Patent Publication Number: US-2023158834-A1

Title: Non-pneumatic tire spoke with impproved elastomeric joint body

Description:
FIELD OF THE INVENTION 
     The subject matter of the present invention relates to a support structure for a nonpneumatic tire and specifically to improvements to the elastomeric joint bodies of such a support structure. 
     BACKGROUND 
     Composite spoke structures have been used to support non-pneumatic tires and may be comprised of an elastomer and a second material having a relatively higher bending stiffness than the elastomer, the composite spring having a first hinge side and a second hinge side comprised of the second material, and a joint body comprised of the elastomer, where the second material comprising the first hinge side and second hinge side are discontinuous or otherwise separated from one another by the joint body connecting the first hinge side and the second hinge side. 
       FIG.  2    provides a sectional view of one such prior art spoke  100 ′. The nose portion, or otherwise referred to as the “joint body”  130  of the spoke  100 ′ is comprised of an elastomeric material and acts to connect a first support element and a second support element, here comprising a radially outer support element or “leg”  144  and a radially inner support element or “leg” 142  respectively. The nose joint body is thicker, as measured in the circumferential direction (“C”), between the radially inner leg  142  and radially outer leg  144  than it is closer to the radially inner or radially outer portions of the joint body  130 . In reference to a single spoke as shown in this embodiment, the circumferential direction “C” is generally orthogonal to both the radial direction and the lateral direction. 
     When the spoke is compressed, which would occur in this particular spoke by moving the radially outer elastomeric joint body  114  toward the radially inner elastomeric joint body  112 , the elastomeric portion of the nose joint body  130  compresses and tension develops toward the ends  146 ,  148 ,  156 ,  158  of the legs  142 ,  144 . Over prolonged use or under high stress, cracks may develop adjacent to the radial ends  146 ,  148 ,  156 ,  158  of the legs  142 ,  144 , and particularly at the radially outer end  148  of the radially outer leg  142 , and may result in crack formation or other tearing. Particularly, cracks may form at the interface between the support element reinforcements and the rubber they are imbedded in at the radially outer end of the radial outer support element. 
     An improved spoke construction having an improved durability would be useful. It would be particularly useful for an improved spoke construction that would prolong the useful life of the spoke by delaying, reducing or eliminating the likelihood of crack formation or tearing. 
     SUMMARY OF THE INVENTION 
     Aspects 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. 
     The invention disclosed herein possesses an improved geometry aimed at reducing crack initiation at the circumferential distal surface of an elastomeric joint body of a composite non-pneumatic tire support. The improved geometry, inter alia, directs excess adhesive material, when present, away from the circumferential distal surface of the elastomeric joint body preventing adhesive material from attaching at a location at or adjacent to peak stresses along the circumferentially distal surface, increasing its durability and resistance to cracking. 
     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 
       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: 
         FIG.  1    provides a lateral side view of an exemplary embodiment of the present invention where a plurality of resilient composite structures are configured as spokes forming a part of a tire depicted under nominal loading conditions. 
         FIG.  2    provides a perspective view of a prior art structural support in the form of a spoke for a non-pneumatic tire. 
         FIG.  3    provides a lateral view of a finite element model of the stress concentration in the radially outer elastomeric joint body during compression, the embodiment lacking a glue deflecting flap. 
         FIG.  4    provides a lateral cross-section view schematic of the radially outer elastomeric joint body during compression, the embodiment lacking a glue deflecting flap, showing a typical glue distribution and excess glue beading and cracking of the elastomeric joint body. 
         FIG.  5    shows a cutaway perspective view of an embodiment of the invention showing the glue deflecting flap on the radially inner elastomeric joint body and radially outer elastomeric joint body. 
         FIG.  6    provides a close-up cross-section lateral view of the radially outer elastomeric joint body radially outer end of the radially outer support element and outer compliant band of an embodiment of the invention. 
         FIG.  7    shows a finite element model of the stress concentration in the radially outer elastomeric joint body during compression of an embodiment having a glue deflecting flap. 
     
    
    
     The use of identical or similar reference numerals in different figures denotes identical or similar features. 
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention provides an improvement to a mechanical structure for resiliently supporting a load. For purposes of describing the invention, reference now will be made in detail to embodiments and/or methods of the invention, one or more examples of which are illustrated in or with 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 or steps illustrated or described as part of one embodiment, can be used with another embodiment or steps to yield a still further embodiments or methods. 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. 
     The following terms are defined as follows for this disclosure: 
     “Axial direction” refers to a direction parallel to the axis of rotation of for example, the shear band, tire, and/or wheel as it travels along a road surface. 
     “Radial direction” or the letter “R” in the figures refers to a direction that is orthogonal to the axial direction and extends in the same direction as any radius that extends orthogonally from the axial direction. 
     “Equatorial plane” means a plane that passes perpendicular to the axis of rotation and bisects the outer compliant band and/or tire structure. 
     “Circumferential direction” or the letter “C” in the figures refers to a direction that is orthogonal to the axial direction and orthogonal to a radial direction. 
     “Lateral direction” or the letter “L” means a direction that is orthogonal to an equatorial plane. 
     “Elastic material” or “Elastomer” as used herein refers to a polymer exhibiting rubber-like elasticity, such as a material comprising rubber. 
     “Elastomeric” as used herein refers to a material comprising an elastic material or elastomer, such as a material comprising rubber. 
     “Interior angle” or “Internal angle” as used herein means an angle formed between two surfaces that is greater than 0 degrees but less than 180 degrees. An acute angle, a right angle and an obtuse angle would all be considered “interior angles” as the term is used herein. 
     “Exterior angle” or “External angle” or “Reflex angle” as used herein means an angle formed between two surfaces that is greater than 180 degrees but less than 360 degrees. 
     “Nominal load” or “desired design load” is a load for which the structure is designed to carry. More specifically, when used in the context of a wheel or tire, “nominal load” refers to the load for which the wheel or tire is designed to carry and operate under. The nominal load or desired design load includes loads up to and including the maximum load specified by the manufacturer and, in the case of a vehicle tire, often indicated by marking on the side of the tire. A loading condition in excess of the nominal load may be sustained by the structure, but with the possibility of structural damage, accelerated wear, or reduced performance A loading condition of less than nominal load, but more than an unloaded state, may be considered a nominal load, though deflections will likely be less than deflections at nominal load. 
     “Modulus” or “Modulus of elongation” (MPa) was measured at 10% (MA10) at a temperature of 23° C. based on ASTM Standard D412 on dumb bell test pieces. The measurements were taken in the second elongation; i.e., after an accommodation cycle. These measurements are secant moduli in MPa, based on the original cross section of the test piece. 
     “Distal” is a direction away from the mass center of spoke. 
     “Proximal” is a direction toward or closer to the mass center of the spoke. 
       FIG.  1    shows a lateral side view of an exemplary embodiment of the present invention wherein a plurality of resilient composite structures are configured as spokes  100  and are attached to an outer compliant band  200  forming a part of a tire  10 . The tire  10  may be incorporated into a wheel for a vehicle. For example the tire  10  may be part of a non-pneumatic wheel having a hub  12  which is attached to a passenger vehicle allowing the vehicle to roll across a ground surface. Other objects and vehicles may incorporate the invention, including but not limited to: heavy duty truck, trailer, light truck, off-road, ATV, bus, aircraft, agricultural, mining, bicycle, motorcycle and passenger vehicle tires. Such a non-pneumatic wheel would possess a hub  12  that would have a radially outer surface having an axis of revolution about a central axis  20 . The tire  10  may be attached to the hub  12  by any of a number of methods, for example, by mechanical fasteners such as bolts, screws, clamps or slots, and/or by adhesives such as cyanoacrylates, polyurethane adhesives, and/or by other bonding materials or a combination thereof. 
     The tire  10  shown here possesses an axis of rotation  20  about which the tire  10  rotates. In this exemplary embodiment, the radially outer surface  230  of the outer compliant band  200  interfaces with a ground surface  30  over which the tire rolls forming a contact patch, or area of the outer compliant band  200  that conforms to the surface upon which it is in contact with. Under a nominal load, the spokes  100  of the tire flex as the tire enters and exits the contact patch. Smaller deflections occur in the spokes  100  as the spoke rotates about the axis  20  outside the contact patch, but most of the deflection occurs while the spoke  100  enters, exits and travels through the contact patch. 
     Each spoke  100  possesses a “nose” portion  130  which acts as a resilient hinge. The “nose” portion  130  is an elastomeric joint body connecting a support element forming the radially inner portion of the spoke and a support element forming the radially outer portion of the spoke. The support elements of the spoke  100  are initially positioned at an angle relative to each other. The angle between the spoke support elements measuring less than 180 degrees is the interior angle and the angle between the spoke support elements measuring greater than 180 degrees is the exterior angle. The nose elastomeric joint body  130  is comprised of an elastomer attached to each spoke support element and is positioned on the side where of the radially outer spoke element and radially inner spoke element form an interior angle. 
     In this embodiment, the radially inner portion of the spoke possesses a radially inner foot  112  which connects to another surface, which is the radially outer surface of the hub  12  in the present embodiment. Here, the radially inner foot  112  is comprised of an elastomeric joint body that connects the radially outer support to the hub  12 . The radially outer portion of the spoke  100  possesses a radially outer foot  114  which is comprised of another elastomeric joint body which connects the outer support element to yet another surface which is, in the present embodiment, the radially inner surface  202  of the outer compliant band  200 . 
     In the exemplary embodiment shown, the tread band  200  comprises an elastomeric material and allows deformation to form a planar footprint in the contact patch. In the exemplary embodiment shown, the radially outer foot  114  of the spoke  100  is attached to the radially inner surface  202  of the tread band  200  and to the opposite side of the support element from the nose portion  130 . In the exemplary embodiment shown, the spoke is adhered in place by an adhesive. In other embodiments, the spoke may be attached by other methods, including by adhering the elastomeric material together, for instance by using green rubber and curing the rubber components together, or using a strip of green rubber between cured or partially cured rubber components. In some embodiments, the outer compliant band  200  may also possess a reinforcement to help carry the load circumferentially around the tire. 
     For this particular embodiment, the size of the tire  100  is equivalent to a pneumatic tire of the size 215/45R17. In the particular embodiment shown, 64 spokes  100  are attached around the inner circumference of the outer compliant band  200 . Under nominal loading conditions the tire  10  deflects 20 mm from the unloaded state. In the exemplary embodiment, 500 kg of mass load (approximately 4,900 N force) was used to approximate the nominal loading condition of the tire. 
       FIG.  3    provides a lateral elevation view of a finite element model of a spoke  100  undergoing compression, the model showing the tensile stress values within the composite structure with higher values shown in grey and red, and lower values shown in blue and black. Under compression of the spoke  100 , the circumferentially distal portion of the radially outer elastomeric joint body  114  undergoes tension while the circumferentially medial portion of the radially outer elastomeric joint body undergoes compression. It can be observed that tension between the radially outer end of the radially outer support element and the outer compliant band  200  is the highest toward middle portion and relatively less nearer the outer complaint band  200  radially inner surface  202 . 
     When the spoke  100  is attached to the compliant band  200 , a bonding layer  50  is typically used to secure the spoke  100  to the outer surface  202  of the compliant band as shown in  FIG.  4   . In this embodiment, the bonding layer  50  is an adhesive. A small bead  52  usually forms at the distal end of the interface between the spoke and complaint band as a small amount of the material making up the bonding layer  50  is squeezed out. The bead  52  adheres to the first surface  120  of the radially outer elastomeric joint body and to the outer surface  202  of the compliant band. Higher tensile stress at the glue  50 —elastomeric joint body  114  interface create sufficient energy in the material to initiate a crack  60  at a crack initiation location  62  and extending to a terminal end  64 . As the spoke is cycled and the crack is exposed to sufficient stress, the crack will continue to grow until the crack is discovered and intervention is taken or the spoke  100  separates from the outer compliant band  200 . The radially outer elastomeric joint body  112  radially outer surface  160  joins to the radially inner surface  202  of the tread band  200 . 
       FIG.  5    provides a perspective cutaway view of an embodiment of the current invention. In the current embodiment, the circumferentially distal most edge  180  between the elastomeric joint body  112  and the shearband&#39;s  200  radially inner surface  202  is pushed farther away from the first surface of the radially outer joint body  102  by an extension of the joint body  114  forming a glue deflector flap  240 . The glue deflector flap  240  places the bead  52  formed from excess bonding material  50  farther from the first surface  120  of the radially outer joint body  114  reducing the likelihood of it bonding to the first surface  120  creating a stress riser and crack initiation point. 
     The nose portion, or otherwise referred to as the “nose joint body”  130  of the spoke  100  is comprised of an elastomeric material and acts to connect a first support element and a second support element, here comprising a radially outer leg  144  and a radially inner leg  142  respectively. The nose portion becomes circumferentially thicker as measured in the circumferential direction (“C”) between the radially inner leg  142  and radially outer leg  144  as you get closer to the halfway point between the radially inner leg  142  and radially outer leg  144 . The nose elastomeric joint body  130  is radially thicker between the radially inner leg  142  and radially outer leg  144  as you move away from the nose portion of the spoke in the circumferential direction C. In reference to a single spoke as shown in this embodiment, the circumferential direction is generally orthogonal to both the radial direction and the lateral direction. 
     The support elements  112 ,  114  of the spoke  100  are referred herein as having a first side  174 ,  176  and a second side  175 ,  177 . The radially outer elastomeric joint body  114  is positioned on the second side  177  of the radially outer support element  144  and the radially inner elastomeric joint body  112  is positioned on the second side  175  of the radially inner support element  142 . The nose elastomeric joint body is positioned on the first sides  174 ,  176  of both the radially outer support element  144  and the radially inner support element  142 . 
     When the spoke is compressed, which would occur in this particular spoke by moving the radially outer elastomeric joint body  114  toward the radially inner elastomeric joint body  112 , the thicker portion of the nose elastomeric joint body  130  compresses and radial tension develops in the thinner portion of the nose elastomeric joint body as the support elements hinge about the nose elastomeric joint body. During compression of the spoke, the radially outer elastomeric joint body  114  and radially inner elastomeric joint body  112  also undergo compression in the radially thicker portion of the joint body and tension in the radially thinner portion of the joint body closer to the ends of the support element  142 ,  144  ends  146 ,  148 . 
     Likewise, when the spoke  100  is deformed radially inward, undergoing compression between the radially outer foot  114  and radially inner foot  112 , the nose elastomeric joint body  130  undergoes compression between the radially inner support element  142  and radially outer support element  144  of the spoke while the distal portion of the nose elastomeric joint body  130  undergoes tension between the radially inner support element  142  and the radially outer support element  144 . 
     Reinforcements  150  in the support elements  142 ,  144  provide flexural stiffness beyond that which the surrounding material can provide alone. The reinforcements may be constructed from any resilient material having a flexural stiffness greater than the elastomeric joint bodies. In this particular embodiment the reinforcements  150  are comprised of pultruded fiberglass reinforced resin. Other materials may be used, including metal, including spring steel, carbon fiber, fiber reinforced resins or fiber reinforced plastics. The reinforcements  150  of the current embodiment are oriented along the length of the support element  142 ,  144  and generally along the length of the spoke such that they lie parallel to the equatorial plane of the tire. 
     The spoke  100  of the embodiment shown, including the elastomeric joint bodies  112 ,  114 ,  130  and the material surrounding the reinforcement  150 , is comprised of rubber of the general type used in the construction of conventional rubber pneumatic radial tires. 
     The rubber used in the embodiment shown is of a relatively soft rubber having a modulus of 3.2 MPa in the areas of the radially inner elastomeric joint body  112  and radially outer elastomeric joint body  114 . Each elastomeric joint body  112 ,  114  is attached to the radially inner leg  142  and radially outer leg  144  respectively. The radially inner leg  142  and radially outer leg  144  are constructed to give them flexural rigidity, that is, to allow them to resiliently deform when the spoke  100  is under compression or tension. In the current embodiment, radially outer end  148  of the radially outer leg  144  is attached to the elastomeric joint body  114 , but is otherwise “free” and may move to compress or stretch the elastomeric joint body  114  when the spoke is being stretched or compressed. Likewise the radially inner end  146  of the radially inner leg  142  is attached to the elastomeric joint body  112 , but is otherwise “free” and may move to compress or stretch the elastomeric joint body  112  when the spoke  100  is under compression or tension. The radially inner elastomeric joint body  112  generally becomes thicker in the circumferential direction nearer the hub  12  to which it is attached than it is near the radially outer portion of the elastomeric joint body. It should be understood, however, as in the embodiment shown, it may become circumferentially thinner at points due to the profile of the geometry near the surface of the hub. In the embodiment shown, the elastomeric joint body  112  flairs outward forming a protrusion  116  nearest the hub  10 . Likewise, the radially outer elastomeric joint body  114  generally becomes thicker in the circumferential direction nearer the outer band  200  to which it is attached compared to the radially inner portion of the elastomeric joint body  114 . In the embodiment shown, the elastomeric joint body  114  flairs outward forming a protrusion  118  nearest the outer band  200 . 
     The legs  142 ,  144  of the spoke  100  may be comprised of fiber reinforced plastic reinforcements surrounded by a rubber to form a membrane. In this embodiment the leg membranes  142 ,  144  possess a flexural rigidity of approximately 40 GPa. In this particular embodiment, the filaments have a diameter of approximately 1 mm with a pace of about 2 mm apart. The filaments of the particular embodiment shown are glass reinforced resin formed by pultrusion. The filaments of the embodiment have a modulus of approximately 10 MPa to 40 GPa. Alternatively other reinforcements may be used, including carbon fiber such as graphite epoxy, glass epoxy or aramid reinforced resins or epoxy or combinations thereof. Unreinforced plastic reinforcements or metallic reinforcements may also be used, provided they have sufficient flexural rigidity for the nominal loads intended to be supported. Alternatively other pacing and other diameters of the membranes and reinforcements may be used. The legs  142 ,  144  of the spoke  100  have a relatively large stiffness compared to the other components comprising the spoke  100 . The legs  142 ,  144  act resiliently and have a large bending stiffness allowing the nose portion  130  of the spoke to act as a joint body connecting the radially inner leg  142  with the radially outer leg  144 . The feet  112 ,  114  act as second and third joint bodies, connecting the radially inner leg  142  to the hub and the radially outer leg  144  with the outer band  200 . 
     In  FIG.  6   , the distance in the radial direction R from the end  148  of the support element reinforcement  150  to the radially inner surface  202  outer compliant band  200  is shown as “Y” while the maximum distance in the circumferential direction C from the end  148  of the support element reinforcement  150  to the first surface  120  of the elastomeric joint body  114  is shown as “X”. The edge  180  is the circumferentially distal edge of the elastomeric joint body  114  where it joins with the outer compliant band  200 . The distal surface  120  is the surface of the elastomeric joint body  114  between the support element  140  and the outer compliant band  200 . The edge  180  extends circumferentially out from the distal surface  120  forming a glue deflector flap  240 . In this embodiment, the edge  180  is radially in line with the radially outer end  148  of the radially outer support element  140 . The thickness of the support element reinforcement is shown as “T” in the figure and is measured here in the medial plane of the non-pneumatic tire and perpendicular to the surface of the support element reinforcement. The inventors have found improved durability of the interface between the elastomeric joint body  114  and the outer shear band  200  is achieved when the dimensions Y and X are at least twice that of the thickness T of the support element reinforcement  150 . The inventors have found further improved durability when the spoke dimensions Y and X are at least three times the thickness T of the elongated reinforcement. Durability is further enhanced when a predominantly concave radius R 1  is present between the end  148  of the reinforcement  150  and the edge  180  of the elastomeric joint body  114 . The radius need not be constant as it may have a variable radius value. In this particular embodiment, the radius has an inflection where the concave radius R 1  becomes convex the radially distal surface  120  of the elastomeric joint body  114  possesses a convex curved radius R 2 , as shown near the edge  180  of the current embodiment. 
     The glue deflector flap  240  may extend in the circumferential direction C from the most medial location of the first surface  120  of the radially outer elastomeric joint body  114  a distance equal to or greater than the thickness of the reinforcement  150 . For example, in an alternative embodiment, the glue deflector flap  240  extends in the circumferential direction C from the most medial location of the first surface  120  of the radially outer elastomeric joint body  114  a distance equal to the thickness of the reinforcement  150 . In another alternative embodiment, the glue deflector flap  240  extends in the circumferential direction C from the most medial location of the first surface  120  of the radially outer elastomeric joint body  114  a distance equal to twice the thickness of the reinforcement  150 . In yet another alternative embodiment, the glue deflector flap  240  extends in the circumferential direction C a distance that is circumferentially more distal from the spoke  100  than the radially outer end  148  of the radially outer support element  140 . 
     The inventors have found that spoke endurance performance is particularly good when the reinforcement  150  thickness T is approximately 1 mm and the radial distance Y is approximately 4 mm and the distance X in the circumferential direction is 3 mm. In this embodiment, the glue flap  240  extends further in the circumferential direction than any other part of the first surface  120  of the elastomeric join body  114 . 
       FIG.  7    shows a computer model of a portion of the radially outer portion of the spoke and the outer compliant band under a nominal load deflection, that is, a 20 mm compression of the spoke which simulates a 20 mm displacement of the outer compliant band  200  toward the hub  12 .  FIG.  7    is a computer model of an embodiment where the thickness of the reinforcement is 1 mm and the circumferential distance X between the end of the reinforcement  150  and the circumferentially farthest distance to the distal surface  120  of the radially outer elastomeric joint body  114  from the edge  180  of the adhesive deflector flap  240  is 3 mm and the radial distance Y between the end of the reinforcement and the radially inner surface  202  of the tread band  200  is 4.3 mm. The location of the edge  180  away from the higher stress along the distal surface  120  positions any excess bonding material, such as excessive adhesive, well away from the areas of higher stress. This corresponds to the inventors&#39; observation of improved durability in the experimental testing of the embodiment of the current invention which possesses the adhesive deflector flap  240  as modeled here. 
     The “v-shape” of the embodiments of the spoke shown and described herein allow the adjacent spokes to “nest” and give linear spring rate when deflected radially over a distance approximately equal to the tires vertical deflection. The nesting of the spokes avoid adjacent spokes from clashing under normal loading conditions. 
     It should be understood by a person of ordinary skill in the art that the stiffness of the spoke may be adjusted by adjusting the length of the “v” of the “v-shaped spoke”, the constituent material moduli and the internal architecture of the spoke. 
     It should be understood that other web element configurations and geometries may be used within the scope of the invention, including web elements which are interconnected such as where they may form a honeycomb or other pattern. While when the resilient composite structure is configured as a spoke they are configured to extend in a lateral direction across the width of the tire, it should be understood that they may be configured at other angles, such as at an angle to the lateral direction of the tire. For example, the spoke may extend at a diagonal between the circumferential direction and the lateral direction of the tire. In yet other embodiments, the spoke may be turned 90 degrees to run circumferentially around the diameter of the tire, thereby resembling a sidewall of a pneumatic tire. In such a configuration, the spoke would be configured like a continuous toroid about the hub of the wheel. 
     Selected combinations of aspects of the disclosed technology correspond to a plurality of different embodiments of the present invention. It should be noted that each of the exemplary embodiments presented and discussed herein should not insinuate limitations of the present subject matter. Features or steps illustrated or described as part of one embodiment may be used in combination with aspects of another embodiment to yield yet further embodiments. Additionally, certain features may be interchanged with similar devices or features not expressly mentioned which perform the same or similar function. 
     The dimensions and values disclosed herein are not to be understood as being strictly limited to the exact numerical values recited. Instead, unless otherwise specified, each such dimension is intended to mean both the recited value and a functionally equivalent range surrounding that value. For example, a dimension disclosed as “40 mm” is intended to mean “about 40 mm.” Also, the dimensions and values disclosed herein are not limited to a specified unit of measurement. For example, dimensions expressed in English units are understood to include equivalent dimensions in metric and other units (e.g., a dimension disclosed as “1 inch” is intended to mean an equivalent dimension of “2.5 cm”). 
     The terms “a,” “an,” and the singular forms of words shall be taken to include the plural form of the same words, such that the terms mean that one or more of something is provided. The terms “at least one” and “one or more” are used interchangeably. Ranges that are described as being “between a and b” are inclusive of the values for “a” and “b.”