonance frequency when force is input is 69 Hz, and the resonance frequency when force displacement is input is 80 Hz. From this result, it can be seen that when a force is input to the response analysis model ground contact region, the value is lower than the experimental value, but when a forced displacement is input, a value almost equal to the experimental value is obtained.

  FIG. 20 is a diagram showing the relationship between the rolling speed and the vertical axial force, and FIG. 21 is a diagram showing the relationship between the rolling speed and the longitudinal axial force. The solid line Ex in FIGS. 20 and 21 is based on the experiment, and the dotted line Si is based on the tire simulation method according to the present embodiment. The unit of the vertical axial force and the front / rear axial force is dB, and 1N is 0 dB. The unit of rolling speed is km / h. The result of the experiment is a result of frequency response analysis using a tire and extracting vertical and longitudinal axial forces for each rolling speed. The result of the tire simulation method according to the present embodiment is a result of extracting the vertical and front / rear axial forces for each rolling speed by applying a frequency response analysis by applying a forced displacement to the response analysis model ground contact region. 20 and 21, it can be seen that the tire simulation method according to the present embodiment provides almost the same result as the experiment.

  As described above, the tire simulation method, the tire analysis computer program, and the analysis apparatus according to the present invention are useful for the tire analysis using the computer, and the calculation accuracy is improved while suppressing an increase in the calculation time. Suitable for suppressing the decrease.

DESCRIPTION OF SYMBOLS 1 Tire 10 Response analysis model 11 Element 12 Response analysis model ground contact area 13 Ground boundary 15 Second node 16 Area 20 Tire model 25a, 25b, 25c, 25d First node 30, 41 Road surface model 31 Protrusion 42 Ground contact part 50 Analyzing device 51 Input / output device 52 Processing unit 52a Model creation unit 52b Analysis unit 52c History setting unit 52d Displacement input setting unit 54 Storage unit

Claims (8)

A model creation procedure in which a computer creates a response analysis model for obtaining a dynamic response of the tire based on a tire to be analyzed;
A force history setting procedure in which the computer sets a history of forces acting on the response analysis model in a region of the response analysis model corresponding to a contact area with the road surface of the tire;
A displacement history setting procedure for obtaining a displacement history of the response analysis model in the region based on the force history;
A forced displacement input setting procedure in which the computer sets an input of forced displacement input to the response analysis model based on the history of displacement;
A response calculation procedure in which the computer gives an input of the set forced displacement to the region to obtain a dynamic response of the response analysis model;
A tire simulation method comprising: The computer
In the force history setting procedure, a history of forces acting on the ground contact area is acquired from a result of quasi-static rolling a tire model that can be analyzed by a computer created based on the tire,
2. The forced displacement input setting procedure according to claim 1, wherein the forced displacement history or the force history is used after being converted into a fluctuation in a rolling speed set in a dynamic response analysis in the response calculation procedure. Tire simulation method. The computer
The tire simulation method according to claim 1, wherein a transformation matrix linearized in a prescribed state is used in the displacement history setting procedure. The computer
The tire simulation method according to claim 3, wherein a stiffness matrix of the response analysis model is used as the transformation matrix. In the force history setting procedure, the computer obtains a history of forces acting on the ground contact area from a result of quasi-static rolling a tire model that can be analyzed by a computer created based on the tire. ,And,
5. The tire simulation method according to claim 1, wherein the response analysis model has a rougher element division of the region than the tire model. The computer
6. The forced displacement input setting procedure according to claim 5, wherein the forced displacement history or force history is converted into a change in rolling speed set in a dynamic response analysis in the response calculation procedure. Tire simulation method.   The response analysis model is a model that is converted into a modal model by a restraint mode method using at least the nodes of the region in which the input of the forced displacement is set as the degree of freedom in holding. Tire simulation method.   A computer program for tire simulation, which causes a computer to execute the tire simulation method according to any one of claims 1 to 7.