Abstract:
A method of improving the snow traction and off-road performances of a tire and tire constructed according to such method are provided. More specifically, a method is provided for constructing the tread of a tire into inner and outer portions by extending a connecting sipe from the free edge of a tread feature that, connects to an inner sipe that surrounds a boss or projection within the tread feature. In some eases, this geometry is further optimized by designing She inner and outer portions of the other performance features. The present invention further relates to a tire having such tread constructions.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to method of improving the snow traction performance of a tire and relates to a tire constructed according to such method. More specifically, the present invention relates to a method of constructing the tread of a tire into inner and outer portions by extending a connecting sipe from the free edge of a tread feature that connects to an inner sipe that surrounds a boss or projection within the tread feature. In some cases, this geometry is further optimized by designing the inner and outer portions of the tread feature so that they experience different radial deformations under operating conditions so as to improve snow traction and other performance features. The present invention further relates to a tire having such tread constructions. 
       BACKGROUND OF THE INVENTION 
       [0002]    The performance of a tire in snow conditions is determined primarily by the amount of biting edge on the tread and the identity of the tread material. For purposes of explanation, consider tread block  100  in  FIG. 1A , where x represents the direction of travel and y represents a direction perpendicular thereto (i.e., the axial direction). If the contribution of the tread material to traction is discounted, the snow traction along the x direction of a tire having tread block  100  depends upon the biting edges  105  and  110  of tread block  100 . To improve snow traction without changing the tread compound, more edges such as  105  and  110  are needed. Accordingly, as shown in  FIG. 1B , sipe  115  is introduced into tread block  100 . However, the addition of sipe  115  has the undesirable effect of decreasing the rigidity of tread block  100  along the x direction, which will result in degrading the highway performance of the tire. 
         [0003]    A compromise between the tread blocks of  FIGS. 1A and 1B  is shown in  FIG. 1C . Here, tread block  100  includes a partial sipe  120  that extends only partly across the tread block  100  in the y-direction. The tread block of  FIG. 1C  will provide higher rigidity than the tread block of  FIG. 1B  but with less snow traction due to the reduced amount of biting edges. Therefore, the tread block of  FIG. 1C  will exhibit highway wear and snow traction performance that is between the performance of the tread blocks shown in  FIGS. 1A and 1B . However, in off-road applications, a tire tread can experience tearing due to the interaction with gravel and stones. In such situations, sipe  120  may experience stress concentrations at terminal portion  125 , which can generate undesired cracks in tread block  100 . As a result, part of tread feature  100  may be torn off after a period of usage in such off-road conditions. 
         [0004]    Accordingly, a tire having improved snow traction performance without an undesirable decrease in highway performance would be useful. A tire that also provides improved snow traction and suitable performance in off-road applications would also be useful. 
       SUMMARY OF THE INVENTION 
       [0005]    Objects and advantages of the invention will be set forth in part in the following description, or may be obvious from the description, or may be learned through practice of the invention. In one exemplary aspect of the invention, a method is provided for improving the traction and off-road performances of a tire, the tire defining radial and axial directions. The method includes the steps of providing a tread feature having an inner portion, an outer portion and a free edge, wherein the inner portion and outer portion are created by defining an inner sipe that surrounds the inner portion and a connecting sipe that extends to the inner sipe from the free edge of the tread feature. 
         [0006]    The method may also include the following steps such as applying an operating load to the tread feature; determining the difference in radial deformation along the radial direction of the inner portion relative to the outer portion under the operating load; modifying the construction of the inner portion, outer portion, or both of the tread feature if the difference in radial deformation between the inner portion and the outer portion is not equal to, or greater than, 0.1 mm; and repeating one or more of the steps of applying, determining, and modifying until the difference in radial deformation between the inner portion and the outer portion during an operating load is equal to, or greater than, 0.1 mm. 
         [0007]    This exemplary method may include other steps or modifications. For example, the method may also include the steps of operating the tire while repeatedly subjecting the outer portion of the tread feature to a radial deformation that is at least 0.1 mm or greater than the radial deformation of the inner portion of the tread feature. Alternatively, the method may also include the steps of operating the tire while repeatedly subjecting the inner portion of the tread feature to a radial deformation that is at least 0.1 mm or greater than the radial deformation of the outer portion of the tread feature. The defining sipe may have a tubular shape of predetermined radius, and the tubular shape can have a length that extends along the radial direction of the tire. 
         [0008]    The method may include the step of providing a connecting sipe that extends through the outer portion from a single, exterior edge of the tread feature and connects to the defining sipe. The connecting sipe may extend along the axial direction of the tire. For some exemplary embodiments, the predetermined radius of the defining sipe may be greater than or equal to about 1.5 mm and/or the defining sipe may have a width of about 0.2 mm. The defining sipe may include undulations along the radial direction of the tire. The tire may be constructed so that the distance between any exterior edge of the tread feature and the defining sipe is greater than or equal to about 3 mm. 
         [0009]    According to this exemplary method of the present invention, the providing step may include a simulated tread feature, and the applying step may include simulating the application of an operating load to the tread feature. The determining step, for example, may include the application of finite element analysis to the simulated tread feature from the providing step. The step of modifying the construction may include changing the physical dimensions of the inner portion, outer portion, or both of the tread feature. Alternatively, or in addition thereto, the step of modifying the construction may include changing the physical properties of the inner portion, outer portion, or both of the tread feature. Alternatively, or in addition thereto, the step of modifying the construction may include changing the composition of the material used for the inner portion, outer portion, or both of the tread feature. 
         [0010]    In another exemplary aspect, the present invention provides for a tire having improved traction and off-road performances, the tire defining axial and radial directions. This exemplary embodiment of the tire includes at least one tread feature, the tread feature having an inner portion, an outer portion and a free edge, wherein said inner and outer portions are created by defining an inner sipe that surrounds the inner portion and a connecting sipe that extends to the inner sipe from the free edge of the tread feature, forming an angle with the free edge of the tread feature. 
         [0011]    The inner portion and outer portions may be constructed so that the difference in radial deformation of the inner and outer portions when the tire is subjected to an operating load is greater than, or equal to, about 0.1 mm. The defining sipe may include a tube defined by the inner and outer portions of the tread feature with the tube having a width of no less than about 0.2 mm, and the tube having a predetermined radius of no less than about 1.5 mm. The inner sipe and connecting sipe may include undulations along the radial direction of the tire. Also, the connecting sipe may undulate in a direction that is substantially perpendicular to the radial direction of the tire. In some cases, the angle the connecting sipe forms with the free edge of the tread feature is ninety degrees. 
         [0012]    These and other features, aspects and advantages of the present invention will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]    A full and enabling disclosure of the present invention, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures, in which: 
           [0014]      FIGS. 1A-1C  are schematics of tread blocks, illustrating differences in biting edges. 
           [0015]      FIG. 2A  is a schematic of an exemplary embodiment of a tread feature—specifically, a tread block—constructed according to the present invention showing a connecting sipe that is undulating in a direction that is substantially perpendicular to the radial direction of the tire. 
           [0016]      FIG. 2B  is a schematic of an exemplary embodiment of a tread feature—specifically, a tread block—constructed according to the present invention showing a connecting sipe that forms an angle with the free edge of the tread feature that is not perpendicular thereto and an inner sipe that has an arbitrary perimeter. 
           [0017]      FIG. 2C  is a schematic of an exemplary embodiment of a tread feature—specifically, a tread block—constructed according to the present invention showing a connecting sipe that forms an angle with the free edge of the tread feature that is perpendicular thereto and an inner sipe that has tubular shape. 
           [0018]      FIGS. 3A and 3B  are schematic, side views of an exemplary embodiment of a tread block constructed according to the present invention taken along lines  3 A- 3 A and  3 B- 3 B of  FIG. 2A . 
           [0019]      FIG. 4  is a perspective view of a simulated tread block for description of exemplary methods of the present invention. 
           [0020]      FIGS. 5 ,  6 , and  7  are plots of data for purposes of illustrating aspects of the present invention. 
           [0021]      FIGS. 8 and 9  are treads that were compared for purposes of testing aspects of the present invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0022]    Reference now will be made in detail to embodiments of the invention, one or more examples of which are illustrated in the drawings. Each example is provided by way of explanation of the invention, not limitation of the invention. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the scope or spirit of the invention. For instance, features illustrated or described as part of one embodiment, can be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present invention covers such modifications and variations as come within the scope of the appended claims and their equivalents. 
         [0023]      FIG. 2A  illustrates an exemplary embodiment of a tread feature i.e., a tread block  150  constructed according to the invention. Tread block  150  includes biting edges  155  and  160 . In addition thereto, tread block  150  includes a defining or inner sipe  165 —i.e., a sipe  165  that defines tread block  150  into an inner portion  170  and an outer portion  175 . As such, sipe  165  creates additional biting edges created by the surfaces  180  and  185  and thereby improves snow traction. Additional biting edges are provided by connecting sipe  242  to improve snow traction. As shown, the connecting sipe  242  is wavy or undulating to provide additional tread block stiffness in the general direction in which the sipe  242  extends. When compared to the tread block  100  of  FIG. 1B , tread block  150  has increased tread block rigidity and, therefore, improved highway wear performance because of sipe  165  and undulating connecting sipe  242 . Compared to the tread block  100  of  FIG. 1C , tread block  150  decreases stress concentrations and, consequently, decreases the likelihood of tread tearing in off-road conditions such as gravel. Also, the extra biting edges provided by sipe  242  is an improvement over the tread block  100  of  FIG. 1C , helping the tread block  150  of  FIG. 2A  match the snow traction of the tread block  100  of  FIG. 1B . 
         [0024]    Similarly,  FIG. 2B  shows a similar tread block  150  where the connecting sipe  242  is relatively straight and forms an angle with the free edge of the tread block  150 . In this case, the angle is not ninety degrees and it is contemplated that the connecting sipe can extend from any free edge that has any orientation and form any desired angle therewith. Also, the general direction that the sipe extends may be anything that is desired including axial, circumferential or any other direction of the tire. Looking at inner or defining sipe  165 , it forms an arbitrary perimeter that surrounds a complimentary shaped inner portion  170 . It is also contemplated that the perimeter could be polygonal as well. Thus, this embodiment shows that the inner or defining sipe can have any shape as long as inner and outer portions of the tread feature are created. 
         [0025]    Further improvement to tread block  150  can also be achieved by the addition of a linear sipe  242  as shown in  FIG. 2C . The addition of linear sipe  242  can result in improvement to tread noise by providing an exit channel through which air may vent that would otherwise be trapped in sipe  165 . Linear sipe  242  will also further improve snow traction by providing additional biting edges. As has been shown, the orientation and path of any connecting sipe may be altered in virtually any manner that is desired. Also, a plurality of inner or defining sipes can be used within a tread feature, each may have one or more connecting sipes extending from them. It is also contemplated that geometry of a connecting sipe and/or inner sipe may vary by having other features such as undulations. Likewise, the thickness of the sipes can be within typical ranges used in industry, such as 0.1 mm and larger. A construction that provides the required difference in radial deformation between the inner and outer portions  170  and  175  can be determined by the inventive methods as will be described hereafter. 
         [0026]    The inventors have discovered that the snow traction performance of a tire utilizing tread block  150  can be dramatically improved without compromising highway and off-road performance. As will be more fully described herein, such improved performance is achieved by carefully designing a tread feature such as tread block  150  so that under operating loads the inner and outer portions  170  and  175  will deform by different amounts along the radial direction. More specifically, the inventors have determined that improved snow traction is achieved by constructing the inner and outer portions  170  and  175  so that a difference in radial deformation between such portions of at least about 0.1 mm occurs during operation. The inventors have also discovered methods of constructing such a tread feature so as to ensure that at least 0.1 mm difference in radial deformation occurs during operation. 
         [0027]      FIG. 3A  is a cross-sectional view of tread block  150  taken along the y-axis i.e., the transverse direction. Tread block  150  is connected to belt  200  at one side and contacts snow  190  on the traveling surface  195 . Sipe  165  separates tread block  150  into outer portion  175  and inner portion  170 . In  FIG. 3A , tread feature  150  is shown without any load applied. 
         [0028]      FIG. 3B  shows tread block  150  under an operating load as represented by arrows L. In this state, load L pushes the belt  200  downward while compressed snow  190  exerts an equal and opposite force upward against the contact surfaces  205  and  210  of the outer and inner portions  175  and  170 . By properly sizing such portions of tread block  150 , the outer portion  175  will experience a different amount of radial deformation (i.e., deformation along the z-axis) than the inner portion  170 . For purposes of illustration), this difference in deformation has been exaggerated in  FIG. 3B  and is shown in phantom lines. The inventors have determined that the inner and outer portions  170  and  175  should be constructed so that a difference in deformation of a least about 0.1 mm occurs during operation in order to improve traction performance. 
         [0029]    As shown in  FIG. 3B , outer portion  175  is deforming more along the radial direction than the inner portion  170 . In such case, the inner portion  170  operates as a stud to penetrate into the snow  190  and provide more traction. Tread block  150  can also be designed so that the inner portion  170  will deform more than the outer portion  175  so as to create a depression at surface  210 . In this construction, when the tread block  150  leaves the ground as the tire rotates, if properly sized, the inner portion  170  will operate as a cleaner—i.e., ejecting the snow packed into the sipe  165  and the depression at surface  210 . 
         [0030]    Again, tread block  150  should be constructed so that a difference in radial deformation of at least about 0.1 mm occurs during operation. As stated, the required difference in radial deformation can be achieved through careful design of the size of sipe  165 , inner portion  170  and outer portion  175  of tread block  150 . By way of example and further description of the invention, a process of designing tread block  150  through simulations with finite element analysis will now be described. Using the teachings disclosed herein, one of skill in the art will understand that the present invention applies not only to tread blocks but to other tread features as well such as e.g., tread ribs. Also, this phenomenon applies equally to tread features that have and do not have connecting sipes. 
         [0031]      FIG. 4  shows a three-dimensional view of a simulated model for tread block  150  for use with finite element analysis. Inner portion  170  has a radius  215 . Sipe  165  is defined by sipe width  220  and sipe depth  225 . Tread block  150  has a depth  230  along the radial or z direction, a width  235  along the direction of travel or x direction (sometimes referred to as the circumferential direction of the tire), and a transverse width  240  along the axial or y direction. 
         [0032]    Sipe  165  is tubular in shape as shown in  FIG. 4 . However, other shapes for sipe  165  can be used. By way of example, sipe  165  could be shaped as a star, cross, circle, ellipse, and other shapes as well. In addition, the shape of sipe  165  along the radial or z-direction can also be varied between straight, curved, and undulating walls such that the three-dimensional construction of sipe  165  creates a cone, cylinder, baffles, and various other shapes. 
         [0033]    In order to simulate conditions of operation, a nominal pressure of five 0.05 daN/mm 2  (5 bar) was applied to the tread surface (surfaces  205  and  210 ) of tread block  150 , and the tread block was restrained from any displacement along the surface connecting with belt  200  (see  FIGS. 3A and 3B ). A modulus for the tread block rubber of 5.47 MPa at 10 percent strain was selected. In addition, tread block  150  was simulated having widths  235  and  240  of 28 mm in both the x and y directions, a sipe width  220  of 0.4 mm, a sipe depth  225  of 8 mm, and a tread block depth  230  of 13 mm. Using finite element analysis, the radial deformation of the inner and outer portions  170  and  175  with various sipe radii  215  was determined and the results are shown in Table 1. Table 1. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Displacement of tread block surface with different sipe radius 
               
             
          
           
               
                   
                   
                 Inner 
                 Outer 
                   
               
               
                 Sipe 
                 Radius 
                 sub-block 
                 sub-block 
                 Inner − Outer 
               
               
                 Radius 
                 Divided by 
                 displacement 
                 Displacement 
                 Difference 
               
               
                 (mm) 
                 Block width 
                 (mm) 
                 (mm) 
                 (mm) 
               
               
                   
               
             
          
           
               
                 10 
                 0.36 
                 −0.47 
                 −0.83 
                 0.36 
               
               
                 8 
                 0.29 
                 −0.53 
                 −0.71 
                 0.18 
               
               
                 6 
                 0.21 
                 −0.55 
                 −0.64 
                 0.09 
               
               
                 4 
                 0.14 
                 −0.58 
                 −0.58 
                 0.00 
               
               
                 2 
                 0.07 
                 −0.64 
                 −0.53 
                 −0.11 
               
               
                   
               
               
                 (Block depth = 13 mm, Block width = 28 mm, Sipe gap = 0.2 mm, Sipe depth = 8 mm, Modulus = 5.47 MPa) 
               
             
          
         
       
     
         [0034]    As indicated by Table 1, as the sipe radius  215  increases, deformation of the outer portion  175  for a given load also increases while the deformation of the inner portion  170  decreases. However, in a manner unexpected, note also that the difference in radial deformation between the inner and outer portions  170  and  175  decreases and then increases as the sipe radius  215  increases. As a result, for the tread block simulated in Table 1, sipe radii between 4 mm and 6 mm do not provide a sufficient difference in radial deformation (at least about 0.1 mm) to appreciably improve snow traction. Accordingly, the inventors also discovered that not every tread feature having inner and outer portions will experience radial deformations that improve snow traction and, instead, must be specifically designed as described herein to experience the desired amount of radial deformation—i.e., at least about 0.1 mm. 
         [0035]    The results of Table 1 also indicate that for this particular configuration of tread block  150 , when the sipe radius  215  is less than or equal to 2 mm, the inner portion  170  deforms more along the radial or z-direction than the outer portion  175  and, therefore, operates as a cleaner. When the sipe radius  215  is greater than or equal to 6 mm, the inner portion  170  deforms less along the radial or z direction than the outer portion  175  and, therefore, operates as a stud. 
         [0036]    As used herein, about 0.1 mm deformation difference between the inner and outer tread blocks  170  and  175  is used to define a cleaner or a stud. More specifically, a stud is created by tread block  150  when the outer portion  175  deforms 0.1 mm more along the radial direction than the inside portion  170 , and a cleaner is created when the inner portion  170  deforms 0.1 mm more along the radial direction than the outside portion  175 . Increasing the deformation difference between the inside and outside portions  170  and  175  results in improvement in snow traction. 
         [0037]    For off-road performance, stress concentrations should be minimized to decrease tearing. As such, generally the sipe radius  215  should not be less than about 1.5 mm and the distance between sipe  165  and outer edges, such as  245  and  250 , should be greater than 3 mm. Therefore, for a head block similar to that in  FIG. 4  with dimensions as used in Table 1, sipe radius  215  should fall in one of the following two ranges:
       Range 1: 1.5 mm≦sipe radius  215 ≦2 mm   Range 2: 6 mm≦sipe radius  215 ≦9.5 mm       
 
         [0040]    As compared to the design shown in  FIG. 1B , both of these ranges will deliver improved snow traction without compromising off-road tearing or highway wear. However, Range 2 will provide better snow traction because this range will provide a larger amount of biting edge. However, the highway wear of Range 2 may not perform as well as Range 1 because the rigidity of the tread block  150  resulting from Range 2 will be less than that of Range 1. Accordingly, Range 1 and Range 2 offer selections for different applications with Range 2 being more appropriately suited for a tire intended for more snow or winter use. 
         [0041]    The depth  225  of sipe  165  is also an important parameter influencing the design of sipe radius  215 . Table 2 presents the simulation results for a sipe depth  225  of 11 mm with all other parameters the same as those used in the simulation of Table 1. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Displacement of tread block surface with different sipe radii 
               
             
          
           
               
                   
                   
                 Inner 
                 Outer 
                   
               
               
                 Sipe 
                 Radius 
                 sub-block 
                 sub-block 
                 Inner − Outer 
               
               
                 Radius 
                 Divided by 
                 displacement 
                 Displacement 
                 Difference 
               
               
                 (mm) 
                 Block width 
                 (mm) 
                 (mm) 
                 (mm) 
               
               
                   
               
             
          
           
               
                 10 
                 0.36 
                 −0.53 
                 −0.77 
                 0.25 
               
               
                 8 
                 0.29 
                 −0.58 
                 −0.70 
                 0.12 
               
               
                 6 
                 0.21 
                 −0.61 
                 −0.64 
                 0.03 
               
               
                 4 
                 0.14 
                 −0.65 
                 −0.57 
                 −0.08 
               
               
                 2 
                 0.07 
                 −0.71 
                 −0.51 
                 −0.21 
               
               
                   
               
               
                 (Block depth = 13 mm, Block width = 28 mm, Sipe gap = 0.2 mm, Sipe depth = 11 mm, Modulus = 5.47 MPa) 
               
             
          
         
       
     
         [0042]    As compared to Table 1, the deformation of the outer portion  175  still increased with an increase in sipe radius  215  while the deformation of inner portion  170  decreased. However, in a manner that was unexpected, the difference in radial deformation between the inner and outer portion as a function of sipe radius  215  for the tread block of Table 2 is different than the tread block of Table 1,  FIG. 5 , for example, shows that the increased sipe depth  225  changes the rate at which increases in sipe radius  215  affect the difference in radial deformation between the inner and outer portions  170  and  175 . 
         [0043]    Using the design guidelines previously stated, Table 2 and  FIG. 5  show that for a sipe with a depth of 11 mm, the design of sipe radius  215  should follow one of the following two ranges:
       Range 1: 1.5 mm≦sipe radius  215 ≦3.5 mm   Range 2: 7.5 mm≦sipe radius  215 ≦9.5 mm       
 
         [0046]    For the examples of Tables 1 and 2, a sipe width  220  of 0.2 mm was simulated. Table 3 presents the results when a sipe width  220  of 0.4 mm was simulated. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Displacement of tread block surface with different sipe radius 
               
             
          
           
               
                   
                   
                 Inner 
                 Outer 
                   
               
               
                 Sipe 
                 Radius 
                 sub-block 
                 sub-block 
                 Inner − Outer 
               
               
                 Radius 
                 Divided by 
                 displacement 
                 Displacement 
                 Difference 
               
               
                 (mm) 
                 Block width 
                 (mm) 
                 (mm) 
                 (mm) 
               
               
                   
               
             
          
           
               
                 10 
                 0.36 
                 −0.45 
                 −0.88 
                 0.43 
               
               
                 8 
                 0.29 
                 −0.48 
                 −0.77 
                 0.29 
               
               
                 6 
                 0.21 
                 −0.52 
                 −0.67 
                 0.15 
               
               
                 4 
                 0.14 
                 −0.57 
                 −0.59 
                 0.02 
               
               
                 2 
                 0.07 
                 −0.64 
                 −0.53 
                 −0.11 
               
               
                   
               
               
                 (Block depth = 13 mm, Block width = 28 mm, Sipe gap = 0.4 mm, Sipe depth = 8 mm, Modulus = 5.47 MPa) 
               
             
          
         
       
     
         [0047]      FIG. 6  provides a plot of the simulation results of Table 3, which demonstrates the differences when sipe width  220  is changed.  FIG. 6  indicates that for a sipe width  220  of 0.4 mm, sipe radius  215  should not be between 3 mm and 5 mm because the difference in radial deformation is not at least about 0.1 mm. Otherwise, the radius should be greater than 1.5 mm and the distance between the sipe and the tread block outer edge  250  should be greater than 3 mm to avoid off-road tearing degradation. Using the design guidelines previously stated, Table 3 and  FIG. 6  show that for this tread block  150 , the design of sipe radius  215  should fall into one of the following two ranges:
       Range 1: 1.5 mm≦sipe radius  215 ≦3 mm   Range 2: 5 mm≦sipe radius  215 ≦9.5 mm       
 
         [0050]    It was also determined that block width  235  and  240  also influences the design of sipe  165  and inner and outer portions  170  and  175 . Table 4 presents the results when block widths  235  and  240  are 20 mm, whereas the previous tables were for block widths of 28 mm. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Displacement of tread block surface with different sipe radius 
               
             
          
           
               
                   
                   
                 Inner 
                 Outer 
                   
               
               
                 Sipe 
                 Radius 
                 sub-block 
                 sub-block 
                 Inner − Outer 
               
               
                 Radius 
                 Divided by 
                 displacement 
                 Displacement 
                 Difference 
               
               
                 (mm) 
                 Block width 
                 (mm) 
                 (mm) 
                 (mm) 
               
               
                   
               
             
          
           
               
                 8 
                 0.4 
                 −0.58 
                 −1.06 
                 0.48 
               
               
                 6 
                 0.3 
                 −0.62 
                 −0.92 
                 0.30 
               
               
                 4 
                 0.2 
                 −0.67 
                 −0.83 
                 0.17 
               
               
                 2 
                 0.1 
                 −0.72 
                 −0.77 
                 0.05 
               
               
                   
               
               
                 (Block depth = 13 mm, Block width = 20 mm, Sipe gap = 0.4 mm, Sipe depth = 8 mm, Modulus = 5.47 MPa) 
               
             
          
         
       
     
         [0051]      FIG. 7  shows a plot comparing the results for different tread block widths where the tread block  150  is square in shape such that widths  235  and  240  are identical for each simulated width of 20 mm and 28 mm. As shown from the results in Table 4 and  FIG. 7 , block widths  235  and  240  influence the design of tread block  150 . More specifically, for a tread block  150  with dimensions of 20×120×13 mm, the sipe radius  165  should be greater than 3 mm. As stated previously, the distance between the sipe  165  and the block outer edge  245  should be greater than 3 mm. Accordingly, the methods of the present invention reveal that only a stud scenario exists for this kind of tread block such that the range of acceptable radii for radius  215  is
       Range 1: 3 mm≦sipe radius  215 ≦17 mm       
 
         [0053]    Using the teachings disclosed herein, one of skill in the art will understand that other variables can be applied and adjusted using the present invention in order to achieve the desired amount of radial deformation (i.e., at least about 0.1 mm). For example, the materials of construction used for block  150  can be changed in order to select different block material modulii, which in turn will lead to changes in e.g., the sipe radius  165 . Additionally, different materials could also be used for the inner and outer portions  170  and  175  in order to obtain the desired difference in radial deformation. Regardless, in each case a tread block  150  can be simulated using e.g., finite element analysis so as to determine the required sipe radii and/or other parameters of block  150  in order to achieve at least 0.1 mm radial deformation difference between inner and outer portions  170  and  175 . 
         [0054]    In order to further test and demonstrate the effectiveness of a tread feature constructed as previously described, two tread patterns as shown in  FIGS. 8 and 9  were compared. Tread  500  of  FIG. 8  contains linear sipes as previously described with regard to  FIG. 1B . Tread  600  of  FIG. 9  contains tread features  605 ,  610  and  615  having tubular sipes similar to that previously described with respect to tread block  150 . Tread features  605  perform as a cleaner while features  610  and  615  perform as a stud. Note that tread  500  and tread  600  have about the same amount of biting edge with the exception of the tubular sipes which give tread  600  slightly more biting edges. The normalized results of the testing of tires having these tread features is shown in Table 5: 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Results of field tests 
               
             
          
           
               
                 Field Tests 
                 Normal Design (FIG. 9) 
                 Tubular Sipe (FIG. 10) 
               
               
                   
               
               
                 Snow Traction 
                 100 
                 104 
               
               
                 Off-Road Tearing 
                 100 
                 107 
               
               
                 Highway Wear 
                 100 
                 107 
               
               
                   
               
             
          
         
       
     
         [0055]    The tests demonstrate that the tread  600  is improved as compared to tread  500  because it has slightly more biting edges as compared to tread  500  and because of the effects of these sipes acting as a cleaner and stud as previously described. In addition, performances in highway wear and off-road tearing were also improved due to increased block rigidity. 
         [0056]    While the present subject matter has been described in detail with respect to specific exemplary embodiments and methods thereof it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing may readily produce alterations to, variations of, and equivalents to such embodiments. Accordingly, the scope of the present disclosure is by way of example rather than by way of limitation, and the subject disclosure does not preclude inclusion of such modifications, variations and/or additions to the present subject matter as would be readily apparent to one of ordinary skill in the art.