Patent Publication Number: US-2007120365-A1

Title: Apparatus and Method for Joining Tubulars

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
      This application is a continuation of U.S. patent application Ser. No. 10/945,728 filed Sep. 21, 2004 which is a continuation of U.S. patent application Ser. No. 10/259,337 filed Sep. 27, 2002 now abandoned. 
    
    
     BACKGROUND OF THE INVENTION  
      1. Field of the Invention  
      The present invention relates to joint restraints for tubular members. More particularly, the present invention relates to systems and methods for controlling the relative movement of components making up a joint restraint and controlling the clamping force applied to tubular members.  
      2. Description of the Related Art  
      Joint restraints are typically used to couple two axially-aligned tubular members such as pipes. A conventional joint restraint includes an annular body or gland fitted with a plurality of evenly spaced pads or wedges. Each pad has an associated bolt that, when rotated, urges the pad radially inward from a retracted position to an extended position. During extension, the teeth projecting out of the pad contact an outer surface of a first tubular member. The gland becomes substantially fixed onto the first tubular member as bolt rotation generates a clamping force that causes the teeth to penetrate or bite into the first tubular member. Mechanisms, such as a bolt or fastener, are used to connect the gland to a flange formed on a second pipe. Thus, a mechanical connection is established between the two tubular members.  
      Conventional joint restraints have certain drawbacks. For example, in many conventional joint restraint arrangements, the pads are disposed in pockets formed within the gland. To prevent relative movement between the gland and the pad during, for example, shipment or handling, a frangible material such as paint, epoxy, or wax is used to retain the pad in a retracted position within the pocket. Once the pad is extended, however, the frangible material is disturbed in such a way that it can no longer effectively retain the pad. In certain other joint restraint arrangements, the teeth may produce penetration or incision patterns that affect the integrity of the tubular member. Still other joint restraint arrangements are not readily adapted to accommodate variations in tubular member material or geometry.  
      The present invention addresses these and other shortcomings of conventional joint restraint arrangements.  
     SUMMARY OF THE INVENTION  
      The present invention provides a robust joint restraint that incorporates features and arrangements that enhance joint restraint reliability and produce a stable clamping force for joining tubular members. The invention may be advantageously applied to a restraint that has a gland that fits around a tubular member, a plurality of pads adapted to apply a clamping force on the tubular member, and a plurality of bolts that move the pads from a retracted position to an extended position.  
      In a first aspect, the present invention provides selective and controlled relative movement between the pad and the gland of the joint restraint. The relative movement between the pad and the gland is controlled by use of a dampening force. This dampening force can be generated by a mechanical device, a chemical, or by known natural forces such as a magnetic field. In a preferred embodiment, a flexible member associated with the pad applies a compressive force against an interior surface of the gland. This flexible member dampens relative movement between the pad and the gland. Further, the flexible member can extend into and be captured by a recess formed into the interior surface. The material and configuration of the flexible member can be adjusted to provide a selective amount of dampening force.  
      In a second aspect, the present invention provides a retaining device that permits a controlled retraction and extension of the pad by the bolt. The retaining device selectively connects the pad to an end of the bolt. In a preferred embodiment, the flexible member is a deformable ring that nests within a cavity formed in the pad. The flexible member surrounds a portion of the bolt when the bolt is inserted into the pad and thereby connects the pad to the bolt.  
      In a third aspect, the present invention provides an articulated wedging interface between the pad and the bolt. This wedging interface includes a frustoconical section formed on a tip of the bolt and a generally planar surface on the pad. Relative movement between the tubular member and the pad causes the pad to wedge against the bolt tip in a controlled fashion. This action can cause supplemental penetration of the teeth into the surface of the tubular member and/or generate an enhanced clamping force.  
      In a fourth aspect, the present invention provides a tooth arrangement that enhances the clamping action of the pad. A preferred arrangement includes a plurality of teeth that are offset from the edges of the pad with a landing. Additionally, a predetermined amount of spacing is provided between the teeth in order to produce a discontinuous or intermittent penetration or incision pattern on the outer surface of the tubular member. This incision pattern reduces the risk that the incisions will affect the structural integrity of the tubular member. Preferably, at least two teeth are substantially aligned along a first circumference. In a related embodiment, a third tooth is substantially aligned on a second circumference that is different from said first circumference to form a tripod arrangement.  
      In a fifth aspect, the present invention provides a spacing member that tunes the clamping force generated by a coupling to accommodate variations tubular member diameters or materials.  
      In a sixth aspect, the present invention provides a method of designing and arranging a joint restraint that uses pipe expansion to provide an enhanced gripping action. For a preferred joint restraint, the geometry of the gland, the pad and the teeth are set such that pre-characterized pipe expansion, in addition to pad extension, causes a predetermined amount of tooth penetration. In one preferred method, the geometry of the joint restraint is based on target tooth penetration at predetermined operating conditions. Preferably, an initial penetration of about 3% to 10% is obtained by pad teeth at about 10%-25% percent of a rated working pressure of the pipe. Further, it is preferred that at the rated working pressure, the tooth penetration be generally in the range of 30%-70%.  
      It should be understood that examples of the more important features of the invention have been summarized rather broadly in order that detailed description thereof that follows may be better understood, and in order that the contributions to the art may be appreciated. There are, of course, additional features of the invention that will be described hereinafter and which will form the subject of the claims appended hereto.  
    
    
     DESCRIPTION OF THE FIGURES  
      For a detailed description of an embodiment of the invention, reference will now be made to the accompanying drawings wherein:  
       FIG. 1  illustrates a schematic side view of a preferred joint restraint made in accordance with the present invention;  
       FIG. 2A  illustrates an end view of a section of a preferred joint restrain made in accordance with the present invention;  
       FIG. 2B  illustrates a sectional view B-B taken from  FIG. 2A ;  
       FIG. 3A  illustrates an end view of a preferred pad made in accordance with the present invention;  
       FIG. 3B  illustrates a bottom view of a preferred pad made in accordance with the present invention;  
       FIG. 3C  graphically illustrates an exemplary penetration or incision pattern formed on a tubular member surface by a preferred pad made in accordance with the present invention;  
       FIG. 4A  illustrates a side view of a preferred bolt made in accordance with the present invention;  
       FIG. 4B  schematically illustrates a tip of a preferred bolt made in accordance with the present invention;  
       FIG. 5A  illustrates a preferred flexible member made in accordance with the present invention;  
       FIG. 5B  illustrates a preferred flexible member made in accordance with the present invention that has been deformed;  
       FIG. 6A  illustrates an exemplary spacer member functionally disposed in an embodiment of a joint restraint made in accordance the teachings of the present invention;  
       FIG. 6B  illustrates an exemplary spacer member made in accordance the teachings of the present invention;  
       FIG. 7A  graphically illustrates test data relating to pressure tests conducted on 6″ DR18 PVC Pipe;  
       FIG. 7B  graphically illustrates test data relating to pressure tests conducted on 12″ DR18 PVC Pipe;  
       FIG. 7C  graphically illustrates one preferred relationship between joint configuration and working pressure; and  
       FIG. 8  illustrates an exemplary joint restraint geometry relevant to a preferred method of arranging a joint restraint.  
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
      The present invention relates to devices and methods providing rugged and cost-effective joint restraint that provides an enhanced clamping force for joining tubular members. The present invention is susceptible to embodiments of different forms. There are shown in the drawings, and herein will be described in detail, specific embodiments of the present invention with the understanding that the present disclosure is to be considered an exemplification of the principles of the invention, and is not intended to limit the invention to that illustrated and described herein.  
      Referring initially to  FIG. 1 , there is schematically illustrated an exemplary coupling  10  made in accordance with the present invention. The coupling  10  is shown positioned about an end of a tubular member T. In the following description of the advantageous features of the coupling  10 , the term “radial” movement denotes movement along axis R and “axial” movement denotes movement along axis A. Further, terms such as “downward” movement or “extension” are defined as movement in the direction of arrow A 2  and terms such as “upward” movement or “retraction” are defined as movement in the direction of arrow A 1 .  
      The coupling  10  includes a gland  12 , a pad  14  and a bolt  16 . A preferred coupling  10  is provided with (a) a dampening device  18  that controls relative movement between the pad  14  and the gland  12 ; and (b) a retaining device  20  that selectively connects the pad  14  to the bolt  16 . It will, of course, be understood that the pad  14  and bolt  16  are merely representative of a plurality of pads and bolts that are circumferentially arrayed within the gland  12 .  
      The pad  14  is adapted to apply a clamping force onto the outer surface of the tubular member T. The pad  14  is ordinarily disposed within the gland  12  and can move between the shown retracted position and an extended position  14   a  (shown in phantom lines). While retraction and extension are desired forms of movement, the pad  14  and gland  12  can be susceptible to undesired relative movement. For example, the pad  14  could vibrate or chatter within the gland  12 . Moreover, the pad  14  could simply fall out of the gland  12 . The dampening device  18 , however, dampens or reduces the likelihood and/or magnitude of such movement. In a preferred arrangement, the dampening force  18  applies a dampening force each time the pad  14  moves into the retracted position. Thus, in contrast to the temporary force produced by frangible materials, the dampening device  18  provides a substantially persistent force. That is, the dampening device  18  controls relative movement throughout at least one cycle wherein the pad  14  moves into a retracted position or state after being moved to an extended state.  
      The dampening force provided by the dampening device  18 , however, can be selectively applied to other situations or conditions. For example, the dampening force may be applied while the pad  14  is in the extended position or moves between the extended and retracted positions or states. In the context of the present invention, it should be understood that the term movement between a retracted position or state and an extended position or state encompasses movement from a retracted position to an extended position and movement from an extended position to a retracted position.  
      The bolt  16  moves the pad  14  between the retracted and extended state and applies a downward axial force that urges the pad  14  against the tubular member T. The bolt  16  has an end portion  17  that selectively engages or coupled to the pad  14  by the retaining device  20 . By substantially fixing the pad  14  to the bolt  16 , the retaining device  20  can stabilize the motion of the bolt  16  and pad  14  during extension of the pad  12 . Moreover, because of the bolt  16  is coupled to the pad  14 , the retaining device  20  enables the retraction or upward movement of the pad  14 . In a preferred arrangement, the movement of the bolt  16  activates the retaining device  20 . For example, the downward movement of the bolt  16  can activate the retaining device  20  by applying a first predetermined amount of thrust. The retaining device  20  can fix the pad  14  to the bolt  16  until it is deactivated by, for example, upward movement of the bolt  16  that applies a second predetermined amount of thrust.  
      The dampening device  18  and retaining device  20  can be any number of devices, systems, mechanisms and materials. Exemplary forces and associated devices include, but are not limited to: frictional or compressive forces provided by devices such as deformable members (e.g., coil springs, gaskets or o-rings); a locking force utilizing interlocking members using a detent mechanism (e.g., a detent ball biased with a spring) or common devices such as VELCRO®; and a chemical force provided by suitable adhesives and resins that remain sticky or viscid for a predetermined time; e.g., until shipment/installation or throughout service life. In these arrangements, it will be seen that there is some form of direct or indirect contact between the pad  14  and the gland  12  and/or bolt  16 . Such type of contact, however is not necessary. For example, the dampening device  18  can produce a magnetic force provided by a magnetic field (e.g., by magnetizing portions of the pad  14  and the gland  12  and/or bolt  16 ). In still another arrangement, a vacuum or negative pressure may be induced between the pad  14  and the gland  12  and/or bolt  16  (e.g., by using a vacuum chamber).  
      It should also be appreciated that the dampening force provided by the dampening device  18  need not be applied strictly between the gland  12  and the pad  14 . For example, the bolt may be used as an intermediate component through which the dampening device  18  acts on the pad  12 . Preferably, however, the dampening force is not applied via the bolt  16 . Having the dampening device  18  independent of the bolt  16  permits greater flexibility in the manufacturing, assembly, shipment and installation of the coupling  10 . For example, the bolts  16  can be shipped separately from the gland  12  and pads  14  while still providing controlled relative movement between the gland  12  and pad  14 .  
      Referring now to FIGS.  2 A-B there is shown a preferred embodiment of a restraint  100  made in accordance with the present invention. The preferred restraint  100  includes a gland  110 , a pad  130 , a bolt  160 , and a flexible member  190 . The pad  130  and the bolt  160  are shown in their retracted position. For convenience, a pad  130   a  and bolt  160   a  are shown in an extended position. In this extended position, pad  130   a  is shown engaging a tubular member T.  
      The gland  110  is of substantially conventional design and includes a generally ring-like body  112 . The body  112  includes a pocket  114 , a threaded radial bore  116 , a recess  118  and an interior surface  120 . The body  112  also includes known features such as flanges  122  and through holes that are of conventional design and known to those of ordinary skill in the art. Such features will not be discussed in detail. The pocket  114  is generally formed to receive the pad  130  and the threaded radial bore  116  is formed complimentary to the threads formed on the bolt  160 . The recess  118  is a depression along the interior surface  120  that is shaped to receive the flexible member  190  in a manner to be described later.  
      Referring now to  FIGS. 2A  to  4 A-B, the pad  130  is adapted to apply a clamping force onto the tubular member T. The pad  130  includes a chamber  132 , a clamping surface  138 , teeth  140   a - c  and a landing  142 . The chamber  132  includes a first portion  134 , a second portion  136  for receiving the flexible member  190 , and a bearing surface  139 . The first portion  134  is a generally radially aligned cavity that is shaped to receive the bolt  160 . The second portion  136  is a channel-like opening that is elongated along the axis A ( FIG. 1 ). The bearing surface  139  includes a planar section  139 A and a sloped section  139 B that coact with the bolt  160  in a manner described below.  
      The teeth  140   a - c  are adapted to penetrate and grip the tubular member T. The teeth  140   a - c , which project out of the clamping surface  138 , have a predetermined spatial interrelationship that enhances the grip or clamping force applied to the tubular member T. In a preferred arrangement, the teeth  140   a - c  are arranged to produce intermittent or discontinuous penetration into the surface of the tubular member T along a functional circumference. That is, a row of teeth can be arranged along one circumference or can be arranged along two or more circumferences and function effectively as one circumference because of their dimensions or proximity. For example, a space  141  is provided between teeth  140   a  and  140   c . The benefits of this arrangement are described below. Further, the teeth  140   a - c  are arranged in a tripod-fashion to enhance stability of the pad  140 . To minimize undue pressure on the pad, the axial offset or distance between teeth  140   a,c  and teeth  140   b  is at least one-half of the bolt diameter and no greater that twice the bolt diameter. In certain embodiments, however, other offsets may be adequate to provide bolt stability and optimal pad pressure distribution. Although  FIG. 3B  shows that the lengths of teeth  140   a  and  140   c  do not overlap the length of tooth  140   b , such an arrangement is not necessary to obtain the benefits of the present invention. Referring now to  FIG. 3C , there is shown a portion of a tubular member T “unwrapped” or “unrolled” as it were to an illustrate full circumferential contact pattern of the teeth  140   a - c  associated with six pads. Representative teeth  140   a,c  produce the indentations or bite pattern designated  146  and representative tooth  140   b  produces the indentations or bite pattern designated with numeral  148 . As can be seen, the bite of the teeth  140 A,C does not create a substantially continuous line of penetration or incision into the tubular surface T. Rather the bite pattern includes spacing  149  that interrupts the incision made by the teeth of one pad  130  into the tubular member surface. It is believed that staggering of the pad teeth as described above minimizes a risk that a tubular member T will suffer a structural failure along the line or penetration or incision. Referring back to  FIG. 3B , landings  142  provide a space or an area into which the material of the tubular member T can flow as the teeth  140   a - c  penetrate into the surface of the tubular member T. The landing  142  is a generally planar portion on the clamping surface  138  that separates the teeth  140   a - c  from a contact edge  144 . The contact edge  144  comes into contact with the tubular member T upon full penetration of the teeth  140   a - c . It is preferred that the contact edge  144  is rounded to reduce the stress concentrations that may occur during contact of the contact edge  144  and the surface of the tubular member T. Referring now to  FIG. 4A  there is shown a preferred bolt  160  for actuating the pad  130 . The bolt  160  is generally of conventional design and is used to move the pad  130  between a retracted and extended position. The bolt  160  includes a head  162 , a shank  164 , and a torque limiting section  166 . The head  162  and torque limiting section  166  are of conventional design and will not be described in further detail.  
      Referring now to FIGS.  3 A and  4 A-B, the shank  164  includes a threaded portion  169  that is complementary to the radial bore  116  of the gland  110  (FIG.  2 A). The shank  164  also includes an end portion  168  adapted to engage the pad  130 . The end portion  168  includes a reduced diameter section  170  and a tip  172 . The tip  172  includes a base  174 , a frustoconical section  176 , and a wedge section  178 . The frustoconical section  178  has a first angle θ 1  that is selected to expand the flexible member  190  such that the flexible member  190  can slide onto the shank  164  and eventually become nested in the reduced diameter section  190 . The wedge section  178  has an angle θ 2  that is selected to allow a controlled wedging action between the pad  140  and the bolt  160 . The base  174  is a substantially planar portion nominally seats flatly against the planar section  139 B of the bearing surface  139 A. As will be discussed in more detail later, the wedge section  178  enables the pad  140  to apply a predetermined supplemental gripping force on a shifting tubular member T.  
      Referring now to FIGS.  3 A and  5 A-B, the flexible member  190  deforms to provide a selected amount of both a dampening force and a retaining force for the restraint  100 . The flexible member  190  includes a deformable body  192  made of a suitable material such as rubber. The deformable nature of the body  92  performs at least two functions. First, the body  192  deforms to provide a desired amount of dampening force. In one preferred embodiment, a normally circular flexible member  190 , when disposed in the chamber second portion  136 , deforms to assume an elongated oval-type of shape shown in  FIG. 5B . This deformation creates extended sections  195  and  196  that extend into the recess  118  of the gland  110  ( FIG. 2B ). Thus, the pad  130  is retained within the gland  110  because the extended sections  195  and  196  are captured within the recess  118 . Additionally, these extended sections  195 , 196  can provide an initial or first amount of compressive (dampening) force against the interior surface  120  of the gland  110 .  
      Referring now to  FIGS. 2A and 4A , secondly, the body  192  deforms to provide a retaining force. When the bolt  160  is installed into the gland  110 , the frustoconical section  176  enters a hole  194  formed in the body  192 . The flexible member  190  deforms a predetermined amount to accommodate the shank  164  until the flexible member  190  reaches the reduced diameter section  170 . Once the flexible member  190  nests into the reduced diameter portion  170 , the flexible member  190  acts as a collar that retains the bolt  160  within the chamber second portion  136 . This connection need not be permanent; i.e., the bolt  160  can be configured to disconnect from the flexible member  190  upon a predetermined amount and type of upward movement. For example, a threaded engagement can be used to selectively uncouple these components. Alternatively, threading can be used to for a partial release and a radial pulling action for a final release. This may be advantageous to prevent an unintended decoupling of the bolt  160  and the pad  130  as when the bolt  160  is rotated during an adjustment or servicing task. In addition to providing the retaining force, the diameter of the reduced diameter section  170  can be selected to provide additional expansion of the deformable body  192  and further force the extended sections  195  and  196  into the recess  118 . This additional expansion can, therefore, create a supplemental dampening force between the flexible member  190  and the interior surface  120 .  
      It should be understood that the above arrangement is merely one of numerous designs that take advantage of the teachings of the present invention. For instance, the flexible member need not be disposed within the pad. Rather, the flexible member can be fixed in the interior surface of the gland or between the gland and the pad. The flexible member can include a ring, a rod bent into a “U” shape, a two-piece member, a Teflon® spacer, a Bellville-type spring or other member having a selected amount of stiffness. Moreover, a first member (flexible or otherwise) may be used for providing a dampening force and a second member (flexible or otherwise) may be used for providing a retaining force. For example, the first member can be disposed in a groove formed in the gland and the second member can be disposed in the pad or even the bolt itself. Moreover, the materials of the first and second flexible members need not be the same. For instance, one member can be a metal-coiled spring and the second member can be an epoxy resin that “glues” or “molds” the bolt end into the pad. Furthermore, in other arrangements, the device for producing the dampening force and retaining force can be applied after assembly of the restraint. For instance, a polymer, resin or other suitable material can be “shot” down through a bore in the bolt. This material, upon flowing between the spacing in the pad and gland and setting, can provide a frictional force as well as locking the pad to the bolt.  
      In an alternate arrangement, the extended sections  195  and  196  enter into the recess  118  only after the flexible member  190  has engaged the bolt  160 . In yet another alternate arrangement, the extended sections  195  and  196  do not provide a compressive contacting force between the flexible member  190  and the interior surface  120  until after the flexible member  190  has engaged the bolt  160 . Thus, it can be seen that the dampening force and retaining force can be selectively applied to the several components of the restraint  100 .  
      Presuming familiarity with the described embodiments of the present invention, the following description of use and operation dispenses with the numerals associated with the described features of the joint restraint. During installation of the joint restraint, the gland is placed over a tubular member (e.g., pipe). Thereafter, the bolts are advanced in a predetermined fashion to extend the pads against the surface of the tubular member. As the pads move to their extended position, their teeth penetrate and bite into the surface of the tubular member to a predetermined depth or percentage of penetration. In instances where the teeth fully penetrate the surface, the material of the tubular member will be pressed against the landings that surround the teeth.  
      Upon or after introduction of a pressurized fluid into the tubular member, the tubular member may shift or move axially. The axial movement of the tubular member can cause a corresponding movement of the pad. The joint restraint accommodates this motion by allowing the pad to slide about the tip of the bolt. The pad slides axially along the planar section of the pad bearing surface until the wedge section of the bolt tip engages the sloped section of the bearing surface. Additional movement by the pad causes the pad to wedge against the sloped section of the bolt tip in a controlled fashion. Thus, for example, as the pad moves axially, the wedge section urges the pad generally downward at a rate substantially corresponding to the angle or inclination of the slope portion. This downward motion can cause supplemental penetration of the teeth into the surface of the tubular member and/or generate an enhanced clamping force. It should be appreciated a plurality of pads in a joint restraint can provide this controlled wedging action simultaneously, in unison, or separately to accommodate the movement of the tubular member. Stated differently, the pads can either independently or cooperatively provide local stabilization for a shifting tubular member as well as stabilization along the full circumference of the shifting tubular member. Further, this enhanced stabilization can be permanent or temporary.  
      Referring now to  FIG. 6A -B, there is shown an exemplary spacer  300  made in accordance with the present invention. The spacer  300  provides enhanced control and selectivity over the clamping force generated by bolt  302 . In one aspect, the spacer  300  limits the radial travel of a bolt  302  in the direction R to thereby control the degree of compression imposed on the tubular member by the pad  304 . In another aspect, the spacer stabilizes the movement of the bolt  302 . A preferred spacer  300  fits about a shank  304  of a bolt  302  and is interposed between a bolt shoulder  306  and a gland  308 .  
      The preferred spacer  300  includes a resilient U-shaped ring body  310  having a mouth  320  and an opening  330 . The opening  330  is diametrically sized to receive the bolt shank  304 . In a preferred arrangement, the gap provided by the mouth  320  is smaller than the diameter of the shank  304 . The resilient body  310 , however, flexes to increase this gap and to thereby allow the shank  304  to enter or leave the opening  330 . After the shank  304  enters the opening  330 , the mouth  320  returns to its nominal size and captures the shank  304  within the opening  330 . The spacer also includes a tab  340  for centering the shank  304  in the opening  330  and access recesses  350 . The access recesses  350  accommodate tools such as a rod or screwdriver than can be used to pry the spacer  300  from the shank  304 .  
      The body  310  further includes an outer surface for seating the bolt shoulder  306 . The outer surface provides a generally flat or planar area against which the bolt shoulder applies pressure during rotation. Proper seating will, for example, increase the likelihood that sufficient torque will build up during rotation to activate known bolt torque limiting features provided on the bolt  302 .  
      The spacer  300  has a predefined thickness TK for controlling the radial travel of the bolt. In certain embodiments, the thickness TK can be a function of the material of the tubular member. For example, it may be determined that a pipe of a first material (e.g., PVC pipe) requires a bolt to travel a radial distance of D in order for the pad teeth to properly engage the pipe surface. It may further be determined that a second material (e.g., ductile iron) of different hardness than the first material requires the bolt to travel a radial distance of E in order for proper engagement of the teeth. An exemplary spacer  300  can then be provided with a thickness of (D minus E). Thus, the spacer  300  is used when the coupling is fitted on a pipe made of the second material but removed when fitted on a pipe made of the first material. In other embodiments, the thickness TK can be made to accommodate variations or differences in the diameter of tubular members.  
      It should be appreciated that the spacer of the present invention may be advantageous used with the couplings made in accordance with the present invention or conventional pipe couplings.  
      It is generally known that flexible tubular members, such as pipe formed of PVC (hereafter “PVC Pipe”), tend to swell or expand circumferentially when subjected to internal hydrostatic pressure. While even tubular members made of ductile iron also can swell under such pressure, the magnitude of this swell is substantially negligible given the dimensions of conventional pipes and associated joint restraints. For convenience, such tubular members are referred to as inflexible tubulars. For the purposes of this discussion, PVC pipe is considered exemplary of substantially flexible pipe that radially deforms an appreciable amount when exposed to internal hydrostatic pressure. The inventors of the present invention have recognized that swelling of substantially flexible pipe can be advantageously used to provide an enhanced and more reliable gripping action by a joint restraint. In order to characterize pipe swell, the inventors have conducted tests on PVC pipe.  FIGS. 7A and 7B  graphically illustrate certain test data relating to pressure tests conducted on sample 6″ PVC pipe and sample 12″ PVC pipe, respectively. During these tests, a PVC pipe was subjected to incremental amounts of internal hydrostatic pressure. At predetermined pressures, the outside diameter of the PVC pipe was measured.  
      In  FIGS. 7A and 7B , the horizontal axis represents incremental pressures and the vertical axis represents the measured outside diameter of the test PVC pipe. The inventors have observed that PVC Pipe expands diametrically even at relatively low hydrostatic pressures. Furthermore, the PVC Pipe continues to diametrically expand upon incremental increases in the hydrostatic pressure. The inventors have, therefore, concluded that the diametrical expansion of PVC pipe is (a) appreciable even at relatively low hydrostatic pressures, and (b) that this diametrical expansion can be quantified or characterized. The inventors, of course, recognize that other factors can influence the diametrical expansion: e.g., wall thickness, physical properties, ambient temperature of the test sample, etc. In view of these conclusions, methods of designing and arranging a joint restraint are provided that use pipe expansion to provide an enhanced gripping action.  
      In one preferred method, the geometry of the pipe restraint is based on target tooth penetration at predetermined operating conditions. Referring now to  FIG. 7C , there is shown a graph that illustrates one preferred relationship between joint configuration and working pressure. In the  FIG. 7C  arrangement, it is preferred that a tooth on a pad penetrate at least 3% into a PVC Pipe but no more than 10% at 10%-25% percent of a rated working pressure. For many applications, a tooth penetration of about 50% into the tubular member at the rated working pressure is believed to be adequate. However, it is believed that tooth penetration at rated working pressure between about 30%-70% will also be adequate in most instances. Under conventional arrangements, the maximum rate of pressure of a PVC Pipe may be several multiples of the rated working pressure. Accordingly, it is preferred that a certain amount of penetration be provided for in the event that the hydrostatic pressure exceeds the rated working pressure.  
      Referring now to  FIG. 8 , there is schematically illustrated an exemplary pad  800  having a tooth  802  positioned over a section of flexible pipe  810 . The flexible pipe  810  has an axial center line designated CL. Numerals R 1 , R 2  and R 3  represent radial distances from the centerline CL. Numeral R 1  represents the operational radial location of the pad  800  during use. Numeral R 2  represents the nominal radius of the outside surface of the flexible pipe  810  before the application of hydrostatic pressure. Reference Numeral R 3  represents the expanded radius of the flexible pipe (shown as a hidden figure labeled  820 ). In accordance with one embodiment of the present method, a target percentage penetration is set for the joint restraint, for example 50%, at rated working pressure. Reference to pressure versus circumferential expansion charts will provide the expanded diameter R 3  at the rated pressure. With R 3  established, a length for the tooth or teeth can be selected (for example 0.0080). Because 50% tooth penetration is desired, 0.0040 inches of the tooth will remain outside of the tube surface. Thus, the length of the exposed tooth when added to R 3  generally provides the value of R 1 . Thus, it can be seen that the tendency for flexible pipe to swell or circumferentially expand can be integrated into the gripping mechanism employed by a joint restraint.  
      It should be understood that the terms “circumferential expansion,” “diametrical expansion,” and “radial expansion” are used interchangeably to describe the swelling of a flexible member.  
      The foregoing description is directed to particular embodiments of the present invention for the purpose of illustration and explanation. It will be apparent, however, to one skilled in the art that many modifications and changes to the embodiment set forth above are possible without departing from the scope and the spirit of the invention. It is intended that the following claims be interpreted to embrace all such modifications and changes.