JP5705425B2 - Tire performance simulation method, tire performance simulation apparatus, and tire performance simulation program - Google Patents

Description

  The present invention relates to a tire performance simulation method, a tire performance simulation apparatus, and a tire performance simulation program. More specifically, the present invention relates to a tire performance simulation method and tire performance for analyzing tire performance by a numerical analysis method such as a finite element method. The present invention relates to a simulation apparatus and a tire performance simulation program.

  Conventionally, as a method for simulating tire performance, the tire to be evaluated is approximated by a tire finite element model obtained by dividing a tire into a finite number of elements, and characteristics such as density and elastic modulus are given to each finite element. The Finite Element Method (Finite Element Method) is often used to give boundary conditions such as internal pressure and load to a model and calculate the deformation state of each of the above elements to numerically analyze the tire dynamics such as tire deformation and rolling resistance. ing.

  By the way, the cause of tire rolling resistance may be due to friction between the tire and the road surface or due to air resistance, but in normal driving, the effect of hysteresis loss caused by deformation when the tire rolls is the most. It is said to be big. As a method of simulating the rolling resistance of a tire, a tire finite element model (called a tire model) in which a rubber material such as tread rubber and a bead core are modeled as a three-dimensional solid element and a fiber composite such as a carcass or a belt is used as a membrane element. ) Is grounded on a road surface model that is modeled with a flat rigid surface element and travels under predetermined driving conditions, and a history of strain amount of each element of the tire model is obtained. Specifically, the energy loss of the rubber member is calculated by calculating the storage elastic modulus, loss (tan δ) and maximum amplitude strain of the rubber material, or determining the area surrounded by the hysteresis loop. A method for calculating rolling resistance from energy loss has been proposed (see, for example, Patent Documents 1 and 2).

  Specifically, for example, a tire model in which a rubber material, a carcass, a belt, a bead core, etc. are continuous in the same cross-sectional shape in the tire circumferential direction is set, a road surface model is set, and a longitudinal load, a road surface friction coefficient, etc. Based on the boundary conditions, the tire model is grounded and deformed without rolling, the strain amount of each rubber element constituting the tread portion of the deformed tire model is calculated, and the rubber Obtain the strain distribution in the circumferential direction of the element, calculate the strain history of the rubber element when the tire rotates once from this strain distribution, then calculate the energy loss from the strain history and simulate the rolling resistance .

  In this way, if the tire finite element model is grounded on the road surface model and deformed, and the magnitude of hysteresis loss caused by the deformation when the tire rolls is numerically analyzed, the tire rolling resistance can be obtained. it can.

  However, in the above conventional simulation method, when calculating the energy loss from the obtained strain amount, the rubber member is handled as a viscoelastic body. However, the tire model is grounded on the road surface model and each element constituting the rubber member is grounded. When analyzing the amount of strain, since the rubber member is an elastic body, there is a problem that the analysis accuracy is not good.

  In addition, the conventional tire model described above cannot calculate a portion that is not continuous in the tire rotation direction due to a calculation method, and a portion where the tire is in contact with the road surface due to rolling resistance proceeds in a discontinuous portion in the tire rotation direction. Since the effect of deformation so as to move backward in the direction cannot be considered, it is difficult to accurately determine the rolling resistance.

  By the way, in a tire model, it is conceivable to perform simulation by giving a viscoelastic coefficient to each element constituting the rubber member from the beginning, but since the viscoelastic coefficient of rubber differs depending on the strain amount and the frequency, various strain amounts and Not only is it necessary to perform viscoelastic property tests for each rubber member at the frequency, but it is not only necessary to measure a lot, but also to set the viscoelastic coefficient in the rolling state, a considerable number of simulations are required. Since it had to be repeated, there was a problem that the analysis efficiency was remarkably bad.

  In order to solve this problem, the road surface is modeled with a drum, the rubber member of the tire is modeled as an elastic body, and the tire rolls at a constant speed on the road surface. After obtaining the strain amplitude and frequency of the rubber material from the strain waveform generated in the rubber element, the viscoelasticity test of the rubber material is performed with the obtained strain amplitude and frequency to obtain the viscoelasticity of the rubber material. A tire model is created using this viscoelastic modulus, and a numerical analysis model of the tire / wheel assembly is created using this tire model, and a rolling analysis is performed to obtain a rolling resistance value. Has been proposed (see, for example, Patent Document 3).

  In addition, as a calculation method of strain energy loss, there are a phase delay method for obtaining strain energy loss based on a phase difference between strain and stress, a Warholic method described in Non-Patent Document 1, and the like. In these methods, hysteresis is generated by giving a constant phase lag with respect to strain to the stress obtained by elastic analysis or superelastic analysis, and strain energy loss is calculated based on this.

JP 2003-118328 A JP 2005-186900 A JP 2007-131209 A

“Tire Rolling Loss Prediction from the Finite Element Analysis of a Statically Loaded Tire”, Warholic, T. C., Master Thesis, University of Akron, 1987

  However, the method described in Patent Document 3 does not calculate the tire rolling resistance after calculating the energy loss, but performs a viscoelasticity test of the rubber material to calculate the viscoelasticity of the rubber material. A tire model is created using the viscoelastic modulus, a numerical analysis model of the tire / wheel assembly is created using the tire model, and a rolling resistance value is directly obtained by performing a rolling analysis. It does not require energy loss. Moreover, since the viscoelasticity test of a rubber material must be implemented, it becomes a big scale.

  In addition, strain energy loss occurs due to hysteresis between strain and stress due to viscoelastic characteristics, so it is necessary to perform viscoelasticity analysis (time-dependent). There is no example of applying the method of or Warholic's method.

  The present invention has been made to solve the above problems, and an object of the present invention is to provide a tire performance simulation method, a tire performance simulation apparatus, and a tire performance simulation program capable of accurately obtaining a strain energy loss. .

In order to achieve the above object, the tire performance simulation method according to the first aspect of the present invention is a step of analyzing deformation for each element by executing rolling analysis on a tire model obtained by dividing a tire into a plurality of elements. If, Hazuki group to the analysis result of the rolling analysis, time history profile deformation by displacement of the element, and the time history distribution of Cauchy stress for the elements corresponding to the time history profile of the displacement for each of the elements a step of obtaining, Hazuki group time history distribution of the displacement, and determining the Green strain time history distribution of the elements corresponding to the time history profile of the displacement in accordance with the Cauchy stress for each of the elements, the displacement time history profile, and the Cauchy Hazuki group time history distribution of stress, 2ndPiora-Kirhihoff stress on the elements corresponding to the time history profile of the displacement in accordance with the Green strain Determining a time history profile of each said element, a phase difference imparted previously set between the time history profile of the Green strain time history distribution and before Symbol 2ndPiora-Kirhihoff stress imparted with phase difference and determining from the time history distribution of Green strain time history distribution and 2ndPiora-Kirhihoff stress strain energy loss of the element for each of the elements, by adding the strain energy loss of each of the elements, the strain of the tire Determining an energy loss.

According to the present invention, a phase difference is imparted between the Green strain obtained from the result of the rolling analysis and the 2ndPiora-Kirhihoff stress , the time history distribution of the Green strain to which the phase difference is imparted, and the time of the 2ndPiora-Kirhihoff stress. Since the strain energy loss of the element is obtained from the history distribution, even if the rolling analysis of the tire is an elastic analysis, the strain energy loss can be obtained in the same manner as the viscoelastic analysis is performed, and the strain energy loss can be accurately calculated. Can be sought.

The G reen strain is the amount of displacement based on the length of the initial state of the element (the state before deformation) , the Cauchy stress is the stress after deformation , and the 2nd Piora-Kirhihoff stress is a stress relative to the stress in the initial state of the elements, Ru determined from displacement and Cauchy stress factors.

Incidentally, as described in claim 2, based on the strain energy loss of the tire, by further comprising the step of determining the rolling resistance of the tire can be accurately simulated to obtain the rolling resistance of tires.

According to a third aspect of the present invention, there is provided a tire performance simulation apparatus, comprising: analyzing means for analyzing deformation of each element by executing a rolling analysis on a tire model obtained by dividing a tire into a plurality of elements; and analyzing by the analyzing means. First time history distribution calculating means for obtaining, for each element, a time history distribution of displacement due to deformation of the element and a time history distribution of Cauchy stress for the element corresponding to the time history distribution of the displacement based on a result; Second time history distribution calculating means for obtaining, for each element, a time history distribution of Green strain for the element corresponding to the time history distribution of the displacement according to the Cauchy stress based on the time history distribution of the displacement; , Based on the time history distribution of the displacement and the time history distribution of the Cauchy stress , 2ndPiora− for the element corresponding to the time history distribution of the displacement according to the Green strain A third time history distribution calculating means for obtaining a time history distribution of Kirhihoff stress for each element, and providing a predetermined phase difference between the time history distribution of Green strain and the time history distribution of 2ndPiora-Kirhihoff stress Energy loss calculating means for obtaining the strain energy loss of each element from the time history distribution of Green strain and the time history distribution of 2ndPiora-Kirhihoff stress to which the phase difference is given, and the strain energy of each of the elements Adding means for calculating a strain energy loss of the tire by adding a loss.

According to the present invention, a phase difference is given between the Green strain obtained from the result of the rolling analysis and the 2nd Piora-Kirhihoff stress, and the time history distribution and the second time history distribution of the Green strain to which the phase difference is given. Since the strain energy loss of the element is obtained, even if the rolling analysis of the tire is an elastic analysis, the strain energy loss can be obtained in the same manner as the viscoelastic analysis is performed, and the strain energy loss can be obtained with high accuracy. it can.

A tire performance simulation program according to a fourth aspect of the invention includes a step of analyzing a deformation for each element by executing a rolling analysis on a tire model obtained by dividing a tire into a plurality of elements, and an analysis of the rolling analysis. results Hazuki group, a step of obtaining time histories distribution deformation by displacement of the element, and the time history distribution of Cauchy stress for the elements corresponding to the time history profile of the displacement for each of the elements, the time of the displacement Hazuki group gravel distribution, said determining a time history profile of Green strain for each of the elements of the element in which the corresponding to the time history distribution of displacement in accordance with the Cauchy stress, time history profile of the displacement, and the Cauchy Hazuki group time history distribution of stress, the time history distribution of 2ndPiora-Kirhihoff stress on the elements corresponding to the time history profile of the displacement in accordance with the Green strain essential A step of obtaining the Motogoto, preset phase difference grant you, Green strain time history distribution of grants phase difference between the time history profile of the Green strain time history distribution and before Symbol 2ndPiora-Kirhihoff stress a method and from time history distribution of 2ndPiora-Kirhihoff stress seek strain energy loss of the element for each of the elements, by adding the strain energy loss of each of the elements, and determining the strain energy loss of the tire The computer is caused to execute processing including

According to the present invention, a phase difference is given between the Green strain obtained from the result of the rolling analysis and the 2nd Piora-Kirhihoff stress, and the time history distribution and the second time history distribution of the Green strain to which the phase difference is given. Since the strain energy loss of the element is obtained, even if the rolling analysis of the tire is an elastic analysis, the strain energy loss can be obtained in the same manner as the viscoelastic analysis is performed, and the strain energy loss can be obtained with high accuracy. it can. In addition, as described in claim 5, the tire rolling resistance can be obtained with high accuracy by further including the step of obtaining the rolling resistance of the tire based on the strain energy loss of the tire.

  According to the present invention, there is an effect that energy loss can be obtained with high accuracy.

It is the schematic of the personal computer for implementing performance prediction of a tire. It is a schematic block diagram of a computer main body. It is a flowchart of a tire performance simulation program. It is a perspective view showing an example of a tire model. It is a figure which shows the relationship between stress and distortion. It is a figure for demonstrating the phase difference of a stress and a distortion | strain.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

FIG. 1 shows an outline of a personal computer as a tire performance simulation apparatus for creating a tire model of a pneumatic tire and performing performance prediction as an example. This personal computer includes a keyboard 10 for inputting data and the like, a computer main body 12 for creating a three-dimensional tire model and predicting performance according to a pre-stored processing program, calculation results and various screens by the computer main body 12 And a mouse 16 for moving the cursor displayed on the CRT 14 to a desired position, and selecting, deselecting, or dragging a menu item or object at the cursor position. It is configured to include.

  As shown in FIG. 2, the computer main body 12 includes a CPU (Central Processing Unit) 12A, a ROM (Read Only Memory) 12B, a RAM (Random Access Memory) 12C, a nonvolatile memory 12D, and an input / output interface (I / O). 12E is connected to each other via a bus 12F.

  Connected to the I / O 12E are a keyboard 10, a CRT 14, a mouse 16, a hard disk 18, and a flexible disk unit (FDU) into which a flexible disk (FD) as a recording medium can be inserted and removed.

  The hard disk 18 stores a tire performance simulation program, which will be described later, and various parameters and data necessary for the execution thereof. The CPU 12A reads and executes a tire performance simulation program stored in the hard disk 18.

Incidentally, tire performance simulation program to be described later, for example because it may be a read-write with respect to the flexible disk FD by using the FDU, tire performance simulation program section later may record in advance FD, the FDU The tire performance simulation program recorded in the FD may be read and executed. As recording media, there are optical discs such as CD-ROM and DVD-ROM, and magneto-optical discs such as MD and MO. When these are used, a CD-ROM device or DVD-ROM is used instead of or in addition to the FDU. A ROM device, MD device, MO device, or the like may be used.

  Next, as a function of the present embodiment, a processing routine of a tire performance simulation program executed by the CPU 12A of the computer main body 12 will be described with reference to a flowchart shown in FIG.

  First, in step 100, a tire for dropping a tire design plan into a numerical analysis model based on tire design data that defines a tire design plan (tire shape, structure, material, etc.) to be subjected to tire performance analysis. Create a model.

For example, the hard disk 18, CAD data to be subjected to tire performance analysis stored in advance tire design data, such as (tire shape, structure, design data of the material, etc.), reads it. Based on the read tire design data, a three-dimensional tire model 20 as shown in FIG. 4 is created.

  The creation of the tire model 20 differs slightly depending on the numerical analysis method used. In this embodiment, a finite element method (FEM) is used as a numerical analysis method.

  Therefore, the tire model 20 created in the above step 100 is divided into a plurality of elements 22 by element division corresponding to the finite element method (FEM), for example, mesh division, as shown in FIG. This is a digitized input data format for a computer program created based on an analytical method. This element division refers to dividing an object such as a tire and a road surface into several small (finite) small parts, that is, elements. After calculating each element and calculating all the elements, the whole response can be obtained by adding all the elements.

After as described above to create a tire model 20 containing Tires finite element model (analysis model), the process proceeds to step 102, the input of the road surface condition is carried out with Generating Configuration namely road model of a road surface. In this step 102, the road surface is modeled and input for setting the modeled road surface to an actual road surface state. The road surface is modeled by dividing the road surface shape into elements and selecting the road surface friction coefficient μ and inputting the road surface state. For example, depending on the road surface condition, there is a road friction coefficient μ corresponding to dry (DRY), wet (WET), on ice, snow, unpaved, etc., so by selecting an appropriate value for the friction coefficient μ, The road surface condition can be reproduced.

When the road surface condition is thus input, the rolling analysis of the tire model 20 is executed in the next step 104. This rolling analysis is performed by a known method using a finite element method. First, boundary conditions are set. The boundary conditions are necessary for analysis of the tire model 20 , that is, for simulating the behavior of the tire, and are various conditions given to the tire model 20 . In the setting of the boundary conditions, firstly, the tire model 20 giving pressure, rotational displacement and the straight displacement in the tire model 20 (displacement force, which may be a velocity) and at least one of the applied load a predetermined, of Give at least one. In addition, when considering friction with the road surface, only one of rotational displacement (or force or speed) or straight displacement (or force or speed) may be used.

And the tire model 20 is rolled with respect to a road surface model , and the deformation | transformation calculation of the tire model 20 is performed by the well-known rolling analysis method based on a finite element method.

  In the present embodiment, a tire model of the entire tire including the tread pattern is created and subjected to rolling analysis. However, tire rolling analysis is not limited to this. For example, a tire model obtained by creating a tire body model such as a smooth tire without a tread pattern or a simple pattern rib pattern tire, and a tread pattern model, and performing a rolling analysis of the tire body model. From the deformed shape, a trajectory in the rolling state of the tread pattern model may be created, and detailed analysis may be performed by rolling the tread pattern model along the trajectory.

  Further, as a method of performing a rolling analysis of a tire model in a pseudo manner, as a method of analyzing a steady rolling state of a tire in a simulated manner without actually rolling the tire model in a simulation, for example, the following Non-Patent Document 1 is provided. Steady State Transport analysis described in (1) may be performed.

(Non-Patent Document 2)

  ABAQUS Version 6.6 Analysis User's Manual 6.4.1

  By executing the above rolling analysis, physical quantities at the time of tire deformation such as displacement and stress of each element 22 of the tire model 20 are obtained. In addition, said rolling analysis is an elastic analysis which handles a tire as an elastic body.

  In step 106, the time history distribution of the displacement of each element is acquired based on the result of the rolling analysis in step 104.

  In step 108, based on the result of the rolling analysis in step 104, the time history distribution of the stress of each element, in this embodiment, the Cauchy stress (stress after deformation) as the first stress is acquired.

  In step 110, based on the time history distribution of the displacement of each element obtained in step 106, the time history distribution of the Green strain of each element is calculated. The Green strain is a displacement amount based on the length of the element 22 in the initial state (the state before the deformation is applied), and is calculated from the displacement obtained in Step 106 by a predetermined calculation formula.

  In step 112, based on the time history distribution of displacement of each element 22 and the time history distribution of Cauchy stress obtained in step 106, the time history distribution of 2ndPiora-Kirhihoff stress as the second stress of each element is calculated. .

  The 2nd Piora-Kirhihoff stress is a stress based on the stress of the element 22 in the initial state, and is calculated from a displacement obtained in step 106 and a Cauchy stress by a predetermined calculation formula. Thus, the 2nd Piora-Kirhihoff stress is a stress based on the initial state stress of the element 22, and the Green strain is a displacement amount based on the length of the initial state of the element 22 as well. Is a common physical quantity. Thereby, the distortion energy loss mentioned later can be calculated correctly.

  In step 114, the strain energy loss of each element 22 is calculated based on the time history distribution of the Green strain of each element 22 obtained in step 110 and the time history distribution of the 2nd Piora-Kirhihoff stress of each element 22 obtained in step 112. calculate.

  Here, since the rubber of the tire is viscoelastic, it is inherently necessary to perform a viscoelastic analysis (time-dependent). However, as described above, the rolling analysis in step 104 is an elasticity that treats the rubber of the tire as an elastic body. Since this is an analysis, there is no phase difference between strain and stress. That is, when treating rubber as elastic, there is no phase difference between strain and stress, so the relationship between strain and stress is linear, as shown by the broken line 24 in FIG. 5, but when treating rubber as viscoelastic, As indicated by the solid line 26 in FIG. 5, hysteresis occurs in the relationship between strain and stress. The hysteresis loss, that is, the strain energy loss can be calculated by obtaining the area of the region surrounded by the solid line 26 in FIG.

  Therefore, in the present embodiment, the strain energy loss is calculated using a phase lag technique as a strain energy loss calculation method. That is, as shown in FIG. 6, since the stress 28 is delayed with respect to the strain 30, by setting the phase difference a, hysteresis is generated in the relationship between the strain and the stress as shown by the solid line 26 in FIG. The hysteresis loss, that is, the strain energy loss is calculated by calculating the area of the region surrounded by the solid line 26. The phase difference a varies depending on the material and temperature of the tire rubber, the temperature of the tire, the frequency of the tire, the frequency, and the like, and is given a predetermined value by, for example, experiments. The phase difference a may be input by the user.

  In step 116, the strain energy loss of the entire tire is calculated by adding the strain energy loss of each element 22 obtained in step 114.

  In step 118, the rolling resistance of the tire is calculated by a predetermined calculation formula based on the strain energy loss obtained in step 116.

  In step 120, the calculation result is output. For example, the strain energy loss obtained at step 116 and the rolling resistance of the tire obtained at step 118 are displayed on the CRT 14 or recorded on the hard disk 18.

  As described above, in the present embodiment, Green strain and 2nd Piora-Kirhihoff stress, which are physical quantities having a common reference, are obtained from the result of rolling analysis in which tire rubber is treated as an elastic body, and a phase difference is given to these physical quantities. Then, the hysteresis energy is generated and the strain energy loss is calculated in the same manner as the viscoelasticity analysis. Thereby, the strain energy loss can be obtained easily and accurately. Further, since the strain energy loss can be obtained with high accuracy, the rolling resistance of the tire can be obtained with high accuracy.

  In the present embodiment, the case of using the phase lag technique as the technique for calculating the strain energy loss has been described. However, the present invention is not limited to this, and the strain energy is calculated using the Warholic technique described in Non-Patent Document 1. Loss may be calculated.

10 Keyboard 12 Computer body 14 CRT
16 Mouse 18 Hard disk

Claims (5)

Analyzing the deformation for each element by performing rolling analysis on a tire model obtained by meshing a tire into a plurality of elements; and
Based on the analysis result of the rolling analysis, obtaining a time history distribution of displacement due to deformation of the element and a time history distribution of Cauchy stress for the element corresponding to the time history distribution of the displacement for each element;
Based on the time history distribution of the displacement, obtaining a Green strain time history distribution for the element corresponding to the displacement time history distribution according to the Cauchy stress for each element;
Based on the time history distribution of the displacement and the time history distribution of the Cauchy stress, the time history distribution of the 2ndPiora-Kirhihoff stress is obtained for each element for the element corresponding to the time history distribution of the displacement according to the Green strain. Steps,
Giving a preset phase difference between the time history distribution of the Green strain and the time history distribution of the 2nd Piora-Kirhihoff stress, the time history distribution of the Green strain and the time history of the 2nd Piora-Kirhihoff stress to which the phase difference was applied Obtaining a strain energy loss of the element for each element from a distribution;
Determining the strain energy loss of the tire by adding the strain energy loss of each of the elements;
A tire performance simulation method including:   The tire performance simulation method according to claim 1, further comprising a step of obtaining a rolling resistance of the tire based on a strain energy loss of the tire. Analyzing means for analyzing deformation for each element by executing rolling analysis on a tire model obtained by meshing a tire into a plurality of elements,
A first time for obtaining, for each element, a time history distribution of displacement due to deformation of the element and a time history distribution of Cauchy stress for the element corresponding to the time history distribution of displacement based on the analysis result by the analyzing means. History distribution calculating means,
A second time history distribution calculating means for obtaining, for each element, a time history distribution of Green strain for the element corresponding to the time history distribution of the displacement according to the Cauchy stress , based on the time history distribution of the displacement;
Based on the time history distribution of the displacement and the time history distribution of the Cauchy stress , the time history distribution of the 2ndPiora-Kirhihoff stress is obtained for each element for the element corresponding to the time history distribution of the displacement according to the Green strain. A third time history distribution calculating means;
Preset phase difference grant that the time history of time history distribution and 2ndPiora-Kirhihoff stress strain Green imparted with phase difference between the time history distribution of the time history profile of the Green strain the 2ndPiora-Kirhihoff stress Energy loss calculating means for obtaining the strain energy loss of the element from the distribution for each element;
Adding means for determining the strain energy loss of the tire by adding the strain energy loss of each of the elements;
Tire performance simulation equipment including Analyzing the deformation for each element by performing rolling analysis on a tire model obtained by meshing a tire into a plurality of elements; and
Based on the analysis result of the rolling analysis, obtaining a time history distribution of displacement due to deformation of the element and a time history distribution of Cauchy stress for the element corresponding to the time history distribution of the displacement for each element;
Based on the time history distribution of the displacement, obtaining a Green strain time history distribution for the element corresponding to the displacement time history distribution according to the Cauchy stress for each element;
Based on the time history distribution of the displacement and the time history distribution of the Cauchy stress, the time history distribution of the 2ndPiora-Kirhihoff stress is obtained for each element for the element corresponding to the time history distribution of the displacement according to the Green strain. Steps,
Giving a preset phase difference between the time history distribution of the Green strain and the time history distribution of the 2nd Piora-Kirhihoff stress, the time history distribution of the Green strain and the time history of the 2nd Piora-Kirhihoff stress to which the phase difference was given Obtaining a strain energy loss of the element for each element from a distribution;
Determining the strain energy loss of the tire by adding the strain energy loss of each of the elements;
Tire performance simulation program for causing a computer to execute processing including   The tire performance simulation program according to claim 4, further comprising a step of obtaining a rolling resistance of the tire based on a strain energy loss of the tire.

Images