Abstract:
A shear band that may be used as part of a structurally supported wheel is provided. More particularly, a shear band constructed from resilient, cylindrical elements attached between inextensible members is described. In certain embodiments, the shear band may be constructed entirely or substantially without elastomeric or polymer-based materials. Multiple embodiments are available including various arrangements of the cylindrical elements between the members as well as differing geometries for the cylindrical elements.

Description:
TECHNICAL FIELD OF THE INVENTION 
       [0001]    The present invention relates to a shear band that may be used as part of a structurally supported wheel. More particularly, a shear band constructed from resilient, cylindrical elements attached between circumferential members is provided. In certain embodiments, the shear band may be constructed entirely or substantially without elastomeric or polymer-based materials, which allows for application in extreme environments. 
       BACKGROUND OF THE INVENTION 
       [0002]    The use of structural elements to provide load support in a tire without the necessity of air pressure has been previously described. For example, U.S. Pat. No. 6,769,465 provides a resilient tire that supports a load without internal air pressure. This tire includes a ground contacting tread portion, a reinforced annular member, and sidewall portions that extend radially inward from the tread portion. By way of further example, U.S. Pat. No. 7,201,194 provides a structurally supported non-pneumatic tire that includes a ground contacting tread portion, a reinforced annular element disposed radially inward of the tread portion, and a plurality of web spokes extending transversely across and radially inward from the reinforced annular element and anchored in a wheel or hub. For each of these references, the constructions described are particularly amenable to the use of elastomeric materials including rubber and other polymeric materials. The use of such materials has certain limitations, however. For example, extreme temperatures levels and large temperature fluctuations can make such elastomeric materials unsuitable for certain applications. Accordingly, constructions that can be created in whole or in part with non-elastomeric materials would be advantageous. Also, constructions from materials such as carbon-based elements may also result in reduced weight and lower materials costs. These and other advantages are provided by certain exemplary embodiments of the present invention. 
       THE SUMMARY OF THE INVENTION 
       [0003]    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. 
         [0004]    In one exemplary embodiment of the invention, a shear band is provided that defines axial, radial, and circumferential directions. The shear band includes an outer member extending along the circumferential direction, an inner member extending along the circumferential direction, and a plurality of resilient, cylindrical elements connected with the outer and inner members and each extending between the members along the radial direction. The arrangement of cylindrical elements between the members may be varied. For example, in one variation, the cylindrical elements are arranged into multiple, overlapping rows along the axial direction. The overlapping rows are positioned about the circumferential direction between the outer and inner inextensible members. In another variation, the cylindrical elements are arranged into a series of axially-aligned, non-overlapping rows and are positioned about the circumferential direction between the members. The cylindrical elements may be constructed as circular shapes; however, elliptical or oblong constructions may also be used. 
         [0005]    Each cylindrical element defines an axis. The axis of the cylindrical elements may be arranged in a manner that is parallel to the axial direction of the shear band, or the cylindrical elements may be arranged in non-parallel orientations. The cylindrical elements may be attached directly to the outer and inner members or may be attached to other components that are in turn connected with the outer and inner members. More specifically, a variety of different means may be used for connecting the cylindrical elements to the outer and inner inextensible members. The inner and outer inextensible members as well as the cylindrical elements may be constructed from a variety of different materials. Traditional elastomeric and polymer-based materials may be used. In addition, the present invention allows for the application of a variety of other materials including, for example, metal and/or carbon-fiber based materials. 
         [0006]    In another exemplary embodiment, the present invention provides a wheel that defines axial, radial, and circumferential directions. The wheel includes a hub, a shear band, and a plurality of support elements connected between the hub and the shear band. The shear band includes an outer circumferential member extending along the circumferential direction at a radial position R 2 , and an inner circumferential member extending along the circumferential direction at a radial position R 1 . The ratio of R 1  to R 2  is about 0.8≦(R 1 /R 2 )&lt;1. A plurality of substantially cylindrical elements are connected with the inner circumferential member and the outer circumferential member. In certain embodiments, the shear band has a shear efficiency of at least about 50 percent. In addition, other variations as previously described may also be applied. 
         [0007]    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 
         [0008]    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: 
           [0009]      FIG. 1A  is an exemplary embodiment of the present invention that includes a non-pneumatic wheel incorporating an embodiment of a shear band. 
           [0010]      FIG. 1B  is a perspective view of a section of the exemplary shear band of  FIG. 1A  taken at the location so identified in  FIG. 1A . 
           [0011]      FIG. 2A  is another exemplary embodiment of the present invention that includes a non-pneumatic wheel incorporating an embodiment of a shear band. 
           [0012]      FIG. 2B  is a perspective view of a section of the exemplary shear band of  FIG. 2A  taken at the location so identified in  FIG. 2A . 
           [0013]      FIG. 2C  is a cross-sectional view taken along lines  3 - 3  of the exemplary embodiment of  FIG. 3A . 
       
    
    
     DETAILED DESCRIPTION 
       [0014]    Objects and advantages of the invention will be set forth in the following description, or may be apparent from the description, or may be learned through practice of the invention. Repeat use of reference characters throughout the present specification and appended drawings is intended to represent same or analogous features or elements of the invention. 
         [0015]    An exemplary embodiment of a wheel  110  according to the present invention is shown in  FIG. 1A  with a portion of wheel  110  being shown in  FIG. 1B . Wheel  110  defines radial directions R, circumferential directions C ( FIG. 1A ), and axial directions A ( FIG. 1B ). Wheel  110  includes a hub  120  connected to a shear band  140  by multiple support elements  130 . Shear band  140  includes multiple cylindrical elements  170  that are spaced circumferentially about shear band  140 . Hub  120  provides for the connection of wheel  110  to a vehicle and may include a variety of configurations for connection as desired. For example, hub  120  may be provided with connecting lugs, holes, or other structure for attachment to a vehicle axle and is not limited to the particular configuration shown in  FIG. 1A . Support elements  130  connect hub  120  to shear band  140  and thereby transmit the load applied to hub  120 . As with hub  120 , support elements  130  may take on a variety of configurations and are not limited to the particular geometries and structure shown in  FIG. 1A . In addition, using the teachings disclosed herein, one of skill in the art will understand that tread or other features may be readily added to the outer circumferential surface  155 . 
         [0016]    Cylindrical elements  170  are positioned between an outer member  150  and an inner member  160 . In one embodiment, for example, members  150  and  160  may be constructed from a metal element encircled as shown in  FIG. 1A . By way of further examples, steel as might be used in the construction of springs, or carbon based filaments may also be utilized for the fabrication of members  150  and  160 . While elastomeric materials can also be used, the utilization of non-elastomeric materials for members  150  and  160  provides for extreme temperature applications such as a polar or lunar environment where elastomeric materials may become too rigid or brittle. For example, shear bands (including wheels incorporating such members) capable of functioning at temperatures as low as 100 degrees Kelvin should be achievable where elastomeric constructions are avoided. 
         [0017]    Focusing on  FIGS. 1A and 1B , for this particular exemplary embodiment, cylindrical elements  170  are each constructed from a relatively short cylinder. Although shown as perfectly circular cylinders in the figures, other configurations may be used. For example, oval or elliptical configurations may be employed and “cylinder” or “cylindrical” as used herein encompasses these and other shapes for a cylinder that may not be perfectly circular and may have different relative lengths from that shown. As with members  150  and  160 , cylindrical elements  170  may be constructed from a variety of relatively resilient, materials including again, for example, metal or carbon-based filaments, as well as elastomeric and polymer based materials where temperatures so allow. In addition, the present invention is not limited to cylindrical elements  170  having the relative widths along the axial direction that are shown in the figures. Instead, different widths may be use relative to the axial width of the cylindrical members  150  and  160 . For example, whereas five cylindrical elements  170  are shown across the axial width of members  150  and  160 , a different number of cylindrical elements  170  may be used with varying widths for the cylindrical elements  170 . Furthermore, although cylindrical elements  170  may be positioned immediately adjacent to one another along the axial direction as shown in  FIG. 3 , larger gaps or spacing may also be used along the axial direction. Alternatively, elements  170  may be constructed to overlap as discussed with regard to another exemplary embodiment below. 
         [0018]      FIG. 1B  illustrates a perspective, sectional view of shear band  140 . Notably, fasteners are not used in this exemplary embodiment. Instead, cylindrical elements  170  are connected directly to the circumferential, outer and inner members  150  and  160 . By way of example, cylindrical elements  170  could be welded or adhered to members  150  and  160 , or cylindrical elements  170  could be formed integrally with such members. Alternatively, various mechanical fasteners may be employed to connect cylindrical elements  170  as will be discussed below. 
         [0019]    Turning now to  FIGS. 2A ,  2 B, and  2 C, cylindrical elements  270  are shown arranged in rows  276  and  278  ( FIG. 2 ) that are overlapping along the axial directions A. Again, however, the present invention includes multiple other arrangements of cylindrical elements  270  between members  250  and  260 . For example, cylindrical elements  270  could be random, parallel, staggered, offset, overlapping rows, non-overlapping rows, aligned in rows that are not parallel to axial directions A, and so forth. As will be discussed later, cylindrical elements  270  provide a shear layer during operation that may be achieved by a variety of geometries and configurations that are within the scope of the present invention. Additionally, the axis of each cylindrical element  270  is shown as basically parallel to axial directions A. However, orientations that are not parallel may also be employed. As such, the configuration of  FIGS. 2A through 2C  emphasizes yet another exemplary embodiment of the present invention. Again, using the teachings disclosed herein, one of skill in the art will understand that multiple constructions and geometries may be used to provide the cylindrical elements between outer and members to create a shear band according to the present invention. 
         [0020]      FIG. 2B  illustrates a perspective, sectional view of shear band  240 , and  FIG. 2C  illustrates a cross-section. Notably, fasteners  274  are used in this exemplary embodiment. More specifically, cylindrical elements  270  are secured by fasteners  274  that extend through the outer and inner members  250  and  260 . It should be understood that multiple other types of fasteners or techniques may be used to secure the position of cylindrical elements  270 , and the present invention is not limited to the use of fasteners  274 . More specifically, for connecting cylindrical elements  270  to members  250  and  260 , constructions may include rivets, epoxy, or molding as unitary constructions as previously discussed. 
         [0021]    Although not limited thereto, the shear band of the present invention has particular application in the construction of wheels including, but not limited to, non-pneumatic tires and other wheels that do not require pneumatic pressure for structural support. For example, in a pneumatic tire, the ground contact pressure and stiffness are a direct result of the inflation pressure and are interrelated. However, a shear band of the present invention may be used to construct a wheel or tire that has stiffness properties and a ground contact pressure that are based on their structural components and, advantageously, may be specified independent of one another. Wheels  110  and  210  provide examples of such constructions. In addition, and advantageously, because the present invention includes structures and geometries for a shear band construction that are not limited to elastomeric (e.g. rubber) or polymer-based materials, the present invention provides for the construction of a wheel that may be used in extreme temperature environments. As used herein, extreme temperature environments includes not only environments experiencing temperatures that would be unacceptable for elastomeric or polymer-based materials but also includes environments where large temperature fluctuations may occur. 
         [0022]    Returning to  FIG. 1A , for example, it will be understood from the figures and description provided above that outer member  150  is longer circumferentially than the inner member  160  and both are relatively inextensible. Accordingly, in operation under an applied load to wheel  110 , the shearing of cylindrical elements  170  between the members  150  and  160  allows the shear band  140  to deform to provide a greater contact area with the travel surface (e.g. ground). 
         [0023]    More specifically, cylindrical elements  170  collectively act as a shear layer having an effective shear modulus G eff . The relationship between this effective shear modulus G eff  and the effective longitudinal tensile modulus E im  of the outer and inner members  150  and  160  controls the deformation of the shear band  140  under an applied load. When the ratio of E im /G eff  is relatively low, deformation of the shear band under load approximates that of the homogeneous member and produces a non-uniform contact pressure with the travel surface. However, when the ratio E im /G eff  is sufficiently high, deformation of the annular shear band  140  under load is essentially by shear deformation of the shear layer (i.e. cylindrical elements  170 ) with little longitudinal extension or compression of the inextensible members  150  and  160 ). Perfectly inextensible members  150  and  160  would provide the most efficient structure and maximize the shear displacement in the shear layer. However, perfect inextensibility is only theoretical: As the extensibility of members  150  and  160  is increased, shear displacement will be reduced as will now be explained in conceptual terms below. 
         [0024]    In the contact region, the inner member  160 , located at a radius R 1 , is subjected to a tensile force. The outer member  150 , located at a radius R 2 , is subjected to an equal but opposite compressive force. For the simple case where the outer and inner members  150  and  160  have equivalent circumferential stiffness, the outer member  150  will become longer by some strain, e, and the inner member  160  will become shorter by the some strain, −e. For a shear layer having a thickness h, this leads to a relationship for the Shear Efficiency of the bands, defined as: 
         [0000]    
       
         
           
             
               
                 
                   
                     Shear 
                      
                     
                         
                     
                      
                     Efficiency 
                   
                   = 
                   
                     ( 
                     
                       1 
                       - 
                       
                         
                           e 
                            
                           
                             ( 
                             
                               
                                 R 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                               + 
                               
                                 R 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             ) 
                           
                         
                         h 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    It can be seen that for the perfectly inextensible members, the strain e will be zero and the Shear Efficiency will be 100%. 
         [0025]    The value of the strain e can be approximated from the design variables by the equation below: 
         [0000]    
       
         
           
             
               
                 
                   e 
                   = 
                   
                     
                       
                         G 
                         eff 
                       
                        
                       
                         L 
                         2 
                       
                     
                     
                       8 
                        
                       
                           
                       
                        
                       
                         R 
                         2 
                       
                        
                       Et 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0026]    For example, assume we have a proposed design with the following values:
       h=10 mm (radial distance between bands  50  and  60 )   G eff =4 N/mm2 (effective shear stiffness between the bands)   L=100 mm (contact patch length necessary for design load)   R 2 =200 mm (radial distance to outer member)   R 1 =190 mm (radial distance to inner member)   E=20,000 N/mm2 (tensile modulus for both members  150  and  160 )   t=0.5 mm (thickness for both members  150  and  160 )
 
Calculating for e using E:
       
 
         [0000]    
       
         
           
             e 
             = 
             
               
                 
                   
                     ( 
                     10 
                     ) 
                   
                    
                   
                     
                       ( 
                       100 
                       ) 
                     
                     2 
                   
                 
                 
                   8 
                    
                   
                     ( 
                     200 
                     ) 
                   
                    
                   
                     ( 
                     
                       20 
                       , 
                       000 
                     
                     ) 
                   
                    
                   
                     ( 
                     0.5 
                     ) 
                   
                 
               
               = 
               0.0025 
             
           
         
       
     
         [0000]    The shear efficiency can then be calculated as: 
         [0000]    
       
         
           
             
               
                 
                   
                     Shear 
                      
                     
                         
                     
                      
                     efficiency 
                   
                   = 
                   
                     
                       1 
                       - 
                       
                         
                           0.0025 
                            
                           
                             ( 
                             
                               190 
                               + 
                               200 
                             
                             ) 
                           
                         
                         10 
                       
                     
                     = 
                     0.9025 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Thus, the efficiency in this case is approximately 90%. 
         [0034]    The above analysis assumes that outer and inner members  150  and  160  have identical constructions. However, the thickness and/or the modulus of members  150  and  160  need not be the same. Using the principles disclosed herein, one skilled in the art can readily calculate the strains in members  150  and  160  and then calculate the shear efficiency, using the above approach. A Shear Efficiency of at least 50% should be maintained to avoid significant degradation of the contact pressure with the travel surface. Preferably, a Shear Efficiency of at least 75% should be maintained. 
         [0035]    Accordingly, as sufficient Shear Efficiency is achieved, contact pressure with the travel surface becomes substantially uniform. In such case, an advantageous relationship is created allowing one to specify the values of shear modulus G eff  and the shear layer thickness h for a given application: 
         [0000]        P   eff   *R   2   =G   eff   *h    (4) 
       Where: 
       [0000]    
       
         
           
             P eff =predetermined ground contact pressure 
             G eff =effective shear modulus of columnar elements  170  within members  150  and  160   
             h=thickness of the shear layer—i.e. radial height of posts  170   
             R 2 =radial position of the outer member  150 
 
As one of skill in the art will appreciate using the teachings disclosed herein, the above relationship is useful in the design context because frequently P eff  and R 2  are known—leaving the designer to optimize G eff  and h for a given application.
 
           
         
       
     
         [0040]    The behavior of shear layer  140  and, more specifically, the effective shear modulus G eff  may be modeled using an approach as will now be described. Assuming that inextensible member  150 , inextensible member  160 , and cylindrical elements  170  are each uniform in physical properties along the axial directions A and that cylindrical elements  170  deform predominantly in shear along circumferential directions C, wheel  110  can be modeled as a wire-based structure (i.e. beam and truss elements) with a two-dimensional planar model that is one unit (e.g. one mm) in width along the axial directions A. As part of such approach, a single cylindrical element is modeled as a single cylinder that is constrained at one point (node) and then subjected to a non-rotational, tangential displacement at a point (node) on the opposite side of the cylinder (i.e. the nodes are located on the respective ends of a diameter to the two-dimensional, planar model of the cylinder). Using this model, the reaction force can be calculated and used to determine the equivalent effective shear modulus as follows: 
         [0000]        G=τ/γ   (5) 
       Where: 
       [0000]    
       
         
           
             G=shear modulus, in N/mm 2 , 
             τ=shear stress, in N/mm 2 , 
             γ=shear angle, in radians.
 
The shear stress τ is calculated using the following familiar equation:
 
           
         
       
     
         [0000]      τ= F/A    (6) 
       Where: 
       [0000]    
       
         
           
             F=reaction force computed by finite element analysis on the single cylinder model described above, in N, 
             A=tributary area in the circumference and depth directions for one cylinder, in mm 2 . 
           
         
       
     
         [0046]    Limiting the finite element model to 1.0 mm in depth as mentioned above, area A can be calculated in terms of the radius of the annular member and the number of cylinders using the following equation: 
         [0000]        A= 2 πR/N    (7)       where:   R=radius of the annular member, in mm,   N=number of cylinders.
 
The shear angle is determined in terms of the predefined displacement imposed on the cylinder and the diameter of the cylinder, as follows:
         
         [0000]      γ=tan −1 (δ/ h )   (8)       where:   δ=displacement imposed at the top node of the cylinder, in mm,   h=diameter of a cylinder, in mm.         
         [0053]    Combining Equations 2 to 5, the effective shear modulus is given by the following equation: 
         [0000]        G=FN /(2 πR  tan −1 (δ/ h ))   (9) 
         [0000]    The reaction force F depends on the material properties of the cylinder (i.e. Young&#39;s modulus E and Poisson&#39;s ratio v) and the thickness of the cylinder t. The designer of a shear band can therefore choose design variables E, v, t, h, and N, select a displacement δ, and then compute the reaction force F by finite element analysis of a single cylinder (using the model just described above) in order to obtain the desired effective shear modulus. 
         [0054]    Using this approach, modeling of a two dimensional wheel  110  having a construction similar to  FIG. 1  was undertaken as will be understood by one of skill in the art using the teachings disclosed herein. The geometry of wheel  110  was defined into wire based structures having the components of cylindrical elements  170 , outer and inner members  150  and  160  (each modeled using Timoshenko quadratic beam finite elements), support elements  130  (modeled as a linear truss element with no compression), and a ground represented as a rigid wire with a reference point. Boundary conditions included the radially inner end of each support element  130  constrained in displacement, and the interaction between the ground and outer member  150  was defined as a contact with frictionless tangential behavior and hard contact normal behavior. During simulation, the ground was moved upward gradually by a predetermined distance. As will be understood by one of skill in the art using the teachings disclosed herein, commercial software sold under the name Abaqus/CAE (Version 6.6-1) was used to conduct the finite element analysis and the following results were obtained: 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE ONE 
               
               
                   
               
               
                   
                   
                   
                   
                   
                 Shear 
               
               
                 Displacement d 
                 Thickness t 
                 Diameter D 
                 Reaction force F 
                 Area (depth = 1 mm), A 
                 Modulus G 
               
               
                 (mm) 
                 (mm) 
                 (mm) 
                 (N) 
                 (mm{circumflex over ( )}2) 
                 (MPa) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 20 
                 0.5 
                 40 
                 8.21 
                 40 
                 0.44 
               
               
                 20 
                 1 
                 40 
                 57.1 
                 40 
                 3.08 
               
               
                 20 
                 1.5 
                 40 
                 212.2 
                 40 
                 11.44 
               
               
                 20 
                 2 
                 40 
                 523.3 
                 40 
                 28.22 
               
               
                 20 
                 0.5 
                 60 
                 2.22 
                 60 
                 0.11 
               
               
                 20 
                 1 
                 60 
                 17.7 
                 60 
                 0.92 
               
               
                 20 
                 1.5 
                 60 
                 59.8 
                 60 
                 3.10 
               
               
                 20 
                 2 
                 60 
                 141.4 
                 60 
                 7.32 
               
               
                 20 
                 0.5 
                 48.26 
                 4.43 
                 48.26 
                 0.23 
               
               
                 20 
                 1 
                 48.26 
                 35.5 
                 48.26 
                 1.87 
               
               
                 20 
                 1.5 
                 48.26 
                 119.5 
                 48.26 
                 6.30 
               
               
                 20 
                 2 
                 48.26 
                 283 
                 48.26 
                 14.93 
               
               
                   
                   
                   
                   
                 Area is larger to 
               
               
                   
                   
                   
                   
                 account for space 
               
               
                   
                   
                   
                   
                 between tubes 
               
               
                 20 
                 0.5 
                 48.26 
                 4.43 
                 55 
                 0.23 
               
               
                 20 
                 1 
                 48.26 
                 35.5 
                 55 
                 1.85 
               
               
                 20 
                 1.5 
                 48.26 
                 119.5 
                 55 
                 6.23 
               
               
                 20 
                 2 
                 48.26 
                 283 
                 55 
                 14.75 
               
               
                   
               
             
          
         
       
     
         [0055]    By way of example, the results indicate that the effective shear modulus G eff  increases as the thickness t of the cylindrical elements  170  increases and decreases as the diameter of the cylindrical elements  170  increases. More importantly, a method whereby a designer can develop an acceptable shear modulus G eff  for a shear band constructed according to the present invention is provided. 
         [0056]    Finally, it should be noted that advantages of the present invention are principally obtained where the relative radial distance between the inner and outer members fall within a certain range. More specifically, preferably the following relationship is constructed: 
         [0000]      0.8≦( R   1   /R   2 )&lt;1   (10) 
         [0000]    where: 
         [0057]    R 2 =radial position of the outer member (e.g. the distance to the outer member from the axis of rotation or focus of the radius defined by such member) (see  FIG. 2C ) 
         [0058]    R 1 =radial position of the inner member (e.g. the distance to the inner member from the axis of rotation or focus of the radius defined by such member) (see  FIG. 2C ) 
         [0059]    While the present subject matter has been described in detail with respect to specific embodiments 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.