Patent Publication Number: US-6711969-B2

Title: Methods for designing rotary drill bits exhibiting sequences of substantially continuously variable cutter backrake angles

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a divisional of application Ser. No. 09/730,983, filed Dec. 6, 2000, now U.S. Pat. No. 6,536,543, issued Mar. 25, 2003. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to rotary bits for drilling subterranean formations. More specifically, the invention relates to fixed cutter, or so-called “drag” bits, employing superabrasive cutters exhibiting continuously varying cutter backrake angles along different locations or zones on the face of the bit, the variations being tailored to improve the transition between portions of the bit which may contain different cutter backrake angles as well as optimize the performance of the drill bit. 
     2. State of the Art 
     Conventional rotary-type earth-boring drill bits typically include cutting elements, or “cutters,” arranged thereon so as to facilitate the cutting away of a subterranean formation in a desired manner. Cutters, typically including polycrystalline diamond compacts (PDCs), are oriented in cutter pockets of the bit, which are oriented so as to protect the cutter and provide clearance at the trailing edge of the cutter as it moves axially while drilling. The angle at which a cutting face of a cutter is oriented relative to a wall of a bore hole being formed is referred to as “rake.” If the angle between a bore hole surface and a cutter face is 90°, the rake is said to be neutral, or zero degrees. If the angle between the cutting face of a cutter and the adjacent surface of the bore hole being formed is less than 90°, the rake angle is negative, and is typically termed “backrake.” The amount of backrake is equal to the angle the cutting face of the cutter is tilted from the neutral rake position. For example, a cutter oriented with its cutting face at a 70° angle to the adjacent surface of the bore hole being formed has a 20° backrake (90°−70°=20°). When the rake angle between the cutting face of a cutter and the adjacent bore hole surface is greater than 90°, the cutter is oriented with a positive, or aggressive, rake angle, or a “frontrake,” which is measured in a similar manner to that in which backrake is measured. 
     Recent laboratory testing and modeling have demonstrated that cutter backrake angles may affect drilling performance characteristics. Specifically, increasing the backrake angle of a cutter appears to improve drilling performance after the cutter begins to wear. The wear flat of a cutter oriented at a larger backrake angle is smaller than the wear flat of a cutter oriented at a smaller (i.e., closer to neutral) backrake angle for a given amount of diamond volume removed. This means that as the diamond begins to wear away from the cutter, cutters oriented at larger backrake angles have smaller “flat” areas than do cutters oriented at smaller backrake angles. Smaller wear flats on cutters essentially provide a more effective cutting geometry. A sharp cutter (i.e., small wear flat) contacts a formation with less area and the same amount of force, thereby inducing larger stresses in the formation, increasing cutting efficiency. In addition, it has been found that orienting cutters to have larger backrake angles does not detrimentally affect the performance of the bit as cutter wear increases. Moreover, cutters that are oriented to have larger backrake angles typically provide better impact resistance than cutters that are oriented to have smaller backrake angles. 
     Although the aforementioned increased impact resistance and advantageous wear flat behavior is beneficial, the detriment to large backrake angles is that more weight on bit (WOB) is required to drill at a given rate of penetration (ROP). Therefore, generally, an all-encompassing increase in cutter backrake angles may cause the drill bit to require such a great WOB so as to render the bit undrillable. 
     Cutter rake not only affects the relationship between the ROP and the WOB but also determines the aggressiveness of the bit. Thus, the rakes of the cutters on a drag bit can affect the performance and drilling characteristics of the bit. The cutters on many drag bits are oriented so as to be backraked due to the increased fracture resistance of cutters with relatively large backrakes. 
     Current PDC drag bit design typically includes cutters oriented at different backrake angles depending upon their locations upon the bit. For example, cutters that are located within about a third of the bit radius from the bit&#39;s longitudinal axis are typically oriented with nominal 15° backrake angles. Cutters located in the shoulder area of the bit are oriented with backrake angles of about 20°. Cutters that are positioned near the gage section of the bit are typically oriented so as to have even higher backrake angles, for instance, about 30°. This discontinuous change in cutter backrake angle abruptly changes cutter behavior and performance between each area of the bit. This discontinuity may be exaggerated by the effective rake angles of the cutters. 
     Each cutter located on a bit crown at a given radial distance from the longitudinal axis of the bit will traverse a helical path upon rotation of the bit. The geometry (pitch) of the helical path is determined by the ROP of the bit (i.e., the rate at which the bit drills into a formation) and the rotational speed of the bit. Mathematically, it can be shown that the helical angle traversed by a cutter relative to a horizontal plane (i.e., a plane normal to the longitudinal axis of the bit) depends upon the distance the cutter is spaced apart from the longitudinal axis of the bit. For a given ROP and rotary speed, cutters located closer to the longitudinal axis have greater helical angles than those of cutters positioned greater distances from the longitudinal axis of the bit. Essentially, the greatest change in helical angles occurs for cutters positioned about 1½ inches to about 2 inches from the bit&#39;s longitudinal axis. In this region, the helical angles of the cutters during rotation of the bit vary from near 90° for cutters nearest the longitudinal axis of the bit to about 7° for cutters positioned about 2 inches from the longitudinal axis. The change in helical angle for cutters spaced about 2 inches from the longitudinal axis up to the bit gage is relatively small. 
     Effective cutter backrake is the angle between the cutter and the formation after correcting for the aforementioned helical angle during drilling (i.e., subtracting the helical angle of a cutter during drilling from the rake angle of the cutter). Since cutters may be at different radial locations, their cutting speeds will vary linearly with their radial position. This phenomenon of variance in “effective rake” of a cutter with radial location, bit rotational speed, and ROP is known in the art and a more detailed discussion thereof may be found in U.S. Pat. No. 5,377,773, assigned to the assignee of the present invention, the disclosure of which is hereby incorporated herein in its entirety by this reference. 
     Planar state of the art PDCs, as well as thermally stable products (TSPs) and other known types of cutters, are typically set at a given backrake angle on the bit face to enhance their ability to withstand axial loading of the bit, which is caused predominantly by the downward force applied to the bit during drilling, WOB. By comparing the effective backrake of a cutter, it is easy to see that cutters positioned within about 2 inches of the longitudinal axis of a bit are angled more aggressively than more distantly positioned cutters with the same or similar actual backrake angles. 
     As a result of the different effective rake angles of cutters that are oriented on a bit so as to have the same actual rake angles, these cutters wear differently, depending upon their radial distances from the longitudinal axis of the bit. Attempts have been made to correct for this problem through cutter redundancy, but the effectiveness of cutter redundancies is limited by the number of blades on the bit and by space constraints. 
     U.S. Pat No. 5,979,576 to Hansen et al. (hereinafter “Hansen”), assigned to the assignee of the present invention, discloses anti-whirl drag bits with “flank” cutters placed in a so-called “cutter-devoid zone” at or near the gage area thereof. Typically, a bearing pad would be positioned on the bit in this region, and would accept the imbalance force, thereby keeping the bit stable. Instead, it is proposed in Hansen to place cutters located within the normally cutter-devoid area at a lesser height from the bit profile than other cutters and at positive, neutral, or negative rake angles. These cutters only engage the formation when the cutting zone cutters dull and the bit has a reduced tendency to whirl, or when the cutting zone cutters achieve relatively high depths of cut, such as when reaming or under high rates of penetration. Under high depths of cut, these cutters engage the formation and prevent damage to the bearing zone and thereby extend the life of the anti-whirl drag bit. While Hansen discloses flank cutters oriented at specific angles, Hansen does not disclose orienting the flank cutters on a bit at different rake angles from one another. 
     U.S. Pat No. 5,549,171 to Mensa-Wilmot et al. discloses drag bits with sets of cutters which are generally spaced the same radial distance from the longitudinal axis of the bit position but have differing backrakes. This may be accomplished by placing cutters with different backrakes onto different blades of the drag bit. Each set of cutters includes cutters oriented at the same rake angles. The cutters of different sets on a single blade may each have the same rake angles, or longitudinally adjacent sets of cutters offset, with a single blade of the bit including cutters oriented at different rake angles. The different rake angles of the cutters on each blade are not, however, angles that vary continuously (i.e., increase or decrease) along the height of the drag bit or with various radial distances from a longitudinal axis of the drag bit. 
     U.S. Pat No. 5,314,033 to Tibbitts (hereinafter “Tibbitts”), assigned to the assignee of the present invention, discloses the use of “positive”-raked cutters in combination with negative or neutral rake cutters in such a manner that the cutters work cooperatively with one another. Effectively positive raked cutters are disclosed as aggressively initiating the cutting of the formation, whereas effectively negative raked cutters are disclosed as skating or riding on the formation. This causes two vastly different cutting mechanisms to coincide on the drill bit, with sudden changes at the coincident boundary between areas with different effective backrakes. Tibbitts does not, however, disclose a bit that includes regions on the face thereof with cutters oriented at different, continuously varying positive or negative rake angles. 
     The inventors are not aware of any art that discloses drag bits with fixed cutters at a particular region of the bit that are oriented so as to have different, continuously varied rake angles. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention includes rotary drag bits with fixed cutters having substantially continuously varied rake angles corresponding to the locations of the cutters relative to the longitudinal axis of the drag bit. As used herein, the term “rake” refers to the radial angle of a cutting face of a cutter relative to a reference line perpendicular to a surface of a formation being drilled, as described previously herein. 
     In one embodiment of a drag bit incorporating teachings of the present invention, cutters are oriented to have rake angles that increase proportionately with an increase of the radial distance of cutter locations from the longitudinal axis of the drag bit. 
     In another embodiment of the present invention, a drag bit includes a face with a plurality of radially separate cutter zones or regions thereon. Each cutter zone includes a number of cutters oriented so as to have the same backrake angle. The cutters of one zone on the face of the drag bit will, however, be oriented to have rake angles that differ from the cutters located within the one or more other zones on the face of the drag bit. In regions where two adjacent zones border one another, cutters adjacent to the border are oriented so as to have rake angles that provide a smooth transition between the rake angles of cutters in each of the adjacent zones. In addition, a given zone or region may include a sequence of cutters having increasing, decreasing, increasing then decreasing, decreasing then increasing, or cyclical variations in rake angles. 
     Another embodiment of drag bit according to the present invention also includes fixed cutters within at least a region or zone over the bit face which are oriented to have rake angles that vary continuously, but not necessarily proportionately to the radial distance of each of the cutters from the longitudinal axis of the drag bit. Rather, other factors, such as the longitudinal location or the angle of the helical path of each cutter, may be taken into account in determining the rake angle at which each of the cutters is oriented. 
     A drag bit incorporating teachings of the present invention may include at least three cutters oriented so as to have rake angles that increase or decrease sequentially based upon the relative radial locations of the cutters on the drag bit, the relative longitudinal positions of the cutters on the drag bit, or the relative positions of the cutters on a blade of the drag bit. 
     The rake angles of cutters on drag bits of the present invention may take into account the angle of the helical path each cutter travels during rotation of the drag bit. The angle of the helical path may be accounted for by continuously varying the effective rake angles of the cutters depending upon their position on the drag bit so as to counteract the effective rakes of the cutters caused by the angles of the helical paths of the cutters. 
     It is also contemplated that the rake angles of different cutters may be varied in response to bit performance factors. By way of example, weight on bit as a function of torque data may be analyzed and cutters within at least one region on the face of a drag bit may be oriented at rake angles that are continuously varied so as to provide a torque response as a function of weight on bit. As another example, the rake angles at which different cutters within a particular region of a face of a drag bit are oriented may be selected in response to bit stability data. Directional drilling criteria may also be used to determine the different, continuously varied rake angles of cutters within a particular region on a face of a drag bit. Other examples of factors that may be considered to determine the specific, continuously varied rake angle of different cutters on a face of a drag bit include, but are not limited to, wear characteristics, formation type, cutter loading, rock stresses, filtration and filtration gradients versus design depth of cut in permeable rocks, and thermal loading. 
    
    
     Other features and advantages of the present invention will become apparent to those of ordinary skill in the art through consideration of the ensuing description, the accompanying drawings, and the appended claims. 
     DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
     FIG. 1 is a side cross-sectional elevation of a five-bladed earth-boring rotary-type drag bit; 
     FIG. 2 is a bottom elevation of the drag bit of FIG. 1; 
     FIG. 3A is a side cross-sectional elevation of a bit blade section containing one cutter pocket; 
     FIG. 3B is a side cross-sectional elevation of the bit blade section illustrated in FIG. 3A, with a cutter disposed in the cutter pocket and illustrating the rake angle of the cutter; 
     FIGS. 4A-4E are side elevations of each of the five blades of the drag bit of FIG. 1, depicting radial cutter placement in accordance with the present invention; 
     FIGS. 4F-4T graphically depict embodiments for the radial position relationships of the cutters shown in FIGS. 4A-4E and the rake angles of each of these cutters; 
     FIG. 5A schematically depicts a cutter design layout for a drill bit and illustrates radial and longitudinal cutter positions; 
     FIGS. 5B-5E graphically depict embodiments for vertical position relationships of the cutters shown in FIG.  5 A and the rake angles of these cutters; 
     FIG. 6A is a side elevation of a bit blade depicting the radial positions of cutters along the blade; 
     FIGS. 6B-6G graphically depict the relationships between the radial positions of the cutters shown in FIG. 6A along a single blade and the rake angles of each of these cutters; 
     FIG. 7A is a side elevation of a bit blade depicting the vertical positions of the cutters carried thereby; 
     FIGS. 7B-7F graphically depict the relationships between the vertical positions of the cutters on the blade shown in FIG.  7 A and the rake angles of each of these cutters; 
     FIG. 8 graphically depicts the amount of wear exhibited by each of the cutters of the drag bit that is schematically represented in FIG. 5A; 
     FIG. 9A graphically illustrates that the cutters of the drag bit of FIG. 5A have cutting faces oriented at substantially the same backrake angles; and 
     FIGS. 9B and 9C graphically depict reorientation of the cutters of the drag bit of FIG. 5A in response to the wear data shown in FIG.  9 A. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     With reference to FIGS. 1 and 2, an exemplary rotary-type earth-boring fixed cutter drill bit  10 , which is also referred to simply as a “drag bit,” is illustrated. FIG. 1 depicts drag bit  10  as it could be oriented while drilling a formation. FIG. 2 illustrates a face  12  of drag bit  10 , which leads drag bit  10  in drilling a formation. 
     As shown in FIG. 1, drag bit  10  may comprise a bit body formed as a mass of erosion-resistant and abrasion-resistant particulate material  200 , such as tungsten carbide (WC), infiltrated with a tough and a ductile binder material  201 , such as an iron-nickel alloy, formed over a steel blank  202 . Alternatively, drag bit  10  may comprise a steel body. In either event, drag bit  10  includes a shank  204  with a threaded region  206  configured to attach drag bit  10  to a drill string (not shown). 
     As depicted in FIG. 2, drag bit  10  includes five blades  20  that extend generally radially over bit face  12  toward the gage  22  of drag bit  10 . Blades  20  may include recesses formed therein, which are referred to as cutter pockets  30  (FIG.  3 A), that carry cutting elements, which are also referred to herein as cutters  150  (FIG. 3B) for simplicity. Cutters  150  are oriented so as to cut into a formation upon rotation of drag bit  10 . The recessed areas located between gage pads  18  at upper ends of adjacent blades  20  extending radially beyond the bit body are referred to as junk slots  16 . 
     Referring back to FIG. 1, drag bit  10  also includes internal passages  80 , which communicate drilling fluid from the drill string (not shown), through shank  204 , to face  12 . Passages  80  communicate with face  12  by way of apertures  14  formed in face  12 . Apertures  14  are preferably configured to receive nozzles  82 . Nozzles  82  may be positioned adjacent to face  12  at the ends of passages  80  so as to aim drilling fluid ejected from passages  80  in directions that will facilitate the cooling and cleaning of cutters  150 , as well as the removal of formation cuttings and other debris from face  12  of drag bit  10  via junk slots  16 . 
     FIG. 3A, which illustrates a section of a blade  20  that includes one cutter pocket  30 , the sides of which (see FIG. 2) have been omitted for clarity. Each cutter pocket  30  includes a back surface  32 , which is oriented at an angle that imparts a cutting face  160  of a cutter  150  disposed within cutter pocket  30  with a desired rake angle  40  relative to a surface of a formation being drilled, as shown in FIG.  3 B. Cutter  150  may be secured within cutter pocket  30  by known processes, such as by brazing or, in some particulate-based drag bits, by positioning cutters  150  carrying TSP compacts within pockets  30  prior to infiltrating the particulate matrix of the bit body. As illustrated in FIG. 3B, cutting face  160  is oriented with a negative rake angle  40 , or backrake. In the present invention, however, cutters  150  may also be oriented on drag bits  10  with neutral rake angles or with positive rake angles relative to a surface of the formation being drilled. 
     The specific manner in which rake angles  40  may be continuously varied in different design embodiments may depend on many factors, including, without limitation, the design of drag bit  10  (e.g., the shape of the profile of drag bit  10 ), the degree of cutter  150  redundancy, the thickness of the compact, or diamond table, on each cutter  150 , the formation to be drilled, the formation pressure (i.e., bore hole stress), and the depth to which a bore hole is to be drilled in the formation. Desired weight on bit or torque responses, as well as directional drilling considerations, may influence embodiments of continuously varying rake angles  40  of cutters  150 . Stability data may also be a basis for designing a drag bit  10  with cutters  150  oriented with their cutting faces  160  at continuously varying rake angles  40 . 
     In one exemplary embodiment of the present invention, which is illustrated by FIGS. 4A-4M, a drag bit  10  may carry cutters  150  that are oriented so as to have rake angles that are at least partially dependent upon the radial distances of these cutters  150  from a longitudinal axis  44  of drag bit  10 . 
     FIGS. 4A-4E respectively illustrate each of the different blades  20  ( 20   a ,  20   b ,  20   c , etc.,) of drag bit  10  (FIGS. 1 and 2) and the cutters  150  ( 150 A- 150 V) carried thereby. As shown in FIGS. 4A-4E, cutters  150  are labeled A-V in sequence, depending upon their respective radial distances from longitudinal axis  44 , cutter  150 A being located closest to longitudinal axis  44  and cutter  150 V being most distant from longitudinal axis  44 . 
     FIGS. 4F-4M are graphs that depict different exemplary relationships between the rake angles of cutters  150  and their relative radial distances from longitudinal axis  44 . As indicated in each of FIGS. 4F-4M, drag bits according to each of these embodiments include at least one region  70  with cutters  150  having cutting faces  160  that are oriented at rake angles  40  (FIG. 3B) that continuously vary within that region  70 . Where appropriate, regions  72  of the graphs are labeled in which a drag bit  10  includes at least two cutters  150  positioned sequential distances (e.g., cutters  150 C and  150 D) from longitudinal axis  44  that have cutting faces  160  with rake angles  40  that are unequal and vary by less than about five degrees. 
     As shown in FIG. 4F, the relationship between the radial distances of cutters  150  from longitudinal axis  44  and the rake angles  40  (FIG. 3B) of cutter  150  may be substantially linear. While FIG. 4F depicts cutters  150  being oriented with cutting faces  160  at more negative rake angles  40  the more radially distant cutters  150  are spaced from longitudinal axis, the rake angles  40  of cutting faces  160  of cutters  150  may alternatively become less negative (i.e., more positive) the greater the radial distance between cutters  150  and longitudinal axis  44 , as shown in FIG.  4 F. 
     As an alternative, cutting faces  160  of cutters  150  may be positioned at rake angles that vary, in a somewhat cyclical relationship, as depicted in FIG.  4 G. As illustrated in FIG. 4G, the rake angles  40  of cutting faces  160  of cutters  150  are independent of the radial distance of each cutter  150  from longitudinal axis  44 . Rather, the rake angle  44  of each cutter  150  (e.g., cutter  150 C) may be related to the rake angle  40  of the previous, more closely spaced cutter  150  (e.g., cutter  150 B) or upon the rake angle  40  of the next, more distantly spaced cutter  150  (e.g., cutter  150 D). By way of example, FIG. 4G depicts cutters  150 B and  150 D as having cutting faces  160  that are oriented with a negative rake of about 25°, while cutting face  160  of cutter  150 C, which is spaced a radial distance from longitudinal axis  44  that lies between the distances that cutters  150 B and  150 D are spaced radially from longitudinal axis  44 , is oriented with a negative rake of about 15°. 
     FIG. 4H graphically depicts the orientation of cutters  150  on a drag bit  10  that includes three regions. Cutting faces  160  of cutters  150 A- 150 G, which are located in a first region of drag bit  10  and are located closest to longitudinal axis  44  thereof, are oriented so as to have substantially the same rake angles  40 . A second, intermediate region  70 / 72  of drag bit  10  includes cutters with cutting faces  160  oriented at a variety of different rake angles  40 . As shown, the rake angles  40  of cutting faces  160  of cutters  150 H- 150 P become less negative the further cutters  150 H- 150 P in second intermediate region  70 / 72  are radially spaced from longitudinal axis  44 . Cutters  150  within region  70 / 72  are arranged with their cutting faces  160  oriented at different rake angles  40 , the rake angle  40  of cutting face  160  of each sequential cutter  150 H,  150 I,  150 J, etc. varying by less than about five degrees from the rake angles  40  of the cutting faces  160  of the previous and subsequent cutters  150 . A third region of drag bit  10 , which is most distantly radially spaced from longitudinal axis  44 , includes cutters  150 Q- 150 V having cutting faces  160  that are oriented at substantially the same rake angles  40  relative to a surface of a formation to be drilled. The rake angles  40  of the cutting faces  160  of cutters  50 A- 150 G, located in the first region of face  12  of drag bit  10 , are less negative than the rake angles  40  of the cutting faces  160  of cutting elements  150 Q- 150 V, which are located in the third region of face  12 . 
     FIG. 4I graphically represents another drag bit  10  with cutters  150  located in three regions of face  12 . Conversely to the arrangement of cutters  150  illustrated in FIG. 4H, the cutting faces  160  of cutters  150 A- 150 G in a first region of face  12  are oriented with more negative rake angles  40  than are cutting faces  160  of cutters  150 Q- 150 V located in the third region of face  12 . To provide a transition between the rake angles  40  of the cutting faces  160  of cutters  150  of the first and third regions, the rake angles  40  of cutting faces  160  of cutters  150 H- 150 P within the second, intermediate region  70 / 72  of face  12  become less negative the more distantly each cutter  150  is positioned from longitudinal axis  44  of drag bit  10 . As in the graphical illustration of FIG. 4H, FIG. 4I illustrates that rake angles  40  of cutting faces  160  of cutters  150  within region  70 / 72  are arranged with their cutting faces  160  oriented at different rake angles  40  and that the rake angle  40  of cutting face  160  of each sequential cutter  150 H,  150 I,  150 J, etc. varies by less than about five degrees from the rake angles  40  of the cutting faces  160  of the previous and subsequent cutters  150 . 
     FIG. 4J also graphically represents the rake angles  40  of the cutting faces  160  of cutters  150  arranged in three regions of a face  12  of a drag bit. Cutters  150 A- 150 F, which are located closest to a longitudinal axis  44  of drag bit  10 , are carried upon a first region of face  12 . Cutters  150 G- 150 N are spaced a greater radial distance from longitudinal axis  44  than are cutters  150 A- 150 F and are located on an intermediate, second region of face  12 . The third region of face  12  carries cutters  150 O- 150 V, which are spaced even greater radial distances from longitudinal axis  44 . While FIG. 4J depicts cutters  150 A- 150 F and cutters  150 O- 150 V as having cutting faces  160  that are oriented at substantially the same rake angles  40 , cutters  150  within the second region of face  12  that are spaced sequential radial distances from longitudinal axis  44  (e.g., cutters  150 G and  150 H) have cutting faces  160  that are oriented at different rake angles  40  commencing with a decrease in backrake followed by an increase in a nonlinear progression, with cutting faces  160  of cutters  150  spaced intermediate radial distances from longitudinal axis  44  (e.g., cutter  150 K) being oriented at the most negative rake angles  40 . 
     FIGS. 4K-4T graphically depict other arrangements of cutters  150  including regions with continuously variable rake angles  40  that incorporate teachings of the present invention. 
     FIGS. 5A-5L schematically and graphically depict another embodiment of a design layout for cutters  150 ′ for a drag bit  10 ′, wherein rake angles  40  of the cutting faces  160 ′ of cutters  150 ′ are related, at least in part, to the vertical positions of cutters  150 ′ relative to a longitudinal axis  44 ′ of drag bit  10 ′. 
     As illustrated in FIG. 5A, drag bit  10 ′ includes a face  12 ′ and blades  20 ′ upon which a plurality of cutters  150 A′- 150 V′, which are collectively referred to as cutters  150 ′, are oriented. Although all of cutters  150 ′ are depicted in FIG. 5A as being located on a single blade  20 ′, FIG. 5A merely depicts the positions of cutters  150 ′ relative to one another with respect to both a longitudinal axis  44 ′ of drag bit  10 ′ and a vertical position along longitudinal axis  44 ′. In actuality, cutters  150 ′ are carried on various blades  20 ′ , the cutter positions having been rotated into a single plane for clarity. The sequence of cutters  150 A′- 150 V′ is, however, based on the relative radial distances of cutters  150 A′- 150 V′ from longitudinal axis  44 ′, with cutter  150 A′ being located closest to longitudinal axis  44 ′ and cutter  150 V′ being radial spaced the greatest distance from longitudinal axis  44 ′. 
     FIGS. 5B-5E depict various exemplary relationships between the vertical position of each cutter  150 ′ along the longitudinal axis  44 ′ of drag bit  10 ′ and the rake angle  40  of the cutting face  160 ′ of each cutter  150 ′. As shown in FIGS. 5B-5E, each of the exemplary relationships between the vertical positions of cutters  150 ′ and the rake angles  40  at which cutting faces  160 ′ of cutters  150 ′ are oriented includes regions  70  on face  12 ′ that carry sets of two or more sequentially positioned cutters  150 ′ that are oriented such that the rake angles  40  of their respective cutting faces  160 ′ vary continuously. In at least some regions  72 , the rake angles  40  of sequentially positioned cutters  150 ′ vary by less than about five degrees. 
     As shown in FIG. 5A, of cutters  150 A′- 150 V′, cutter  150 G′ is in the lowermost position along longitudinal axis  44 ′, while cutter  150 V′ is in the uppermost position along longitudinal axis  44 ′. The exemplary cutter  150 ′ arrangements depicted in FIGS. 5B-5E illustrate that the rake angle  40  of cutting face  160 ′ of the lowermost cutter  150 G′ may be the maximum rake angle or the minimum rake angle of all of cutters  150 ′. Nonetheless, other rake angle orientations of cutters  150 ′ that are related to the relative vertical positions of at least some cutters on a drag bit  10 ′ are also within the scope of the present invention. 
     Turning now to FIGS. 6A-6G, an embodiment of a cutter  150 ″ rake angle  40  arrangement is illustrated that takes into account the relative positions of cutters  150 ″ along a single blade  20 ″ of a drag bit  10 ″. 
     As shown in FIG. 6A, drag bit  10 ″ includes a blade  20 ″ that carries cutters  150 A″- 150 F″, which are collectively referred to herein as cutters  150 ″. FIGS. 6B-6G illustrate different possible relationships between the positions of cutters  150 ″ along blade  20 ″, or the radial distances of cutters  150 ″ on a single blade  20 ″ from a longitudinal axis  44 ″ of drag bit  10 ″, and the rake angles  40  at which cutting faces  160 ″ of cutters  150 ″ are oriented. Again, the rake angles  40  of at least some cutters  150 ″ sequentially positioned within a region  70  of blade  20 ″ are continuously varied. Blade  20 ″ may also include adjacently positioned cutters  150 ″, which are identified in FIGS. 6B-6G by reference numeral  72 , that have cutting faces  160 ″ oriented at rake angles  40  that differ by less than about five degrees from one another. 
     In FIGS. 7A-7F, yet another embodiment of a continuously varied cutting face  160 ′″ rake angle  40  arrangement incorporating teachings of the present invention is illustrated. 
     FIG. 7A depicts a blade  20 ′″ of a drag bit  10 ′″ that carries cutters  150 A′″- 150 F′″. In this embodiment, the rake angles  40  of the cutting faces  160 ′″ of cutters  150 A′″- 150 F′ 41   are at least partially determined as a function of the vertical position of each cutter  150 A′″- 150 F′″ on a single blade  20 ′″ relative to a longitudinal axis  44 ′″ of drag bit  10 ′″. Thus, the rake angles  40  of cutting faces  160 ′″ are independent of the positioning of cutters on other blades of drag bit  10 ′″. While rake angles  40  of the present embodiment are at least partially dependent upon the vertical locations of cutters  150 A′″- 150 F′″, the sequence of identification of cutters  150 A′″- 150 F′″ is based on the relative distance each of cutters  150 A′″- 150 F′″ on blade  20 ′″ is radially spaced from longitudinal axis  44 ′″. 
     Various exemplary rake angle  40  arrangements of cutters  150 A′″- 150 F′″ are illustrated in the graphs of FIGS. 7B-7F. As shown in FIGS. 7B-7F, in each of these rake angle  40  arrangements, sequentially positioned cutters  150 ′″ on at least a portion of blade  20 ′″, which is referred to as region  70 , are oriented with their cutting faces  160 ′″ at different, continuously varying rake angles  40 . Where appropriate, regions  72  of a blade  20 ′″ are designated in which at least two sequentially adjacent cutters  150 ′″ have cutting faces  160 ′″ that are oriented at different rake angles that vary by less than about five degrees. 
     As aforementioned, rake angles  40  of cutting faces  160  of cutters  150  may be advantageously designed to improve the individual wear characteristics of a cutter at one or more positions on a face  12  of a drag bit  10  or the overall wear characteristics of drag bit  10 . In so designing a drag bit  10 , wear data may be collected, either from worn drag bits, computer simulations, or extrapolation of laboratory data. Then, upon analysis of the wear data, the rake angles  40  at which cutting faces  160  of cutters  150  on the bit may be modified to adjust the relative wear of one or more cutters  150  or of the entire drag bit  10  so as to extend the useful life of cutters  150  or of drag bit  10 . 
     For illustration purposes only, FIG. 8 depicts an example of the relative wear of cutters  150 A′- 150 V′ of drag bit  10 ′ illustrated in FIG.  5 A. Each of cutters  150 A′- 150 V′ was oriented with its cutting face  160 ′ having a negative rake angle  40 , or backrake, of about 15°, as depicted in the graph of FIG.  9 A. The observed performance of individual cutters  150 ′ or of the entire drag bit  10 ′ is compared to desired performance criteria. The orientations of cutters  150 ′ on drag bit  10 ′ may then be modified to provide regions on drag bit  10 ′ where sequentially adjacent cutters  150 ′ have cutting faces  160 ′ that have rake angles  40  that vary continuously so as to compensate for disparities between the desired and measured performance of cutters  150 ′ or of drag bit  10 ′. 
     As an example of a response to the observed wear data, cutters  150 ′ that were subject to increased wear (e.g., cutters  150 I′- 150 V′) may be reoriented, as shown in the graph of FIG. 9B, so as to decrease the wear thereof, with cutting faces  160 ′ of these cutters  150 ′ (e.g. cutters  150 I′- 150 V′) oriented at rake angles  40  that will counteract the tendencies of cutters  150 ′ in these locations to wear at increased rates relative to the wear rates of cutters  150 ′ at other positions on drag bit  10 ′. In FIG. 9B, the rake angles  40  of cutting faces  160 ′ of cutters  150 A′- 150 H′, which FIG. 8 shows exhibited very little wear (less than about five percent), were not changed, while the negativity of the rake angles  40  of cutting faces  160 ′ of the remaining cutters  150 I′- 150 V′ was increased with the increased amount of wear illustrated in FIG.  8 . 
     Alternatively, as depicted in FIG. 9C, rake angles  40  may be modified by reducing the negativity of rake angle  40  for the cutting faces  160 ′ of cutters  150 A′- 150 H′, which exhibit low wear, and increasing the negativity of rake angles  40  for the cutting faces  160 ′ of cutters  150 I′- 150 V′ in the higher wear areas of face  12 ′ of drag bit  10 ′. One motivation for this strategy would be to prevent the weight on bit from increasing excessively due to the average increase in the negativity of rake angle  40  (i.e., backrake) of cutters  150 ′. 
     In this embodiment of the invention, FIGS. 9B and 9C depict modification of rake angles  40  in a manner that generally follows the wear pattern function. The modifications depicted in FIGS. 9B and 9C are not intended to limit the scope of the invention; rather, these modifications are only provided as exemplary embodiments of the invention. 
     Although most evident from the graphical representations of FIGS. 6B-6E, mathematical functions may be used to continuously vary the rake angles  40  of the cutting faces  160 ,  160 ′,  160 ″,  160 ′″ of at least some cutters  150 ,  150 ′,  150 ″,  150 ′″ carried upon the face  12 ,  12 ′,  12 ″,  12 ′″ of a drag bit  10 ,  10 ′,  10 ″,  10 ′″. For example, mathematical functions may be employed to generally increase or generally decrease the rake angles  40  of cutters  150 ,  150 ′,  150 ″,  150 ′″ within such a variable region  70 , depending upon the relative positions of these cutters  150 ,  150 ′,  150 ″,  150 ′″. Linear functions or nonlinear functions may also be employed to arrange cutters  150 ,  150 ′,  150 ″,  150 ′″ within a region  70  on the face  12 ,  12 ′,  12 ″,  12 ′″ of a drag bit  10 ,  10 ′,  10 ″,  10 ′″ so that the cutting faces  160 ,  160 ′,  160 ″,  160 ′″ thereof are oriented at continuously varying rake angles  40 . Likewise, polynomials, exponential functions, or cyclic functions may be employed to determine rake angles  40 . The continuously varied rake angles  40  of the cutting faces  160 ,  160 ′,  160 ″,  160 ′″ of cutters  150 ,  150 ′,  150 ″,  150 ′″ sequentially positioned on at least a region  70  of a face  12 ,  12 ′,  12 ″,  12 ′″ of a drag bit  10 ,  10 ′,  10 ″,  10 ′″ may alternatively take the form of repeating or nonrepeating patterns. 
     Each of the herein-described inventive rake angle  40  arrangements of cutters  150 ,  150 ′,  150 ″,  150 ′″ may include providing small changes (i.e., less than about 5°) in the rake angles  40  of cutting faces  160 ,  160 ′,  160 ″,  160 ′″ of sequentially adjacent cutters  150 ,  150 ′,  150 ″,  150 ′″ so as to smooth the transition between regions on face  12 ,  12 ′,  12 ″,  12 ′″ with cutters  150 ,  150 ′,  150 ″,  150 ′″ of different rake angles  40 . By continuously varying the cutter backrake angle, several advantages will be apparent. One advantage of the continuous transition between different cutter backrake angles is smoothing the cutter forces between two areas with differing cutter backrake angles. These cutter forces directly affect bit whirling and the dynamic behavior of the bit. Thus, a smooth transition provides the advantage of smooth and more stable drilling. The reduction of vibration and dynamic loading extends cutter life, thereby extending the bit life as well. Another advantage is that, by varying the backrake angle, drilling performance and wear characteristics can be tailored. 
     As yet another alternative, a drill bit incorporating teachings of the present invention may include cutters with rake angles that continuously vary in a randomly generated manner. For example, the rake angles of the cutters of such a drill bit could be determined by a random number generator, as known in the art, rather than as a function of the radial or axial location of each cutter on the bit. Random rake angles may, for example, be useful for imparting the bit with increased stability or a desired amount of cuttings generation. 
     Many additions, deletions, and modifications may be made to the preferred embodiments of the invention as disclosed herein without departing from the scope of the invention as hereinafter claimed.