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 THE INVENTION 
   1. Technical Field 
   The present invention is related to drill bits for boring earthen formations. The present invention is particularly adapted for rolling cutter earth-boring bits most typically used in oil and gas drilling, but also has application in bits used in blast hole and mining applications. 
   2. Summary of the Prior Art 
   In 1909, Howard R. Hughes invented the rolling cutter rock bit, which revolutionized the exploration and drilling of oil and gas wells. Since that time, countless improvements have been made to Hughes&#39; basic design. 
   One problem that remains to be solved is that of “tracking.” Tracking occurs when a cutting element (tungsten-carbide insert or steel tooth) falls in the same impression that was made previously by the same or another cutting element. This results in loss of drilling efficiency since the primary mode of contact between cutters and formation is between the surface of the cutter and formation rather than between the cutting elements and formation. This results in increased wear of the bit as well as reduction in feet per hour or penetration rate. 
   Conventional solutions to tracking include increasing the weight-on-bit (WOB), but, as can be expected, this reduces bit life because of the additional strain on bit components. Probably the most common way to reduce tracking and vibration is to decrease the pitch between adjacent cutting elements or increase cutting element count, especially for hard rock formations as shown in U.S. Pat. Nos. 6,161,634 and 3,726,350. The disadvantage of such solutions is that overbreak effect is not utilized, specific energy increases and the cost of the drill bit is augmented. 
   Tracking also can be partially reduced by increasing sliding and scraping of cutting elements on the bottom hole by adjusting the geometry of the bit. The drawback of this approach is that the cutting elements that are sliding and scraping will wear faster while tracking will not be completely eliminated. 
   Another solution to the tracking problem is the use of varying pitch (angular distance between the centerlines) between the cutting elements for instance as proposed in U.S. Pat. Nos. 4,248,314, 4,187,922 and 3,726,350. Any deviation from equal pitch, can dramatically increase bit vibration, again causing premature bit wear. Moreover, merely randomly varied pitch drill bits can track just as much as equally spaced drill bits. 
   Tracking can also be reduced through various configurations of cutting elements or teeth, including teeth with “T” shape crest for additional wear resistance wherein the teeth/inserts crush the formation to reduce tracking (for example see UK Patent number 3,326,307). This approach tends to reduce drilling speed and increases specific energy (energy applied per unit of formation broken) because the cutting elements crush the formation with lower penetration rate. Another variation is to group and space cutting elements with varied pitches between groups in combination with changing the orientation of the cutting element crests for various groups. (See for example UK Patent 1,896,251). These approaches may reduce tracking; however they increase manufacturing cost. See U.S. Pat. No. 2,333,746. A change in cutting element orientation as shown in U.S. Pat. No. 4,393,948 without optimal placement on the surface of the cutters can only reduce but not completely eliminate tracking. 
   Methods to optimize drill bit performance using simulations and other statistical data to improve performance parameters of the bit are illustrated in U.S. Pat. Nos. 6,213,225; 6,095,262; 6,516,293; and published patent applications 20,030,051,917; 20,030,051,918; 20,010,037,902. Ad hoc simulation approaches are best implemented in the absence of adequate theory; however, statistical optimization results are limited by the assumptions and biases taken at the beginning of the optimization process. Furthermore, prior-art simulation methods have over-inflated the cutting element count required to optimally drill earthen formations. 
   A need exists, therefore, for an earth-boring bit having anti-tracking characteristics that avoids excessive vibration and can be economically produced. 
   One common drawback of all the prior art solutions is lack of overbreak optimization during drilling of rock formation. The overbreak effect is the investigation of the fact that rock has strong compression properties and has weak bending and distention properties as compared to metal, for instance iron. 
   Another common drawback all the prior art solutions is misunderstanding by those knowledgeable in the art of actual cause for detrimental axial resonance frequency vibration of the cutter drill bit by boring rock. Inventors found the actual cause for detrimental axial resonance frequency vibration for roller cutter drill bits for the first time since long history of improvements made to Hughes&#39; basic roller cutter drill bits; found cause is eliminated in the present invention. 
   SUMMARY OF THE INVENTION 
   The main object of the invention is creation of earth-boring roller cutter drilling tool design which simultaneously increases footage drilled, durability and rate of penetration while reducing the number of cutting element count, in one embodiment tungsten-carbide inserts, compared to conventional earth-boring roller cutter drilling tools which are presently manufactured around the globe. 
   Another object of the present invention is modification of conventional designs of roller cutter drill bits to simultaneously increase footage drilled, durability and rate of penetration while reducing the cutting element count compared conventional earth-boring roller cutter drilling tools which are presently manufactured around the globe. 
   The above mentioned objects can be achieved according to the proposed invention via mathematically determined optimal placement of cutting elements on the surface of each cutter rotatably mounted on a drill tool or drill bit through simultaneous utilization of the following concepts:
         1. Complete elimination of tracking during drilling on the bottom hole by means of independent rolling cutter with use of varied pitch between adjacent cutting elements.   2. Maximization of volume of formation broken due to optimization of overbreak through optimal spacing between subsequent penetrations taking into account mechanical properties of rock to be drilled and the geometry of cutting elements and orientation of cutting elements centerline with respect to the surface of the cutter.   3. Substantial reduction of detrimental axial resonance frequency vibration of drill bit or tool which are restrictive to the process of drilling the formation through optimal placement of cutting elements along cutter generatrices.       

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a perspective view of a prior-art rolling cone drill bit that is of the general type contemplated by the present invention. 
       FIG. 2  shows a side view of a cutter designed according to the teaching of the present invention. 
       FIG. 3  is a schematic drawing illustrating a preferred arrangement of tungsten-carbide inserts on the surface of the cutting member according to the teachings of present invention. 
       FIG. 4  is a schematic layout showing a preferred arrangement of cutting elements comprising milled teeth. 
       FIG. 5  shows volume of formation broken without overbreak optimization (prior art). 
       FIG. 6  shows volume of formation broken with overbreak due to optimal spacing between previous and subsequent penetrations of cutting elements in rock. 
       FIG. 7  illustrates volume of formation broken as a generally convex function of spacing between previous and subsequent penetrations of cutting elements for a given formation. 
       FIG. 8  is a schematic layout showing placement of mathematically determined pitch pairs in a circumferential row according to the teachings of the present invention. 
       FIG. 9  is a schematic layout showing a preferred arrangement of cutting elements comprising a combination of milled teeth and tungsten-carbide inserts on the surface of the cutting member. 
       FIG. 10  is a schematic layout showing a preferred arrangement of cutting elements arranged in groups according to the teachings of the present invention. 
       FIG. 11  is a perspective view of a cutting member constructed in accordance with the teachings of the present invention employed, for instance, by bits of the reaming type which in practice used for Tunnelling, Mining and Raise-Boring. 
       FIG. 12  is schematic layout and a perspective view showing the preferred arrangement of the cutting elements in accordance with the teachings of the present invention for rotatable cutter with one circumferential row. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Referring now to the FIGS., and specifically to  FIG. 1 , a conventional rolling cutter (also called rolling-cone or three-cone) drill bit  50  conventionally used for drilling a bore in an earthen formation is illustrated. Bit  50  is typical of those contemplated by the present invention. Bit  50  comprises a bit body  51  that is threaded at its upper extent  52  for connection into a drill string. Bit  50  optionally may be provided with a lubricant compensator  53 . A nozzle  55  is provided in bit body  51  to cool and lubricate the drill bit during drilling. Bearing pins or arms  54  extend from bit body in a cantilevered, downwardly depending fashion. At least one cutter  101  is mounted on bit arm  54  and is carried for rotation by each section of bit body with a plurality of cutting elements  107  thereon arranged in generally circumferential rows. Tungsten-carbide inserts  107  are secured by interference fit in holes or apertures formed in cutters  101  to define the cutting elements. The cutting elements may also be formed of the material of the cutter  173  (a steel-tooth bit) as shown in  FIG. 4 . When connected into a drillstring, bit  50  is rotated about its axis  115  in the direction  206  to disintegrate earthen formations. 
   Referring to  FIG. 2 , a side view of multi-cone rolling cutter  101  according to the teachings of present invention is illustrated. The cutter  101  comprises a multiplicity of cutting elements, in one embodiment tungsten-carbide inserts  107 , embedded in insert holes formed in the body of the cone and arranged in generally circumferential rows  102 – 106  about the axis  114  of the cutter. Geometrical parameters of cutting elements  107  can be different in shape, size, and orientation of the crest. 
   Each cutting element  107  has its centerline  500 ; centerline  500  simultaneously intersects the surface of the cutter and the circumferential row in which the cutting element is placed. Pitch is defined as the length of arc in circumferential row between points of intersection of centerlines  500  with circumferential row curve on the cutter  101  surface for adjacent cutting elements along the circumferential row or alternatively defined as the angle between adjacent cutting elements&#39; axes  500  for each circumferential row. 
   Radiuses r 1 –r 5  of each circumferential row are defined as the shortest distance from the cutter axis  114  to the any point in circumferential rows  102 – 106  on the surface of the cutter  101 . Radiuses R 1 –R 5  are the maximum distance from a selected point of circumferential row to the axis  115  of the drill bit  50  measured perpendicular to axis  115  of the drill bit  50 . It is conventionally known that the ratio Kv defined as Ri divided by ri should not be equal to an integer to reduce tracking, where i=1, 2, 3 . . . 
   100% tracking is achieved in cases where Kv ratio is equal to an integer regardless of pitch selection between cutting elements  107 . In order to avoid tracking with varied pitch and optimize overbreak of formation, the decimal part of Kv is preferably in the 0.3–0.7 range. Overbreak optimization of the cutter  101  according to the teachings of the present invention mathematically determines optimum pitch between the cutting elements  107  arranged in circumferential rows to produce the largest chips possible for selected cutters  101  and formations to be drilled. The larger the chips, the more rock formation is removed per unit of energy and the greater is cost reduction, time and energy savings. Placement of cutting elements  107  closer than this optimum distance results in less volume broken per unit of energy; subsequent penetration farther than this optimum distance results in increased power consumption as chipping is replaced by indentation. 
   The cutter  101  is mounted on the bit arm  54  and is rotated about bit central axis  115  in the direction  206 . Multiplicity the generatrices  400  defined as the geometric locus on the surface of the cutter  101  formed when the plane containing the central axis  114  of the cutter  101  intercrosses the centerline  500  of at least one selected cutting element  107  and the geometric surface of the cutter  101 . In other words, a generatrix is a curve that forms the surface of the cutter as it is rotated about the cutter&#39;s axis. At each moment during drilling, main force interactions between the cutter  101  and formation being disintegrated occur along a generatrix  400 . Therefore, optimal placement of cutting elements with respect to their density along generatrices is crucial for reduction of harmful vibration. 
   Referring now to  FIG. 3 , which depicts View A, looking upwardly at the cutting structure, the pitches between the cutting elements  107 , defined as the angle between adjacent cutting elements&#39; axis  500 , on each circumferential row, are progressively increasing from minimum pitch  108  to the maximum pitch  109 , moreover, all pitches are different and the minimum pitch  108  and the maximum pitch  109  are adjacent to each other. Additionally, the minimum pitches  108  on all circumferential rows  102 - 106  start along a randomly chosen generatrix  113  of the rolling cutter member  101 ; furthermore, the deviation from the generatrix  113  cannot exceed 45 degrees and is preferably less than half the minimum pitch  110 . The same direction  111  is maintained for all circumferential rows  102 – 106  of said cutting member  101  from said minimum pitches  108  starting along said generatrix  113  and increasing to maximum pitches  109 . 
   The minimal pitches  108  in all circumferential rows  102 – 106  of said cutting member  101  could be equal or different. The maximum pitches  109  and on all circumferential rows  102 – 106  of said cone  101  could be equal or different. The increase from the minimal pitch  108  to the maximum pitch  109  can be defined as arithmetical, geometrical, exponential, logarithmical or any other mathematical function or a combination thereof. 
   For illustrative purposes, several generatrices  400  are shown along which cutting elements  107  in each circumferential row  102 – 106  are being aligned with deviation from generatrices  400  less than half the selected maximum pitch  109  of the circumferential row occupied by the cutting element  107 . 
   To illustrate selection of optimal varied pitch for overbreak optimization according to the teachings of the present invention, for circumferential row  103  pitch  203  is selected and its pair varied pitch  204  is computed as detailed below. Arc  450  shown as a dashed curve is a part of the circumferential row  103 . The arc  450  is measured from point A defined as midpoint of selected pitch  203  in circumferential row  103  in the direction  208 , which is opposite to the direction  205  of cutter  101  rotation. The origin of direction  208  is line  207 , which intersects pitch  203  at midpoint A. The end of arc  450  falls within a certain pitch, labelled computed pitch  204 . The arc  450  denoted as L equals to the length of said circumferential row  103  (2*ρ*r2) multiplied by the decimal part of Kv which will be denoted as KvD for the purposes of present invention. For instance, for r=5 units and R=7 units, Kv equals 7 divided by 5 or 1.4. The decimal part of Kv denoted as KvD equals 0.4.
 
 L=KvD *(2*ρ* r 2)
 
KvD may not equal zero to avoid tracking and may be within from 0.15 to 0.85. KvD is preferably in the 0.3–0.7 range. The overbreak effect of rock formation during drilling exists when the absolute difference between selected pitch  203  and its computed pair varied pitch  204  is greater than 10% of the absolute difference between maximum pitch  109  and minimum pitch  108 , both of which are selected for circumferential row  103 . The above definition for circumferential row  103  can be restated in mathematical form:
 
|203−204|&gt;0.1*|109−108|
 
   In one class of embodiments according to the principals of the current invention, the pitches are calculated as an arithmetical progression of the form “minimal pitch” +D*n, wherein D is a constant which is determined as the optimal value to maximize overbreak effect and n is a consecutive positive integer (n=1, 2, 3 . . . ) 
   Yet in another class of the embodiments according to the principals of the current invention, D can be varied such as to allow optimal placement of the cutting elements to reduce vibration. 
   Referring now to  FIG. 4 , the cutter is illustrated according to the teachings of the present invention. Annotations similar to those in  FIG. 3  are used except in this embodiment of the present invention cutting elements are made of the same material as the cutter or milled teeth  173 . For illustrative purposes, selected pitch  203  and its pair computed varied pitch  204  are illustrated for circumferential row  105  versus circumferential row  103  in  FIG. 3 . The overbreak effect of rock formation during drilling exists when the absolute difference between selected pitch  203  and its calculated pair varied pitch  204  is greater than 10% of the absolute difference between maximum pitch  109  and minimum pitch  108 , both of which are selected for circumferential row  105 . The above definition for circumferential row  105  can be restated in mathematical form:
 
|203−204|&gt;0.1*|109−108|
 
   To illustrate selection of optimal varied pitch for overbreak optimization according to the teachings of the present invention, for circumferential row  105  select pitch  203  and compute its pair varied pitch  204 . Arc  450  shown as a dashed curve is a part of the circumferential row  105 . The arc  450  is measured from the point A defined as midpoint of selected pitch  203  in circumferential row  105  in the direction  208 , which is opposite to the direction  205  of cutter  101  rotation. The end of arc  450  falls within a certain pitch, labelled computed pitch  204 . The arc  450  denoted as L equals to the length of said circumferential row  105  (2*ρ*r2) multiplied by the decimal part of Kv which will be denoted as KvD.
 
 L=KvD* (2*ρ* r 4)
 
     FIG. 5  illustrates the volume of the formation broken without overbreak optimization (prior art). If the spacing between previous and subsequent penetrations of cutting elements is not optimized, the volume of the formation broken and depth of penetration are insignificant lacking overbreak effect. Based on the definition of overbreak according to the teachings of the present invention, it is impossible to create overbreak with constant pitch conventionally used in roller cutter drill bits of prior art. 
   Referring now to  FIG. 6  volume of the formation broken with overbreak due to optimal spacing between previous and subsequent penetrations of cutting elements is shown. Overbreak is optimized for a given circumferential row when at least 20% of pitches have mathematically determined pair, which satisfy the definition of overbreak according to the teachings of the present invention. In one preferred embodiment, all pitches of given circumferential row have a pair satisfying the definition of overbreak according to the teachings of the present invention. 
     FIG. 7  illustrates volume of formation broken as a generally convex function of spacing between previous and subsequent penetrations of cutting elements for a given formation. Each type of formation has its own spacing-volume curve (soft, medium or hard) that depends on physical and mechanical properties of formation for given type of cutting elements and drilling conditions. Overbreak is optimized when volume of formation broken is maximized. 
   Referring now to  FIG. 8 , a schematic layout of a single-cone rolling cutter  101  and placement of mathematically determined pitch  204  with respect to selected pitch  203  of circumferential row  106  is illustrated according to the teachings of the present invention as described in  FIGS. 1–3 . 
   The cutting element  107  of the circumferential row  106  of the cutter  101  interacts with the bottom hole along path  300  making impressions  310  in the bottom hole resulting from penetration of cutting elements during the drilling process. The distance between adjacent the impressions  310  on the circular path  300  with radius R 5  is equal to the distance between respective adjacent cutting elements  107  on the circumferential row  106 . If the pair of pitches  203  and  204  on the circumferential row  106  is calculated according of the teachings of the present invention, than for any random section  340  along path  300  penetrations of the bottom hole by cutting elements defining pitch  204  will follow penetrations of cutting elements defining pitch  203 , optimal pitch difference will create overbreak effect and eliminate tracking during drilling process. Varied pitch improves scraping efficiency during formation drilling, thus even those cutting elements that are engaged in sliding fashion versus complete penetration contribute to better disintegration of formation as compared to constant pitch bits. 
   In one embodiment of the present invention, cutting elements  107  in all of circumferential rows of cutter  101  are being aligned along the generatrix  400  with deviation from generatrix  400  of less then 51% of the selected minimum pitch  108  for every circumferential rows occupied by cutting elements  107  resulting in substantial elimination of detrimental axial  115  resonance frequency vibration of bit  50 . 
   If cutting elements  107  are not aligned along said generatrix  400  in accordance with the teachings of the present invention, detrimental axial resonance vibration of bit  50  offsets benefits of overbreak effect; therefore, objectives of the present invention cannot be achieved. 
     FIG. 9  shows another embodiment of the cutter  101  designed according to the teachings of the present invention. The cutting elements comprise both tungsten-carbide inserts  107  and milled teeth  173  and as illustrated for circumferential row  104  have selected pitch  203  and its calculated pair varied pitch  204 . The beginning of minimum pitches  108  for both types of cutting elements  107  and  173  starts along one generatrix  113  for all circumferential rows of the cutter  101 . Pitches in all circumferential rows progressively increase in one direction and maximum and minimum pitches for all circumferential rows are adjacent to each other. For each circumferential row maximum deviation from generatrices is less than 0.51 of the respective minimum pitch selected for that circumferential row. 
     FIG. 10  illustrates another class of the preferred embodiments, wherein cutting elements  107  are arranged in groups  112  wherein the pitch within the group is constant and the pitches between groups are varied. The direction  111  of increase in varied pitch is maintained similar for all groups; furthermore, minimal pitches  108  are adjacent to maximum pitches  109  along a chosen generatrix  113  of the cutter  101  with deviation less than 45 degrees and preferably with deviation is less than 51% of the selected minimum pitch  108 . 
     FIG. 11  is a schematic perspective view depicting a truncated cone  101  constructed in accordance with the teaching of the present invention as described in  FIG. 2 ,  FIG. 3 ,  FIG. 8  which is typically used for Tunneling, Mining and Raise-Boring for instance by bits of the reaming type. For illustrative purposes, circumferential row  320  shows selected pitch  203  and its pair calculated varied pitch  204 . 
     FIG. 12  is a front view and a side view the cutter  101  with one circumferential row in accordance with the teaching of the present invention as described in  FIG. 3 . This is another embodiment according to the teachings of the present invention.

Summary:
An earth boring drill bit is constructed having rotatable cutter for forming a borehole in earth. At least one circumferential row of cutting elements is optimized to create overbreak of rock and eliminate tracking, wherein selected pitches have mathematically determined pairs and the absolute difference between the selected pitch and its pair is greater than 10% of the difference between maximum and minimum pitch for that circumferential row. Furthermore, cutting elements are placed along pre-selected generatrices with deviation from said generatrices, which is less than half the maximum pitch of circumferential rows occupied by said cutting element. The present invention eliminates tracking and reduces detrimental axial resonance frequency vibration while reducing cutting element count, including tungsten-carbide inserts, as compared to conventional roller cutter drill bits used for oil, gas and shot hole drilling wells and simultaneously increases footage drilled, drilling speed, and durability.