Patent Publication Number: US-10786961-B2

Title: Adjusting expandable rim width using a band

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 14/868,886, filed on Sep. 29, 2015, which claims priority to U.S. Provisional Patent Application No. 62/194,861 filed Jul. 21, 2015 and entitled “Expandable Rim Width Insert”, the entire disclosure of which is incorporated herein by reference. 
    
    
     FIELD OF THE DISCLOSURE 
     The field relates generally to systems and methods for adjusting a rim width of an expandable rim suited for mounting a tire or a casing onto a machine. 
     BACKGROUND 
     Retreaded tires provide an economical way to gain additional use from tire casings after the original tread or retread has become worn. According to a method of retreading sometimes referred to as cold process retreading, a worn tire tread and other materials on a used tire are removed to create a buffed, generally textured, treadless surface along the circumference of the tire casing to which a new tread may be bonded. 
     The tire casing may be inspected for injuries, some of which may be skived and filled with a repair gum while others may be severe enough to warrant rejection of the tire casing. After completion of the skiving process, the buffed surface may be sprayed with cement that provides a tacky surface for application of bonding material and new tread. Next, a layer of cushion gum may be applied to the back, i.e., the inside surface of a new tread, or alternatively, the layer of cushion gum may be applied directly to the tacky surface on the tire casing. There are other methods that may eliminate the need for cement or cushion gum. The cushion gum is a layer of uncured rubber material. The cushion gum and tread may be applied in combination about the circumference of the tire casing to create a retreaded tire assembly for curing. As an alternative, a length of tire tread may be wrapped around the tire casing with the cushion gum already applied. The cushion gum may form the bond between the tread and the tire casing during curing. 
     Certain retreading processes such as the buffing of the tire casing may be carried out on specialized equipment that rotatably mount the casing onto an expandable rim. The expandable rim may include various sections that move radially outwardly with respect to a central hub to expand to a circumference of the rim and sealably engage the beads of the casing, which is inflated to provide a resilient surface that can be buffed or otherwise processed. The machine may include a rasp that can be applied to the surface of the tire to remove rubber. Because the circumference of a tire casing can more easily be measured by the operator, the desired final radius of the tire casing may be identified in relation to the final circumference of the tire. 
     Expandable rims have a rim width that is fixed for a given machine. However, such fixed widths are not suitable for processing tires or casings having different widths, thus necessitating the purchase and installation of expandable rims having different widths between production runs of different tires. In some instances, the width of such rims maybe adjusted by cutting and welding the expandable rims to adjust an initial width of the rim, for example shorten the initial width of the rim. This is costly and also permanently changes the width of the expandable rim so that the rim is no longer usable with tires having a width equal to the initial width. 
     SUMMARY 
     Some embodiments include systems and methods for adjusting a width of a rim enabling mounting of tires of various widths on the rim, and in particular to adjusting a width of an expandable rim by positioning a band around the expandable rim contiguous with a flange segment of the rim so that the band has an adjusted rim width different than an original rim width. 
     In some embodiments, an expandable rim for mounting a tire thereon includes a base portion including a cylindrical structure and a rim portion. The base portion defines an axial channel therethrough. A rotatable hub is positionable through the axial channel to mount the rim thereon. The rim portion includes a rim segment, a first flange segment positioned on one side of the rim segment and a second flange segment positioned on an opposite side of the rim segment. The rim segment defines a circular curvature. The rim segment has an original rim width measured along a rotation axis of the rim between inward facing surfaces of the first flange segment and the second flange segment. The expandable rim is configured so that it may be expanded in a direction perpendicular to the rotation axis of the rim. A band is positioned around a circumference of the rim segment. The band is positioned contiguous with an inward facing surface of the first flange segment. The rim portion has an adjusted rim width measured along the rotation axis between a band inward facing surface and the inward facing surface of the second flange segment. The adjusted rim width is different from the original rim width. 
     In some embodiments, a machine for retreading tires includes a hub being rotatable with respect to the machine. The hub has a generally conical shape that is moveable axially along a rotation axis. An expandable rim is disposed around the moveable hub. The expandable rim includes a plurality of shoes arranged symmetrically around the hub. Each of the plurality of shoes includes a base portion and a rim portion. The base portion is positioned on the hub. The rim portion includes a rim segment and a flange segment on either side of the rim segment. The rim segment has an original rim width measured along the rotation axis between inward facing surfaces of the flange segments. A belt surrounds each of the plurality of shoes. The belt is disposed along the rim segment of the plurality of shoes. A band is positioned around a circumference of the rim segment on the belt. The band is positioned contiguous with an inward facing surface of the flange segment. The expandable rim is configured so that it may be expanded in a direction perpendicular to the rotation axis of the rim. An adjusted rim width measured along the rotation axis between a band inward facing surface and an inward facing surface of the flange segment at another side of the rim portion is different than the original rim width. 
     In some embodiments, a method for modifying a width of an expandable rim for use in a tire retreading machine includes assembling a plurality of shoes to form a cylindrical rim structure. Each of the plurality of shoes includes a rim portion and a base portion. The rim portion includes a rim segment, a first flange segment on one side of the rim segment and a second flange segment on an opposite side of the rim segment. The rim segment has an original rim width measured along the rotation axis between inward facing surfaces of the first flange segment and the second flange segment. A band is positioned around a circumference of the cylindrical rim structure on the rim segment of each of the plurality of shoes. The band is positioned contiguous with the first flange segment of each of the plurality of shoes. The expandable rim has an adjusted rim width measured along the rotation axis between a band inward surface and an inward facing surface of the second flange segment which is different than the original rim width. 
     In some embodiments, a process for buffing tires having varying widths using a buffing machine including an expandable rim for mounting the tire thereon is provided. The expandable rim includes a base portion and a rim portion. The rim portion includes a rim segment and a pair of flange segments positioned orthogonally to the rim segment on either side of the rim segment. The expandable rim has an original rim width measured between the flange segments. The process includes the steps of positioning a band contiguous with an inward facing surface of any one of the flange segment of the pair of flange segments. The positioning of the band causes the rim segment to have an adjusted rim width measured between a band inward facing surface of the band and an inward facing surface of the opposite flange segment. A tire having a tire width equal to the adjusted rim width is mounted on the rim segment. A first bead of the tire is positioned adjacent to the band inward facing surface and a second bead of the tire opposite the first bead is positioned adjacent to the inward facing surface of the opposite flange segment. The tire is the buffed on the buffing machine. 
     All combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being included within this disclosure. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being included within this disclosure. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The foregoing and other features of the present disclosure will become more fully apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. Understanding that these drawings depict only several implementations in accordance with the disclosure and are therefore, not to be considered limiting of its scope, the disclosure will be described with additional specificity and detail through use of the accompanying drawings. 
         FIG. 1  is a side cross-section view of a rim having an adjustable rim width, according to an embodiment. 
         FIG. 2  is a front cross-section of the rim of  FIG. 1  taken along the line AA shown in  FIG. 1 . 
         FIG. 3A  is a side view of one embodiment of a band, and  FIG. 3B  is a side view of another embodiment of a band that can be used to adjust a width of a rim. 
         FIG. 4  is a schematic illustration of a tire buffing machine according to an embodiment. 
         FIG. 5  is an exploded view of an embodiment of an expandable rim assembly that can be used in the tire buffing machine of  FIG. 4 . 
         FIG. 6  is a perspective view of an embodiment of a shoe which can be included in the expandable rim assembly of  FIG. 5 . 
         FIG. 7  is a side cross-section of the shoe of  FIG. 6  with a belt and a band for adjusting a width of a rim segment of the shoe positioned thereon. 
         FIG. 8  is a schematic flow diagram of an embodiment of a method for modifying the width of an expandable rim. 
         FIG. 9  is a schematic flow diagram of a process for buffing a tire, according to an embodiment. 
     
    
    
     Reference is made to the accompanying drawings throughout the following detailed description. In the drawings, similar symbols typically identify similar components, unless context dictates otherwise. The illustrative implementations described in the detailed description, drawings, and claims are not meant to be limiting. Other implementations may be utilized, and other changes may be made, without departing from the spirit or scope of the disclosure. It will be readily understood that the aspects of the present disclosure, as generally described herein, and illustrated in the figures, can be arranged, substituted, combined, and designed in a wide variety of different configurations, all of which are explicitly contemplated and made part of this disclosure. 
     DETAILED DESCRIPTION 
     Some embodiments relate to systems and methods for adjusting a width of a rim enabling mounting of tires of various width on the rim, and in particular to adjusting a width of an expandable rim by positioning a band around the rim contiguous with a flange segment of the rim so that the band has an adjusted rim width different than an original rim width. 
       FIG. 1  is a side-cross section and  FIG. 2  is a front cross-section of a rim  10  which has an adjustable rim width. The rim  10  is configured to be mounted on a rotatable hub (not shown), for example the hub  110  included in the buffing machine  100  described with respect to  FIG. 4 . The rim  10  includes a base portion  20  and a rim portion  40 . The base portion  20  includes a generally cylindrical structure defining an axial channel  22  therethrough. The rim  10  can be mounted on the hub by inserting the hub through the axial channel  22  and securing the hub to an inner surface of the axial channel  22 . In some embodiments, notches, grooves, indents, mounting apertures, holes, a snap-fit mechanism or any other structures can be defined on an inner surface of the axial channel  22  for securing the rim  10  to the hub. Furthermore, fasteners (e.g., screws, bolts, nuts, etc.) can be used to removably couple the rim  10  to the hub. 
     The rim  10  also includes a rim portion  40  positioned around the base portion  20 . The rim portion  40  includes a rim segment  42 , a first flange segment  44   a  and a second flange segment  44   b  (collectively referred to herein as “the flange segments  44 ”) positioned orthogonally on either side of the rim segment  42  and extending away from the rim segment  42 . The rim segment  42  and the flange segments  44  generally define a U-shape for securing a tire on the rim segment  20  between the flange segments  44 . An outer surface or drum surface  45  of the rim segment  42  defines a circular curvature. A generally circular tire can be mounted on the drum surface  45  of the rim segment  42 . 
     The rim segment  42  has an original rim width W measured along a rotation axis A R  of the rim  10  between inwards facing surfaces of the opposing flange segments  44 . The flange segments  44  are configured to abut against or be contiguous to at least a portion of edges of a tire having a tire width approximately equal to the width W between a first inward facing surface  47   a  of the first flange segment  44   a  and a second inward facing surface  47   b  of the second flange segment  44   b , thereby securely retaining the tire on the outer surface of the rim segment  42 . However, tires having smaller tire widths than the rim width W will not be securely retained by the flange segments  44 , and can slide along the rotational axis of the rim  10  along the outer surface  45  of the rim segment  42  which is undesirable. 
     A first band  60   a  having a first band width W B  is positioned around the rim segment  42  of the rim portion  40 . The first band  60   a  is positioned contiguous to the first inward surface  47   a  of the first flange segment  44   a , but in some embodiments, the first band  60   a  can be positioned contiguous to the second inward facing surface  47   b  of the second flange segment  44   b . After the positioning of the first band  60   a , the rim segment has an adjusted rim width W′ measured between a first band inward facing surface and the second inward facing surface  47   b  of the second flange segment  44   b  which is different, for example smaller than the original rim width W. 
     The adjusted rim width W′ can be substantially similar to the width of a tire which has a smaller rim width than the original rim width W. This allows a tire having a smaller width than the original rim width W to be mounted on the rim by securing between the first band  60   a  and the second flange segment  44   b . The first band width W B  can be adjusted or varied to accommodate tires having a range of widths. In some embodiments, the first band  60   a  has a first band thickness T 1  equal to a distance H between a top edge  48   a  of the first flange segment  44   a  and the drum surface  45  of the rim segment  42 . That is the first band  60   a  extends from the drum surface  45  to the top edge  48   a  of the first flange segment  44   a.    
     In some embodiments, a second band  60   b  can also be positioned around the rim segment  42  of the rim portion  40 . The second band  60   b  can be substantially similar to the first band  60   a . In some embodiments, the second band  60   b  is positioned contiguous to the inward facing surface  47   b  of the second flange segment  44   b . The adjusted rim width W′ is then measured along the rotation axis of the rim  10  between a first band inward facing surface of the first band  60   a  and a second band inward facing surface of the second band  60   b.    
     Each of the first band  60   a  and the second band  60   b  are unattached to the first flange segment  44   a  and the second band segment  44   b  i.e., are not coupled using any coupling mechanism (e.g., fasteners such as bolts, screws, etc.) to the flange segments  44  or rim segment  42 . The first band  60   a  and the second band  60   b  can be formed from stretchable materials (e.g., include the band  160  as described herein) and configured to exert a compressive force on the rim segment  42  to retain the first band  60   a  and the second band  60   b  thereon. Furthermore, the flange segments  44  also serve as barriers for the first band  60   a  and the second band  60   b  preventing the first band  60   a  and the second band  60   b  from slipping off the rim segment  42 , thereby retaining the first band  60   a  and the second band  60   b  on the rim segment  42 . 
     In some embodiments, the rim  10  can include an expandable rim (e.g., the expandable rim  200  described with respect to  FIGS. 5-7 ). In some embodiments, the expandable rim  10  includes a plurality of shoes (e.g., the shoes  200  or  300  described with respect to  FIGS. 5 to 7 ) configured to be positioned symmetrically around the hub to form a cylindrical rim structure. Each of the plurality of shoes define a segment of the base portion  20  and the rim portion  40  which includes the rim segment  42  and the flange segment  44 , as described before herein. Each shoe has a circular curvature such that when the shoes are symmetrically positioned around the hub, each shoe defines a segment of the circular curvature of the rim segment  42 . In some embodiments, the first band  60   a  and/or the second band  60   b  is positioned on the rim segment of each of the plurality of shoes and adjacent to a flange segment of each of the plurality of shoes. Each shoe is radially displaceable relative to the hub, thereby adjusting a diameter of the rim  10 . 
     In some embodiments, a belt  70  or skirt can be positioned around the circumference of the expandable rim  10  on the rim segment of each of the plurality of shoes. The belt  70  can have a width equal to the width of the rim segment of each of the plurality of shoes and thereby, the rim segment of the expandable rim  10 . The belt  70  is configured to retain each of the plurality of shoes on the hub. For example, the belt  70  can be formed from a stretchable or elastic material and configured to exert a radially inward force on each of the plurality of shoes relative to the hub. The belt  70  therefore retains each of the plurality of shoes on the hub, but is stretchable to allow the shoes to be radially displaced outward relative to the hub, thereby allowing adjustment (e.g., increase) of the diameter of the rim  10  (i.e., allowing expansion of the rim). In some embodiments, the belt  70  is configured to a form a sealing contact with a tire positioned on the rim segment  42 , thereby allowing air to be filled and retained within the tire. 
     The belt  70  has a thickness T 2  which is substantially smaller than the distance H between the drum surface  45  of the rim segment  42  and the top edge (e.g., the top edge  48   a  of the first flange segment  44   a ) of the flange segments  44 . In some embodiments, the first band  60   a  and/or the second band  60   b  are positioned around the rim segment  42  on the belt  70  and in contact with a belt outer surface  75  which faces away from the drum outer surface  45 . Furthermore, a thickness T 1  of the first band  60   a  and/or the second band  60   b  can be equal to a distance measured from the top edge (e.g., the top edge  48   a  of the first flange segment  40   a ) of the flange segments  44  to the belt outer surface  75 . In some embodiments, the belt  70  has a belt width less than the original rim width and the first band  60   a  and/or the second band  60   b  are positioned adjacent to the belt  70  on the drum surface  45 . 
     Other suitable bands can be positioned around the rim segment  42  of the rim  10  to adjust the original rim width. For example,  FIG. 3A  shows a side view of a band  160  according to an embodiment. The band  160  can be used as the first band  60   a , the second band  60   b  or any other band described herein. The band  160  can include a continuous circular ring which is positioned circumferentially on a rim segment of a rim (e.g., the rim segment  42  of the rim  10 ) as described herein. In some embodiments, the band  160  can be formed from a stretchable material, for example rubber, vulcanized rubber, silicone, a molded polymer or any other suitable stretchable and strong material. The band  160  can be stretched radially outwards and over the first flange segment  44   a  to position the band  160  on the rim segment of the rim (e.g., the rim segment  42  of the rim  40 ) or otherwise a belt (e.g., the belt  70 ) positioned on the rim segment. In some embodiments in which the rim includes an expandable rim, the position of the band  160  is performed while the expandable rim is in an unexpanded configuration. In some embodiments, the band  160  is positioned on the expandable rim once the expandable rim is in its expanded configuration. Expanding of the rim to a larger diameter also stretches the band so that the band continues to be retained on the rim segment of the rim while allowing the expandable rim to expand. In some embodiments, the band  160  is stretchable to allow a change in an initial diameter of the band by 1 inches, 2 inches, 3 inches, 4 inches or 5 inches inclusive of all ranges and values therebetween. The band may be configured such that its initial smaller diameter may be increased to a larger diameter while still maintaining substantially the same wall thickness or reducing the rim width by a predetermined amount. 
       FIG. 3B  is a side view of a band  260  according to an embodiment which can be used to adjust the width of a rim segment of a rim, for example the rim  10 . The band  260  includes a plurality of band segments  262  which can be positioned around the circumference of a rim (e.g., the rim  10 ). Each of the plurality of band segments  262  can define a circular curvature corresponding to the circular curvature of the rim segment (e.g., the rim segment  42  of the rim  10 ). Each of the plurality of band segments  262  are configured to be positioned on a segment of the circumference of the rim segment. For example, the rim can include an expandable rim including a plurality of shoes (e.g., the plurality of shoes  202  or  300 ), and each of the plurality of band segments  262  and can have an arc length which is smaller or equal to an arc length of each shoe of the plurality of shoes. 
     Furthermore, each of the plurality of band segments  262  can have the same circular curvature as the rim segment of each of the plurality of shoes. It should be appreciated that while  FIG. 3B  shows the plurality of band segments  262  positioned adjacent to each other with a gap therebetween, in some embodiments, each of the plurality of band segments  262  can define an arc length so that each of the plurality of band segments  262  abut against an adjacent band segment  262 , for example when the plurality of band segments  262  are positioned on an expandable rim in its unexpanded configuration. Any number of band segments  262  can be included in the band  260 , for example 6, 8, 10, 12 or even more. In some embodiments, the number of band segments  262  corresponds to a number of shoes included in an expandable rim (e.g., the shoes  202  included in the expandable rim  200 ). Furthermore, the band  260  can be positioned on an expandable rim in its expanded or unexpanded configuration. 
     In some embodiments, the band segments  262  can be formed from an inelastic material such as metals (e.g., stainless steel, aluminum), plastics, rigid rubber, polymers, etc. Each of the plurality of band segments  262  are securely retained on the rim segment via a retaining member  264  can include, for example an O-ring, a garter spring, a band clamp or any other retaining member. The retaining member  264  is configured to retain or otherwise maintain the plurality of band segments  262  positioned around the circumference of the rim. 
     In some embodiments, each band segment  262  can be linked or coupled to an adjacent band segment  262  by a stretchable member (e.g., a rubber string or cord, a bungee cord, a spring, etc.) positioned on an end of the adjacent band segments  262 . In some embodiments, the stretchable member can be positioned through a channel (not shown) defined through each of the band segments  262 . In some embodiments, the stretchable member operatively couples the plurality of band segments  262  while allowing the band segments  262  to be radially displaced outwardly relative to each other for positioning or mounting on the rim segment of the rim, as described herein. Once mounted the stretchable member exerts a radially inward force on each of the band segments  262  to urge the band segments  262  towards the rim, thereby retaining each of the band segments  262  on the rim. In this manner, some embodiments permit the wall thickness to remain substantially the same (for reducing the rim width) while the rim is expanded from a smaller diameter to a larger diameter. 
       FIG. 4  is a schematic illustration of a buffing machine  100  having a tire  102  mounted on a rotating, expandable rim  104 . As shown, the machine  100  may be a standalone, dedicated machine for buffing tires prior to a retreading operation, or may alternatively be part of a retreading machine that can perform other operations, such as installing a new tread onto the casing. 
     During operation, the expandable rim  104  and tire  102  rotate at a constant angular rate of rotation, for example, 60-90 revolutions per minute (RPM), but may also rotate at a variable speed. An electric motor  106  is connected to a hub  108  of the expandable rim  104  to provide the rotation of the tire  102 , but any other type of rotary actuator may be used, such as hydraulically or pneumatically powered motors, or even mechanical arrangements providing a rotating output. As shown, the hub  108  includes timing features that are picked up by an angular displacement encoder  110  associated with the machine  100 . A control signal of the motor  106  may be provided by an electronic controller  112  via a motor control conduit  114 , while information indicative of the rotation of the hub  108  may be provided to the controller  112  by the encoder  110  via a tire rotation information conduit  116 . 
     The machine  100  further includes a buffing tool or rasp  118 . The rasp  118  may be any device capable of cutting material from the tire  102  as it rotates. In an embodiment, the rasp  118 , can include a laminated steel drum having saw teeth arranged around its outer cylindrical surface. 
     Although many configurations are possible, the rasp  118  is connected to the machine  100  at the end of an arm  122 . A rasp rpm sensor  132  is communicatively coupled to the rasp motor  130  and the electronic controller  112  via rasp rpm conduit  134 , and configured to provide information on rasp  118  rotational speed to the electronic controller  112 . The position of the arm  122  and of the rasp  118  relative to the tire  102  can be adjusted by a rasp actuator  124 . The rasp actuator  124  positions a rasp head to sweep a circular arc across a face of the tire  102  at a defined radius. A force thus derived is caused by the interference between the a face of the rasp  118  and the circumference of the tire  102  being buffed. There are other arrangements of the arm  122 , rasp actuator  124 , and other parts of the cutting assembly that are known in the art and incorporated herein. This pressing or normal force effects removal of material from the tire  102  and is carried out in response to command signals provided by the electronic controller  112  via a rasp actuator control conduit  125 . In  FIG. 4 , an outer circumference  126  of the tire  102  is illustrated by dashed line. In that same figure, a cutting depth  128 , which is located radially inward from the outer circumference  126  relative to a center of the tire  102 , is shown in dash-dot-dashed line. 
     The electronic controller  112  is communicatively coupled to an operation panel  142  via an input panel conduit  148 . The input panel  142  includes an input device  146  (e.g., an alphanumeric keyboard, switches, buttons, etc.) and a display  144 . A user can input commands, for example rasp  118  cutting depth, tire rotation speed, tread pattern, etc. via the input device  146 . A cutting depth sensor  136  which can include a small rotatable wheel is positioned in contact with an outer surface of the tire  102  via a depth sensor mounting arm  138 . The cutting depth sensor  136  is communicatively coupled to the electronic controller  112  via depth sensor conduit  140 . While various sensors included in the buffing machine  100  are depicted as communicatively coupled to the electronic controller  112  via conduits, in some embodiments, each of the sensors, input panel  142  or otherwise electronic components can be wirelessly coupled to the electronic controller  112  (e.g., via Bluetooth®, Wi-Fi, or any other wireless communication protocol). 
     During a cutting operation, the rasp  118  is driven by a rasp motor  130  in a counter-rotational direction relative to the tire  102 . The motor  130  is controlled and monitored by the electronic controller  112  through a motor control conduit  131 . When the rasp  118  is in position at the cutting depth  128  and the rasp motor  130  is operating, material is removed from the outer portion of the tire  102  as the teeth or other cutting mechanism of the rasp  118  are pressed against the outer circumference  126  of the tire. To prevent rotation and to retain the tire  102  firmly on the expandable rim  104  during the cutting operation, the expandable rim  104  is placed in an expanded position such that a rubber skirt or belt (not shown) placed around an outer rim thereof sealably engages a bead of the tire  102  to seal the inner cavity of the tire  102  and inflate the tire  102  when air is pumped in its interior. The expandable rim  104  also laterally engages the bead of the tire  102  to ensure that the tire  102  maintains a proper inflated shape and is securely retained by the expandable rim  104  during the various operations that are performed on the tire  102 . 
     An exploded view of an expandable rim assembly  200  is shown in  FIG. 5 . The expandable rim assembly  200  may be associated with a machine (e.g., the buffing machine  100 ) in much the same way as the expandable rim  104  described above and shown in  FIG. 4 . The expandable rim assembly  200  is configured for use with a hub (e.g., the hub  108 ), which includes surfaces that push radially ramped portions of a plurality of shoes  202  that make up the expandable rim  200  radially outward, thus pushing them apart to expand the rim assembly  200 . 
     In the embodiment, the expandable rim assembly  200  includes the plurality of segmented shoes  202  that together, form a cylindrical rim structure  204 . Each of the plurality of segmented shoes  202  extends over an angle around the cylindrical rim structure  204 . As shown in  FIG. 5 , expandable rim includes twelve shoes  202  forming cylindrical structure  204  and the angle is about 30 degrees, but other angles and number of shoes can be used. Radially extending slits  206  extending through the cylindrical rim structure  204  result at the interfaces between adjacent shoes  202 . Each slit  206  is covered by a respective support plate  208 , which has a generally curved shape that is consistent with an outer drum surface  210  of the cylindrical rim structure  204 . In the embodiment shown, each support plate  208  forms two posts  212 , each of which locates the support plate  208  on the outer surface  210  of the cylindrical structure  204  (also referred to herein as “drum surface  210 ”) by being inserted into a corresponding opening  214  formed by shallow cutouts or detents in the edges of the shoes  202  along the slits  206 . 
     A belt or skirt  216  having a generally cylindrical shape is placed around and covers the outer drum surface  210  of the cylindrical rim structure  204 . One or more (two shown) air conduits  220  provide compressed air to and from a nipple  222  through a series of aligned openings along an air path  224  to an air nozzle  226  that is connected to the belt  216  and disposed within the interior of a tire (e.g., the tire  102 ) when the tire is mounted onto the expandable rim assembly  200 . In this way, the tire can be inflated and deflated, as desired, by providing or evacuating air to/from the air nozzle  226 . Bolts  228  that engage nuts  230 , or a different fastening arrangement, can be used to retain the belt  216  around the cylindrical rim structure  204  such that the belt  216  is prevented from rotating relative to the cylindrical rim structure  204  and the shoes  202  are held together. 
       FIG. 6  is a perspective view of a shoe  300  and  FIG. 7  is a side cross-section thereof. The shoe  300  is suitable for use in an expandable rim, for example, in place of one or each of the shoes  202  that make up the expandable rim assembly  200  shown in  FIG. 5  and described above. The shoe  300  includes a base portion  302 , which is sometimes referred to as the shank and which is generally plate-shaped, and a rim portion  304 , which defines a circular segment of an expandable rim. The rim portion  304  includes a rim segment  306  and a flange segment  308 , which together form a structure having a generally U-shaped cross section, into which a tire is accommodated, in the known fashion. The rim segment  306  includes a drum surface  310  onto which other structures may be disposed such as, for example, the support plates  208  and/or portions of the inner belt  216 , when the shoe  300  has been assembled into an expandable rim assembly such as the expandable rim assembly  200  ( FIG. 5 ). 
     At the radially inward part of the shoe  300 , on the end of the base portion  302 , various features are formed that facilitate the mounting, retention, and relative motion of the shoe  300  with respect to a conical hub (e.g., the hub  108 ) around which the shoes  300  are positioned, when the rim is expanding or contracting during operation. It should be appreciated that although the interface features shown may be common across different expandable rim assemblies, other features than those shown here can be used. In the embodiment illustrated in  FIGS. 6 and 7 , the end of the base portion  302  that is the furthest away from the rim portion  304  forms a step  312  that is disposed next to a notch  314 . A ramp  316  formed at the bottom of a V-shaped channel  318  extends away from the end of the base portion  302 , towards the rim portion  304 , in a direction away from the step  312  along the bottom edge of the base portion  302 . When the shoe  300  is assembled into an expandable rim assembly, for example, the expandable rim assembly  200  ( FIG. 5 ), the ramp  316  and channel  318  matingly and slidably engage a rib  322  of a conical hub  324  that actuates the shoe  300  in the known fashion. 
     A perspective view of the shoe  300  with a portion of a set of bands  412  configured to be positioned adjacent to opposing flange segments  308  of the shoe  300 , is shown in  FIG. 6 . The bands  412  can include a continuous circular ring (e.g., the band  160 ) configured to be positioned around the cylindrical rim structure (e.g., the cylindrical rim structure  204 ) formed by the plurality of shoes  300  positioned adjacent to each other. In some embodiments, the bands  412  can include a plurality of band segments (e.g., the plurality of band segments  262 ) having an annular shape and a curvature that matches the curvature of the inside face  420  of each flange segment  308 . 
     In some embodiments, the set of bands  412 , for example, a circular ring or a band segment forming each of the set bands  412  has a rectangular cross section. The bands  412  have a bottom surface  432  and a top surface  434  such that the curvature of the bottom surface  432  is generally concentric with the curvature of the top surface  434 . The bands  412  extend over the same circular segment of the shoe  300  they are installed on to preserve unobstructed operation of the expandable rim assembly, for example, the assembly  200  discussed above. In some embodiments, the bands  412  can be formed from a stretchable material (e.g., rubber, vulcanized rubber, silicone rubber, polymers etc.) such that the bands  412  exert an inwardly radial force on the rim assembly which retains the bands  412  on the rim assembly. In embodiments in which the bands  412  include a plurality of band segments (e.g., the band segments  262 ), a retaining member, for example an O-ring, a garter spring, or a band clamp (e.g., the retaining member  264 ) can be positioned around the band segments. The retaining member exerts an inward radial force on the plurality of band segments thereby, retaining the band segments forming the bands  412  on the rim assembly. Each band segment can have an arc length equal or substantially equal to of an arc length of the rim segment  306  of the rim portion  304  of each shoe  300  (e.g., within +/−5% of the arc length of the each shoe  300 ). 
     Each of the bands  412  are unattached to the flange segments  308  i.e., are not coupled using any coupling mechanism (e.g., fasteners such as bolts, screws, etc.) to the flange segments  308  or rim segment  306 . For example, the bands  412  can be formed from stretchable materials (e.g., include the band  160  as described herein) and configured to exert a compressive force on the rim segment  306  to retain the bands  412  thereon. Furthermore, the flange segments  308  also serve as barriers for the bands  412  preventing the bands  412  from slipping off the rim segment  306 , thereby retaining the bands  412  thereon. 
     In some embodiments, the bands  412  can be positioned over a belt  216  disposed around the plurality of shoes  300 , as shown in  FIG. 7 , which can be assembled to form a rim, for example expandable rim assembly  200 . In some embodiments, a height H of the band  412  can extend from an outer surface of the belt disposed over the rim segment to a top edge of the flange segments  308 . Alternatively, the bottom surface  432  of the insert  412  may have a height H extending from the drum surface  310  to the top edge of the flanges segments  308  and provide a flush contact between the bottom surface  432  of the bands  412  and the drum surface  310 . In this alternate configuration, the bands  412  can be positioned adjacent the belt  216 . 
     In some embodiments in which the bands  412  include a plurality of band segments  412  a wall thickness T of each of the band segments  412 , which is measured as a distance between each band segment  412  extends from the inside face  420  of the respective flange segment  308  contiguous to which the band segment  412  is positioned to, is the same for the band segments  412  positioned contiguous to all of the shoes  300  for a given expandable rim assembly  200 , such that a width of the drum surface  310  that accommodates the bead of a tire is reduced. Similarly, a height H of the band or band segment  412 , as measured by how far the band  412  extends from the top surface  434  towards the drum surface  310 , can have any height sufficient to laterally retain the bead and/or sidewall of the tire or casing disposed between the bands  412  while still allowing the insertion and removal of the tire or casing onto the expandable rim assembly. For illustration, the height can be at minimum, the distance from the top surface  326  of the flange segment  308  to a clearance above the belt  216  and at maximum, the distance that the flange segment  308  extends radially from the drum surface  310  so that normal or expected operation of the expandable rim is not affected. Other heights may also be used. 
     The bands  412  can be made from a stretchable material which can be radially expanded outwardly for positioning over the drum surface  310  or the belt  216  positioned over the drum surface  310  of the rim portion  304 . Once positioned the band  412  exerts an inwardly radial force directed towards the drum surface  310 , thereby securing the band  412  on the drum surface  310 . In some embodiments in which the band  412  includes a plurality of band segments  412 , the band segments  412  can be made from plastic, steel, aluminum, rubber, vulcanized rubber or any other suitable material. The plurality of band segments  412  can be retained on the drum portion  410  of the rim portion  304  via a retaining member positioned over the band segments, as described before. Once positioned, the bands  412  modify the original rim width W, which extends between inward facing surfaces of the flange segments  308 , to a new shorter adjusted rim width W′, which extends between band inward facing surfaces of the bands  412 . The bands  412  can be positioned on the drum surface  310  or otherwise the belt  216  positioned on the drum surface  310  while the rim is in in its unexpanded or expanded configuration or position, as described before herein. The bands may be configured such that the expansion does not substantially alter (e.g., decrease) the wall thickness of the bands, thereby curtailing variations in the width W′ as the rim is expanded. 
       FIG. 8  is a flowchart of a method  500  of modifying an original rim width of an expandable rim according to an embodiment. The method  500  includes assembling a plurality of shoes at  502 . Each of the plurality of shoes includes a rim portion. Each rim portion includes a rim segment with a first flange segment positioned on one side and a second flange segment positioned opposite the first flange segment. For example, the plurality of shoes can include the shoes  200  or  300  described before herein which are assembled on a hub, e.g., the hub  108 , as described in detail with respect to  FIGS. 4-7 . The rim portion has an original rim width measured between inward facing surfaces of opposing flange segments of each of the plurality shoes. 
     In some embodiments, a belt is positioned around the shoes to retain the shoes in the cylindrical rim structure at  504 . For example, the belt  216  is positioned on the plurality of shoes  202  included in rim  200 , as described before herein. A band is positioned around a circumference of the cylindrical rim structure on a rim segment of the plurality of shoes at  506 . For example, the band  412  is positioned on the cylindrical rim structure formed by assembling the plurality of shoes  300  on the belt positioned on the rim segment or adjacent to the belt on the drum surface  310  of the rim segment  306  of the plurality of shoes  300 . The band  412  is positioned contiguous to a first flange segment (e.g., the flange segment  308  of each of the plurality of shoes  300 ). By positioning the band on the rim portion, the rim portion has an adjusted rim width measured between a band inward facing surface of the band and the inward facing surface of the opposite flange segment which is less than the original rim width. This allows a tire having width smaller than the original rim width to be securely mounted on the rim, as described herein. 
     In some embodiments, a second band is positioned around a circumference of the cylindrical rim structure on the rim segment of the plurality of shoes at  508 . The second band is positioned contiguous to the second flange segment of the rim portion. In some embodiments, the adjusted rim width is measured between a first band inward facing surfaces and a second band inward facing surface. Positioning of two bands allows centering of the tire on the rim segment, for example to center the tire relative to a hub on which the tire is mounted and/or a rasp used to buff the tire, eliminate any wobbling or undue vibrations that might be encountered if the tire is not centered on the rim. 
       FIG. 9  is a schematic flow diagram of a process  600  for buffing tires having varying widths using a buffing machine. The buffing machine (e.g., the buffing machine  100 ) includes a hub (e.g., the hub  108 ) and an expandable rim (e.g., the expandable rim  104  or  200 ). The expandable rim includes a base portion configured to be mounted on the hub, and a rim portion. The rim portion includes a rim segment and a pair of flange segments positioned orthogonally to the rim segment on either side of the rim segment. The expandable rim has an original rim width measured between the flange segments. 
     The process  600  includes positioning a band contiguous with an inward facing surface of any one of the flange segment of the pair of flange segments at  602 . The positioning of the band (e.g., the band  60   a ,  60   b ,  160 ,  260 ,  412  or any other band described herein) causes the rim segment to have an adjusted rim width measured between a band inward facing surface of the band and an inward facing surface of the opposite flange segment. In some embodiments, the band can include a stretchable or otherwise elastic band (e.g., a rubber band) which is stretched over the flange segment of expandable rim with the expandable rim in an initial unexpanded configuration, and positioned on a drum surface of the rim segment. In some embodiments, a belt is positioned on the drum surface of the rim segment as described herein, and the band is positioned on an outer surface of the belt. 
     A tire having a tire width equal to the adjusted rim width is mounted on the rim segment of the expandable rim at  604 . For example, the tire is positioned on the expandable rim with the expandable rim being in the unexpanded configuration. The expandable rim is then expanded to secure the tire on the rim segment. During such expansion, the rim width remains substantially the same with the thickness of the band remaining substantially the same as the expandable rim is moved from the unexpanded to the expanded configuration. The belt which can be positioned on the drum surface can contact a first bead and a second bead of the tire opposite the first bead to form an air tight seal between the belt and the tire. Air can then be filled in the tire using any suitable means. 
     The first bead of the tire is positioned adjacent to the band inward facing surface and a second bead of the tire is positioned adjacent to the inward facing surface of the opposite flange segment. Thus a tire having a tire width less than the original rim width is secured on the rim segment by adjusting the rim width. The tire is buffed on the buffing machine at  606 , for example as described with respect to the buffing machine  100 . In some embodiments, the band is a first band and a second band is positioned contiguous with the inward facing surface of the opposite flange segment. In some embodiments, the adjusted rim width is measured between a first band inward facing surface and a second band inward facing surface. Positioning a band adjacent to each of the pair of flange segments allows the tire to be mounted substantially centered on the rim segment of the expandable rim. 
     The use of the terms “a” and “an” and “the” and similar referents in the context of describing embodiments (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The terms “comprising,” “having,” “including,” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate embodiments and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention 
     It should be noted that the term “example” as used herein to describe some embodiments is intended to indicate that some embodiments are possible examples, representations, and/or illustrations of possible embodiments (and such term is not intended to connote that some embodiments are necessarily extraordinary or superlative examples). 
     The terms “coupled,” “connected,” and the like as used herein mean the joining of two members directly or indirectly to one another. Such joining may be stationary (e.g., permanent) or moveable (e.g., removable or releasable). Such joining may be achieved with the two members or the two members and any additional intermediate members being integrally formed as a single unitary body with one another or with the two members or the two members and any additional intermediate members being attached to one another. 
     Some embodiments are described herein. Variations of those embodiments may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate, and the inventors intend for the embodiments to be practiced otherwise than as specifically described herein. Accordingly, embodiments include all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the embodiments unless otherwise indicated herein or otherwise clearly contradicted by context. 
     It is important to note that the construction and arrangement of the various embodiments are illustrative only. Although some embodiments have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter described herein. 
     While this specification contains many specific implementation details, these should not be construed as limitations on the scope of this disclosure or of what may be claimed, but rather as descriptions of features specific to particular implementations. Certain features described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.