EP1500781A2 - Verfahren zum Entwurf eines Rollenbohrmeissels - Google Patents

Verfahren zum Entwurf eines Rollenbohrmeissels Download PDF

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Publication number
EP1500781A2
EP1500781A2 EP04025560A EP04025560A EP1500781A2 EP 1500781 A2 EP1500781 A2 EP 1500781A2 EP 04025560 A EP04025560 A EP 04025560A EP 04025560 A EP04025560 A EP 04025560A EP 1500781 A2 EP1500781 A2 EP 1500781A2
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Prior art keywords
bit
tooth
cone
teeth
formation
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Application number
EP04025560A
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English (en)
French (fr)
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EP1500781A3 (de
Inventor
Shilin Chen
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Halliburton Energy Services Inc
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Halliburton Energy Services Inc
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH DRILLING; MINING
    • E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B10/00—Drill bits
    • E21B10/08—Roller bits
    • E—FIXED CONSTRUCTIONS
    • E21—EARTH DRILLING; MINING
    • E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B10/00—Drill bits
    • E21B10/08—Roller bits
    • E21B10/16—Roller bits characterised by tooth form or arrangement

Definitions

  • the present invention relates generally to the drilling of oil and gas wells, or similar drilling operations, and in particular to orientation of tooth angles on a roller cone drill bit.
  • Oil wells and gas wells are drilled by a process of rotary drilling, using a drill rig such as is shown in Figure 10 .
  • a drill bit 10 is mounted on the end of a drill string 12 (drill pipe plus drill collars), which may be more than a mile long, while at the surface a rotary drive (not shown) turns the drill string, including the bit at the bottom of the hole.
  • roller cone bit an example of which is seen in Figure 11 .
  • a set of cones 16 two are visible
  • teeth or cutting inserts 18 are arranged on rugged bearings on the arms of the bit.
  • the second type of drill bit is a drag bit, having no moving parts, seen in Figure 12 .
  • Drag bits are becoming increasingly popular for drilling soft and medium formations, but roller cone bits are still very popular, especially for drilling medium and medium-hard rock.
  • roller cone bits There are various types of roller cone bits: insert-type bits, which are normally used for drilling harder formations, will have teeth of tungsten carbide or some other hard material mounted on their cones. As the drill string rotates, and the cones roll along the bottom of the hole, the individual hard teeth will induce compressive failure in the formation.
  • the bit's teeth must crush or cut rock, with the necessary forces supplied by the "weight on bit” ( WOB ) which presses the bit down into the rock, and by the torque applied at the rotary drive. While the WOB may in some cases be 100,000 pounds or more, the forces actually seen at the drill bit are not constant: the rock being cut may have harder and softer portions (and may break unevenly), and the drill string itself can oscillate in many different modes. Thus the drill bit must be able to operate for long periods under high stresses in a remote environment.
  • WOB weight on bit
  • the individual elements of a drill string appear heavy and rigid. However, in the complete drill string (which can be more than a mile long), the individual elements are quite flexible enough to allow oscillation at frequencies near the rotary speed. In fact, many different modes of oscillation are possible. (A simple demonstration of modes of oscillation can be done by twirling a piece of rope or chain: the rope can be twirled in a flat slow circle, or, at faster speeds, so that it appears to cross itself one or more times.)
  • the drill string is actually a much more complex system than a hanging rope, and can oscillate in many different ways; see WAVE PROPAGATION IN PETROLEUM ENGINEERING, Wilson C. Chin, (1994).
  • the oscillations are damped somewhat by the drilling mud, or by friction where the drill pipe rubs against the walls, or by the energy absorbed in fracturing the formation: but often these sources of damping are not enough to prevent oscillation. Since these oscillations occur down in the wellbore, they can be hard to detect, but they are generally undesirable. Drill string oscillations change the instantaneous force on the bit, and that means that the bit will not operate as designed. For example, the bit may drill oversize, or off-center, or may wear out much sooner than expected. Oscillations are hard to predict, since different mechanical forces can combine to produce "coupled modes"; the problems of gyration and whirl are an example of this.
  • the "cones" in a roller cone bit need not be perfectly conical (nor perfectly frustroconical), but often have a slightly swollen axial profile. Moreover, the axes of the cones do not have to intersect the centerline of the borehole. (The angular difference is referred to as the "offset" angle.) Another variable is the angle by which the centerline of the bearings intersects the horizontal plane of the bottom of the hole, and this angle is known as the journal angle. Thus as the drill bit is rotated, the cones typically do not roll true, and a certain amount of gouging and scraping takes place. The gouging and scraping action is complex in nature, and varies in magnitude and direction depending on a number of variables.
  • roller cone bits can be divided into two broad categories: Insert bits and steel-tooth bits. Steel tooth bits are utilized most frequently in softer formation drilling, whereas insert bits are utilized most frequently in medium and hard formation drilling.
  • Steel-tooth bits have steel teeth formed integral to the cone.
  • a hardmetal is typically applied to the surface of the teeth to improve the wear resistance of the structure.
  • Insert bits have very hard inserts (e.g. specially selected grades of tungsten carbide) pressed into holes drilled into the cone surfaces. The inserts extend outwardly beyond the surface of the cones to form the "teeth" that comprise the cutting structures of the drill bit.
  • the design of the component elements in a rock bit are interrelated (together with the size limitations imposed by the overall diameter of the bit), and some of the design parameters are driven by the intended use of the product. For example, cone angle and offset can be modified to increase or decrease the amount of bottom hole scraping. Many other design parameters are limited in that an increase in one parameter may necessarily result in a decrease of another. For example, increases in tooth length may cause interference with the adjacent cones.
  • the teeth of steel tooth bits are predominantly of the inverted "V" shape.
  • the included angle i.e. the sharpness of the tip
  • the length of the tooth will vary with the design of the bit. In bits designed for harder formations the teeth will be shorter and the included angle will be greater.
  • Gage row teeth i.e. the teeth in the outermost row of the cone, next to the outer diameter of the borehole
  • inserts The most common shapes of inserts are spherical, conical, and chisel.
  • Spherical inserts have a very small protrusion and are used for drilling the hardest formations.
  • Conical inserts have a greater protrusion and a natural resistance to breakage, and are often used for drilling medium hard formations.
  • Chisel shaped inserts have opposing flats and a broad elongated crest, resembling the teeth of a steel tooth bit. Chisel shaped inserts are used for drilling soft to medium formations.
  • the elongated crest of the chisel insert is normally oriented in alignment with the axis of cone rotation.
  • the chisel insert may be directionally oriented about its center axis. (This is true of any tooth which is not axially symmetric.) The axial angle of orientation is measured from the plane intersecting the center of the cone and the center of the tooth.
  • Soft formations were originally drilled with "fish-tail" drag bits, which sheared the formation away.
  • Roller cone bits designed for drilling soft formations are designed to maximize the gouging and scraping action. To accomplish this, cones are offset to induce the largest allowable deviation from rolling on their true centers. Journal angles are small and cone-profile angles will have relatively large variations. Teeth are long, sharp, and widely-spaced to allow for the greatest possible penetration. Drilling in soft formations is characterized by low weight and high rotary speeds.
  • Hard formations are drilled by applying high weights on the drill bits and crushing the formation in compressive failure. The rock will fail when the applied load exceeds the strength of the rock. Roller cone bits designed for drilling hard formations are designed to roll as close as possible to a true roll, with little gouging or scraping action. Offset will be zero and journal angles will be higher. Teeth are short and closely spaced to prevent breakage under the high loads. Drilling in hard formations is characterized by high weight and low rotary speeds.
  • Medium formations are drilled by combining the features of soft and hard formation bits.
  • the rock breaks away (is failed) by combining compressive forces with limited shearing and gouging action that is achieved by designing drill bits with a moderate amount of offset. Tooth length is designed for medium extensions as well. Drilling in medium formations is most often done with weights and rotary speeds between that of the hard and soft formations. Area drilling practices are evaluated to determine the optimum combinations.
  • bit lateral vibration which can be caused by radial force imbalances, bit mass imbalance, and bit/formation interaction among other things.
  • This condition includes directional reversals and gyration about the hole center often known as whirl. Lateral vibration results in poor bit performance, overgage hole drilling, out-of-round, or "lobed" wellbores, and premature failure of both the cutting structures and bearing systems of bits.
  • roller cone bit designs remain the result of generations of modifications made to original designs.
  • the modifications are based on years of experience in evaluating bit records, dull bit conditions, and bottom hole patterns.
  • each cone On the outermost rows of each cone, the teeth are encountering impressions in the formation left by teeth on other cones.
  • the staggered teeth are just as likely to track an impression as any other tooth.
  • Another disadvantage to staggered designs is that they may cause fluctuations in cone rotational speed, resulting in fluctuations in tooth impact force and increased bit vibration. Bit vibration is very harmful to the life of the bit and the life of the entire drill string.
  • This orientation is designed to provide the inserts with a higher resistance to breakage.
  • the inserts in the heel row are oriented at an axial angle between 300 degrees and 330 degrees, while the inserts in the second row are axially oriented between 30 degrees and 60 degrees.
  • This orientation is designed to provide the inserts with a broader contact area with the formation for increased formation removal, and thereby an increased rate of penetration of the drill bit into the formation.
  • the present application describes bit design methods (and corresponding bits, drilling methods, and systems) in which tooth orientation is optimized jointly with other parameters, using software which graphically displays the linearized trajectory of each tooth row, as translated onto the surface of the cone.
  • the speed ratio of each cone is precisely calculated, as is the curved trajectory of each tooth through the formation.
  • linear approximations to the tooth trajectory are preferably displayed.
  • roller cone drill bit design methods and optimizations which can be used separately from or in synergistic combination with the methods disclosed in the present application. That application, which has common ownership, inventorship, and effective filing date with the present application, is:
  • Figures 1A-1C show a sample embodiment of a bit design process, using the teachings of the present application. Specifically, Figure 1A shows an overview of the design process, and Figures 1B and 1C expand specific parts of the process.
  • bit geometry is input (step 102 ).
  • bit layout is displayed (step 104 ).
  • transformation matrices from cone to bit coordinates must be calculated (step 106 ).
  • step 106 The number of bit revolutions is input (step 108 ), and each cone is counted (step 110 ), followed by each row of teeth for each cone (step 112 ).
  • step 114 the type of teeth of each row is identified (step 114 ), and the teeth are counted (step 116 ).
  • step 118 a time interval delta is set (step 118 ), and the position of each tooth is calculated at this time interval (step 120 ).
  • step 122 If a given tooth is not "cutting" (i.e., in contact with the hole bottom), then the algorithm continues counting until a cutting tooth is reached (step 122 ).
  • the tooth trajectory, speed, scraping distance, crater distribution, coverage ratio and tracking ratios for all rows, cones, and the bit are calculated (step 124 ).
  • This section of the process gives the teeth motion over the hole bottom, and displays the results (step 126 ).
  • bit mechanics are calculated. (See Figure 1C .) Again transformation matrices from cone to bit coordinates are calculated (step 128 ), and the number of bit revolutions and maximum time steps, delta, are input (step 130 ). The cones are then counted (step 132 ), the bit and cone rotation angles are calculated at the given time step (step 134 ), and the rows are counted (step 136 ). Next, the 3D tooth surface matrices for the teeth on a given row are calculated (step 138 ). The teeth are then counted (step 140 ), and the 3D position of the tooth on the hole bottom is calculated at the given time interval (step 142 ). If a tooth is not cutting, counting continues until a cutting tooth is reached (step 144 ).
  • the cutting depth, area, volume and forces for each tooth are calculated, and the hole bottom model is updated (based on the crater model for the type of rock being drilled). Next the number of teeth cutting at any given time step is counted. The tooth force is projected into cone and bit coordinates, yielding the total cone and bit forces and moments. Finally the specific energy of the bit is calculated (step 146 ).
  • Figure 13 shows a sample XYZ plot of a tooth tip (in tooth local coordinates). Tooth coordinates will be indicated here by the subscript t. (Of course, each tooth has its own tooth coordinate system.) The center of the X t Y t Z t coordinate system, in the presently preferred embodiment, is located at the tooth center. The coordinate of a tooth's crest point P t will be defined by parameters of the tooth profile (e.g. tooth diameter, extension, etc.).
  • Figure 14 shows axial and sectional views of the i-th cone, and illustrates the enumeration of rows and teeth.
  • Cone coordinates will be indicated here by the subscript c.
  • the center of the cone coordinates is located in the center of backface of the cone.
  • the cone body is fixed with respect to these coordinates, and hence THESE COORDINATES ROTATE WITH THE CONE. (Of course, each cone has its own cone coordinate system.)
  • the axis Z c coincides with the cone axis, and is oriented towards to the bit center.
  • Cone axes Y c and X c together with axis Z c , follow the right hand rule.
  • H c , R c , ⁇ c and ⁇ c are the same.
  • a set of bit axes X b Y b Z b is aligned to the bit.
  • the bit is fixed with respect to these coordinates, and hence THESE COORDINATES ROTATE WITH THE BIT.
  • Axis Z b preferably points toward the cutting face, and axes X b and Y b are normal to Z b (and follow the right-hand rule).
  • FIG. 1 The simplest coordinate system is defined by the hole axes X h Y h Z h , which are fixed in space. Note however that axes Z b and Z h may not be coincident if the bit is tilted.
  • Figure 2 shows the tangential and radial velocity components of tooth trajectory, viewed through the cutting face (i.e. looking up). Illustrated is a small portion of a tooth trajectory, wherein a tooth's crest (projected into an X h Y h plane which approximates the bottom of the hole) moves from point A to point B, over an arc distance ds and a radial distance dr.
  • the cone has a rotation angle ⁇ around its negative axis (-Z c ). Any point on the cone moves to a new position due to this rotation.
  • the new position of P c in X c Y c Z c can be determined by combining linear transforms.
  • R cone cos( ⁇ )I + (1-cos( ⁇ ))NcNc' + sin( ⁇ )Mc, where N c is the rotation vector and M c is a 3*3 matrix defined by N c .
  • the formation is modeled, in the presently preferred embodiment, by multiple stepped horizontal planes. (The number of horizontal planes depends on the total number of rows in the bit.) In this way, the trajectory of any tooth on hole bottom can be determined.
  • Figures 3A, 3B, 3C, and 3D show plots of planar tooth trajectories, referenced to the hole coordinates X h Y h , for teeth on four different rows of a particular roller cone bit.
  • the teeth on the outermost row (first row) scrapes toward the leading side of the cone. Its radial and tangential scraping distances are similar, as can be seen by comparing the first bar in Figure 4A with the first bar in Figure 4B. However for teeth on the second row the radial scraping motion is much larger than the tangent motion.
  • the teeth on the third row scrape toward the trailing side of the cone, and the teeth on the forth row scrape toward the leading side of the cone.
  • Figures 4A and 4B show per-bit-revolution tangential and radial distances, respectively, for the four tooth trajectories shown in Figures 3A-3D. Note that, in this example, the motion of the second row is almost entirely radial, and not tangential.
  • the tooth trajectories described above are projected on the hole bottom which is fixed in space. In this way it is clearly seen how the tooth scrapes over the bottom.
  • the teeth orientation angle on the cone coordinate in order either to keep the elongate side of the tooth perpendicular to the scraping direction (for maximum cutting rate in softer formations) or to keep the elongate side of the tooth in line with the scraping direction (for durability in harder formations).
  • the tooth trajectories are projected to the cone coordinate system.
  • roller cone design There are numerous parameters in roller cone design, and experienced designers already know, qualitatively, that changes in cone shape (cone angle, heel angle, third angle, and oversize angle) as well as offset and journal angle will affect the scraping pattern of teeth in order to get a desired action-on-bottom.
  • One problem is that it is not easy to describe a desired action-on-bottom quantitatively.
  • the present application provides techniques for addressing this need.
  • the arcuate (or bulged) shape of the cone primarily affects the ETSD value, and the offset determines the ERSD value.
  • the ERSD is not equal to zero even at zero offset. In other words, the teeth on a bit without offset may still have some small radial scraping effects.
  • the radial scraping direction for all teeth is always toward to the hole center (positive). However, the tangential scraping direction is usually different from row to row.
  • the leading side of the elongated teeth crest should be orientated at an angle to the plane of the cone's axis, which is calculated as described above for any given row.
  • Figure 2 shows the procedure in which a tooth cuts into (point A) and out (point B) the formation. Due to bit offset, arcuate cone shape and bit and cone rotations, the motion from A to B can be divided into two parts: tangent motion ds and radial motion dr. Notice the tangent and radial motions are defined in hole coordinate system XhYh. Because ds and dr vary from row to row and from cone to cone, we derive an equivalent tangent scraping distance (ETSD) and an equivalent radial scraping distance (ERSD) for a whole cone (or for an entire bit).
  • ESD equivalent tangent scraping distance
  • ERSD equivalent radial scraping distance
  • Nc is the total tooth count of a cone and Nr is the number of rows of a cone.
  • Nb is the total tooth count of the bit.
  • Figures 15A-15D show how the planarized tooth trajectories vary as the offset is increased. These figures clearly show that with the increase of the offset value, the radial scraping distance is increased. Surprisingly, the radial scraping distance is not equal to zero even if the offset is zero. This is due to the arcuate shape of the cone.
  • Figures 16A-16D show how the ERSD and ETSD values vary for all rows of a given cone as offset is increased. From these Figures, it can be seen that the tangent scraping distance of the gage row, while very small compared to other rows but is not equal to zero. It means that there is a sliding even for the teeth on the driving row. This fact may be explained by looking at the tangent speed during the entry and exit of teeth into and out of the rock. ( Figure 6 shows time-domain plots of tooth tangential speed, for the five rows of a sample cone, over the duration of the trajectory for each row.) During the cutting procedure the tangent speed is not equal to zero except for one instant. Because the sliding speed changes with time, the instantaneous speed is not the best way to describe the teeth/rock interaction.
  • Figure 5 is a sectional view of a cone (normal to its axis), showing how the tooth orientation is defined in the present application: the positive direction is defined as the same direction as the bit rotation. This means that the leading side of tooth on one row may be different from that on another row.
  • the ERSD increases almost proportionally with the increase of the bit offset. However, ERSD is not zero even if the bit offset is zero. This is because the radial sliding speed is not always zero during the procedure of tooth cutting into and cutting out the rock.
  • Figures 7A and 7B show how optimization of tooth orientation can perturb the width of uncut rings on the hole bottom.
  • the width of uncut rings is one of the design constraints: a sufficiently narrow uncut ring will be easily fractured by adjacent cutter action and mud flows, but too large an uncut ring will slow rate of penetration.
  • tooth orientation should not be adjusted in isolation, but preferably should be optimized jointly with the width of uncut rings.
  • Figures 9A, 9B and 9C show the screen views which a skilled bit designer would see, according to some embodiments of the invention, while working on a bit optimization which included optimization of tooth orientation. These three views show representations of tooth orientation and scraping direction for each tooth row on each of the three cones. This simple display allows the designer to get a feel for the effect of various parameter variations
  • the present application also teaches that the ratio between the rotational speeds of cone and bit can be easily checked, in the context of the detailed force calculations described above, simply by calculating the torques about the cone axis. If these torques sum to zero (at a given ratio of cone and bit speed), then the given ratio is correct. If not, an iterative calculation can be performed to find the value of this ratio.
  • a method of designing a roller cone bit comprising the steps of: adjusting the orientation of at least one tooth on a cone, in dependence on an expected trajectory of said tooth through formation material at the cutting face, in dependence on an estimated ratio of cone rotation to bit rotation; recalculating said ratio, if the location of any row of teeth on said cone changes during optimization; recalculating the trajectory of said tooth in accordance with a recalculated value of said cone speed; and adjusting the orientation of said tooth again, in accordance with a recalculated value of said tooth trajectory.
  • a method of designing a roller cone bit comprising the steps of: calculating the trajectory of at least one tooth on each cone through formation material at the cutting face; and jointly optimizing both the orientations of said teeth and the width of uncut rings on said cutting face, in dependence on said trajectory.
  • a method of designing a roller cone bit comprising the steps of: a) adjusting the orientation of at least one row of teeth on a cone, in dependence on an expected trajectory of said tooth through formation material at the cutting face; b) calculating the width of uncut rings of formation material, in dependence on the orientation of said row of teeth, and adjusting the position of said row of teeth in dependence on said calculated width; and c) recalculating the rotational speed of said cone, if the position of said row is changed, and accordingly recalculating said trajectory of teeth in said row.
  • a method of designing a roller cone bit comprising the steps of: calculating the respective trajectories, of at least two non-axisymmetric teeth in different rows of a roller cone bit, through formation material at the cutting face; and graphically displaying, to a design engineer, both said trajectories and also respective orientation vectors of said teeth, as the engineer adjusts design parameters.
  • a method of designing a roller cone bit comprising the steps of: calculating the curved trajectory of a non-axisymmetric tooth through formation material at the cutting face, as the bit and cones rotate; calculating a straight line approximation to said curved trajectory; and orienting said tooth with respect to said approximation, and not with respect to said curved trajectory.
  • a roller cone drill bit designed by any of the methods described above, singly or in combination.
  • a rotary drilling system comprising: a roller cone drill bit designed by any of the methods described above, singly or in combination. a drill string which is mechanically connected to said bit; and a rotary drive which rotates at least part of said drill string together with said bit.
  • a method for rotary drilling comprising the actions of: applying weight-on-bit and rotary torque, through a drill string, to a drill bit designed in accordance with any of the methods described above, singly or in combination.
  • the various teachings can optionally be adapted to two-cone or four-cone bits.
  • the orientations of teeth can be perturbed about the optimal value, to induce variation between the gage rows of different cones (or within an inner row of a single cone), to provide some additional resistance to tracking.
  • bit will also normally contain many other features besides those emphasized here, such as gage buttons, wear pads, lubrication reservoirs, etc. etc.
EP04025560A 1998-08-31 1999-08-31 Verfahren zum Entwurf eines Rollenbohrmeissels Withdrawn EP1500781A3 (de)

Applications Claiming Priority (4)

Application Number Priority Date Filing Date Title
US9844298P 1998-08-31 1998-08-31
US98442P 1998-08-31
EP03021139A EP1371811B1 (de) 1998-08-31 1999-08-31 Rollenbohrmeissel, zugehöriges Entwurfsverfahren und Drehbohrsystem
EP99945376A EP1117894B2 (de) 1998-08-31 1999-08-31 Rollenmeissel, systeme, bohrverfahren und konstruktionsmethoden mit optimierung der zahnorientierung

Related Parent Applications (1)

Application Number Title Priority Date Filing Date
EP03021139A Division EP1371811B1 (de) 1998-08-31 1999-08-31 Rollenbohrmeissel, zugehöriges Entwurfsverfahren und Drehbohrsystem

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EP1500781A2 true EP1500781A2 (de) 2005-01-26
EP1500781A3 EP1500781A3 (de) 2006-04-12

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Application Number Title Priority Date Filing Date
EP04025561A Withdrawn EP1500782A3 (de) 1998-08-31 1999-08-31 Verfahren zum Entwurf eines Rollenbohrmeissels
EP03021139A Expired - Lifetime EP1371811B1 (de) 1998-08-31 1999-08-31 Rollenbohrmeissel, zugehöriges Entwurfsverfahren und Drehbohrsystem
EP04025560A Withdrawn EP1500781A3 (de) 1998-08-31 1999-08-31 Verfahren zum Entwurf eines Rollenbohrmeissels
EP99945376A Expired - Lifetime EP1117894B2 (de) 1998-08-31 1999-08-31 Rollenmeissel, systeme, bohrverfahren und konstruktionsmethoden mit optimierung der zahnorientierung
EP04025562A Withdrawn EP1500783A3 (de) 1998-08-31 1999-08-31 Verfahren zum Entwurf eines Rollenbohrmeissels
EP04025232A Withdrawn EP1498572A3 (de) 1998-08-31 1999-08-31 Rollenmeissel, Systeme, Bohrverfahren und Konstruktionsmethoden mit Optimierung der Zahnorientierung

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EP04025561A Withdrawn EP1500782A3 (de) 1998-08-31 1999-08-31 Verfahren zum Entwurf eines Rollenbohrmeissels
EP03021139A Expired - Lifetime EP1371811B1 (de) 1998-08-31 1999-08-31 Rollenbohrmeissel, zugehöriges Entwurfsverfahren und Drehbohrsystem

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EP99945376A Expired - Lifetime EP1117894B2 (de) 1998-08-31 1999-08-31 Rollenmeissel, systeme, bohrverfahren und konstruktionsmethoden mit optimierung der zahnorientierung
EP04025562A Withdrawn EP1500783A3 (de) 1998-08-31 1999-08-31 Verfahren zum Entwurf eines Rollenbohrmeissels
EP04025232A Withdrawn EP1498572A3 (de) 1998-08-31 1999-08-31 Rollenmeissel, Systeme, Bohrverfahren und Konstruktionsmethoden mit Optimierung der Zahnorientierung

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EP (6) EP1500782A3 (de)
AU (1) AU5798499A (de)
ID (1) ID28893A (de)
MX (1) MXPA01002208A (de)
WO (1) WO2000012860A2 (de)

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WO2000012860A9 (en) 2000-11-23
EP1371811A3 (de) 2004-01-02
EP1371811A2 (de) 2003-12-17
WO2000012860A2 (en) 2000-03-09
WO2000012860A3 (en) 2000-06-08
EP1117894A4 (de) 2002-08-14
EP1500783A3 (de) 2006-04-12
EP1500783A2 (de) 2005-01-26
EP1498572A2 (de) 2005-01-19
EP1117894B1 (de) 2003-12-03
EP1498572A3 (de) 2006-04-12
EP1371811B1 (de) 2011-03-30
AU5798499A (en) 2000-03-21
ID28893A (id) 2001-07-12
EP1117894A2 (de) 2001-07-25
MXPA01002208A (es) 2003-03-27

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