Abstract:
A method of simulating a tire rolling on a road at a certain speed by using a computer apparatus  1  comprises the steps of: modeling a flexible tire model  2  for numerical calculation by using finite elements having at least one elastic element (step S 1 ), changing at least one elastic element of the flexible tire model  2  to rigid elements so as to make a rigid tire model  5  (step S 6 ), accelerating the rigid tire model  5  (step S 7 ), returning the elasticity of each element of the rigid tire model into the original elasticity when the speed of the rigid tire model  5  has reached the certain speed (step S 8 ), and obtaining at least one physical parameter related to the flexible tire model  2  (step S 10 ).

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to a method of rolling tire simulation capable of simulating a situation of a tire rolling at a certain speed and of calculating it in shorter time with high accuracy. 
         [0003]    2. Related Art 
         [0004]    In recent years, a computer simulation is used for development of a tire. It is known that various method for simulating a rolling tire at a certain speed with the computer as disclosed in Japanese unexamined Published Applications Nos. 2003-127622, 2004-20229, 2004-322971, and 2002-67636. The computer simulation enables performance to some extent to be predicted without experimentally manufacturing the tire. As the computer simulation has been known, for example, a rolling simulation, in which a tire model is made to roll on a road model. Each model consists of the finite elements. Most of the finite elements are elements having similar elasticity to the rubber, cords and the like comprising a tire. 
         [0005]    The tire model is given various boundary conditions such as a rim, inner pressure, and load, and contacts with the road model; and then, an accelerating step of accelerating the tire model up to a certain speed is conducted. AS to the acceleration step, it takes approximately 1.4 seconds to accelerate to 50 km/h even when the tire model is accelerated sizably to 1 G (nearly equal to 9.8 m/s 2 ) in view of actual service condition, for example. Then, after reaching the predetermined certain speed, necessary physical parameters are calculated from the rolling tire model. 
         [0006]    For simulating characteristics of a tire rolling at a constant speed, the above-mentioned accelerating is wasted time. To shorten the amount of simulation time, it is effective to accelerate the tire model enormously and accelerates to a predetermined speed in a short time. 
         [0007]    However, when the acceleration is too large, deformational amount of elastic elements of the tire model becomes notably large, and the elements may be damaged and calculation errors may occur. 
         [0008]    The finite element method (FEM) is often used in the above-described simulation. In the finite element method, calculation runs by dividing time into short time steps. The state of each element at the end of a time step is adopted as initial values of a next time step, and the calculation is performed in chronological order. In each time step, some errors are observed since a calculation result is rounded off to a predetermined digits. Usually in the number of time steps, the number of digit is secured sufficiently not to affect the errors. However, the increase of acceleration time causes inevitably increases of the number of time steps, thereby possibly accumulating errors and reducing accuracy of calculation, so called underflow. 
       SUMMARY OF THE INVENTION 
       [0009]    The present invention has been accomplished to solve the above-described problems. Therefore, a principal object of the present invention is to provide a method of simulating rolling tire capable of shortening the amount of calculation time while keeping accuracy of calculation high. 
         [0010]    A method of simulating rolling tire according to the present invention comprises the following steps: modeling a flexible tire model for numerical calculation by using finite elements having at least one elastic element, changing at least one elastic element of the flexible tire model to rigid element so as to make a rigid tire model, accelerating the rigid tire model, returning the elasticity of each element of the rigid tire model into the original elasticity when the speed of the rigid tire model has reached the certain speed, and obtaining at least one physical parameter related to the flexible tire model. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]      FIG. 1  is a perspective view showing a computer apparatus for using a simulation method in a present preferred embodiment; 
           [0012]      FIG. 2  is a flowchart illustrating one example of processing procedures of a simulation method for use in the present preferred embodiment; 
           [0013]      FIG. 3  is a perspective view showing one example of a tire model; 
           [0014]      FIG. 4  is a cross sectional view of the tire model along the tire meridian section including the tire axis; 
           [0015]      FIG. 5  is a perspective view of the road model; 
           [0016]      FIG. 6  is a perspective view showing one example of a rolling simulation of a flexible tire model contacting with the road model; 
           [0017]      FIG. 7  is a side view illustrating the rolling simulation of the flexible tire model; 
           [0018]      FIG. 8  is a side view illustrating a rolling situation of a rigid tire model. 
           [0019]      FIG. 9  is a graph illustrating the relationship between a rolling speed of the tire model and a time; 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0020]    A description will be given below of preferred embodiments according to the present embodiment in reference to the attached drawings. 
         [0021]      FIG. 1  shows a computer apparatus  1  for carrying out a simulation method according to the present embodiment. The computer apparatus  1  includes a main unit  1   a,  a keyboard  1   b  and a mouse  1   c  serving as input means, and a display  1   d  serving as output means. Although not shown, the main unit  1   a  is appropriately provided with a central processing unit (abbreviated as “a CPU”), a ROM, a working memory, a large-capacity storage device such as a magnetic disk, and drives  1   a   1  and 1a2 for a CD-ROM or a flexible disk. The large-capacity storage device stores therein processing procedures (i.e., programs) for executing a method, described later. 
         [0022]      FIG. 2  illustrates one example of processing procedures in the present preferred embodiment. In the present preferred embodiment, a flexible tire model  2  is first modeled (step S 1 ).  FIG. 3  shows one example of the flexible tire model  2  visually in a three-dimensional fashion. In the flexible tire model  2 , a tire as an analysis object is illustrated by replacing with finite elements (e). 
         [0023]    The flexible tire model  2  is modeled by dividing a radial tire for passenger cars to be analyzed (irrespective of the actual presence) into the finite elements (e) . . . . Each of the elements (e) can be defined as numerically analyzable. The “numeric analyzable” signifies to available to carry out modification calculation by at least one numerically analyzing method. The numerically analyzing methods include the finite element method, the finite volume method, calculus of finite differences, and the boundary element method, for example. 
         [0024]    Specifically describing, for example, a coordinate value of a point in a X-Y-Z coordinate system, the shape of the element, the properties of a material (e.g., a density, a modulus of elasticity, a loss tangent and a damping coefficient) and the like are defined with respect to each of the elements (e). Consequently, the substance of the flexible tire model  2  is expressed by numerical data, which can be operated in the computer apparatus  1 . 
         [0025]      FIG. 4  shows a cross sectional view of the tire model  2  along the tire meridian section including the tire axis (not shown). As modeled rubbers, the flexible tire model  2  of the present embodiment comprises: a tread rubber model portion E 1  made of first elements (e 1 ) having predetermined elastic modulus in relation to a tread rubber; a side rubber model portion E 2  made of second elements (e 2 ) having predetermined elastic modulus in relation to a sidewall rubber; an apex model portion E 3  made of third elements (e 3 ) having predetermined elastic modulus in relation to a bead apex rubber; and an inner liner model portion E 4  made of fourth elements (e 4 ) having predetermined elastic modulus in relation to an inner liner. The elements (e 1 )-(e 4 ) are treated as elastic bodies in which strain occurs in proportion to stress. The elastic bodies have characteristics of deformed by force and becoming normal again after unloading, and comprising the hyperelastic body in concept. 
         [0026]    The flexible tire model  2  also comprises as modeled fiber cords: a carcass model portion E 5  made of fifth elements (e 5 ) having predetermined elastic modulus in relation to a carcass cords and orthotropy along longer direction of the carcass cords; and a belt model portion E 6  made of sixth elements (e 6 ) having predetermined elastic modulus in relation to a belt cords and orthotropy along longer direction of the belt cords. The elements (e 5 ) and (e 6 ) are also treated as elastic bodies in which strain occurs in proportion to stress. 
         [0027]    Moreover, the flexible tire model  2  comprises a bead core model portion E 7  made of fifth elements (e 7 ) having predetermined elastic modulus in relation to a bead core. The elements (e 7 ) are treated as a rigid body, which is never deformed by external force. 
         [0028]    For the elements (e 1 )-(e 4 ) and (e 7 ), three-dimensional solid elements of a tetrahedral or hexahedral are preferably used, for example. For the elements (e 5 ) and (e 6 ), planar shell elements are also used preferably in addition to those three-dimensional solid elements. The flexible tire model  2  is not provided with grooves in the tread rubber model portion E 1  in the present embodiment, but not to be limited. 
         [0029]    Next, a road model  3  is modeled in the present preferred embodiment (step S 2 ).  FIG. 5  shows one example of the road model  3 . In the present embodiment the road model  3  is modeled by one or more rigid surface elements (e 8 ), which comprise a single flat surface. Since the road model  3  is formed of a rigid surface, the road model  3  cannot be deformed even if external force acts on the road model  3 . Moreover, unevenness (for example, irregular steps, grooves, undulation, ruts or the like) may be provided in the road model  3 , as required. Additionally, the road model  3  may be formed into a cylindrical surface used to resemble a drum test machine. 
         [0030]    Subsequently, various kinds of boundary conditions are applied to each of the flexible tire model  2  and the road model  3  (step S 3 ) in the present preferred embodiment. The conditions comprises a rim on which the flexible tire model  2  is mounted, inner pressure of the tire, normal load, a certain rolling speed, slip angle and camber angle, and a frictional coefficient between the flexible tire model  2  and the road model  3 . The frictional coefficient values depend on a road condition. 
         [0031]    And then, deformational simulation of calculating a shape of the flexible tire model  2  contacting the road model  3  and loaded at in the z-axis direction (normal loading) as shown in  FIG. 6  (step S 4 ). 
         [0032]    In the above-described deformational simulation, a tire mounted on a rim, inflated at a certain inner pressure, loaded at a certain normal load, and pressed vertically on a road surface in finite element method is calculated in accordance with the conditions set in the step S 3 . For example, the situation of the flexible tire model  2  mounted on the rim can be calculated by deforming intervals of the bead core model E 7  of the flexible tire model  2  in width in accordance with rim width. The inflated situation of the flexible tire model  2  can be also calculated by the deforming under a certain uniformly-distributed load on a cavity inner surface of the flexible tire model  2 . The deformed situation of the flexible tire model  2  can be calculated by applying the normal load on the rolling axis of the flexible tire model  2 . 
         [0033]    As to the steps of a procedure and ways in order to provide with boundary conditions in a finite element model and to calculate physical parameters such as the entire system force and displacement and the like, the finite element calculation can be conducted in accordance with well known examples. In the present embodiment, the above-mentioned computer apparatus  1  calculates with a general analysis program (general explicit method software “LS-Dnya”, for example). 
         [0034]      FIG. 7  is a side view illustrating the flexible tire model  2  obtained by such a deformation simulation where the flexible tire model  2  is statically contact with the road model  3  in the present embodiment. As is obvious from  FIG. 7 , the ground contact area (A) of contacting with the road model  3 , which is rigid, deforms flatly in the tread rubber model portion E 1  of the flexible tire model  2 . 
         [0035]    The information on the deformation of each element of the flexible tire model  2  is stored in the above-mentioned computer apparatus  1  (step S 5 ). That is to say, the information on each deformation such as stress, strain, and energy etc. is stored in the storage of the computer apparatus  1  since the elements (e 1 )-(e 6 ) are deformed elastically. The information may comprise various parameters, if needed. 
         [0036]    In step S 6 , the flexible tire model  2  is rigidized. In the present embodiment, all the elastic elements (e 1 )-(e 6 ) are rigidized, thereby changing the flexible tire model  2  into a rigid tire model  5 . The elements can be rigidized by changing the values of elastic modulus, which are determined par element up to infinity, for example. The rigid tire model  5  keeps a shape shown in  FIG. 7 , that is to say, keeping the shape of the tread rubber model portion E 1  including the ground contact area (A) flatly-deformed. 
         [0037]    The rigid tire model  5  is accelerated up to a certain speed (step S 7 ). In the present embodiment,  FIGS. 7 and 8  show that the rigid tire model  5  is rotatable around the tire axis CL and is movable only in the z-axis direction and that the road model  3  is set to move at the certain speed. The rigid tire model  5  is therefore accelerated by the frictional force caused by contacting with the road model  3 . The embodiment for applying acceleration is not to be considered limited to such an aspect. 
         [0038]    The rigid tire model  5  is not deformed by any outer force and rotates while keeping the deformed state obtained in the above-mentioned deformation simulation. Therefore, the rigid tire model  5  can be accelerated up to the predetermined certain speed at short times neither crushing of the elements (e 1 )-(e 6 ) nor miscalculation even when the rigid tire model  5  is accelerated unrealistically enormously (not less than 100 G, for example). Moreover, there is no need for the deformation calculation of the accelerating rigid tire model  5 , so that computational load may decrease. 
         [0039]    The time to accelerate the rigid tire model  5  is not limited in the present embodiment. However, as the rigid tire model  5  comprises the flatly-deformed ground contacting area (A), the external diameter is not constant. Therefore, when accelerating tire is longer, large vibration in the z-axis direction possibly occurs in the rigid tire model  5 . For suppressing such vibration, it is preferable to diminish moving distance of the accelerating rigid tire model  5 . Notably, to set the rigid tire model  5  to having a length of not more than one-half of a circumferential ground contacting length L of the rigid tire model  5  at the condition of before acceleration (“L/2” means a length between positions P 1 -P 2  of the ground contacting area). The relation between an acceleration and a time is described by the formula (1): 
         [0000]      ∫ T    at·dt≦L/ 2   (1), 
         [0000]    where, “a” is an acceleration (m/s 2 ) for the rigid tire model  5 , “T” is a time (sec.) to accelerate the rigid tire model  5 , and “L” is a circumferential ground contacting length (meter) of the rigid tire model  5  with the road model  3  at the condition of before acceleration. 
         [0040]    By calculating the above-mentioned formula (1), the time for accelerating the rigid tire model  5  is preferably described by the formula (2): 
         [0000]        T ≦( L/a ) 0.5    (2). 
         [0000]    In order to set the rigid tire model  5  to be having the moving distance of not more than one third of the circumferential ground contacting length L, it is in particular preferably described by the formula (3) 
         [0000]        T ≦(2 L/ 3 a ) 0.5    (3). 
         [0000]    The rigid tire model  5  is never deformed by the acceleration. In the formulae (2) and (3), the acceleration time is therefore determined in priority to the acceleration (a). 
         [0041]    For example, when the length L is set to 150 mm, the predetermined speed is 50 km/h, the moving distance of the rigid tire model  5  is set to be not more than one third of the length L, and the time T for accelerating the rigid tire model  5  is set to be very short time, 7 msec, for example. In accordance with the formula (3) the acceleration is as follows: 
         [0000]        a ≦(2 L/ 3 T   2 ). 
         [0000]    Therefore, the acceleration (a) in this case is set to become approximately 2040.8 m/s 2 . 
         [0042]    Meanwhile, after the speed of the rigid tire model  5  reaching at the predetermined speed in accordance with step S 7 , the acceleration will return into zero, and the rigid tire model  5  will roll at the constant speed. 
         [0043]    Then, the elasticity of each element of the rigid tire model  5  is returned into the original elasticity (step S 8 ). The information of deformation stored in step S 5  is brought back to each of the elements (e 1 )-(e 6 ) of the flexible tire model  2  (step S 9 ); namely, the elastic modulus of the elements (e 1 )-(e 6 ) is brought back to the original determined elastic modulus in relation to each of the rubbers or fiber cord materials and are regained as same stress, strain, and energy as before the rigidization. Therefore, the flexible tire model  2  can roll at a target speed and may change into a shape that is formed by equation of motion and equilibrium of force. 
         [0044]    In step S 10 , necessary physical parameters are obtained from the flexible tire model  2 . As the physical values, for example, there are circumferential force, lateral force, vertical force, and/or cornering power; these values can be output in chronological order. It makes possible to forecast performances in the target tire rolling on a road at a certain speed. 
         [0045]    It may be possible to change the present embodiment to other embodiments. For example, it may deform the flexible tire model  2  by contacting with the road model  3  and loading after the acceleration steps S 6  to S 8 . At this moment of the contact, the speeds of the flexible tire model  2  and the road model  3  are preferably the same. 
         [0046]    In the present embodiment of the above, all the elastic elements (e 1 )-(e 6 ) are rigidized, but it is possible to rigidize principle elements only. For example, an embodiment will be fully effective when rigidizing only the elements related to deformable rubber. 
       Comparison Test: 
       [0047]    Pneumatic tires for test of 235/45R17 were made and cornering power during test tire rolling calculated in the undermentioned simulation method of the present embodiment. Table 1 and  FIG. 9  show the test result. The rolling tests were conducted as follows: 
         [0048]    Rolling speed: 20 km/h or 50 km/h, 
         [0049]    Inner Pressure: 200 kPa, 
         [0050]    Slip angle: 1 degree, and 
         [0051]    Load: 4.5 kN. 
         [0052]    In the accelerating step of comparative Examples 1 and 2, the tire model being expressible of elastic deformation was subjected to acceleration of 1 G. In Examples 1 and 2, simulations were conducted according to the procedures shown in  FIG. 2 ; and the acceleration was 113 G and 283 G, respectively. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Ex. 1 
                 Ex. 2 
                 Com. Ex. 1 
                 Com. Ex. 2 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Change from a flexible 
                 Yes 
                 Yes 
                 No 
                 No 
               
               
                 tire model into a rigid 
               
               
                 tire model 
               
               
                 Predetermined speed 
                 20 
                 50 
                  20 
                 50 
               
               
                 (km/h) 
               
               
                 Acceleration in 
                 113 G 
                 283 G 
                 1 G 
                 1 G 
               
               
                 Accelerating step 
               
               
                 Calculated value of 
                 1400  
                 1450  
                 1400  
                 incalculable 
               
               
                 Cornering power (N) 
               
               
                 Time of calculation 
                 38 
                 38 
                 100 
                 — 
               
               
                 (Index) 
               
               
                   
               
             
          
         
       
     
         [0053]    As shown in Table 1, the Examples shortened the calculation time by approximately 62%. Moreover, in view of calculation accuracy, the difference between the Examples and comparative Examples is about 4%; therefore, the accuracy was kept sufficiently in the present embodiment.