Abstract:
A threaded connection includes a continuous pin thread including at least a first step, a mid-step, and a second step formed sequentially thereon. A continuous box thread includes at least a first step, a mid-step, and a second step formed sequentially thereon, wherein the steps on the box thread correspond generally in axial position with the steps on the pin thread. The first step has a first wedge ratio, the mid-step has a transition wedge ratio, and the second step has a second wedge ratio, wherein thread leads are substantially constant within each of the steps. The connection is designed such that at make-up of a pin member with a box member, a clearance exists between at least one of corresponding load flanks and corresponding stab flanks on at least one of the first step, the mid-step, and the second step.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is related to co-pending United States patent applications filed concurrently herewith titled “Threads with Perturbations” having U.S. patent application Ser. No. 11/027,014, and titled “Floating Wedge Thread for Tubular Connection” having U.S. patent application Ser. No. 11/027,015, all assigned to the assignee of the present application and all incorporated herein by reference in their entireties. 
     BACKGROUND OF INVENTION 
     Casing joints, liners, drill pipe, and drill collars (collectively referred to as “tubulars”) are often used in drilling, completing, and producing a well. Casing joints, for example, may be emplaced in a wellbore to stabilize a formation, to protect a formation against elevated wellbore pressures (e.g., wellbore pressures that exceed a formation pressure), and the like. Casing joints may be coupled in an end-to-end manner by threaded connections, welded connections, and other connections known in the art. The connections may be designed so as to form a seal between an interior of the coupled casing joints and an annular space formed between exterior walls of the casing joints and walls of the wellbore. The seal may be, for example, an elastomeric seal (e.g. an o-ring seal), a metal-to-metal seal formed proximate the connection, or similar seals known in the art. In some corrections, seals are formed between the internal and external threads. Connections with this characteristic are said to have a “thread seal.” As used herein, a “thread seal” means that a seal is formed between at least a portion of the internal thread on the box member and the external thread on the pin member. 
     It will be understood that certain terms are used herein as they would be conventionally understood where tubular joints are being connected in a vertical position along a central axis of the tubular members such as when making up a pipe string for lowering into a well bore. Thus, the term “load flank” designates the side wall surface of a thread that faces away from the outer end of the respective pin or box member on which the thread is formed and supports the weight (i.e., tensile load) of the lower tubular member hanging in the well bore. The term “stab flank” designates the side wall surface of the thread that faces toward the outer end of the respective pin or box member and supports forces compressing the joints toward each other such as the weight of the upper tubular member during the initial makeup of the joint or such as a force applied to push a lower tubular member against the bottom of a bore hole (i.e., compressive force). The term “face” of the box is the end of the box member facing outward from the box threads and the term “nose” of the pin is the end of the pin member facing outward from the threads of the connection. Upon makeup of a connection the nose of the pin is stabbed into and past the face of the box. 
     One type of thread commonly used to form a thread seal is a wedge thread. In  FIG. 1 , a connection having a wedge thread is shown. “Wedge threads” are characterized by threads that increase in width (i.e., axial distance between load flanks  125  and  126  and stab flanks  132  and  131 ) in opposite directions on the pin member  101  and box member  102 . Wedge threads are extensively disclosed in U.S. Pat. No. RE 30,647 issued to Blose, U.S. Pat. No. RE 34,467 issued to Reeves, U.S. Pat. No. 4,703,954 issued to Ortloff, and U.S. Pat. No. 5,454,605 issued to Mott, all assigned to the assignee of the present invention and incorporated herein by reference. On the pin member  101 , the pin thread crest  122  is narrow towards the distal end of the pin member  101  while the box thread crest  191  is wide. Moving along the axis  105  (from right to left), the pin thread crest  122  widens while the box thread crest  291  narrows. In  FIG. 1 , the thread surfaces are tapered, meaning that the pin thread  106  increases in diameter from beginning to end while the box thread  107  decreases in diameter in a complimentary manner. Having a thread taper improves the ability to stab the pin member  101  into the box member  102  and distributes stress in the connection. 
     Generally, thread seals are difficult to achieve with free-running threads having broad crests and roots, however, the same thread forms may have thread seals when used for wedge threads. Various thread forms may be used for embodiments of the invention disclosed below. One example of a suitable thread form is a semi-dovetailed thread form disclosed in U.S. Pat. No. 5,360,239 issued to Klementich, and incorporated herein by reference. Another thread form includes a multi-faceted load flank or stab flank, as disclosed in U.S. Pat. No. 6,722,706 issued to Church, and incorporated herein by reference. An open thread form with a generally rectangular shape is disclosed in U.S. Pat. No. 6,578,880 issued to Watts. Each of the above thread forms are example thread forms that may be used for embodiments of the invention having either wedge threads or free running threads. Those having ordinary skill in the art will appreciate that the teachings contained herein are not limited to particular thread forms. 
     For wedge threads, a thread seal is accomplished by the contact pressure caused by interference over at least a portion of the connection between the pin load flank  126  and the box load flank  125  and between the pin stab flank  132  and the box stab flank  131 , which occurs when the connection is made-up. Close proximity or interference between the roots  192  and  121  and crests  122  and  191  completes the thread seal when it occurs over at least a portion of where the flank interference occurs. Higher pressure may be contained with increased interference between the roots and crests (“root/crest interference”) on the pin member  101  and the box member  102  and by increasing flank interference. This particular connection also includes a metal-to-metal seal that is accomplished by contact between corresponding sealing surfaces  103  and  104  located on the pin member  101  and box member  102 , respectively. 
     A property of wedge threads, which typically do not have a positive stop torque shoulder on the connection, is that the make-up is “indeterminate,” and, as a result, the relative position of the pin member and box member varies more for a given torque range to be applied than connections having a positive stop torque shoulder. As used herein, “make-up” refers to threading a pin member and a box member together. “Selected make-up refers to threading the pin member and the box member together with a desired amount of torque, or based on a relative position (axial or circumferential) of the pin member with the box member. For wedge threads that are designed to have both flank interference and root/crest interference at a selected make-up, both the flank interference and root/crest interference increase as the connection is made-up (i.e. increase in torque increases flank interference and root/crest interference). For wedge threads that are designed to have root/crest clearance, the clearance decreases as the connection is made-up. Regardless of the design of the wedge thread, corresponding flanks and corresponding roots and crests come closer to each other (i.e. clearance decreases or interference decreases) during make-up. Indeterminate make-up allows for the flank interference and root/crest interference to be increased by increasing the torque on the connection. Thus, a wedge thread may be able to thread seal higher pressures of gas and/or liquid by designing the connection to have more flank interference and/or root/crest interference or by increasing the torque on the connection, however, this also increases stress on the connection during make-up, which could lead to failure during use. 
     Free-running threads used for oilfield tubular connections typically do not form thread seals when the connection is made-up.  FIG. 2  shows a prior art connection having free-running threads. The free-running threads include load flanks  154  and  155 , stab flanks  157  and  158 , crests  159  and  162 , and roots  160  and  161 . As is typical of a connection with free-running threads, this connection relies on a positive stop torque shoulder formed by the contact of surfaces  151  and  152  disposed on the pin member  101  and the box member  102 , respectively. The positive stop torque shoulder shown in  FIG. 2  is commonly referred to as a “pin nose shoulder.” In other connections, the positive stop torque shoulder may instead be formed by the box face  163  and a mating shoulder (not shown) on the pin member  101 . The positive stop torque shoulder also provides a seal. Unlike wedge threads, which make-up by the wedging of the pin thread ( 106  of  FIG. 1 ) and the box thread ( 107  of  FIG. 1 ), free-running threads rely on the positive stop torque shoulder to load the connection during make-up. To make-up the connection shown in  FIG. 2 , the pin member  101  and the box member  102  are screwed together until the surfaces  151  and  152  are brought into abutment, at which point the pin load flank  154  and box load flank  155  are also in abutment. Additional torque is applied to the pin member  101  and the box member  102  to load the surfaces  151  and  152  and the pin load flank  154  and box load flank  155  until the desired amount of make-up torque has been applied to the connection. 
     The connection shown in  FIG. 2  does not accomplish a thread seal because of the large gap  153  that exists between the pin stab flank  157  and box stab flank  158 . The gap  153  occurs because of how free-running threads with positive stop torque shoulders are loaded. Applying torque to the connection during make-up against the positive stop torque shoulder causes the pin member  101  to be compressed while the box member  102  is stretched in tension. Note that when a box face shoulder is used, the box member  102  is compressed while the pin member  101  is stretched in tension. The force between the pin member  101  and the box member  102  is applied through the pin load flank  154  and box load flank  155 . The pin stab flank  157  and the box stab flank  158  are not loaded during make-up. This results in contact pressure between the load flanks  154  and  155  and a gap between stab flanks  157  and  158 . As discussed above, a wedge thread (as shown in  FIG. 1 ) is able to form a thread seal in part because of the interference between the load flanks  125  and  126  and the stab flanks  132  and  131 . For wedge threads, this occurs near the end of the make-up of the connection because of the varying width of the pin thread  106  and the box thread  107 . To have similar interference between the load flanks  154  and  155  and stab flanks  157  and  158  on a cylindrical (i.e. non-tapered) free-running thread, the interference would exist substantially throughout the make-up of the connection because the pin thread  106  and the box thread  107  have a continuous width. Further, root/crest interference, if any, would exist substantially throughout the make-up of the connection. This could lead to galling of the threads and difficulty in making up the connection. 
     The variance in thread width for a wedge thread occurs as a result of the load flanks having different leads than the stab flanks. A thread lead may be quantified in inches per revolution. Note that this is the inverse of a commonly used term “thread pitch,” which is commonly quantified as threads per inch. A graph of the leads for a prior art wedge thread is shown in  FIG. 3A . For this connection, the load lead  14  is constant over the length of the connection and greater than the stab lead  12 , which is also constant. The nominal lead is shown as item  10 . As used herein, “nominal lead” refers to the average of the load lead  14  and the stab lead  12 . The thread will widen with each revolution by the difference in the load lead  14  and the stab lead  12 . The difference in the load lead  14  and the stab lead  12  is sometimes referred to as the “wedge ratio.” For a free-running thread (i.e. non-wedge thread), the load lead  14  and the stab lead  12  would be substantially equal causing the free-running thread to have a substantially constant thread width (i.e. a zero wedge ratio). 
     Intentional variances in thread leads have been disclosed in the prior art for the purposes of load distribution, however, the present inventor is unaware of variances in thread leads to form a thread seal for a wedge thread or a free-running thread. One example of a varied thread lead for stress distribution is disclosed in U.S. Pat. No. 4,582,348 issued to Dearden, et al. That patent is incorporated herein by reference in its entirety. Dearden discloses a connection with free-running threads that has the pin thread and box thread divided into three portions with different leads (note that Dearden refers to thread pitch, which is quantified as threads per inch). In  FIG. 3B , a graph of the thread leads for the box member and the pin member is shown. As shown in the graph, at one end of the connection, the pin thread lead  21  is larger than the box thread lead  22 . In the intermediate portion  23 , the pin thread lead  21  and box thread lead  22  are substantially equal. Then, at the other end of the connection, the box thread lead  22  is larger than the pin thread lead  21 . In Dearden, the changes in the pin thread lead  21  and box thread lead  22  are step changes (i.e. substantially instantaneous changes in the lead). The varied thread leads disclosed by Dearden are intended to distribute loading across a greater portion of the connection, and have no effect on the inability of the free-running threads to form a thread seal. Dearden does not disclose varying a load lead or stab lead independent of each other. 
     Another connection is disclosed in U.S. application Ser. No. 10/126,918 entitled “Threaded Connection Especially for Radially Plastically Expandable Conduit,” (“Sivley”) and assigned to the assignee of the present invention. That application is incorporated herein by reference in its entirety. Sivley discloses connections having a variance in load lead and/or stab lead on one or both of the pin member and the box member. A graph of an embodiment disclosed by Sivley is shown in  FIG. 3C . Sivley discloses varying the load lead  14  relative to the stab lead  12  at a selected rate over at least a portion of the pin thread and/or box thread. In  FIG. 3C , the connection is a wedge thread as shown by the difference between the load lead  14  and the stab lead  12 . The load lead  14  and the stab lead  12  converge at a linear rate towards the end of the thread. Sivley discloses various other embodiments having load leads  14  and stab leads  12  that vary at linear rates relative to each other. The variance in the thread leads distributes the loads experienced by the connection over the length of the connection. 
       FIG. 9  shows a prior art two-step connection. The threads that form the connection are separated on two different “steps,” a large step indicated by the bracket  31  and a small step indicated by the bracket  32 . The portion between the large step  31  and the small step  32  is commonly referred to as a mid-step  901 . In some connections, the mid-step  901  may be used as a metal-to-metal seal. The pin thread crest on the small step  32  of the pin member  101 , at its full design height, does not interfere with the box thread crest on the large step  31  of the box member  102  when the pin member  101  is stabbed into the box member  102 . The diameter of the small step  32  of the pin member  101  is smaller than the smallest crest-to-crest thread diameter on the large step  31  of the box member  102 . The pin thread  106  on the small step  32  can be stabbed past the box thread  107  on the large step  31 . The threads on both the small step  32  and the large step  31 , which have substantially the same nominal lead, engage with each revolution to make-up the connection. Thus, the number of revolutions during which the threads slide or rub against each other is reduced for the same number of engaged threads. A two-step connection allows for each of the steps to have threads with different characteristics as long there is little or no variance in the nominal lead of the threads on the steps. 
     A two-step wedge thread connection is disclosed in U.S. Pat. No. 6,206,436 issued to Mallis and assigned to the assignee of the present invention. That patent is incorporated herein by reference. Mallis discloses a two-step wedge thread connection having different wedge ratios, one of which is considered to be an “aggressive” wedge ratio and the other a “conservative” wedge ratio. “Aggressive” refers to the larger wedge ratio, and “conservative” refers to the smaller wedge ratio. Everything else the same, the greater the wedge ratio, the more determinate the make-up. Too large of a wedge ratio may have an inadequate wedging effect, which can allow the connection to back-off during use. Smaller wedge ratios are better able to resist backing-off of the connection. Too small of a wedge ratio may have such an indeterminate make-up that galling may occur over the lengthened make-up distance. Mallis discloses that one of the steps can have a wedge ratio that is optimized for a more determinate make-up (aggressive), while the other step can have a wedge ratio that is optimized for preventing back-off of the connection (conservative). 
     In U.S. Pat. Nos. 6,174,001 and 6,270,127 issued to Enderle and assigned to the assignee of the present invention, two-step, low torque wedge threads for tubular connectors are disclosed. Those patents are incorporated herein by reference in their entirety. One of the steps is provided so that there is interference contact at makeup along at least one of the complementary stab flanks, load flanks, roots, and crests while clearance is provided along another step along at least one of the complementary stab flanks, load flanks, roots, and crests, which reduces the amount of torque required for make-up of the connection while retaining torque sensitivity, scaling capability, and threads necessary for structural purposes. 
     One problem with two-step connections is that the connection must be thick to reach 100 percent pipe body efficiency. As used herein, “pipe body efficiency” is the tensile strength of the connection relative to the tensile strength of the tubular. The primary reason for needing a thicker connection is the unengaged space of the mid-step, which is required so that the threads on the large step can clear the threads on the small step during stabbing. The mid-step, due to the lack of thread engagement, does not contribute to the overall strength of the connection. The advantages of having two separate threads often makes up for the decreased pipe body efficiency, however, it is desirable to have a single step thread that can exhibit the advantages of two-step connections. 
     SUMMARY OF INVENTION 
     In one aspect, the present invention relates to a threaded connection having wedge threads. The threaded connection includes a pin member and a box member having a continuous pin thread and a continuous box thread, respectively. The pin thread has a pin thread crest, a pin thread root, a pin load flank, and a pin stab flank. The pin thread includes at least a first step, a mid-step, and a second step formed sequentially thereon. The box thread has a box thread crest, a box thread root, a box load flank, and a box stab flank. The box thread includes at least a first step, a mid-step, and a second step formed sequentially thereon. The steps on the box thread correspond generally in axial position with the steps on the pin thread. The first step has a first wedge ratio, the mid-step has a transition wedge ratio, and the second step has a second wedge ratio. The thread leads are substantially constant within each of the steps. The connection is designed such that, at make-up of the pin member with the box member, a clearance exists between at least one of the corresponding load flanks and the corresponding stab flanks on at least one of the first step, the mid-step, and the second step. 
     In another aspect, the present invention relates to a method of manufacturing a threaded connection having wedge threads using a machine tool with a programmable control. The method includes forming a pin member and a box member having a continuous pin thread and a continuous box thread, respectively. The pin thread has a pin thread crest, a pin thread root, a pin load flank, and a pin stab flank. The pin thread includes at least a first step, a mid-step, and a second step formed sequentially thereon. The box thread has a box thread crest, a box thread root, a box load flank, and a box stab flank. The box thread includes at least a first step, a mid-step, and a second step formed sequentially thereon. The steps on the box thread correspond generally in axial position with the steps on the pin thread. The first step has a first wedge ratio, the mid-step has a transition wedge ratio, and the second step has a second wedge ratio. The thread leads are substantially constant within each of the steps. The connection is designed such that, at make-up of the pin member with the box member, a clearance exists between at least one of the corresponding load flanks and the corresponding stab flanks on at least one of the first step, the mid-step, and the second step. 
     In another aspect, the present invention relates to a threaded connection having wedge threads. The threaded connection includes a pin member and a box member having a continuous pin thread and a continuous box thread, respectively. The pin thread has a pin thread crest, a pin thread root, a pin load flank, and a pin stab flank. The pin thread includes at least a first step, a mid-step, and a second step formed sequentially thereon. The box thread has a box thread crest, a box thread root, a box load flank, and a box stab flank. The box thread includes at least a first step, a mid-step, and a second step formed sequentially thereon. The steps on the box thread correspond generally in axial position with the steps on the pin thread. The first step has a first wedge ratio, the mid-step has a transition wedge ratio, and the second step has a second wedge ratio. The thread leads are substantially constant within each of the steps. The connection is designed such that, at make-up of the pin member with the box member, a clearance exists between both the corresponding load flanks and the corresponding stab flanks on at least one of the first step, the mid-step, and the second step. 
     Other aspects and advantages of the invention will be apparent from the following description and the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  shows a cross section of a prior art connection having a wedge thread. 
         FIG. 2  shows a cross section of a prior art connection having a free-running thread. 
         FIGS. 3A ,  3 B, and  3 C show graphs of thread leads for prior art connections. 
         FIG. 4A  shows a schematic representation of a threaded connection in accordance with one embodiment of the present invention. 
         FIGS. 4B and 4C  show graphs of thread leads versus axial position corresponding to the embodiment shown in  FIG. 4A . 
         FIG. 5A  shows a schematic representation of a threaded connection in accordance with one embodiment of the present invention. 
         FIGS. 5B and 5C  show graphs of thread leads versus axial position corresponding to the embodiment shown in  FIG. 5A . 
         FIG. 6A  shows a schematic representation of a threaded connection in accordance with one embodiment of the present invention. 
         FIGS. 6B and 6C  show graphs of thread leads versus axial position corresponding to the embodiment shown in  FIG. 6A . 
         FIG. 7A  shows a schematic representation of a threaded connection in accordance with one embodiment of the present invention. 
         FIGS. 7B and 7C  show graphs of thread leads versus axial position corresponding to the embodiment shown in  FIG. 7A . 
         FIG. 8A  shows a schematic representation of a threaded connection in accordance with one embodiment of the present invention. 
         FIGS. 8B and 8C  show graphs of thread leads versus axial position corresponding to the embodiment shown in  FIG. 8A . 
         FIG. 9  shows a cross section of a prior art two-step connection with a free-running thread. 
     
    
    
     DETAILED DESCRIPTION 
     The present invention relates to threads for tubular connections. More specifically, the present invention relates to threads having two-step characteristics formed on a single thread on a tapered connection. 
     For the purpose of clarity, several terms are explicitly defined below. As used herein, “a thread lead” refers generally to the group of leads consisting of the load lead, the stab lead, and the nominal lead. 
     As used herein, “helical length” refers to the number of turns of the thread that the contactor is disposed, and may be expressed in the number of degrees about the axis of the tubular (i.e. 360 degrees is one thread pitch). 
     Embodiments of the present invention have variations in wedge ratios on a single thread such that the connection has at least some characteristics of a two-step connection. Embodiments of the present invention are characterized by at least two distinct portions joined by a transition zone between the two distinct portions. The two distinct portions may be referred to using the same terminology used for two-step connections although embodiments of the present invention have a single step. In some embodiments, one step may have a different thread height (as measured from root to crest) in order to form a higher pressure thread seal. 
     Turning to  FIGS. 4A-C , a pseudo two-step thread in accordance with one embodiment of the present invention is shown.  FIGS. 4A-C  provide an exaggerated example of a pseudo two-step for illustrative purposes. In  FIG. 4A , the pin thread  406  that corresponds to the graph in  FIG. 4C  is shown at a selected make-up with the box thread  407  that corresponds to the graph in  FIG. 4B . In this particular embodiment the pin thread  406  and the box thread  407  have been designed to have interference between the load flanks  225  and  226  and the stab flanks  231  and  232  on both a first step  401  (compare to the small step  32  in  FIG. 9 ) and a second step  403  (compare to the large step  31  in  FIG. 9 ), while having a selected clearance between the flanks on the mid-step  402 . In one embodiment, flank interference may occur on one step before the other step during make-up, with both the first step  401  and the second step  403  having interference at the selected make-up. Further, in one embodiment, one or both the small step  32  and the large step  31  may have interference between only the load flanks or the stab flanks instead of both. 
     To achieve the pseudo two-step configuration shown in  FIG. 4A , the load lead  314  and the stab lead  312  may be varied in a complementary manner on both the pin thread  406  and the box thread  407 , as shown in  FIGS. 4B and 4C . The nominal lead  310  has been kept substantially constant over the length of both the pin thread  406  and the box thread  407 . Along the first step  401 , the difference between the load lead  314  and the stab lead  310  (i.e. wedge ratio  411 ) is substantially constant. At the end of the first step  401 , the wedge ratio  411  increases to wedge ratio  412  by increasing the load lead  314  by a selected amount while proportionally decreasing the stab lead  312  such that the nominal lead  310  is substantially maintained. The wedge ratio  412  is larger than both the wedge ratio  411  on the first step  401  and the wedge ratio  413  on the second step  403 . This length of the threads at the heightened wedge ratio  412  provides the transition between the first step  401  and the second step  403 , and may be referred to as the mid-step  402  using the terminology for two-step connections. The mid-step  402  is minor in helical length compared to the first step  401  and the second step  403 . In some embodiments, the helical length of the mid-step  402  may be in increments of about 360 degrees to prevent eccentric loading of the connection. After the mid-step  402 , the wedge ratio  412  decreases to the wedge ratio  413  on the second step  403 , which is about equal to the wedge ratio  411  on the first step  401  in this embodiment. 
     Continuing with  FIGS. 4A-4C , this embodiment has an offset  405  between the mid-step  402  on the pin thread  406  and the box thread  407 . The mid-step  402  on the box thread  407  begins at a slightly earlier selected axial position than the mid-step  402  on the pin thread  406 . This causes the box thread  407  to “open up” or widen slightly earlier than the pin thread  406 , which causes the selected clearance between flanks to occur on the mid-step  402 . To return the threads to having flank interference on the second step  403 , the second step  403  may also begin at an earlier selected axial position on the box thread  407 , which allows the pin thread  406  to “catch up” in width. The variations in the load lead  314  and the stab lead  312  over the length of the threads allows for the connection to behave as if it has two separate steps and a mid-step, as in a two-step connection. This allows for a connection to be designed to have different behavior in each portion of the connection. Those having ordinary skill in the art will appreciate that after using the teachings of the present disclosure, many combinations of first steps  401 , mid-steps  402 , and second steps  403  may be achieved using features for two-step connections known in the art. Examples of such connections are discussed below. 
     In  FIGS. 5A-5C , a pseudo two-step thread in accordance with one embodiment of the present invention is shown. In  FIG. 5A , the pin thread  406  that corresponds to the graph in  FIG. 5C  is shown at a selected make-up with the box thread  407  that corresponds to the graph in  FIG. 5B . In this particular embodiment, the pin thread  406  and the box thread  407  have been designed to have interference between the load flanks  225  and  226  and the stab flanks  231  and  232  on both a first step  401  and a second step  403 , while having a selected clearance between the flanks on the mid-step  402 . The thread shown in  FIGS. 5A-5C  differs from the one shown in  FIGS. 4A-4C  because the wedge ratio  413  of the second step  403  is greater than wedge ratio  411  of the first step  401 . Two-step connections having differential wedge ratios are disclosed in U.S. Pat. No. 6,206,436 issued to Mallis, which was discussed above. Mallis&#39; teachings (including all of the advantages), as they apply to two-step connections having two different wedge ratios, are generally applicable to the pseudo two-step connection disclosed herein. Using the terminology from Mallis, in the embodiment shown in  FIGS. 5A-5C , the second step  403  has the “aggressive” wedge ratio  413 , while the first step  401  has the “conservative” wedge ratio  411 . 
     Turning to  FIGS. 6A-6C , another pseudo two-step thread in accordance with one embodiment of the present invention is shown. In this particular embodiment, the pin thread  406  and the box thread  407  have been designed to have interference between the load flanks  225  and  226  and the stab flanks  231  and  232  on the mid-step, while selected clearances exist between the flanks on the first step  401  and the second step  403 . The embodiment shown in  FIG. 6A  may be desirable for forming a thread seal at the mid-step  402 . In one embodiment, the mid-step  402  may also have increased root/crest interference as disclosed in the concurrently filed U.S. patent application titled “Threads with Perturbations.” In this particular embodiment, the helical length of the mid-step  402 , which experiences load before the first step  401  and the second step  403 , is about 360 degrees in order to prevent eccentric loading. Although  FIG. 6A  shows the selected clearances between flanks on the first step  401  and the second step  403  as about equal, those having ordinary skill in the art will appreciate that, in other embodiments, the selected clearances may be different. For example, the connection may be designed such that the second step  403  has a smaller selected clearance than the first step  401 . In such an embodiment, the second step  403  would be loaded under tension before the first step  401 . In other embodiments, the selected clearances may be different between load flanks and stab flanks on the same step. 
     In  FIGS. 7A-7C , another pseudo two-step thread in accordance with one embodiment of the present invention is shown. In this particular embodiment, the pin thread  406  and the box thread  407  have been designed to have interference between the load flanks  225  and  226  and the stab flanks  231  and  232  on the first step  401 , while selected clearances exist between the flanks on the mid-step  402  and the second step  403 .  FIGS. 7B and 7C  show how the pseudo two-step thread in  FIG. 7A  can be achieved. In this embodiment, the mid-step  402  on the box thread  407  has an offset  405  from the mid-step  402  on the pin thread  406 , which causes the box thread  407  to open up before the pin thread  406  widens. This causes a selected clearance to occur between the flanks on the mid-step  402 . To maintain at least some clearance between the flanks on the second step  403 , the mid-step  402  on the pin thread  406  has a shorter helical length than the mid-step  402  on the box thread  407  such that it ends at about the same axial position as the mid-step  402  on the box thread  407 . The configuration shown in  FIG. 7A  allows for stresses to be distributed along the connection based on the amount of stress experienced by the connection. For example, a pseudo two-step connection may be designed to initially load the first step  401  when pulled in tension, and then load the second step  403  prior to yielding the threads in the first step  401 . Such a design is disclosed for two-step connections in the concurrently filed U.S. patent application titled “Floating Wedge Thread for Tubular Connection.” 
     Turning to  FIGS. 8A-8C , another pseudo two-step thread in accordance with one embodiment of the present invention is shown. In this particular embodiment, the pin thread  406  and the box thread  407  have been designed to have alternating interference and clearance between the load flanks  225  and  226  and the stab flanks  231  and  232  on the steps. In designing the thread shown in  FIG. 8A , the first step  401  is made to have interference between the stab flanks  231  and  232 , while having clearance between the load flanks  225  and  226 . To alternate between interference and clearance, the load lead  314  and the stab lead  312  of one of the pin thread  406  and the box thread  407  may be offset from each other in their axial positions. In this embodiment, the pin thread  406  has the offset  408 . In another embodiment, the offset  408  may be on the box thread  407 . 
     Continuing with the embodiment shown in  FIGS. 8A-8C , the increase in the load lead  314  of the pin thread  406  begins before the increase in the load lead  314  of the box thread  407 . This causes the pin thread  406  to widen on the load flank side, which brings the load flanks  225  and  226  into interference at the mid-step  402 . Then, the decrease in the stab lead  312  of the box thread  407  begins before the decrease in the stab lead  312  of the pin thread  406 , which brings the stab flanks  231  and  232  out of interference at the mid-step  402 . The flank interference is then reversed back at the end of the mid-step  402  by decreasing the load leads  314  and increasing the stab leads  312  with the same offsets in axial position. This causes the second step  403  to have interference between the stab flanks  231  and  232 , while having clearance between the load flanks  225  and  226 . In another embodiment, the alternating of interference and clearance may be reversed (i.e. having interference between the load flanks  225  and  226  on first step  401 , while having clearance between the stab flanks  231  and  232 ). 
     While each of the above embodiments shows at least some clearance between flanks, it should be noted that some embodiments of the pseudo two-step connection may be designed to have varying amounts of interference between flanks on each of the first step, the mid-step, and the second step at a selected make-up. A pseudo two-step connection may be made such that interference occurs in a sequential manner between load flanks and stab flanks on the first step, the mid-step, and the second step. For example, by using the offsetting methods of load lead and stab lead changes discussed with respect to the above embodiments, a pseudo two-step connection may be designed such that during make-up, the flanks on the second step come into interference. Then as the make-up continues, the flanks on the first step come into interference, with flanks on the mid-step coming into interference last. As discussed above, flank interference increases during make-up of a wedge thread connection. As a result, at a selected make-up, the step on which flank interference occurs first will have the most interference. Those having ordinary skill in the art will appreciate that many combinations and sequences of interference and clearance between flanks are possible using the teachings of the present invention. Thus, the scope of the present invention should not be limited to the select number of embodiments disclosed herein. 
     Another variation that is possible is the relative helical lengths of the first step, the mid-step, and the second step. While the above embodiments have shown first steps that are substantially equal in helical length to the second steps, those having ordinary skill in the art will appreciate the first step and second step may be unequal in helical length. For example, on a connection having about 10 thread turns (i.e. about 3600 degrees in helical length), the first step may be about 4 thread turns (i.e. about 1440 degrees in helical length), while the mid-step may be about 1 thread turn and the second step may be about 5 thread turns. 
     It should be noted that the graphs of thread leads for the above embodiments are idealized as step changes in the thread leads. In practice, the changes in the thread leads may not be as instantaneous as shown in the graphs due to the manufacturing process used to make the threads. For example, in one embodiment, a computer numerically controlled (“CNC”) lathe may be used. CNC machines may be controlled by CNC programs. Typically, the CNC program consists of positions for each axis of control. For example, if the CNC lathe has an axial position and a rotational position, the program would have an axial position value corresponding with each rotational position. Because a CNC lathe is usually rotating at a set speed measured in rotations per minute (“RPM”), the CNC program typically has the rotational positions in order and at set increments as the part is rotated in the machine. The increments at which the rotational positions are spaced is commonly referred to as the “resolution” of the lathe. For example, if the resolution is about 90 degrees, a data point will exist for each sequential increment of about 90 degrees. An axial position would be selected for each increment. Typically, the CNC lathe will move the axial position at a substantially constant speed between points. The speed is selected as required to reach the next axial position at substantially the same time as the corresponding rotational position. The thread lead can be selected by calculating the value for the increments such that for each revolution, the axial position advances by a distance substantially equal to the thread lead. For example, a lead of 1 inch per revolution would advance by a ¼ inch every 90 degrees. Those having ordinary skill in the art will be able to apply the above teachings for use with other manufacturing methods. The resolution of the lathe used may effect the amount of offset between steps. Another result of using machine tools is that the momentum of the moving parts and response time in the controls may result in a more smoothed out change in thread leads. Although the precise changes in thread leads between the first step, the mid-step, and the second step may vary by production method, the benefits of the pseudo two-step connection may still be realized. 
     It should be noted that embodiments of the present invention have at least a first step and a second step with a transition zone (i.e. mid-step) joining the first step and the second step. The first step, the mid-step, and the second step are formed sequentially on both the pin thread and the box thread. Those having ordinary skill in the art will appreciate that additional steps may be added to the pin thread and the box thread without departing from the scope of the present invention. Further, embodiments of the present invention may be formed on an actual two-step connection. For example, a pseudo two-step in accordance with the above disclosure may be formed on one of the small step and the large step of a two-step connection such that the connection essentially has three steps. 
     While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as disclosed herein. Accordingly, the scope of the invention should be limited only by the attached claims.