You are an expert at summarizing long articles. Proceed to summarize the following text:

You are an expert at summarizing long articles. Proceed to summarize the following text: 
BACKGROUND OF INVENTION 
     1. Field of the Invention 
     The invention relates generally to stators for use with positive displacement drilling motors. More specifically, the invention relates to selecting an optimized liner thickness for a stator so as to increase the power available from a positive displacement motor while increasing longevity of the stator. 
     2. Background Art 
     Positive Displacement Motors (PDMs) are known in the art and are commonly used to drill wells in earth formations. PDMs operate according to a reverse mechanical application of the Moineau principle wherein pressurized fluid is forced though a series of channels formed on a rotor and a stator. The channels are generally helical in shape and may extend the entire length of the rotor and stator. The passage of the pressurized fluid generally causes the rotor to rotate within the stator. For example, a substantially continuous seal may be formed between the rotor and the stator, and the pressurized fluid may act against the rotor proximate the sealing surfaces so as to impart rotational motion on the rotor as the pressurized fluid passes through the helical channels. 
     Referring to FIG. 1, a typical rotor  10  includes at least one lobe  12  (wherein, for example, channels  14  are formed between lobes  12 ), a major diameter  8 , and a minor diameter  6 . The rotor  10  may be formed of metal or any other suitable material. The rotor  10  may also be coated to withstand harsh drilling environments experienced downhole. Referring to FIG. 2, a typical stator  20  comprises at least two lobes  22 , a major diameter  7 , and a minor diameter  5 . Note that if the rotor ( 10  in FIG. 1) includes “n” lobes, the corresponding stator  20  used in combination with the rotor  10  generally includes either “n+1” or “n−1” lobes. Referring to FIG. 3, the stator  20  generally includes a cylindrical external tube  24  and a liner  26 . The liner  26  may be formed from an elastomer, plastic, or other synthetic or natural material known in the art. The liner  26  is typically injected into the cylindrical external tube  24  around a mold (not shown) that has been placed therein. The liner  26  is then cured for a selected time at a selected temperature (or temperatures) before the mold (not shown) is removed. A thickness  28  of the liner  26  is generally controlled by changing the dimensions of the mold (not shown). 
     A lower end of the rotor may be coupled either directly or indirectly to, for example, a drill bit. In this manner, the PDM provides a drive mechanism for a drill bit independent of any rotational motion of a drillstring generated proximate the surface of the well by, for example, rotation of a rotary table on a drilling rig. Accordingly, PDMs are especially useful in drilling directional wells where a drill bit is connected to a lower end of a bottom hole assembly (BHA). The BHA may include, for example, a PDM, a transmission assembly, a bent housing assembly, a bearing section, and the drill bit. The rotor may transmit torque to the drill bit via a drive shaft or a series of drive shafts that are operatively coupled to the rotor and to the drill bit. Therefore, when directionally drilling a wellbore, the drilling action is typically referred to as “sliding” because the drill string slides through the wellbore rather than rotating through the wellbore (as would be the case if the drill string were rotated using a rotary table) because rotary motion of the drill bit is produced by the PDM. However, directional drilling may also be performed by rotating the drill string and using the PDM, thereby increasing the available torque and drill bit rpm. 
     A rotational frequency and, for example, an amount of torque generated by the rotation of the rotor within the stator may be selected by determining a number of lobes on the rotor and stator, a major and minor diameter of the rotor and stator, and the like. An assembled view of a rotor and a stator is shown in FIG.  3 . Rotation of the rotor  10  within the stator  20  causes the rotor  10  to nutate within the stator  20 . Typically, a single nutation may be defined as when the rotor  10  moves one lobe width within the stator  20 . The motion of the rotor  10  within the stator  20  may be defined by a circle O which defines a trajectory of a point A disposed on a rotor axis as point A moves around a stator axis B during a series of nutations. Note that an “eccentricity”e of the assembly may be defined as a distance between the rotor axis A and the stator axis B when the rotor  10  and stator  20  are assembled to form a PDM. 
     Typical stators known in the art are formed in a manner similar to that shown in FIG.  2 . Specifically, an inner surface  29  of the external tube  24  is generally cylindrical in shape and the stator lobes  22  are formed by molding an elastomer in the external tube  24 . Problems may be encountered with the stator  20  when, for example, rotation of the rotor  10  within the stator  20  shears off portions of the stator lobes  22 . This process, which may be referred to as “chunking,” deteriorates the seal formed between the rotor  10  and stator  20  and may cause failure of the PDM. Chunking may be increased by swelling of the liner  26  or thermal fatigue. Swelling and thermal fatigue may be caused by elevated temperatures and exposure to certain drilling fluids and formation fluids, among other factors. Moreover, flexibility of the liner  26  may lead to incomplete sealing between the rotor  10  and stator  20  such that available torque may be lost when the rotor compresses the stator lobe material, thereby reducing the power output of the PDM. Accordingly, there is a need for a stator design that provides increased power output and increased longevity in harsh downhole environments. 
     SUMMARY OF INVENTION 
     In one aspect, the invention comprises a stator for a positive displacement motor. The stator comprises an external tube comprising an outer surface and an inner surface, and the inner surface comprising at least two radially inwardly projecting lobes extending helically along a selected length of the external tube. A liner is disposed proximate the inner surface, and the liner conforms to the radially inwardly projecting lobes formed on the inner surface and to the helical shape of the inner surface. A thickness of the liner is at a maximum proximate the at least two radially inwardly projecting lobes. 
     In another aspect, the invention comprises a positive displacement motor. The positive displacement motor comprises a stator including an external tube comprising an outer surface and an inner surface. The inner surface comprises at least two radially inwardly projecting lobes extending helically along a selected length of the external tube. A liner is disposed proximate the inner surface, and the liner conforms to the radially inwardly projecting lobes formed on the inner surface and to the helical shape of the inner surface. A thickness of the liner is at a maximum proximate the at least two radially inwardly projecting lobes. A rotor is disposed inside the stator, and the rotor comprises at least one radially outwardly projecting lobe extending helically along a selected length of the rotor. The at least one radially outwardly projecting lobe formed on the rotor is adapted to sealingly engage the at least two radially outwardly projecting lobes formed on the liner. 
     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 prior art rotor. 
     FIG. 2 shows a prior art stator. 
     FIG. 3 shows an assembled view of a prior art positive displacement motor. 
     FIG. 4 shows a cross-sectional view of an embodiment of the invention. 
    
    
     DETAILED DESCRIPTION 
     FIG. 4 shows an embodiment comprising at least one aspect of the present invention, A positive displacement motor (PDM)  30  comprises a stator  32  and a rotor  34 . The stator  32  comprises an external tube  38  that may be formed from, for example, steel or another material suitable for downhole use in a drilling environment. The stator also comprises a liner  36  that may be formed from an elastomer, a plastic, or any other suitable synthetic or natural material known in the art. In some embodiments, the liner may also be formed from a fiber reinforced material such as the materials described in co-pending U.S. patent application Ser. No. 10/097,480, and assigned to the assignee of the present application. 
     The external tube  38  comprises a shaped inner surface  44  that comprises at least two lobes  46  formed thereon. The lobes  46  are helically formed along a selected length of the external tube  38  so that the lobes  46  define a helical pattern along the selected length. The helical form of the inner surface  44  generally corresponds to a desired shape for stator lobes. The liner  36  typically comprises at least two lobes  40 , and a thickness  42  of the liner  36  is non-uniform throughout a cross-section thereof. The lobes  40  (and the liner  36 ) are helically formed along a selected length of the external tube  38  such that the liner  36  conforms to the helically shaped inner surface  44  so that the at least two lobes  46  formed on the shaped inner surface  44  correspond to the lobes  40  formed in the liner  36 . The external tube  38 , including the inner surface  44 , may be helically shaped by any means known in the art including machining, extrusion, and the like. 
     In some embodiments, the shaped inner surface  44  of the external tube  38  is adapted to provide additional support for the liner material. The shaped inner surface  44  “stiffens” the liner  36  by providing support for the liner  36  (e.g., by forming a metal backing), thereby increasing power available from the PDM. For example, shaping the inner surface  44  to form a contoured backing for the liner  36  may stiffen the liner material proximate the lobes  40  by reducing an amount by which the liner  36  may be compressed when contacted by the rotor  44  so that a better seal may be formed between the rotor  44  and the stator  32 . Moreover, reduced flexibility increases an amount of torque required to stall the PDM. 
     The thickness  42  of the liner  36  may be increased at selected locations that are exposed to, for example, increased wear and shear (e.g., proximate the lobes  40 ,  46 ), so that the longevity of the stator  32  and, therefore, the longevity of the PDM  30  may be increased. In some embodiments, the thickness of the liner  36  is selected so as to maximize a shear strength of the liner  36  proximate the lobes  46  The shaped form of the inner surface  44  typically results in a thinner liner  36  than is commonly used in prior art stators (such as that shown in FIG.  3 ). Fluid pressure is less likely to deform the liner  36  and, accordingly, the liner  36  is less susceptible to deformation that could reduce the efficiency of the seal formed between de rotor  34  and stator  32  (thereby producing an additional loss in power output of the PDM  30 ). 
     As shown in FIG. 4, the thickness  42  of the liner  36  may be varied so that a thickness TA of the portion of the liner  36  proximate the lobes  46  is greater than a thickness of other portions of the liner  36  (e.g., a thickness TB of the portion of the liner  36  proximate channels  48 ). The thickness  42  of the liner  36  may be selected to generate a desired amount of contact (or, if desired, clearance) between the liner  36  and the rotor  34 . For example, the thickness  42  of the liner  36  may be selected to form a seal between the rotor  34  and the stator  32  while maintaining a desired level of compression between the rotor  34  and stator  32  when they are in contact with each other. Moreover, the thickness  42  of the liner  36  may be selected to permit, for example, swelling or contraction of the liner  36  caused by elevated temperatures, contact with drilling fluids and other fluids, and the like. 
     In some embodiments, the thickness TA of the liner  36  proximate the lobes  46  is selected to be at least 1.5 times the thickness TB of the liner  36  proximate the channels  48 . In other embodiments, the thickness TA of the liner  36  proximate the lobes  46  may be selected to be less than or equal to 3 times the thickness TB of the liner  36  proximate the channels  48 . Other embodiments may comprise other thickness ratios depending on the type of material (e.g., elastomer, plastic, etc.) selected to form the liner  36 . 
     Note that the embodiment in FIG. 4 is generally referred to as a “5:6” configuration including 5 lobes formed on the rotor and 6 lobes formed on the stator. Other embodiments may include any other rotor/stator combination known in the art, including 1:2, 3:4, 4:5, 7:8, and other arrangements. Moreover, as described above, stators may generally be formed using “n+1” or “n−1” lobes, where “n” refers to a number of rotor lobes. Accordingly, the embodiment shown in FIG. 4, and other embodiments described herein, are intended to clarify the invention and are not intended to limit the scope of the invention with respect to, for example, a number of or arrangement of lobes. 
     Accordingly, the present invention allows for an inner surface of an external stator tube to be shaped so as to enable optimization of a liner thickness and to provide a stiff backing for the liner material. Optimizing liner thickness leads to increased power output and increased longevity of the power section. 
     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.

Summary:
A stator for a positive displacement motor including an external tube. The external tube includes an outer surface and an inner surface, and the inner surface includes at least two radially inwardly projecting lobes extending helically along a length of the external tube. A liner is positioned adjacent the inner surface, and the liner conforms to the radially inwardly projecting lobes formed on the inner surface and to the helical shape of the inner surface. A thickness of the liner is at a maximum at the at least two radially inwardly projecting lobes.