Abstract:
There is disclosed a threaded joint for coupling together rods, tubes, pipes etc. The joint consists of helical box and pin thread segments each defined by a pressure flank and a clearance flank spaced apart from each other with alternating roots and crests. The pressure flank is defined by an S-curve extending between the root and the crest, which is defined by a first curvature c 1  adjacent to the root and a second curvature c 2  adjacent to the crest. c 1  and c 2  curve in opposing directions with an inflection point “i” between curvatures c 1  and c 2.

Description:
FIELD 
       [0001]    The invention relates to threaded joints for coupling together of rods, tubes, pipes and shafts, with particular application for subsurface drilling pipes and tubes. 
       BACKGROUND 
       [0002]    Subsurface drilling, particularly for mineral exploration, involves the use of a rotating drill string assembled from multiple individual tubular rods that are coupled together as the drilling progresses. Typically, the rods are threaded together using threading that is provided at opposing ends of each rod. Significant axial and rotational stresses are placed on the threading during the drill rotation and drill string retraction. Furthermore, the rods should be coupled together and decoupled without the need to apply excessive torque or force to the drill rod segments. 
         [0003]    Within the mining industry, there is an ongoing need to provide improved threaded joints that address some of the drawbacks that are present within prior art threaded joints. 
       SUMMARY 
       [0004]    We describe a threaded joint for coupling together first and second members, in which each of said members comprises a central axis between respective ends thereof. The joint consists of threaded segments located on at least one end of the members, in which members may be coupled together by threading the respective segments together. In one aspect, the invention relates to a modified “buttress” thread that is self-locking. 
         [0005]    In one aspect, the joint comprises a pin thread segment at one end of a first of said members and a tubular box thread segment at one end of a second of said members, in which the box thread segment and pin thread segment each comprise a helical thread defined by a pressure flank and a clearance flank. The box thread segment and pin thread segment each further comprises a root and a crest extending between said pressure flank and said clearance flank, wherein the pressure flank comprises an S-curve (when viewed in cross-section along an axial section) extending between the root and the crest. The S-curve is defined by a first curvature c 1  extending from the root and a second curvature c 2  extending from the crest with an inflection point “i” between curvatures c 1  and c 2 . Curvatures c 1  and c 2  are opposed, whereby c 1  is concave and c 2  is convex. The S-shaped curvature of the pressure flank may extend from adjacent to the root to adjacent to the crest. 
         [0006]    In one aspect, curvature c 1  equals c 2  in opposed directions. One or both of c 1  or c 2  may comprise a segment of a circle having a radius r 1 . 
         [0007]    Alternatively, one of both of c 1  or c 2  may comprise a compound curvature comprising a segment of a first circle having a radius r 1  and a segment of a second circle having a radius r 2  wherein r 1  does not equal r 2 . In one aspect, r 2  may be greater than r 1 . 
         [0008]    In another aspect, the crest and root surfaces of said box and pin thread segments may each define a frustoconical surface, in which the angle of taper may be within the range of 0.75° and 1.63° relative to said central axis. 
         [0009]    In a further aspect, the pin thread segment and box thread segment each comprises a first and second unthreaded segments at opposing ends of the helical thread, the first unthreaded segment is at a distal end of the member and having an end face defining the distal end surface of the first member. The second unthreaded segment has a radially inwardly stepped shoulder. The shoulders may each be angled relative to the perpendicular of the central axis within the range of 5 to 15 degrees. Alternatively, the shoulders may each comprise an inner region adjacent to the unthreaded segment comprising a negative slope of 12° to 15° relative to the perpendicular of the central axis and an outer region which is perpendicular to the central axis or has a negative slope of up to 4° relative to the perpendicular. The end face may comprise a mirror-image of the compound slope of the shoulder. 
         [0010]    According to a further aspect, the clearance flanks may have a positive slope relative to the central axis by about 45°, about 60° or between 45° and 60°. 
         [0011]    According to a further aspect, the inflection point i has a tangent with a slope relative to the central axis that is about 45°, about 60° or between 45° and 60°. 
         [0012]    The helical thread may comprise either an unpaired helix comprising single-start thread or a paired helix comprising a double-start thread. 
         [0013]    In a further aspect, the ratio of r 1 : 2  above is about 1:3 or greater. 
         [0014]    In a further aspect, r 1  is within the range of 0.007 inches to 0.015 inches. 
         [0015]    In a further aspect, r 1  is 0.005 inches to 0.012 inches and r 2  is 0.024 inches to 0.060 inches. 
         [0016]    Dimensions herein are normally provided in imperial measurements, unless otherwise specified. Directional references herein are normally with reference to the threaded tubular members being horizontal. The terms “inner”, “inwardly” and similar terms refer to the direction that is radially inwardly towards the central axis of a given threaded member. The terms “outer”, “outwardly” and the like refer to the opposed direction which is radially outwardly from the central axis. 
         [0017]    References herein to angular deviations are generally expressed in terms of an angle from the central axis of the elongate member or, if specified, a plane which is perpendicular to the axis. The assumption is made herein that the central axis of the threaded coupling is linear. However, the present invention is equally applicable to curved members in which the central axis is non-linear. In such case, angular deviations may be considered to be based on a short segment of the central axis which closely approximates a straight line. 
       Definitions 
       [0018]    For purposes of the present specification, the following definitions shall apply unless a different meaning is expressly stated or the context clearly requires a different definition. 
         [0019]    “Rod”: means an elongate member that is threaded at one or both ends for coupling with a similar rod. A rod may be cylindrical or tapered and may have a solid or hollow core. A rod may be fabricated from any suitable material. The term “rod” may in some cases be used interchangeably with one or more of the terms “shaft”, “tube”, or “casing”. 
         [0020]    “Thread” or “threading”: means a projecting rib or recessed groove, usually helical in configuration, which may be coupled together by threading to a similar “mating” thread. 
         [0021]    “Box thread”: refers to the female threaded segment. 
         [0022]    “Pin thread”: refers to the male threaded segment. 
         [0023]    “Pressure flank”: refers to an essentially vertical or somewhat sloping surface on a thread forming between the root and crest surfaces. Normally, a pressure flank is brought into contact with a corresponding pressure flank when opposing threads are engaged with each other. The corresponding pressure flanks bear upon each other when axially load is induced on and the rod during makeup of a connection or a tensile load is applied during retraction of a drill string. 
         [0024]    “Axial cross section”: refers to a cross section on a plane that bisects a rod through a central axis that extends between opposed ends of the rod. 
         [0025]    “Transverse cross section”: refers to a cross section on a plane that is transverse to the central axis of the rod. 
         [0026]    “Clearance flank”: is the flank extending between the root and crest of the threading, opposed to the pressure flank. Normally, a given clearance flank of a threading will remain out of contact with an opposed clearance flank of the mating threading when threaded together. 
         [0027]    “Root”: refers to a cylindrical or frustoconical surface which extends between adjacent portions of a thread. The pin root is radially inward to the crest and the box root is radially outward to the crest and is normally parallel thereto. Normally, the root is co-axial with the central axis of the threading. 
         [0028]    “Crest”: is a frustoconical or cylindrical surface which is normally parallel to the root. A crest is the surface between the pressure flank and clearance flank of a thread. The axis of the crest is normally co-axial with the central axis of the threading. 
         [0029]    “Negative slope”: means a slope that provides an overhang between upper and lower portions of the negatively sloping surface whereby the uppermost portion of the sloping surface overhangs the lowermost portion. A negative slope normally defines a concave space beneath the overhang. For example, in  FIG. 2  it will be seen that shoulder  30  defines a concave space when viewed in cross-section. In some cases, a surface may have multiple angles whereby a negative slope may have a positively sloping portion, even when the slope as a whole is negative. 
         [0030]    “Interference fit”: means a configuration whereby the pin thread has a slightly larger outside diameter than the inside diameter of the contact surfaces of the box thread. The portions of the pin thread that contact the box thread when fully tightened force a slight expansion of the box thread segment, to secure the respective threaded components together. 
         [0031]    “Proximal”: refers to a direction toward a point intermediate between opposing ends of the elongate tubular member  10  as described herein. “Distal” refers to an opposing direction towards one of the respective ends thereof. 
         [0032]    “Buttress thread”: refers to a thread having a trapezoid or saw-tooth profile which is designed to handle high axial force in one direction. A buttress thread has a load-bearing face which is perpendicular to the central axis or a slight slope, such as 7° or less. The opposing face has a relatively shallow slope such as about 45°. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0033]      FIG. 1  is a cross-sectional view of threaded couplings disposed on the respective end segments of an elongate tubular member, according to one embodiment. 
           [0034]      FIG. 2  is an axial cross-sectional view of portions of threaded members showing box and pin threads in expanded view. 
           [0035]      FIG. 3  is an expanded view of box and pin thread portions, showing end sections thereof 
           [0036]      FIG. 4  is a view similar to  FIG. 3  showing opposing end sections thereof. 
           [0037]      FIG. 5  is an enlarged axial cross-sectional view showing portions of the box and pin thread segment of the tubular member. 
           [0038]      FIG. 6  is a further enlarged view showing a box threaded section. 
           [0039]      FIG. 7  is an enlarged view of a pin section. 
           [0040]      FIG. 8  is an axial cross-sectional view showing a pin threading in its entirety. 
           [0041]      FIG. 9  is an axial cross-sectional view showing a box section in its entirety. 
           [0042]      FIG. 10  is an axial partial-cross-sectional view showing a box section in its entirety. 
           [0043]      FIG. 11  is a further axial cross-sectional view showing a pin thread in its entirety. 
           [0044]      FIG. 12  is an axial cross-sectional view showing a pin section, of a double-start thread. 
           [0045]      FIG. 13  is a view similar to  FIG. 12  showing a single start thread. 
           [0046]      FIG. 14  is an enlarged view of a pressure flank of a pin or box thread showing a first embodiment thereof. 
           [0047]      FIG. 15  is an enlarged view as in  FIG. 14  showing a second embodiment thereof. 
           [0048]      FIG. 16  is an enlarged view of an embodiment of  FIG. 14 , showing tangent lines and other aspects thereof. 
           [0049]      FIG. 17  is an axial sectional view showing a shoulder portion of a pin segment according to a further embodiment. 
           [0050]      FIG. 18  is an axial sectional view showing an end face portion of a pin segment according to the embodiment of  FIG. 17 . 
           [0051]      FIG. 19  is an enlarged axial cross section of a shoulder portion of a pin thread according to one aspect; the box thread shoulder is similar. 
           [0052]      FIG. 20  is an enlarged cross section of an end portion of a pin thread according to one aspect; the end portion of the box thread is similar. 
           [0053]      FIG. 21  is an enlarged axial cross-section view of a further embodiment, showing a portion of a box thread. 
           [0054]      FIG. 22  is an enlarged axial cross-sectional view according to the embodiment of  FIG. 21 , showing a portion of a pin thread. 
           [0055]      FIG. 23  is an axial cross sectional view showing pin and box threads according to a still further embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0056]    The following is a detailed description of certain embodiments of the invention. The present description is not intended to limit the scope of the invention in any respect, including limiting the scope thereof to any of the specific aspects, features, details, dimensions or configurations provided in this detailed description. 
         [0057]      FIGS. 1-11  illustrate an embodiment of a modified buttress thread having a self-locking pressure flank. In this embodiment, the thread configuration relates to the threaded joint of a drill rod string. However, the present thread configuration has a range of applications, including use with a range of materials, fabrication methods and industrial applications. For example, without limitation, the thread configuration may be applicable for use with well casings, drilling tools and other components used for mineral and hydrocarbon exploration and environmental drilling. 
         [0058]      FIG. 1  depicts three tubular members  10 ,  12  and  13  which are essentially identical in structure and which may be coupled together in end to end fashion with threading provided at the respective ends thereof. The respective threading comprises a pin thread  1  (seen in more detail in  FIG. 7 ) and a box thread  2  (seen in more detail in  FIG. 6 ). An exemplary pin thread  1  is provided on a first end segment  6  of a first tubular member  10 . A mating box thread  2  is provided on a second end segment  8 , of a second tubular member  12 .  FIG. 1  also shows an opposing end of tubular member  12  comprising a pin thread  1 . Thus, each tubular member  10  and  12  is provided with first and second threaded end segments  6  and  8  on opposing ends thereof. Tubular members  10  and  12  each further comprise a body  14  and  16  respectively, located between segments  6  and  8 . A central longitudinal axis  18  extends axially between end segments  6  and  8  of each of members  10  and  12 . When coupled together, the respective tubular members  10  and  12  are normally axially aligned, with a (normally) linear axis  18  extending between the opposing ends of the respective tubular members. It will be seen that a non-linear configuration may be provided, for example to accommodate a curved or arcuate drill string. 
         [0059]    The outside diameter of tubular bodies  14  and  16  may be between 1.188″ to 6.5″ with a wall thickness of 0.188″ to 0.25″. The invention is not limited to these dimensions, nor to any particular dimensions identified in this specification. 
         [0060]    As shown in  FIG. 2 , pin thread  1  is composed of a root surface  20  and a crest surface  22 . Root and crest surfaces  20  and  22  lie on respective co-axial frustoconical (conical section) surfaces which are essentially planar when seen in cross section. The respective surfaces  20  and  22  are parallel to each other and taper inwardly by an angle of between 0.75 and 1.63 degrees relative to central axis  18  towards the distal end of threaded segment  6 . Box thread  2  has a similar crest surface  26  and root surface  24  each being frustoconical and having a similar angle of taper of between 0.75 to 1.63 degrees inwardly towards the proximal end of segment  8 . The respective threads  1  and  2  are configured to provide an interference fit between the pin crest and box root surfaces and a minimal clearance between the pin root and box crest when threaded together. 
         [0061]    As seen more clearly in  FIG. 8 , body  14  of tubular member  10  is stepped radially inwardly at a shoulder  30 , which defines the proximal margin of pin thread segment  6 . Shoulder  30  has a negative slope of about 5-15° relative to axis  18  whereby body  14  overhangs the proximal margin of segment  6 . A fillet  31  defines the inner corner between shoulder  30  and segment  6 . Fillet  31  merges the surface of segment  6  with shoulder  30 . An outer corner  29  is opposed to fillet  31  and defines the border between shoulder  30  and the outer surface of body  14 . Segment  6  is defined at its opposed, distal end by an end face  32 . End surface  32  has a positive slope similar to shoulder  30  (5-15°) and an outer fillet  33  with a radius of curvature similar to fillet segment  31 . Fillet  33  is located at the radially outer corner of end face  32   
         [0062]    Fillet segments  33  and  50  may have a minimum radius of curvature of about 0.0156″ and fillet segments  31  and  48  may have a maximum radius of curvature of about 0.0156″. These respective dimensions provide minimal or no overlap in the respective radii of curvature so as to minimize or eliminate any interference between these segments when the members  10  and  12  are coupled together. Respective segments  33  and  50  are thus brought into abutting or adjoining relationship when the thread joint is fully made up without generating an interference fit between these respective regions. In more general terms, the radius of curvature of the concave shoulder fillet segments is greater than or equal to the radius of curvature of the corresponding abutting or adjoining convex end segment fillets. 
         [0063]    As seen in  FIGS. 2, 3 and 4 , when the respective box and pin threads are coupled and the tubular members  10  and  12  are initially threaded together to a non-fully tightened position, a stand-off or gap remains between the respective end surface  42  of the box thread and shoulder  30  of the pin thread, and likewise between end surface  32  and box thread shoulder  40 . At this initial pre-torqued stage, this gap is approximately 0.04-0.09 inches (see S 1  in  FIG. 2 ). When torqued to proper requirements, the end surface  42  of the box thread contacts shoulder  30  of the pin thread, while a gap or stand off exists of 0.002 to 0.004 inches between end face  32  of the pin thread and shoulder  40  of the box thread. 
         [0064]    The pin and box threads  1  and  2  are configured to provide an interference fit, whereby the pin crest  22  has an outside diameter of about 0.002 inches larger than the inside diameter of box thread root  24 . When fully made up, the crest  22  of the pin and the root  24  of the box thread has an interference fit of approximately 0.002″ on the diameter while the pin root  20  and the box crest  26  has minor clearance to allow room for thread compound and debris. By increasing the radius in the corner of the root  24  and pressure flank  54 , it decreases the stress concentration of the part. 
         [0065]    The rear flank of the pin and box has the same geometry but the box thread depth is shallower than the pin thread depth by 0.002 to 0.005″ to provide interference between the pin crest and the box root and clearance between the pin root  20  and box crest  26 . The box crest  26  extends off of a secant line and intersects to the rear flank radius. 
         [0066]    As discussed above, the diameter of pin crest  22  is approximately 0.002″ larger than the diameter of box root  24  so when the thread joint is made up “hand tight”, the pin major diameter will contact the box major diameter and there will be approximately 0.04 to 0.09″ standoff between the pin and box. When the joint is pre-torqued to the proper requirements, it will have an interference fit of approximately 0.002″ on the diameter until the box face  42  and pin shoulder  30  fully contacts. At this point there will be a gap of 0.002 to 0.004″ between the pin face  32  and box shoulder  40 . 
         [0067]    The pin and box segments  6  and  8  have a theoretical length relative to the central axis of 1.6 to 2.6″ with the box segment  8  being longer than the pin segment  6  by up to 0.004″ to ensure proper make up. 
         [0068]    As seen in  FIGS. 6 and 7 , pin and box threads have a pitch of 2 to 4 threads per inch, when provided on a single start thread. This value is doubled on an embodiment comprising a two-start thread, which comprises a paired helical threading and which is described below. The thread length relative to the central axis may be 1.6 to 2.6 inches, with the axial distance from the end face  42  to shoulder  40  of the box segment being longer than the corresponding distance of the pin segment by about 0.004 inches to ensure proper makeup. The pin crest diameter is approximately 0.002 greater than the box root diameter, to provide an interference fit. 
         [0069]    Referring to  FIGS. 6 and 7 , box thread pressure flank  54  and corresponding pin thread pressure flank  52  are shown, as well as pin thread clearance flank  56  and box thread clearance flank  58 . Pin thread pressure flank  52  is shown in detail in  FIGS. 14 through 16 . Box thread pressure flanks  54  have identical mating configurations.  FIG. 14  depicts a first embodiment of pressure flank  52  comprising an S-shaped cross-sectional configuration, composed of an inner concave section  60  and an outer convex section  62 . Section  60  and  62  meet at inflection point  64 . Surface  52  is thus continuously curved between root  20  and crest  22 . Concave section  60  has a radius of curvature of R 1 , and convex segment  62  has an identical radius of curvature R 1 . At inflection point  64 , surface  52  has a tangent angle  66 . The slope of tangent angle  66  relative to axis  18 , as well as the length of radius R 1 , determines the thread depth. Tangent  66  may comprise a negative angle of between 45 to 60 degrees relative to axis  18 . The absence of flat surfaces on the respective pressure flanks allows the mating thread to lock while avoiding the compression characteristic of a conventional flat-surface reverse angle pressure flank. 
         [0070]    The corresponding clearance flanks  56  and  58  are only in contact with each other until the pin shoulder  30  meets the box face  42 . At this point, contact between the pin and box threads will shift to the respective rear pressure flanks  52  and  54 . The threaded joint is then fully engaged. The initial relatively shallow attack angles of the clearance flanks  56  and  58  make it easier to start the thread by lining it up and reduce cross-threading. 
         [0071]    The respective pressure and clearance flanks of the pin and box threads each meet the adjoining root and crest surfaces at a curved radius or fillet rather than a sharply-defined angle, as described herein. Turning first to the box thread  2  as seen in  FIG. 6 , a first convex radius or fillet  63  is provided at the intersection where clearance flank  58  meets box crest  26 . A second concave fillet  65  is provided where box clearance flank  58  meets box root  24 . A third convex fillet  69  is provided where box pressure flank  54  meets box crest  26  and a fourth concave fillet  67  is provide where box pressure flank  54  meets box root  24 . 
         [0072]    Turning next to pin thread  1  as seen in  FIG. 7 , pin thread  1  has a first convex fillet  80  where pin thread pressure flank  52  meets pin crest  22 . A second concave fillet  82  defines the junction between pressure flank  52  and pin root  20 . A third convex fillet  84  defines the junction between pin clearance flank  56  and pin crest  22  and a fourth concave fillet  86  defines the junction between pin clearance flank  56  and pin root  20 . 
         [0073]    It will be seen that when the pin and box threads are engaged, the respective convex fillets nest within the concave fillets. The radii of the respective convex fillets  63 , and  84  are larger than the radii of the respective concave fillets  65 , and  86  to ensure proper clearance during makeup of the joint. 
         [0074]    The S-shaped curvature of pressure flank  52  provides a radius of curvature between pressure flank  52  and root  20 . Increasing this radius causes a decrease of the stress concentration of the threading, as shown in the graph of Table 2 (see below). 
         [0075]    In one embodiment, pin and box threads  1  and  2  form a single start thread comprising an unpaired helix. In this embodiment, seen in  FIG. 12 , the thread has a pitch of 2.0 to 4 threads per inch. In a second embodiment, shown in  FIG. 13 , the thread has a double-start configuration that consists of a paired helical threading. In this embodiment, the thread pitch may be doubled from the above. One advantage of a double start thread is to provide increased contact area on the pressure flank which also reduces the distance between the last active thread and the shoulder which makes for a stronger and stiffer thread lead-in without compromising the amount of turns required to fully make up the joint. This can also allow for a shorter thread lead-in adding additional strength to the joint. 
         [0076]    The double start embodiment shown in  FIG. 12  can have a “lead-in distance” x which is shorter than the corresponding “lead-in distance” y of the single start embodiment of  FIG. 13 . In the present embodiment, distance x is about 23% shorter than distance y. The “lead in distances” x and y comprise the axial spacing between the outer corner  29  that defines the edge of face  30  and fillet  52  that defines the margin between pressure flank  54  and crest  22  of pin thread  1 . For purposes of measuring the lead-in distance, this measurement is derived from the proximal margin of pin thread  1 , where pin thread  1  is closest to end face  30 . The corresponding single start and double start embodiments of box threads  2  (not shown) have similar configurations to the pin threads of  FIGS. 12 and 13 . 
         [0077]      FIG. 15  shows a second embodiment wherein pressure flank  70  comprises a similar S-shaped curve extending between root  20  and crest  22 . However, pressure flank  70  differs from pressure flank  52  in that concave segment  72  is composed of a dual radius curved surface. Surface  72  is a compound curvature, a portion of which is comprised of a primary (major) radius of curvature R 3  and the remainder of which is comprises a secondary (partial) radius of curvature R 2 , wherein R 2  is greater than R 3 . One segment of concave portion  72  thus has a radius of curvature of R 2  and is adjacent to root  20 , while a second portion of segment  72  which is adjacent to inflection point  64  has a radius of curvature of R 3 . In a similar fashion, convex segment  74  has a compound curvature, composed of a first segment of radius R 3  and an adjoining second segment of radius R 2 . Convex and concave segment  72  and  74  meet at an inflection point  64 , having a tangent  66 . 
         [0078]      FIG. 16  provides additional details of the single radius curvature of the embodiment of  FIG. 14 . Pressure flank  52  can merge with crest  22  in a continuously curved arc. In one option, shown in a stippled  75  line in  FIG. 16 , pressure flank  52  can meet crest  22  at a flat surface  75  having a slope of 15° to 30° relative to crest  22 . Flat surface  75  may be introduced in a machining process after the initial threading is cut. Flat surface  75  is provided to remove any irregularities that may have been introduced in the initial thread cutting step due to possible difficulties in cutting a smooth, continuously curved transition between flank  52  and crest  22 . In this version, flat surface  75  has little or no significant effect on the performance of the thread. 
         [0079]    Radius R 1  combined with the tangent angle  66  effectively determines the thread depth between the respective root and crest surfaces and the quantum of interference  95  between respective pin and box pressure flanks (see Table 1). 
         [0080]      FIGS. 17 to 20  show a further embodiment of pin thread  100 . In this embodiment, shoulder  102  ( FIG. 17 ) has a compound negatively sloped surface consisting of an outer portion  104  and an inner portion  106 . Outer portion  104  is perpendicular to axis  18  or has a negative slope of up to 4° relative to a perpendicular to axis  18 . Inner portion  106  has a negative slope of between 12-15°. Portions  104  and  106  meet at an inflexion region  108  which is approximately the mid-point of shoulder  102 . In one aspect, inflection region  108  has a minimum radius of curvature of 0.156″. Inner portion  106  meets segment  112  at a curved fillet  110 . End surface  120 , seen in  FIG. 18  comprises a similar compound surface, consisting of an outer portion  121  with the same or similar taper as surface  106  and an inner surface  122  with the same or similar taper as surface  104 . End surface  120  further comprises a rounded corner  124  having a similar radius as fillet  110 . The pin shoulder  102  has a similar inflection region having a minimum radius of curvature of 0.156″. 
         [0081]      FIGS. 21 and 22  provide a further embodiment.  FIG. 21  shows a proximal portion of a box thread  200  adjacent to body  16 . Box thread  200  comprises an outer surface  202  which is continuous with the outer surface of body  16 . Thread  200  comprises a shoulder  204 , which comprises a tapered (frustoconical) annular surface that is undercut relative to the adjacent inner surface  206  of body  16 . Shoulder  204  is perpendicular to the central thread axis or tapers outwardly (towards outer surface  202 ) and proximally and is within an angle of between 0° and 10°, preferably in the range of 5 to 10°, relative to a transverse (radial) plane of body  16 . 
         [0082]    Shoulder  204  merges with a tapered (frustoconical) ramp segment  208  which extends in a distal direction from shoulder  204 . Ramp segment  208  slopes upwardly in a distal direction to merge with crest  210 . As such, ramp segment  208  tapers outwardly in a proximal direction from crest  210  towards shoulder  204  to provide a radially enlarged segment of box thread  200 . Ramp segment  208  is perpendicular to the central thread axis or has a slope of between 0° and 10°, preferably in the range of 5 to 10°, relative to the central elongate axis of body  16 . The length of ramp segment  208  (proximal to distal ends thereof) is in the range of about 0.1500.200 inches. Ramp segment  208  merges with shoulder  204  at a curved radius  212 . 
         [0083]      FIG. 22  shows a distal segment of a pin thread  220  that provides a complementary profile to box thread  200 . Pin thread  220  is provided with a sloping (frustoconical) proximal shoulder  222  adjacent to outer surface  224  of body  16 . Shoulder  222  has configuration that matches shoulder  204  of box thread  200 , whereby shoulder  222  undercuts outer surface  224  and is provided with a taper of about 0-10° relative to a plane that transversely bisects body  16 . Shoulder  222  merges with a ramp segment  226  which comprises a frustoconical surface having a taper of about 0-10° relative to the central elongate axis of body  16 . Segment  16  tapers radially inwardly from adjacent to the innermost (proximal) pin crest surface  230 , to reach a maximum diameter adjacent to shoulder  222 . When seen in axial cross section as in  FIG. 22 , ramp segment  226  slopes downwardly towards proximal shoulder  222 . 
         [0084]    The length of ramp segment  226  matches box ramp segment  208 , namely in the range of about 0.150-0.200 inches from the proximal to distal ends thereof. Ramp segment  226  merges with shoulder  222  at a radius  232 . 
         [0085]    In operation, in the embodiment of  FIGS. 21 and 22 , threads  200  and  220  are threaded together thereby bringing the respective pin and box threads into engagement. The effect of the ramp segments leads to the respective pin and box lead-in being pulled into the ramp rather than pushed out when a high level of torque or torsion is applied to the respective threads. 
         [0086]      FIG. 23  shows box thread  250  and pin thread  252  according to a further embodiment. According to this embodiment, at least one of the pressure flanks of the pin and/or box threads comprises a projecting nose continuous with the pressure flank, such that the nose is adjacent to and merges with the corresponding crest. When the pin and box threads are engaged, the crest adjacent to the projecting nose crest becomes spaced apart from the root of the corresponding box or pin thread when threaded thereto. 
         [0087]    According to this embodiment, the box and pin threads have S-curved pressure flanks  254  and  256  respectively. A flat crest  258  of pin thread  252  (at the major diameter of pin thread  252 ) is in contact with a flat root  260  of box thread  250  (at the major diameter of box thread  250 ) when threaded together. Box thread pressure flank  254  merges with an outer radius  262  at the minor diameter of box thread  250  (i.e. the innermost diameter). Outer radius  262  merges with a tapered segment  264  that angles outwardly towards the major diameter of box thread  250 . As a result, radius  262  comprises a protruding nose when seen in an axial cross section (as in  FIG. 23 ), which protrudes inwardly towards the central axis relative to the adjacent crest  266  of box thread  250 . Crest  266  is thus recessed outwardly away from the central axis, when seen in axial section. In contrast, pressure flank  256  of pin thread  252  merges with a radius  268  which does not provide a similar nose-like projection. 
         [0088]    It will be seen that nose  262  could alternatively or in addition be provided on the pin thread segment. 
         [0089]    When box and pin threads  250  and  252  are threaded together, as seen in  FIG. 23 , crest  266  of box thread  250  is spaced apart from root  270  of pin thread  252 , by a gap  272 . It will be seen that gap  272  is formed and defined by the projecting portion of radius  262 . Furthermore, this structure maximizes the thread flank contact between pressure flanks  254  and  256  without compromising the clearance between the adjacent crest and root segments  266  and  272  of box and pin threads  250  and  252 . 
       Example 1 
       [0090]    Table 1 is a chart that provides an example of thread configurations in which radius R 1  ranges from 0.008 inches to 0.012 inches with tangent  66  comprising either 45 degrees or 60 degrees relative to axis  18 . 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Rear Pressure Flank Chart (See FIG. 16): 
               
               
                   
               
             
             
               
                 Radius (90) 
               
               
                 Adjacent (91)  
               
               
                 Opposite (92) 
               
               
                 Angle (93) 
               
               
                 Depth of Thread (94) 
               
               
                 Interference (95) 
               
               
                 Adjacent = (Radius) × (Cosine of angle) 
               
               
                 Opposite = (Radius) × (Sine of angle) 
               
               
                 Depth of thread = 2(Radius + Adjacent) 
               
               
                 Interference = 2(Radius − Opposite) 
               
               
                   
               
               
                 45 Degree Tangent 
               
               
                   
               
             
          
           
               
                 Radius 
                 .008″ 
                 .009″ 
                 .010″ 
                 .011″ 
               
               
                 Thread Depth 
                 .0274″ 
                 .0308″ 
                 .0342″ 
                 .0376″ 
               
               
                 Interference 
                 .0046″ 
                 .0052″ 
                 .0058″ 
                 .0064″ 
               
               
                   
               
             
          
           
               
                 60 Degree Tangent 
               
               
                   
               
             
          
           
               
                 Radius 
                 .009″ 
                 .010″ 
                 .011″ 
                 .012″ 
               
               
                 Thread Depth 
                 .027″ 
                 .030″ 
                 .033″ 
                 .036″ 
               
               
                 Interference 
                 .0024″ 
                 .0027″ 
                 .0029″ 
                 .0032″ 
               
               
                   
               
             
          
         
       
     
       Example 2 
       [0091]    Table 2 is a graph that illustrates the reduction in internal stress concentration as the radius increases of the fillet between the root and pressure flank of the box and pin threads according to one aspect of the invention. 

 
         [0092]    By increasing the radius in the corner of the root and pressure flank, it decreases the stress concentration of the part 
       Example 3: Measurement of Torsional Strength 
       [0093]    An embodiment was tested for torsional strength. According to this test, three threaded pipe assemblies were provided, each assembly consisting of a pair of pipes threaded together. Each pipe had a 1 inch diameter hole for receiving a torque transfer shaft. An end plate adapter interface was provided for fastening to the torque transfer shaft, consisting of a pair of flanges with pins and holes for connecting the torque transfer shaft to a torsion device. Each assembly was attached at one end, through the flange, to a bearing block shaft and a sprocket. The opposed end of the assembly was secured against rotation by attachment to a vertical post via a pin. Torque was applied to the pipe in a counter-clockwise direction using a servo-hydraulic actuator equipped with a calibrated load cell and displacement transducer, through a chain and a clevis. 
         [0094]    Rotation of the threaded joint was measured using a second calibrated displacement transducer installed directly on the tube at approximately 1 inch from the joint. Torque was applied to the tube using angular displacement control at a constant rate of 10°/minute until failure occurred to the threaded joint. Load and angular displacement at the tube were recorded and used to plot the torque vs. angular displacement curves. 
         [0095]    The scope of the present invention should not be limited by the preferred embodiments set forth in the examples but should be given the broadest interpretation consistent with the description as a whole. The claims are not to be limited to the preferred or exemplified embodiments of the invention.