Patent Grant
8973684
Rotary drill bits employing polycrystalline diamond compact (“PDC”) cutters have previously been employed for drilling subterranean formations. Conventional PDC cutters may comprise a diamond table formed under ultra high temperature, ultra high pressure conditions onto a substrate, typically of cemented tungsten carbide. Conventional drill bit bodies may comprise a so-called tungsten carbide matrix including tungsten carbide particles distributed within a binder material or may comprise steel. Tungsten carbide matrix drill bit bodies may be fabricated by preparing a mold that embodies the inverse of the desired generally radially extending blades, cutting element sockets or pockets, junk slots, internal watercourses and passages for delivery of drilling fluid to the bit face, ridges, lands, and other external topographic features of the drill bit. Particulate tungsten carbide may then be placed into the mold and a binder material, such as a metal including copper and tin, may be melted into the tungsten carbide particulate and solidified to form the drill bit body. Steel drill bit bodies may be fabricated by machining a piece of steel to form generally radially extending blades, cutting element sockets or pockets, junk slots, internal watercourses and passages for delivery of drilling fluid to the bit face, ridges, lands, and other external topographic features of the drill bit. In both matrix-type and steel bodied drill bits, a threaded pin connection may be formed for securing the drill bit body to the drive shaft of a downhole motor or directly to drill collars at the distal end of a drill string rotated at the surface by a rotary table, top drive, drilling motor (pdm) or turbine.
Conventional cutting element retention systems or structures that have been employed generally comprise the following two styles: (1) tungsten carbide studs comprising a cylindrical tungsten carbide cylinder having a face oriented at an angle (back rake angle) with respect to the longitudinal axis of the cylinder, the face carrying a superabrasive cutting structure thereon, wherein the cylinder is press-fit into a recess that is generally oriented perpendicularly to the blades extending from the bit body on the bit face; and (2) brazed attachment of a generally cylindrical cutting element into a recess (e.g., a cutter pocket) formed on the bit face, typically on a blade extending from the bit face. Accordingly, the first cutting element retention style is designed for a stud type cutting element, while the second cutting element retention style is designed for generally cylindrical cutting elements, such as PDC cutters. In either system, the orientation of the cutting elements is held stationary relative to the bit body as the drill bit is used. Of the two different types of cutting element retention configurations utilized in the manufacture of rotary drill bits, cylindrical cutting elements are generally more common. Stud-type cutting elements, on the other hand, are relatively uncommon and may require a brazing or infiltration cycle to affix the PDC or TSPs to the stud.
According to at least one embodiment, a rotary drill bit may comprise a bit body, a cutting pocket defined in the bit body, and a cutting element rotatably coupled to the bit body, the cutting element being positioned at least partially within the cutting pocket. The rotary drill may also comprise a rotation-inducing member adjacent to the cutting element for inducing rotation of the cutting element relative to the cutting pocket. A gap may be defined between the cutting element and the cutting pocket. Optionally, the cutting element may be coupled to the bit body such that the cutting element may be moved within the cutting pocket. The cutting element may be capable of contacting one or more surfaces of the cutting pocket.
The rotation-inducing member may also be disposed at least partially within the cutting pocket. The rotation-inducing member may also comprise at least a portion of a cutting pocket surface. In one embodiment, the rotation-inducing member may be disposed between the cutting element and the cutting pocket defined in the bit body. The rotation-inducing member may be configured to induce rolling contact between the cutting element and the cutting pocket. Further, the rotation-inducing member may be configured such that cutting forces acting on the drill bit actuate the rotation-inducing member to induce rotation of the cutting element relative to the cutting pocket. The rotation-inducing member may optionally be configured to induce a net rotation of the cutting element in a single direction relative to the cutting pocket. The rotation-inducing member may be configured to induce rotation of the cutting element relative to the cutting pocket as the drill bit is rotated relative to a formation. The rotation-inducing member may also be configured to induce vibrational movement of the cutting element relative to the cutting pocket.
According to various embodiments the rotation-inducing member may comprise a resilient support member. The resilient support member may comprise a spring element. The resilient support member may comprise at least one of a wave spring washer, a curved spring washer, or a Belleville spring washer. The resilient support member may bias the cutting element within the cutting pocket. According to additional embodiments, the resilient support member may be configured to vibrate in response to cutting forces and therefore may be referenced as a vibrational member. The resilient support member may also be configured to compress in response to cutting forces. Optionally, the resilient support member may be configured to alternately compress and decompress in response to variations in cutting forces.
According to at least one embodiment, the rotation-inducing member may comprise a vibrational member. The vibrational member may be configured to vibrate such that friction between the cutting element and the cutting pocket is reduced. The vibrational member may be configured such that external forces acting on the drill bit induce vibrations in the vibrational member. External forces acting on the drill bit may include cutting forces acting on the drill bit. The vibrational member may be configured to vibrate sufficiently to induce rotation of the cutting element relative to the cutting pocket. Optionally, the vibrational member may comprise at least two vibrational prongs adjacent to the cutting element. The vibrational member may optionally resiliently support at least a portion of the cutting element.
According to various embodiments, the cutting element may comprise a superabrasive material bonded to a substrate, the substrate extending from an interfacial surface to a back surface of the substrate. The rotation-inducing member may be adjacent to at least one of the substrate and the superabrasive material bonded to the substrate. Optionally, the rotation-inducing member may comprise a resilient support member disposed between a back surface of the cutting element and the cutting pocket.
According to certain embodiments, the rotary drill bit may also comprise a structural element coupled to a back surface of the cutting element. The rotary drill bit may further comprise a through hole defined in the bit body, the through hole defined by the cutting pocket, wherein the structural element is rotatably disposed in the through hole. The structural element may comprise an anchor element positioned adjacent to an anchor surface, the anchor element having an outer diameter greater than a diameter of the through hole.
According to at least one embodiment, the cutting element may have a central axis. The cutting element may be coupled to the bit body such that the cutting element and the central axis may be moved within the cutting pocket. The rotation-inducing member may radially surround at least a portion of the cutting element relative to the central axis. The rotation-inducing member may also comprise a resilient member positioned adjacent to an outer diameter of the cutting element. The resilient member may be configured to compress in a direction that is generally transverse to the rotational axis of the cutting element.
According to additional embodiments, the rotary drill bit may comprise one or more protrusions extending from an interior of the cutting pocket adjacent to an outer diameter of the cutting element. The cutting element and the one or more protrusions may be configured such that the cutting element engages and rolls over the one or more protrusions when the cutting element is forced toward the resilient member. The cutting element may be configured to rotate relative to the cutting pocket as it engages and rolls over the one or more protrusions. Optionally, the cutting element and the protrusions may be configured such that the cutting element slides over the one or more protrusion when the cutting element is forced away from the resilient member.
According to at least one embodiment, a method of drilling a formation may comprise providing a drill bit, the drill bit comprising a bit body, a cutting pocket defined in the bit body, a cutting element rotatably coupled to the bit body, the cutting element being positioned at least partially within the cutting pocket, and a rotation-inducing member adjacent to the cutting element. The method may comprise contacting the drill bit to a formation. The method may comprise moving the drill bit relative to the formation. The rotation-inducing member may induce rotation of the cutting element relative to the cutting pocket as the drill bit is moved relative to the formation.
Moving the drill bit relative to the formation may cause the rotation-inducing member to induce vibrational movement of the cutting element relative to the cutting pocket. Moving the drill bit relative to the formation may cause vibration of the rotation-inducing member sufficiently to induce rotation of the cutting element relative to the cutting pocket. In one embodiment, moving the drill bit relative to the formation may cause vibration of the rotation-inducing member such that friction between the cutting element and the cutting pocket is reduced. Further, the rotation-inducing member may comprise a resilient member configured to compress in a direction that is generally transverse to the rotational axis of the cutting element.
Features from any of the above-mentioned embodiments may be used in combination with one another in accordance with the general principles described herein. These and other embodiments, features, and advantages will be more fully understood upon reading the following detailed description in conjunction with the accompanying drawings and claims.
The accompanying drawings illustrate a number of exemplary embodiments and are a part of the specification. Together with the following description, these drawings demonstrate and explain various principles of the instant disclosure.
Throughout the drawings, identical reference characters and descriptions indicate similar, but not necessarily identical, elements. While the exemplary embodiments described herein are susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and will be described in detail herein. However, the exemplary embodiments described herein are not intended to be limited to the particular forms disclosed. Rather, the instant disclosure covers all modifications, equivalents, and alternatives falling within the scope of the appended claims.
The present invention relates generally to drill bits, such as rotary drill bits used for drilling subterranean formations. “Superhard,” as used herein, refers to any material having a hardness that is at least equal to a hardness of tungsten carbide. Additionally, a “superabrasive material,” as used herein, may refer to a material exhibiting a hardness exceeding a hardness of tungsten carbide, such as, for example, polycrystalline diamond. In addition, as used throughout the specification and claims, the word “cutting” generally refers to any drilling, boring, or the like. The word “cutting,” as used herein, refers broadly to machining processes, drilling processes, or any other material removal process utilizing a cutting element.
Cutting elements 14 may be mounted to various suitable portions of bit blades 16, as illustrated in
Cutting element 14 may include a layer or table 22 affixed to or formed upon a substrate 24. Table 22 may be formed of any material or combination of materials suitable for cutting various types of formations. For example, table 22 may comprise a superhard or superabrasive material such as polycrystalline diamond. In additional embodiments, cutting element 14 may comprise a unitary or integrally formed structure comprising, for example, diamond, silicon carbide, boron nitride, or a combination of the foregoing. Substrate 24 may comprise any material or combination of materials capable of adequately supporting a superabrasive material during drilling of a subterranean formation, including, for example, cemented tungsten carbide. For example, cutting element 14 may comprise a table 22 comprising polycrystalline diamond bonded to a substrate 24 comprising cobalt-cemented tungsten carbide. In at least one embodiment, after formation of table 22, a catalyst material (e.g., cobalt or nickel) may be at least partially removed (e.g., by acid-leaching) from table 22. Table 22 of cutting element 14 may form a cutting face 23, at least a portion of which is generally perpendicular to a central axis 42, and additionally, a circumferential portion of cutting face 23 may be chamfered or may comprise at least one so-called buttress geometry or any other suitable geometry. According to various embodiments, a circumferential portion of cutting face 23 and/or any other suitable portion of table 22 may form a cutting edge. Central axis 42 may be substantially centered (i.e., positioned at a centroid) with respect to a selected cross-sectional area (e.g., a solid cross-sectional area or a cross-sectional area bounded by an exterior surface, without limitation) of cutting element 14.
According to certain embodiments, cutting element 14 may also comprise a base member 25. Base member 25 may be affixed to substrate 24 through any suitable method, such as, for example, brazing. Base member 25 may extend from a back surface of substrate 24 to a back cutting element surface 26 of cutting element 14. According to additional embodiments, back cutting element surface 26 may be defined by substrate 24. Base member 25 and/or substrate 24 may include a recess for facilitating retention of cutting element 14 within cutting pocket 27 of bit blade 16. The recess may be configured for accepting a fastening or support element, wherein the fastening element extends from the recess and may facilitate affixation, support, or securement of the cutting element to a rotary drill bit. The cutting element assembly may embody any of the features disclosed in U.S. patent application Ser. No. 11/148,806, which is incorporated by reference above.
In at least one embodiment, a structural element 30 may be employed in combination with cutting element retention structures or assemblies for securing or supporting cutting element 14 within bit blade 16 of rotary drill bit 10. For example, structural element 30 may include an end portion that is sized and configured to fit within a recess of base member 25 and/or substrate 24. Structural element 30 may also comprise a fastener as known in the art. For example, structural element 30 may comprise a bolt or machine screw (e.g., a socket-head cap screw). Structural element 30 may also comprise any threaded fastener as known in the art, without limitation. Additionally, structural element 30 may comprise a threaded end portion configured to fit within a corresponding threaded recess in base member 25. While structural element 30 is shown attached to base member 25 in
In various embodiments, structural element 30 may comprise a shaft portion 32, which may be positioned within a through hole 36 defined in bit blade 16. Through hole 36 may be sized to allow rotation of shaft portion 32. Additionally, through hole may be coated with at least one coating or may comprise a sleeve, such as a metallic sleeve, to facilitate rotation of shaft portion 32, to reduce friction between shaft portion 32 and/or through hole 36, and/or to reduce wear of shaft portion 32 and/or through hole 36. Structural element 30 may also comprise an anchor portion 34 located at an end portion of structural element 30 opposite cutting element 14. Anchor portion 34 may be adjacent to an anchor surface 38 on bit blade 16. Anchor portion 34 may also be located adjacent an end of through hole 36 opposite cutting pocket 27. In at least one embodiment, anchor portion 34 may be integrally formed with shaft portion 32 of structural element 30. Anchor portion 34 may also be fastened to shaft portion 32. For example, structural element 30 may have a threaded end that engages a threaded aperture in anchor portion 34 comprising a threaded nut. Lock washers or other elements that are used in combination with fasteners (as known in the art) may also be employed in combination with structural element 30.
In at least one embodiment, a biasing element 40 (e.g., a Belleville washer spring or a coil spring) may be positioned between anchor portion 34 and bit blade 16. Biasing element 40 may bias structural element 30 in a selected direction and/or may generate a selected force. For example, biasing element 40 may generally bias cutting element 14 within cutting pocket 27 of bit blade 16. Biasing element 40 may also enable a preload force to be applied to cutting element 14. For example, biasing element 40 may apply a preload force to cutting element 14, which may aid in the rotation of cutting element 14 in response to forces generated during drilling of a formation. Accordingly, biasing element 40 may position cutting element 14 in cutting pocket 27 of bit blade 16 while selectively allowing cutting element 14 to rotate in cutting pocket 27.
In one embodiment, a resilient support member 29 may be positioned between cutting element 14 and cutting pocket 27. Resilient support member 29 may act as a rotation-inducing member, inducing and/or otherwise enabling rotation of cutting element 14 within cutting pocket 27. Resilient support member 29 may be positioned between any suitable portion of cutting element 14 and any suitable portion of cutting pocket 27. For example, as illustrated in
According to various embodiments, vibrations may be induced in resilient support member 29 during a drilling operation. For example, cutting element 14 and/or various other portions of rotary drill bit 10 may contact portions of a formation, such as a subterranean rock formation, during a drilling or other cutting operation, causing vibrations to be induced in cutting element 14 and/or other portions of rotary drill bit 10. Any suitable portion of cutting face 23 may contact a formation such that cuttings are removed from the formation. Cuttings may comprise pulverized material, fractured material, sheared material, a continuous chip, or any cuttings produced by abrading a solid material, such as a rock formation, without limitation. Cutting pocket 27 may be sized such that it has a larger diameter than a diameter of cutting element 14 relative to central axis 42. Accordingly, cutting forces during a drilling operation may cause cutting element 14 to move within cutting pocket 27. The vibrations and/or movement induced in cutting element 14 and/or other portions of drill bit 10 may likewise induce vibrations in resilient support member 29. Vibrations induced in resilient support member 29 may reduce or inhibit frictional forces (e.g., static friction) between resilient cutting element 14 and support member 29 and/or between cutting element 14 and various portions of cutting pocket 27, enabling and/or inducing rotation of cutting element 14 within cutting pocket 27 in response to forces acting on cutting element 14 and/or other portions of drill bit 10. Accordingly, cutting forces acting on cutting element 14 during a drilling operation may cause incremental or continuous movement of cutting element 14 within cutting pocket 27 as resilient support member 29 vibrates.
The rotation of cutting element 14 within cutting pocket 27 may significantly decrease wear on cutting element 14, thereby significantly increasing the usable life of cutting element 14 in comparison with conventional cutting elements. As cutting element 14 rotates relative to cutting pocket 27, a surface portion of cutting element 14 exposed to a formation during drilling, such as a portion of cutting face 23, may be periodically changed or substantially continuously changed, in contrast to a conventional cutting element, where the surface portion of a cutting element exposed to a formation remains constant. Rotation of cutting element 14 during a drilling operation may introduce a greater portion of cutting element 14, including cutting face 23, against a formation, which may reduce wear of the cutting element 14. For example, the volume of diamond worn away from cutting element 14 for a given volume of rock cut may be reduced in comparison with a conventional non-rotatable cutting element.
In various embodiments, cutting element 14 may be substantially cylindrical and may rotate about central axis 42. Cutting element 14 may be rotated about central axis 42 in a clockwise direction, in a counter-clockwise direction, or both (i.e., serially). Such rotation may cause a selected portion of table 22, such as cutting face 23 and/or a cutting edge formed by cutting face 23 or any other suitable portion of table 22, to contact material being cut, such as rock material. Cutting element 14 may be rotated in at least one or more directions, intermittently or substantially continuously, so that various portions of table 22, including cutting face 23, interact with a material being cut during a drilling or other cutting operation. At least one lubricant and/or another fluid may be introduced into cutting pocket 27 to facilitate rotation of cutting element 14 within cutting pocket 27 and/or to flush out various debris from cutting pocket 27, such as particles of rock resulting from drilling a rock formation. Fluids introduced into cutting pocket 27 may include, without limitation, drilling mud, air, oil, and/or water.
Various factors may affect the rotation of cutting element 14 in cutting pocket 27, including the extent and/or speed of rotation of cutting element 14 relative to cutting pocket 27. These factors may include, without limitation, the size of cutting element 14, the size of cutting pocket 27, the ratio of a diameter of cutting pocket 27 to a diameter of cutting element 14, and/or vibrational frequencies and magnitudes resulting from cutting forces acting on rotary drill bit 10. Accordingly, the rotation of cutting element 14 may be configured to suit various drilling situations and to maximize the usable life of cutting element 14.
In at least one embodiment, a structural element 130 may be employed in combination with cutting element retention structures or assemblies for securing or supporting cutting element 114 within bit blade 116 of rotary drill bit 110. Structural element 130 may comprise a shaft portion 132, which may be positioned within a through hole 136 defined in bit blade 116. Structural element 130 may also comprise an anchor portion 134 located at an end portion of structural element 130 opposite cutting element 114. Anchor portion 134 may be adjacent to an anchor surface 138 on bit blade 116. In at least one embodiment, a biasing element 140 may be positioned between anchor portion 134 and bit blade 116.
According to additional embodiments, a resilient support member 129 may be positioned between cutting element 114 and cutting pocket 127. Resilient support member 129 may be positioned between any suitable portion of cutting element 114 and any suitable portion of cutting pocket 127. For example, resilient support member 129 may be positioned between back cutting element surface 126 and back cutting pocket surface 128. Resilient support member 129 may have a natural frequency encompassing frequencies generated in rotary drill bit 110 during cutting. In at least one embodiment, resilient support member 129 may have a natural frequency of between about 200-1000 hertz. For example, resilient support member 129 may have a natural frequency of about 800 hertz.
In another embodiment, rotary drill bit 110 may additionally comprise a vibrational member 144 positioned adjacent to cutting element 114. Vibrational member 144 may be coupled to bit blade 116 by fastener 148. Fastener 148 may comprise any suitable fastener suitable for coupling vibrational member 144 to bit blade 116, such as, for example, a threaded bolt. As illustrated in
Vibrational member 144 may be formed to any suitable shape or size and may be formed of any suitable material, such as, for example, a metallic material. A surface of vibrational member 144 may form at least a portion of a surface of cutting pocket 127 adjacent to cutting element 114. As shown in
Prongs 146 may act as support members supporting cutting element 114 within cutting pocket 127. Prongs 146 may also act as resilient members resiliently supporting and/or deflecting cutting element 114 within cutting pocket 127. For example, prongs 146 may vibrate adjacent to cutting element 114, thereby reducing friction between cutting element 114 and cutting pocket 127. Prongs 146 may be either symmetric or asymmetric relative to each other.
According to additional embodiments, vibrational member 144 may vibrate in a manner and at a frequency suitable to induce continuous or incremental rotation of cutting element 114 within cutting pocket 127. For example, vibration of prongs 146 of vibrational member 144 may induce rolling contact rotation of cutting element 114 along a surface portion of cutting pocket 127. Accordingly, vibrations from vibrational member 144 may induce rolling contact rotation between cutting element 114 and cutting pocket 127 such that cutting element 114 moves in a generally circular pattern around at least a portion of cutting pocket 127 (see, e.g.,
As illustrated in
Various factors may affect the rotation of cutting element 214 in cutting pocket 227, including the extent and/or speed of rotation of cutting element 214 relative to cutting pocket 227. These factors may include, without limitation, the size of cutting element 214, the size of cutting pocket 227, the ratio of a diameter of cutting pocket 227 to a diameter of cutting element 214, the size of gap 250 between cutting element 214 and cutting pocket 227, the natural frequency of vibrational member (not shown for clarity purposes), and/or frequencies and magnitudes of vibrations (e.g., circular vibrations) resulting from cutting forces acting on rotary drill bit 210. Details concerning factors that influence rotation of a cutting element, such as circular vibration, may be described in Vibration-Induced Rotation, Patrick Andreas Petri, Massachusetts Institute of Technology, May 2001, which document is incorporated herein by reference in its entirety.
As indicated above, the rotation of cutting element 214 within cutting pocket 227 may significantly increase the usable life of cutting element 214 in comparison with conventional cutting elements. For example, rotation of cutting element 214 may intermittently or substantially continuously renew a portion of cutting element 214 exposed to a material being cut, thereby reducing an amount and/or depth of wear of cutting element 214 during a cutting period. In another example, rotating the cutting element 214 tends to spread the heat input over a larger volume of the cutting element 214. Spreading the heat input to the cutting element 214 may lead to longer life. Accordingly, the rotation of cutting element 214 may be configured and adjusted to suit various drilling situations and to maximize the usable life of cutting element 214.
In another embodiment, a vibrational member 356 may be positioned adjacent to cutting element 314. For example, as illustrated in
According to at least one embodiment, vibrational member 356 and protrusions 360 may facilitate rotation of cutting element 314 within cutting pocket 327 as cutting element 314 is exposed to external forces, such as cutting forces experienced during a drilling operation. For example, as shown in
As shown in
Additionally, as cutting element 314 moves in direction 366, an exterior portion of cutting element 314 may contact and/or engage protrusions 360, causing cutting element 314 to rotate (e.g., tip, tilt, and/or slide) in direction 364 (counter-clockwise relative to the view in
Protrusions 360 may be formed such that protrusions 360 allow for rotation of cutting element 314 generally in direction 364, and such that protrusions 360 interfere with rotation of cutting element 314 generally in a direction opposite to direction 364. As cutting element 314 rotates in direction 364, cutting element 314 may tend to roll or slide over protrusions 360. Cutting element 314 may continue to move generally in direction 366 until a force in direction 362 is decreased, until cutting element 314 comes in contact with a portion of cutting pocket 327 adjacent to vibrational member 356, and/or until cutting element 314 compresses and/or deflects vibrational member 356 to a maximum degree.
As shown in
According to certain embodiments, protrusions 360 may optionally be formed such that they promote rotation as cutting element moves generally in direction 366, and additionally, protrusions 360 may be formed such that they restrict or inhibit rotation as cutting element 14 moves generally in direction 368. In such an embodiment, cutting element 314 may experience a net rotation about central axis 342 in a direction opposite direction 364.
Another embodiment shown in
Rotation of the cutting element 414 is determined by a line contact 461 between the cutting pocking 427 and cutting element 414. Relatively little force can change a position of the line contact 461. Typically, cutting forces will no act through the line contact 461, which can result in an eccentricity “e” that represents a moment arm for a cutting force applied in direction 462. The cutting force applied in direction 462 acting at a distance “e” from the line contact 461 produces a torque that rotates the cutting element 414 in direction 464. Vibration from the cutting forces tends to reset the cutting element 414 within the cutting pocket 427 and make another incremental rotation possible.
The size and position of the first and second bearings 480, 482 helps minimize a torque that resists rotation of the cutting element 414. An axial preload from the forces FB1 and FB2 helps keep the cutting element 414 from binding in the cutting pocket 427 and helps maintain a quasi stable position of the cutting element 414 in the cutting pocket 427.
The preceding description has been provided to enable others skilled in the art to best utilize various aspects of the exemplary embodiments described herein. This exemplary description is not intended to be exhaustive or to be limited to any precise form disclosed. Many modifications and variations are possible without departing from the spirit and scope of the instant disclosure. It is desired that the embodiments described herein be considered in all respects illustrative and not restrictive and that reference be made to the appended claims and their equivalents for determining the scope of the instant disclosure.
Unless otherwise noted, the terms “a” or “an,” as used in the specification and claims, are to be construed as meaning “at least one of.” In addition, for ease of use, the words “including” and “having,” as used in the specification and claims, are interchangeable with and have the same meaning as the word “comprising.”
This application is a continuation of, and claims priority to U.S. patent application Ser. No. 13/933,883, filed Jul. 2, 2013, now U.S. Pat. No. 8,763,727, issued Jul. 1, 2014, which is a continuation of U.S. patent application Ser. No. 13/645,128, filed Oct. 4, 2012, now U.S. Pat. No. 8,499,859, issued Aug. 6, 2013, which is a continuation of U.S. patent application Ser. No. 13/330,471, filed Dec. 19, 2011, now U.S. Pat. No. 8,286,735, issued Oct. 16, 2012, which is a continuation of U.S. patent application Ser. No. 12/405,585, filed Mar. 17, 2009, now U.S. Pat. No. 8,079,431, issued Dec. 20, 2011, the disclosures of each of which are incorporated by reference herein in their entireties.
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| Vibration-Induced Rotation, Patrick Andreas Petri, Massachusetts Institute of Technology, May 2001. |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 13933883 | Jul 2013 | US |
| Child | 14286550 | US | |
| Parent | 13645128 | Oct 2012 | US |
| Child | 13933883 | US | |
| Parent | 13330471 | Dec 2011 | US |
| Child | 13645128 | US | |
| Parent | 12405585 | Mar 2009 | US |
| Child | 13330471 | US |
