Patent Publication Number: US-2020300293-A1

Title: Self-aligning bearing assembly for downhole tools

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This application claims priority from U.S. Provisional Patent Application Ser. No. 62/822,580, filed on Mar. 22, 2019, incorporated herein by reference in its entirety. 
    
    
     BACKGROUND OF THE DISCLOSURE 
     1. Field of the Disclosure 
     This disclosure relates generally to oilfield downhole tools and more particularly to bearing assemblies utilized for drilling wellbores. 
     2. Background of the Art 
     To obtain hydrocarbons such as oil and gas, boreholes or wellbores are drilled by rotating a drill bit attached to the bottom of a drilling assembly (also referred to herein as a “Bottom Hole Assembly” or (“BHA”). The drilling assembly is attached to the bottom of a tubing, which is usually either a jointed rigid pipe or a relatively flexible spoolable tubing commonly referred to in the art as “coiled tubing”. The string comprising the pipe or the tubing and the drilling assembly is usually referred to as the “drill string”. When jointed pipe is utilized as the tubing, the drill bit is rotated by rotating the jointed pipe from the earth&#39;s surface and/or by a drilling motor such as a mud motor contained in the drilling assembly. In the case of a coiled tubing, the drill bit is rotated by the drilling motor. During drilling, a drilling fluid (also referred to as the “mud”) is supplied under pressure into the tubing. The drilling fluid passes through the drilling assembly and then discharges at the drill bit bottom. The drilling fluid provides lubrication to the drill bit and carries to the earth&#39;s surface rock pieces disintegrated by the drill bit in drilling the wellbore. The drilling motor is rotated by the drilling fluid passing through the drilling assembly. A drive shaft connected to the motor and the drill bit rotates the drill bit. 
     A substantial amount of current drilling activity involves drilling deviated and horizontal wellbores to more fully exploit hydrocarbon reservoirs. Often referred to as directional drilling, this drilling technique can provide boreholes that have relatively complex well profiles. One known deflection tool, a so-called tilted drive sub, for directional drilling has a housing with an inner surface and an outer surface, the inner surface having an inner surface rotational axis and the outer surface having an outer surface rotational axis that is offset and/or at an angle from the inner surface rotational axis. As a result, the outer diameter of the tilted drive sub is remaining straight with comparison to the mud motor&#39;s outer diameter while the internal bearing components are radially offset and/or offset at some predetermined angle. This concept allows to bring the position of the tilt relatively close to the drill bit. The effective bit to bend distance, known as one of the parameters for the design of a directional drilling motor, can be minimized using this approach. The bit to bend distance is defined by the distance from the inclined bearing axis intersection point with the longitudinal tool axis of the drilling tool to the bit face for this concept. One drawback of the prior art tilted drive sub design is the inability to change the tilt or offset angle without parts exchange and also complete disassembly/assembly of the bearing unit. Other known tools for directional drilling are bent subs or adjustable kickoff (AKO) tools. These tools utilize a deflection device that creates a tilt in the outer housing of a BHA. The tilt angle of the AKO can be adjusted on a rig floor. 
     Because bent subs or adjustable kickoff tools are positioned uphole of a bearing section, these assemblies are known to exert high side loads and bending moments at the drill bit, the stabilizer, and the bend, caused by the large bit to bend distance, thus creating high bit offset from the rotational axis of the drilling tool. This is especially the case when they are used for drilling a straight section of the wellbore. In such instances, the housing, which includes the bend, is rotated. High side load in combination with misalignment of the bearing/drive shaft axes and the housing axis contributes to wear and damage of the radial and/or axial bearing. Bearing wear is known to be one major contributor to service limitation and repair costs. 
     Another known tool for directional drilling is a rotary steering system configured for directional drilling with continuous rotation from the earth&#39;s surface. Rotary steering systems may utilize a so-called non-rotating sleeve that is rotatably disposed around the drill string by means of a bearing system. Actuator elements are used to push the non-rotating sleeve outwards to create a deflection on the drill string. The deflections on the drill string create side loads and bending moments on the drill string and/or the non-rotating sleeve which may create a higher probability for damage or wear in the bearing system supporting the non-rotating sleeve. A similar embodiment comprises a non-rotating stabilizer that is rotatably disposed around the drill string utilizing a bearing system. 
     The present disclosure addresses these and other drawbacks of the prior art and generally addresses the need for more robust and durable devices for drilling such wellbores as well as wellbores for other applications such as geothermal wells. 
     SUMMARY OF THE DISCLOSURE 
     In aspects, the present disclosure provides an apparatus for use in a drill string configured for use in a subterranean formation. The apparatus may include a drive shaft coupled to a drill bit, the drill bit configured to continuously rotate and penetrate within the subterranean formation; a drill string housing that houses the drive shaft, the drive shaft continuously rotating within the drill string housing relative to the drill string housing; and a bearing assembly configured bear the drive shaft within the drill string housing, the bearing assembly comprising a first bearing surface having a first curvature. 
     In aspects, the present disclosure further includes a method for drilling a curved borehole in a subterranean formation. The method may include forming a drill string, the drill string comprising: a drive shaft coupled to a drill bit, the drill bit configured to continuously rotate and penetrate within the subterranean formation; a drill string housing that houses the drive shaft, the drive shaft continuously rotating within the drill string housing relative to the drill string housing; a bearing assembly configured bear the drive shaft within the drill string housing, the bearing assembly comprising a bearing surface having a curvature; and penetrating the subterranean formation with the drill string; and drilling the curved borehole with the drill string. 
     Examples of certain features of the disclosure have been summarized rather broadly in order that the detailed description thereof that follows may be better understood and in order that the contributions they represent to the art may be appreciated. There are, of course, additional features of the disclosure that will be described hereinafter and which will form the subject of the claims appended hereto. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a detailed understanding of the present disclosure, reference should be made to the following detailed description of the embodiments, taken in conjunction with the accompanying drawings, in which like elements have been given like numerals, wherein: 
         FIG. 1  illustrates a drilling system made in accordance with one embodiment of the present disclosure; 
         FIG. 2  schematically illustrates a self-aligning bearing assembly made in accordance with one embodiment of the present disclosure; 
         FIG. 3  schematically illustrates an “exploded” view of the  FIG. 2  embodiment; 
         FIG. 4  illustrates an insert having a spheroid bearing surface made in accordance with one embodiment of the present disclosure; 
         FIG. 5A  illustrates the  FIG. 2  embodiment in a section of a drill string providing an adjustable amount of tilt for a drive shaft in accordance with one embodiment of the present disclosure, the tilt is displayed in a straight position; 
         FIG. 5B  illustrates the  FIG. 2  embodiment in a section of a drill string providing an adjustable amount of tilt for a drive shaft in accordance with one embodiment of the present disclosure, the tilt is displayed in an inclined position; 
         FIG. 5C  illustrates the  FIG. 2  embodiment in a section of a drill string in accordance with one embodiment of the present disclosure 
         FIG. 5D  illustrates an adjustable eccentric member for providing an adjustable amount of tilt for a drive shaft in accordance with one embodiment of the present disclosure with the tilt adjusted in an inclined position; 
         FIG. 5E  illustrates an adjustable eccentric member for providing an adjustable amount of tilt for a drive shaft in accordance with one embodiment of the present disclosure with the tilt adjusted in a straight position; 
         FIG. 5F  illustrates a cross section of an adjustable eccentric member for providing an adjustable amount of tilt for a drive shaft in accordance with one embodiment of the present disclosure with the tilt adjusted in an intermediate position; 
         FIGS. 6A , B illustrate a drilling assembly that includes self-aligning bearing assemblies in accordance with embodiments of the present disclosure; 
         FIG. 7  illustrates a self-aligning bearing assembly in accordance with one embodiment of the present disclosure that uses spherical bearing surfaces; 
         FIGS. 8A-C  illustrate the operation of the  FIG. 7  embodiment when encountering no load, axial loading, and a combined axial and being loading, respectively; 
         FIG. 9  illustrates another view of the  FIG. 7  embodiment; 
         FIGS. 10A-C  illustrate in “exploded format” the  FIG. 7  embodiment; 
         FIG. 11  illustrates another self-aligning bearing assembly in accordance with one embodiment of the present disclosure that uses spheroid and cylindrical geometries to define bearing surfaces; 
         FIGS. 12A-D  illustrate the operation of the 11 embodiment when encountering no displacement, axial displacement, angular displacement and a combined axial and angular displacement, respectively; 
         FIG. 13  illustrate yet another self-aligning bearing assembly in accordance with one embodiment of the present disclosure that uses spheroid and cylindrical geometries to define bearing surfaces; and 
         FIGS. 14A-D  illustrate the operation of the 13 embodiment when encountering no displacement, axial displacement, angular displacement and a combined axial and angular displacement, respectively. 
     
    
    
     DETAILED DESCRIPTION OF THE DISCLOSURE 
     As will be appreciated from the discussion below, aspects of the present disclosure provide a steerable system for drilling wellbores. In general, the described steering methodology involves deflecting the angle of the drill bit axis relative to the longitudinal tool axis. 
     Referring now to  FIG. 1 , there is shown one illustrative embodiment of a drilling system  10  utilizing a steerable drilling assembly or bottomhole assembly (BHA)  12  for directionally drilling a wellbore  14 . While a land-based rig is shown, these concepts and the methods are equally applicable to offshore drilling systems. The system  10  may include a drill string  16  suspended from a rig  20 . The drill string  16 , which may be jointed tubulars or coiled tubing (not shown), may include power and/or data conductors (not shown) such as wires for providing bidirectional communication and power transmission. In one configuration, the BHA  12  includes a drill bit  30 , a sensor sub  32 , a communication and/or power module  34 , a formation evaluation sub  36 , and one or more rotary power devices  38  such as drilling motors (e.g. electrical motors or mud motors). The sensor sub  32  may include sensors and tools for measuring a direction of at least a part of the drill string  16  and/or BHA (e.g., BHA azimuth, inclination, toolface, and/or BHA coordinates, etc.). The sensors and tools may be positioned relatively close to the drill bit  30  for measuring near-bit direction or near-bit position. The sensors and tools may be configured for making measurements while the drill string  16  is rotationally stationary or while the drill string  16  is rotating to generate stationary or rotary directional surveys, respectively. The sensor sub  32  may include two (2) or three (3) axis accelerometers, magnetometers, gyroscopic devices and signal processing circuitry. The system may also include information processing devices such as a control unit  50  (aka surface controller) and/or one or more downhole controller  42 . The drill bit  30  may be rotated by rotating the drill string  16  from the surface and/or by using a downhole drilling motor, or other suitable rotary power device  38 . By downhole drilling motor, it is meant mud motors, turbines, electrically powered motors, etc. 
     Communication between the control unit  50  and the BHA  12  may use uplinks and/or downlinks generated by a mud-driven alternator, a mud pulser, a mud siren, or a mud valve as known in the art, and conveyed using the drilling fluid column. Alternatively or in addition, uplinks and/or downlinks may be conveyed using acoustic conductors, electric conductors (e.g., hard wires), electromagnetic transmitter/receiver and/or optical conductors (e.g., optical fibers). The signals used for communication may be drilling fluid pressure variations, drilling fluid flow variations, acoustic signals, electric/electromagnetic signals including radio-frequency signals, and/or optical signals. 
     The BHA  12  may also include a steering system configured to adjust or control a direction of at least a part of the BHA  12  to drill wellbore  14  into a desired direction. Examples of steering assemblies are tilted motors, kickoff motors, adjustable kickoff motors, tilted drive shafts, or rotary steerable systems. As will be discussed in greater detail below, the BHA  12  may include a self-aligning bearing assembly that reduces wear of bearings during directional drilling and other situations. 
     Referring to  FIG. 2 , there is sectionally illustrated a self-aligning bearing assembly  100  for directionally drilling a borehole in a subterranean formation. The term “self-aligning” in this context means that the bearing assembly is configured to adjust its direction in response to forces applied to the bearing assembly. In aspects, the forces applied to the bearing assembly may be caused only by rotating, drilling, bending, or putting axial weight on the bit. In aspects, the term “self-aligning” in this context means that the bearing assembly is configured to adjust its direction in response to forces applied to the bearing assembly in a passive way. The term “in a passive way” in this context means that the bearing assembly is configured to adjust its direction in response to forces applied to the bearing assembly without adding energy to the adjustment other than the forces that are caused only by rotating, drilling, bending, or putting axial weight on the bit. The bearing assembly  100  may be positioned in a section  112  of a drill string  16  ( FIG. 1 ). The section  112  may be subjected to intentional or unintentional misalignment occurring between a shaft or other torque transmitting member  116  and the section  112 . The torque transmitting member  116  may have a rotational axis  115  and the section  112  of the drill string  16  may have a rotational axis  222  which may be inclined with respect to each other. For example rotational axis  115  may be rotated with respect to rotational axis  224  about an axis that is perpendicular to rotational axis  115  or rotational axis  224 . In one embodiment, the bearing assembly  100  includes an inner bearing structure  120  and an outer bearing structure  122 . In one non-limiting embodiment, the outer bearing structure  122  can include mating sections  124 ,  126 . As will be described in greater detail below, the inner bearing structure  120  and the outer bearing structure  122  rotationally slide relative to one another about an axis that is perpendicular to the rotational axis  115  or rotational axis  224  to accommodate shaft misalignments while bearing both axial and radial loading. Advantageously, these misalignments are accommodated while maintaining contact over a large surface area between the contacting and dynamically moving bearing surfaces during continuous rotation about the rotational axis  115  of the torque transmitting member  116  or the rotational axis of section  112  of the drill string. This large contact surface helps to reduce specific surface loading by engaging over a distributed area as opposed to a point loading, which can be damaging. 
     In the embodiments of this disclosure, axial bearing and thrust bearing have the same broad meaning. Axial or thrust bearings prevent movement along a rotation axis while at the same time allow rotation about that rotation axis. Similarly, in the embodiments of this disclosure, the terms radial bearing and journal bearing have the same broad meaning. Radial or journal bearings prevent movement perpendicular to a rotation axis while at the same time allow rotation about the rotation axis. Consequently, the terms “axial” bearing and “thrust” bearing will be used interchangeably in that broad meaning and the terms “radial” and “journal” bearings will be used interchangeably in that broad meaning. For example, the terms “axial” or “thrust” bearings as used herein may comprise bearings with sliding surfaces that are not perpendicular to the rotation axis but may be tapered or tilted with respect to the rotation axis and may comprise sliding surfaces that are plane or curved such as spherical, toroidal, or elliptical surfaces. The terms “curved surface”, “surface with curvature”, or “surface having a curvature”, as used herein, refer to surfaces that are at least partially not plane, linear, or straight. Further, the terms “radial” or “journal” bearings as used herein may comprise bearings with sliding surfaces that are not cylindrical with respect to the rotation axis and may comprise sliding surfaces that are tapered, tilted, or curved with respect to the rotation axis. Moreover, the terms “axial”, “thrust”, “radial”, or “journal” bearings may also be understood to comprise more than one bearing or more than one pair of sliding surfaces. The terms “lower”, “downward”, “downhole”, etc. and “upper”, “upward”, “uphole”, etc. respectively describe axial directions along the wellbore  14  ( FIG. 1 ) towards or away from drill bit  30  ( FIG. 1 ). 
     Referring to  FIG. 3 , there is shown the bearing assembly  100  in an “exploded” format. In one non-limiting embodiment, the inner bearing structure  120  includes a mandrel  130 , which may be a rigid tubular member, and a bearing surface  132  that may be formed by a plurality of inserts  134 . Mandrel  130  is coupled to torque transmitting member  116  and locked with respect to rotation in at least one direction relative to torque transmitting member  116 . That is, rotation of mandrel  130  relative to torque transmitting member  116  is restricted in at least one direction. Locking with respect to rotation can be accomplished by screwing, gluing, welding, or clamping mandrel  130  to torque transmitting member  116  or by using one or more shoulders or keys, such as parallel keys to restrict the rotation. The bearing surface  132  is not parallel to the rotational axis of mandrel  130  and not perpendicular to the rotational axis of the mandrel  130  and, thus, allows to support axial loads as well as radial loads. In the configuration shown in  FIG. 3 , the bearing surface is at an angle with respect to the rotational axis of the mandrel  130  that is approximately between 40° and 50° to allow bearing of comparable loads from both, radial and axial directions, simultaneously at the same time. Depending on the angle of inclination of the bearing surface  132  with respect to the rotational axis of bearing assembly  100 , the bearing can be optimized for axial support, radial support or any combination thereof. For a combined axial and radial bearing surface, the angular offset is between 0° and 90°, for example between 10° and 80°, or even between 20° and 70° if substantial loads from both, radial loads and axial loads, are taken by the bearing surface  132  at the same time. The inserts  134  are circumferentially distributed on outer surfaces of opposing ends  136 ,  138  of the mandrel  130 . Each insert  134  presents an outer spheroid surface that is defined by either a sphere  139  or a sphere  141 . Both of the spheres  139 ,  141  share a center  142  inside of the bearing assembly  100 . The sphere  139  defines a bearing surface  135  and the sphere  141  defines a bearing surface  137 . Bearing surfaces  135  and  137  together are forming bearing surface  132 . In other words, bearing surface  135  and bearing surface  137  have a convex shape that is defined by spheres  139  and  141 . The bearing surface  135  of inserts  134  on the end  138  correspond to an outer spheroid surface defined by the sphere  139  and bearing surface  137  of the inserts  134  on the end  136  correspond to an outer spheroid surface defined by the sphere  141 . Alternatively, instead of utilizing inserts as sliding members, other, preferably hard or super hard surfaces might be utilized for the bearing function. To enhance performance and service life, bearing surfaces, such as opposing surfaces of spherical bearing surfaces with convex and respectively concave shape may include surface treatments and features, including but not limited to flame spray coatings, high velocity oxygen fuel (HVOF) spray coatings, laser weld coatings, ceramic inserts, tungsten carbide inserts (T2A), and diamond bearing elements to reduce abrasive wear. Such coatings or inserts may be characterized by the convex shape of bearing surfaces that are defined by spheres as explained above.  FIG. 3  exemplary illustrates inserts, such as diamond bearing elements  134 , also referred to as polycrystalline diamond compact (PDC) bearing elements (inserts) that may be distributed on bearing surfaces described herein to provide greater resistance to wear. Figures of this application are exemplary showing inserts. It shall be appreciated, that instead of inserts, other sliding members and surfaces could be used to fulfill the same function. 
     The outer bearing structure  122  may include a first section  124  and a second section  126 . The first section  124  includes a mandrel  160 , which may be a rigid tubular member, and a bearing surface  162  that may be formed by a plurality of inserts  164  circumferentially distributed on an inner surface  166 . Likewise, the second section  126  includes a mandrel  170 , which may be a rigid tubular member, and a bearing surface  172  that may be formed by a plurality of inserts  164  circumferentially distributed on an inner surface  174 . Mandrels  160 ,  170  are coupled to section  112  and locked with respect to rotation in at least one direction relative to section  112 . That is, rotation of mandrels  160 ,  170  relative to section  112  is restricted in at least one direction. Locking with respect to rotation can be accomplished by screwing, gluing, welding, or clamping mandrels  160 ,  170  to section  112  or by using one or more shoulders or keys, such as parallel keys to restrict the rotation. The first section  124  and the second section  126  may connect at a connector section  176 , which may be a threaded connection or other mechanical connection such as a glued or welded connection or by means of additional components such as screws or clamps. For assembly purposes, the inner diameters of mandrels  160  and  170  are equal or greater than the maximum inner diameter of mandrel  130 . 
     A bearing surface  162 , which is formed by the inserts  164  of first and second section sections  124 ,  126 , are defined by the spheres  139 ,  141 , respectively. All points defining the bearing surface  162  on the first section  124  have the same distance to the center point  142 . Likewise, all points defining the bearing surface  172  on the second section  126  have the same distance to the center point  142 . This means that the contact area of inserts  164  and  134  have a shape of a spherical cap. The shape of the spherical cap is machined directly into the bearing surfaces of inserts  164  and  134  by grinding or milling. Because the bearing surfaces  135 ,  162  have a complementary spheroid shape and the bearing surfaces  137 ,  172  have a complementary spheroid shape and because the spheroid shapes have a common center point  142 , the bearing surfaces  135  and  162  as well as  137  and  172  can slide in a ball and socket fashion. The spheres  139 ,  141  can have different diameters but share the same center point. While the sphere  139  has a smaller diameter than the sphere  141  in the illustrated embodiment, both can have the same diameters or sphere  141  can have a smaller diameter than sphere  139 . Still, in all cases the spheres share the same center point or substantially the same center point. “Substantially the same center point” in this context means that in case sphere  139  has a different center point than sphere  141 , the distance of these center points is small compared to the diameters of spheres  141  and  139 , e.g. the distance of these center points is smaller than 10% of the diameters of spheres  141  and  139 . The common center point  142  enables a sliding action between the bearing surfaces  135  and the bearing surfaces  162  and between bearing surfaces  137  and bearing surface  172  in a ball joint fashion inside the bearing assembly  100 . The point of bearing tilt is defined at the center point  142 . Due to the spherical curvature of inserts  164  and  134 , the contacting surfaces of inserts  164  and  134  are contacting over an area rather that at a point or a line. For instance, the contacting surfaces are contacting over an area that is higher than 10% of the surface area of the insert, such as 50% of the surface area of the insert or even 80% of the surface area of the insert. 
     Referring to  FIG. 4 , there is shown the insert  134  in contact with the insert  164 , which is shown in hidden lines. The contour of the bearing surfaces  135 ,  162  is in highly exaggerated form to better illustrate the curvature. The bearing surfaces  135 ,  162  conform to a surface of a sphere; i.e., all points defining each bearing surfaces  135 ,  162  have substantially the same distance to a common center point  142 . The common center point  142  is the pivoting point at the intersection of the rotational axis  115  and the rotational axis  224 , which is discussed in connection with  FIG. 5B . Thus, the bearing surfaces  135 ,  162  have curvatures in three dimensions. It should be noted that the bearing surface  135  may be considered discontinuous or segmented because it can be made up of the surfaces of a plurality of separate inserts  134 . This means that the surface areas of inserts  134  have a shape of a spherical cap. The shape of the spherical cap is machined directly into the bearing surfaces of inserts  134  by grinding or milling. It should also be noted that while a spheroid shape defines each bearing surface  135 ,  162 , the nature of the curvatures may be considered opposing in order to allow continuous contact between the two bearing surfaces  135 ,  162 . In one aspect, the bearing surface  135  may be considered convex and the bearing surface  162  may be considered concave, both in a three dimensional fashion. The distance between the bearing surfaces  135 ,  162  defines the bearing play. The nature of sliding bearings for use in downhole drilling and for use in abrasive loaded media such as drilling mud, demands some minimum bearing play. The bearing play may be in the range of up to one mm, e.g. between 0.03 mm and 0.8 mm, or even better defined in a range of 0.1 mm to 0.2 mm. When a force is applied, sliding surfaces come into contact and the gap closes towards the load applied direction. 
     It should be appreciated that the above-described features enable the bearing assembly to maintain alignment between the contacting bearing surfaces by using the center point  142  inside the bearing assembly  100  as a pivot point for the aligning movement. In this context, “maintaining alignment” means that the contacting surfaces are contacting over an area instead of at a point. For instance, the contacting surfaces are contacting over an area that is higher than 10% of the surface area of the insert, such as 50% of the surface area of the insert or even 80% of the surface area of the insert. 
     Additionally, it should be noted that a tangent  144  at the apex  146  of the bearing surface  135  is non-parallel with a rotational axis  115  ( FIG. 2 ) of the drill string section or housing. The tangent  144  may have any angular offset. The angular offset allows the bearing surface  135  of inserts  134 ,  164  to bear axial loadings  150  and radial loadings  152  at the same time. For an ideal radial bearing, the angular offset is 0° while for an ideal axial bearing the angular offset is 90°. For a combined axial and radial bearing surface, the angular offset is between 0° and 90°, for example between 10° and 80°, or even between 20° and 70° if substantial loads from both, radial loads and axial loads, are taken by the bearing surface  135  at the same time. 
     To enhance performance and service life, bearing surfaces, such as bearing surfaces  135 ,  162  may have surface treatments and features that include, but are not limited to, HVOF spray coatings, laser weld coatings, ceramic inserts, and tungsten carbide inserts (T2A) to reduce abrasive wear. Alternatively bearing surfaces can be formed from inserts (e.g. inserts  134  in  FIG. 3 ), preferably from hard or super-hard inserts such as diamond bearing elements, also referred to as polycrystalline diamond compact (PDC) bearing elements (inserts) that may be distributed along bearing surfaces described herein to provide greater resistance to wear. Again alternatively, those inserts may be made from ceramic such as polycrystalline cubic boron nitride (PCBN). 
     Referring to  FIGS. 5A , B, there is shown one non-limiting embodiment of a drilling assembly  300  (also known as bottomhole assembly  300 ) that incorporates the self-aligning bearing assembly  100 . As noted previously, the self-aligning bearing assembly  100  can bear radial and thrust loading with similar effectiveness and allows pitching and yawing degree of freedom (omni-directional tilt) of the rotating and non-rotating bearing elements. In  FIG. 5A , the drive shaft  218  is disposed within a drill string housing  220  that houses the drive shaft  218 . Drive shaft  218  continuously rotates inside the drill string housing  220  and relative to the drill string housing  220  and does not have an intentional or unintentional deflection relative to the drill string housing  220 . “Continuous rotation” in this context means rotation by at least one full circumference. Thus, the rotational axis  222  of the drill string housing  220  is aligned with the rotational axis  224  of the drive shaft  218  below bearing assembly  100 . In this assembly, mandrel  130  of bearing assembly  100  is coupled to drive shaft  218  and locked with respect to rotation in at least one direction relative to the drive shaft  218 . That is, rotation of mandrel  130  relative to drive shaft  218  is restricted in at least one direction. Locking with respect to rotation can be accomplished by screwing, gluing, welding, or clamping mandrel  130  to drive shaft  218  or by using one or more shoulders or keys, such as parallel keys to restrict the rotation. Mandrels  160 ,  170  are coupled to drill string using  220  and locked with respect to rotation in at least one direction relative to drill string housing  220 . That is, rotation of mandrels  160 ,  170  relative to drill string housing  220  is restricted in at least one direction. Locking with respect to rotation can be accomplished by screwing, gluing, welding, or clamping mandrels  160 ,  170  to drill string housing or by using one or more shoulders or keys, such as parallel keys to restrict the rotation. 
     Bearing assemblies according to the present disclosure may be used in a variety of configurations for downhole tools. One non-limiting configuration involves a downhole tool for directional drilling. In particular, the disclosed bearing assemblies may be used with steerable drilling systems that utilize a tilted drive shaft ( FIGS. 5A-F ). In  FIG. 5A , B, there is shown a drill string housing  220  of a bottomhole assembly  300  ( FIG. 1 ) where a drive shaft  218  is located inside the drill string housing  220 , and the bearing assembly  100 . Drive shaft  218  may be made out of several parts that are joined together, for example by thread  219  or other means, such as screws, clamps, or connections that are welded or glued. A mechanical connection above bearing assembly  100  may facilitate exchange of bearing assembly  100  if bearing assembly  100  was subject to excessive wear. Drive shaft  218  is connected to drill bit  30  and configured to be continuously rotated, e.g. by a downhole drilling motor (not shown) that is further up in the drill string or a so-called top drive at the earth&#39;s surface. In  FIG. 5A , the rotational axis  222  of the drill string housing  220  is shown which is aligned with rotational axis  224  of the drive shaft  218 .  FIG. 5B  shows the same section of a bottomhole assembly  300  that is adjusted in a way that the rotational axis  224  of the drive shaft  218  is tilted with respect the rotational axis  222  of the drill string housing  220 . Tilting the drive shaft  218  can be used for a device usable for directional drilling. When the drill bit is rotated by the motor only, the tilt effects a change in drilling direction by influencing the way the drill bit  30  and bottom hole assembly  12  lays in the previously drilled hole. The end effect is that the face  35  of the drill bit  30  points or tilts in a selected orientation for the selected new direction of the hole.  FIG. 5A  shows a section of a bottomhole assembly  300  with the tilt adjusted to a straight position. Such bottomhole assemblies can be used for drilling straight sections of a wellbore or as drive systems for other steering tools (for example, those referred to as Rotary Steerable Systems (RSS) for those skilled in the art) mounted below (between the device shown in  FIGS. 5A-C  and the drill bit  30 ). As explained in the following sections, the device according to  FIG. 5A  and B can be continuously adjusted from a straight to a defined maximum tilt position. The adjustment is being done on surface before the device is lowered in the hole. 
     In embodiments, one or more components of the bottomhole assembly  300  may include one or more eccentricity members having an eccentricity or asymmetric geometry that causes a deflection of the drive shaft  218  and the drill bit  30  ( FIG. 1 ) with respect to the rotational axis  222  of the drill string housing  220 . 
     Referring now to  FIG. 5C , the deflection may cause a tilt that is relatively fixed, e.g., by a tilt that cannot be adjusted without disassembling the bottomhole assembly  300  at the earth&#39;s surface, for instance, by using an eccentricity member  290  constructed to have a wall thickness asymmetric with respect to the rotational axis  222  of the drill string housing  220  that results in a constant angular offset of the rotational axis  224  of the drive shaft  218  with respect to rotational axis  222  of the drill string housing  220 . In order to adjust the tilt to a different angle, such an assembly needs to be disassembled to exchange the eccentric member  290  with one that has a different eccentricity and thus causes a different tilt. A higher tilt would be beneficial to drill narrower curvatures, while a smaller tilt would be beneficial to drill straighter sections or do corrections only. Advantageously, the self-aligning bearing assembly  100  reduces potential damage to bearing surfaces from misalignment. Advantageously, the self-aligning bearing assembly  100  orients according to the tilt as described previously. Also, identical components can be used for bearing assembly  100  regardless of the adjusted tilt. 
     Referring further to  FIG. 5A-F , in embodiments, the bottomhole assembly  300  may be configured to have an adjustable tilt; e.g., a tilt axis adjustable between a nominal or no tilt and about 1°, or a higher value such as 5°.  FIGS. 5A , B and D-F illustrate an adjustable alignment assembly  402  that uses two or more eccentric members to vary the tilt angle. The two eccentric members may move relative to one another such that their eccentricities either offset one another to minimize a tilt angle or complement one another to maximize tilt angle. Of course, the eccentricities may also be set to provide an intermediate tilt angle value. 
     In embodiments, an upper bearing  400  may be configured to have an adjustable tilt; e.g., a tilt axis adjustable between no tilt and a tilt of about 1°, or a higher value such as 5°.  FIGS. 5A , B and D-F illustrate an upper bearing  400  that uses two or more eccentricity members to vary the tilt angle. The two components may move relative to one another such that the eccentricities either offset one another to minimize a tilt angle or complement one another to maximize tilt angle. Of course, the eccentricities may also be set to provide an intermediate tilt angle value. 
     Referring to  FIGS. 5A , B and D-F, in one non-limiting embodiment, the upper bearing  400  generates a first eccentricity using a bearing housing  410  having an eccentric inner surface, creating the first eccentricity member. The bearing housing  410  includes an inner contour  420  that is eccentric and/or at an angle with respect to the rotational axis  222  of the drill string housing  220 . For example, as shown in  FIG. 5B , the bearing housing  410  includes an inner contour  420  that is eccentric and/or at an angle with respect to an outer contour  422  of the housing wall such that a first enlarged portion  423  is formed, hence bearing housing  410  has one side with an enlarged wall thickness and one opposite side with a narrower wall thickness. The eccentric and/or asymmetric inner contour  420  of bearing housing  410  is complementary to the female radial bearing  424 . Referring to  FIGS. 5A , B and E-F, another eccentric and/or asymmetric eccentricity member is formed using a female radial bearing  424  with an outer contour  416  that is eccentric to the inner radial bearing surface  418  and configured to bear drive shaft  218 . Thus, the female radial bearing  424  has a first side with an enlarged wall portion  425  and an opposing side with a narrower wall thickness  426 . The female radial bearing  424  can be rotated and positioned inside the contour  420  and hence relative to the bearing housing  410  about its center line by means of a keyed connection  431  ( FIG. 5E , F) between an upper housing  103  and the female radial bearing  424 . 
     Referring further to  FIG. 5A  and B, in one non-limiting configuration, the upper housing  103  and the bearing housing  410  are connected through a threaded portion  105 . To adjust the tilt, the upper housing  103  is rotated about its rotational axis  222  of the drill string housing  220  with respect to the bearing housing  410 . Referring to  FIG. 5A  and B, one or more rings  430 , or ring segments (for example, half shell rings) may be installed between upper housing  103  and bearing housing  410 . Use of ring  430  with various widths may result in various distances between upper housing  103  and bearing housing  410  and consequently may lead to various eccentricity orientations when screwed together. Use of ring segments, such as half-shell rings allows to exchange rings, for example exchange rings with various thickness, without completely unscrewing threaded portion  105 . 
     It is apparent, that with the pitch of the thread and by use of the one or more the one or more rings  430  clamped between the shoulders of upper housing  103  and bearing housing  410  the housings will have various azimuthal offsets with respect to each other when screwed together. For example, with a pitch of threaded portion  105  of 4 mm per revolution and with a width of the one or more rings  430  reduced by 1 mm, upper housing  103  and bearing housing  410  are rotated about 90° with respect to each other, thus reducing the tilt by rotation of the enlarged portions  423 ,  425 . Referring to  FIG. 5D , the maximum tilt created by aligning both enlarged portions  423 ,  425  towards the same side is exemplary set to 1° and the thread pitch of threaded portion  105  is 4 mm per revolution. A respective rotation of 180°, achieved by a reduction in thicknesses of the one or more ring  430  of 2 mm, would yield to a 0° tilt (straight assembly) as shown in  FIG. 5A  and in  FIG. 5E . 
       FIG. 5B  also shows the distance “bit to bend” from the point of intersection  447 , where the two rotational axis  224  and  222  intersect, which is at the same or substantially the same location as common center point  142  defined by the spherical surface of the self-alignment bearing assembly  100  to the bit face  35  of the drill bit  30 . 
     Thus, it should be appreciated that manipulation of the angle and/or the thickness of the one or more rings  430  and thus of the tilt angle can create and/or define a tilt in the bearing assembly  100 . The bearing surfaces  162  and  132  allow for such adjustment without creating point or line contact in the actual sliding surfaces as explained earlier. 
     Referring to  FIG. 6A , B, there is shown another embodiment of a drilling system  500  according to the present disclosure. The drilling system  500  may include a first self-alignment bearing  100  and a second alignment bearing  600 . The drilling system  500  may also include a bottom hole assembly (BHA) that includes a drill bit  30  connected to and driven by a drive shaft  512  and a sleeve  504  that is rotatably coupled to drive shaft  512  (aka non-rotating sleeve). The sleeve  504  houses the drive shaft  512  (sleeve  504  is a drill string housing  504  for drive shaft  512  similar to drill string housing  220  for drive shaft  218 ) and the drive shaft  512  rotates within and relative to the sleeve  504 . Sleeve  504  supports a bias module  510 , an electronics and sensor module  508 , and a communication module  506 . Bias module  510  comprises one or more eccentricity members, such as actuators, that are configured to create a bias of sleeve  504 , For example, bias module  510  may comprise actuators that can be engaged with the borehole wall to create radial forces on sleeve  504 . This, in turn, will create radial forces on drive shaft  512  that may create deflection and/or misalignment of drive shaft  512  with respect to sleeve  504  via bearing  100  or bearing  600 . Bias module  510  may be in communication with communication module  506  to receive commands based on which actuation will be controlled. It should be understood that the drilling system  500  is not limited to any particular configuration for a BHA. 
     The non-rotating sleeve  504  is supported by the first self-alignment bearing  100  and the second alignment bearing  600 . The non-rotating sleeve  504  is considered “non-rotating” as it may be substantially stationary relative to a borehole wall. Irrespective of the term “non-rotating sleeve”, there may be some slight rotation of the sleeve  504  due to inherent drilling dynamics and frictional contacts. The self-alignment bearing  100  supports axial and radial loadings as described previously. Therefore, the self-alignment bearing  100  axially positions the non-rotating sleeve  504  relative to drive shaft  512 . 
     To prevent an axially over-confined situation, the second alignment bearing  600  is configured to support radial loadings, which may arise during drilling and steering, be self-aligning to account, for instance, for static and dynamic shaft deflection and for manufacturing tolerances, and axially free to some extent to accommodate axial misalignment within the bearing assembly. In both self-alignment bearings, some of the bearing surfaces are not parallel to the rotational axis  224 ,  222  of drive shaft  512  and/or sleeve  504  and not perpendicular to the rotational axis  224 ,  222  of drive shaft  512  and/or sleeve  504  and, thus, simultaneously allow to support axial loads as well as radial loads. In the configuration shown in  FIGS. 6A , B, the bearing surface of self-alignment bearing  100  is at an angle with respect to the rotational axis  224 ,  222  of drive shaft  512  and sleeve  504  that is approximately between 40° and 50° to allow bearing of comparable loads from both, radial and axial directions, at the same time. In contrast, bearing surface of self-alignment bearing  600  is at an angle with respect to the rotational axis  224 ,  222  of drive shaft  512  and sleeve  504  that is much lower—approximately between 5° and 30° to allow bearing of loads mainly from axial directions, at the same time. Depending on the angle of inclination of the bearing surfaces with respect to the rotational axis of  224 ,  222  of drive shaft  512  and sleeve  504 , the bearings can be optimized for axial support, radial support or any combination thereof. Irrespective of the actual angle of inclination, both bearings  100  and  600  have bearing surfaces that are inclined towards the axis of rotation in an upward direction and bearing surfaces that are inclined towards the axis of rotation in a downward direction to restrict axial movement in axial upward and downward direction as well as radial movement at the same time. However, this is not meant to be a restriction. Bearing where the bearing surface are inclined towards the rotational axis  224 ,  222  of drive shaft  512  and sleeve  504  only in upward direction or only in downward direction may also be used. Also, the angle of inclination does not need to be the same in a bearing assembly. Bearing assemblies can be used having bearing surfaces with different angles of inclination. 
     Referring to  FIG. 7 , there is shown the alignment bearing  600  in greater detail. In one embodiment, the alignment bearing  600  includes an inner ring  602 , an outer ring  604 , and an intermediate ring  606 . Outer ring  604  is coupled to drill string housing  220 / 504  and locked with respect to rotation in at least one direction relative to drill string housing  220 / 504 . That is, rotation of outer ring  604  relative to drill string housing  220 / 504  is restricted in at least one direction. Locking with respect to rotation can be accomplished by screwing, gluing, welding, or clamping outer ring  604  to drill string housing  220 / 504  or by using one or more shoulders or keys, such as parallel keys to restrict the rotation. Likewise, inner ring  602  is coupled to drive shaft  218 / 512  and locked with respect to rotation in at least one direction relative to drive shaft  218 / 512 . That is, rotation of inner ring  602  relative to drive shaft  218 / 512  is restricted in at least one direction. Locking with respect to rotation can be accomplished by screwing, gluing, welding, or clamping inner ring  602  to drive shaft  218 / 512  or by using one or more shoulders or keys, such as parallel keys to restrict the rotation. 
     The rings  602 ,  604 ,  606  are telescopically arranged and can, to some extent, slide axially, radially and angularly about an axis perpendicular to the rotational axis  222  of the drill string housing  220 / 504  or the rotational axis  224  of the drive shaft  218 / 512  relative to one another while still allowing continuous rotation (e.g. rotation about one or more circumferences) about the rotational axis  222  of the drill string housing  220 / 504  or the rotational axis  224  of the drive shaft  218 / 512  relative to each other. The mating surfaces of the rings  602 ,  604 , and  606  are made using bearing surfaces formed by inserts. As explained above, also with the alignment bearing  600 , to enhance performance and service life, bearing surfaces may have surface treatments and features that include, but are not limited to, HVOF spray coatings, laser weld coatings, ceramic inserts, and tungsten carbide inserts (T2A) to reduce abrasive wear. Alternatively bearing surfaces can be formed from inserts, preferably from hard or super-hard inserts such as diamond bearing elements ( 134 ), also referred to as polycrystalline diamond compact (PDC) bearing elements (inserts) that may be distributed on bearing surfaces described herein to provide greater resistance to wear. Again alternatively inserts may be made from ceramic such as polycrystalline cubic boron nitride (PCBN), and others. 
     The inner ring  602  includes inserts  610  circumferentially distributed on an outer surface  612  and the outer ring  604  has inserts  614  circumferentially distributed on an inner surface  616 . The intermediate ring  606  includes inserts  620  circumferentially on an outer surface  622  and inserts  624  circumferentially distributed on an inner surface  626 . The inserts  620  and  614  are arranged to slidingly engage one another and the inserts  624  and  610  are arranged to slidingly engage one another. While two rows of inserts are shown, other embodiments may include greater or fewer rows of inserts, or even closed sliding surfaces without inserts. 
     In one embodiment, the inserts  620 ,  614  and inserts  624 ,  610  share complementary curvatures. In one embodiment, the curvatures substantially conform to a surface of one or more spheres  613   a,  c or toroids  613   b,  d, i.e., are spherically or toroidically shaped. This means that the surface area of inserts  620 ,  614  and inserts  624 ,  610  have a shape of a spherical cap. The shape of the spherical cap is machined directly into the bearing surfaces of inserts  620 ,  614  and inserts  624 ,  610  by grinding or milling. The radii of the spheres/toroids  613   a - 613   d  are selected to support radial loads while having sufficient curvature to allow pivoting about an axis perpendicular to the rotational axis  222  of the drill string housing  220 / 504  or the rotational axis  115 / 224  of the drive shaft  218 / 512 . Preferably the intermediate ring  606  has a spherical/toroid-like radius slightly smaller than the respective inner and outer spheres/toroids. The outer set of inserts  620 ,  614  may have a curvature  630  such that a radius defining the surfaces of the inserts  620 ,  614  projects toward a center of spheres  613   a,c  defining the curvature. The center of the spheres  613   a,c  may be located on the rotational axis  222  of the drill string housing  220 / 504  or the rotational axis  115 / 224  of the drive shaft  218 / 512  and may be located close to or at the center of alignment bearing  600 . The inner set of inserts  624 ,  610  may have a curvature  632  such that a radius defining the surfaces of the inserts  624 ,  610  projects away from the rotational axis  222  of the drill string housing  220 / 504  or the rotational axis  115 / 224  of the drive shaft  218 / 512  and the alignment bearing  600 . The pairing of the spheroid/toroid surfaces  613   a - 613   d  of the inserts  620 ,  614  and  624 ,  610  locks the intermediate ring  606  within the inner ring  602  and the outer ring  604 . The curvature of the inserts  620 ,  624  may be considered convex and curvatures of the inserts  614 ,  610  may be considered concave. Thus, in one aspect, inserts  620 ,  624  may be considered to have bearing surfaces with curvatures that are opposing to those of inserts  614 ,  610 . Although not shown, it should be noted that the spheres  613   a  and  613   c  may have different radii. For example, radius of sphere  613   a  may be larger or smaller than radius of sphere  613   c.  Likewise, the radii of toroids  613   d  and  613   b  may be different. For example, radius of toroid  613   d  may be larger or smaller than radius of sphere  613   b.  Also, it should be noted that opposing inserts such as inserts  610  and  624  may have different sizes. For example, inserts  610  may be larger or smaller than insert  624 . In particular, opposing inserts may have different surface areas which may be advantageous depending on the configuration. Further, it should be noted that the curvature are in three dimensions because the curvatures  630 ,  632  are spherical in shape. Thus, the term “complementary curvatures” refers to curvatures that allow surfaces defined by such curvatures to physically engage and slide against one another over an area, as opposed to a point. In aspects, the area is substantially a majority of the bearing surface of the inserts  614 ,  610  and  624 ,  610 . Thus, in the illustrated embodiment, the insert  610  has a surface with a curvature that is complementary to curvature defining the surface of the insert  624 . In this illustrated embodiment, the complementary configuration is obtained by pairing a convex surface with a concave surface. It should be noted that the inner ring  602 , the intermediate ring  606  and/or the outer ring  604  may comprise two single rings for assembly purposes (only shown for outer ring  604  and inner ring  602  in  FIG. 7 . The two single rings are hold together during operation by retaining elements such as screws and clamps. 
       FIGS. 8A-C  illustrate the operation of the alignment bearing  600 . In  FIG. 8A , the alignment bearing  600  is shown in a neutral alignment wherein the intermediate ring with inserts  620 ,  624 , collectively  634 , of the alignment bearing  600  are aligned. By aligned, it is meant that the inserts  634  are centered relative to the inner and outer rings  602 ,  604  in axial direction. Further, there is no angular misalignment between the rotational axis  640  of the outer ring  604  and the rotational axis  642  of the inner ring  602 . In  FIG. 8B , the alignment bearing  600  is shown in an axial misalignment. The axial misalignment is caused by the axial displacement of the inner ring  602  relative to the outer ring  604 . This axial misalignment is accommodated by the paired spheroid surfaces defined by the radii  613   a,c  and  613   b,d  ( FIG. 7 ). In  FIG. 8C , the alignment bearing  600  is shown with axial displacement and angular misalignment. The axial displacement is between the inner ring  602  relative the outer ring  604 . Further, an angular misalignment exists between the rotational axis  640  of the outer ring  604  and the rotational axis  642  of the inner ring  602 . The axial and angular misalignment are accommodated by the paired spheroid surfaces defined by the radii  613   a,c  and  613   b,d  ( FIG. 7 ). Despite the misalignments, the alignment bearing assembly  600  maintaining alignment between the contacting bearing surfaces; i.e., the surfaces contact one another over an area instead of at a point. 
     The nature of sliding bearings as disclosed herein, and in general with traditionally used sliding bearings for drilling applications, demand some minimum radial bearing play. As a consequence of the large curvature radiuses  630 ,  632 , minimum radial play between the inner ring and intermediate ring sliding surfaces (inserts  624 ,  610 ) and between the outer ring and intermediate ring sliding surfaces (inserts  620 ,  614 ), permits comparably large axial displacement as displayed in  FIG. 8B  without mechanically over-constraining the bearing. The small radial play on the other hand also accounts for the possibility for the intermediate ring to pivot according to the angular misalignment and the present radial load scenario as displayed in  FIG. 8C . The radial play may be in the range of up to one mm, e.g. between 0.03 mm and 0.8 mm, or even better defined in a range of 0.1 mm to 0.2 mm. 
     To facilitate assembly of the alignment bearing  600 , one non-limiting arrangement for construction of the alignment bearing  600  uses mating halves of the inner and outer rings  602 ,  604  as discussed below. 
     Referring to  FIGS. 9 and 10A -C, there is shown one non-limiting embodiment of the alignment bearing  600  in an “exploded” format. Referring to  FIGS. 9 and 10C , the inner ring  602  includes a mandrel having mating halves  650 ,  652 . Each half  650 ,  652  may be a rigid tubular member that together present an outer bearing surface formed by the surfaces of the inserts  610 . Referring to  FIGS. 9 and 10A , the outer ring  604  includes a mandrel having mating halves  660 ,  662 . Each half  660 ,  662  may be a rigid tubular member that together present an inner bearing surface  616  formed by the surface of the inserts  614 . 
     Referring to  FIGS. 9 and 10B , the intermediate ring  606  includes a mandrel  670  that presents an inner surface  672  and an outer surface  674 . The intermediate ring  606  includes the inserts  620  circumferentially on the outer surface  674  and the inserts  624  circumferentially distributed on the inner surface  672 . 
     During assembly, the paired inner ring mandrels  650 ,  652  may be inserted from opposing ends into the intermediate ring  606 . Thereafter, the paired outer ring mandrels  660 ,  662  may be slid around the intermediate ring  606  from opposing ends and fastened to one another, e.g. by screwing or axially clamping in a housing. 
     Referring to  FIG. 11 , there is shown another self-aligning bearing  700  according to the present disclosure. In one embodiment, the self-aligning bearing  700  includes an inner ring  702 , an outer ring  704 , and an intermediate ring  706 . The rings  702 ,  704 ,  706  are telescopically arranged and can slide relative to one another about an axis perpendicular to the rotational axis  222  of the drill string housing  220 / 504  or the rotational axis  115 / 224  of the drive shaft  218 / 512  when continuously rotating (e.g. rotation about one or more circumferences) about the rotational axis  222  of the drill string housing  220 / 504  or the rotational axis  115 / 224  of the drive shaft  218 / 512 . The mating surfaces of the rings  702 ,  704 , and  706  are bearing surfaces formed by inserts. The inner ring  702  includes inserts  710  circumferentially distributed on an outer surface  712  of inner ring  702  and the outer ring  704  has inserts  714  circumferentially distributed on an inner surface  716  of outer ring  704 . The intermediate ring  706  includes inserts  720  circumferentially on an outer surface  722  and inserts  724  circumferentially distributed on an inner surface  726 . The inserts  720  and  714  are arranged to slidingly engage one another and the inserts  724  and  710  are arranged to slidingly engage one another. While two rows of inserts are shown, other embodiments may include greater or fewer rows of inserts. 
     In one embodiment, the outer set of inserts  720 ,  714  share complementary curvatures to allow tilting for pitching and/or yawing movements of the intermediate ring with respect to the outer ring. Like explained above, sliding sphere  730  accounts for angular tilt according to axis misalignment and current loading situation. The radius of sphere  730  is selected to support radial loads while having sufficient curvature to allow tilting or pivoting for pitching and/or yawing movements of the inner ring  702  with respect to outer ring  704  and therefore to allow tilting or pivoting for pitching and/or yawing movements of the drive shaft  218 / 512  with respect to drill string housing  220 / 504 . The inserts  720 ,  714  may have a curvature  730  such that a radius defining the surfaces of the inserts  720 ,  714  projects towards the rotational axis  115 / 224 ,  222  of the drill string housing  220 / 504  or the drive shaft  218 / 512 . The spheroid surfaces of the inserts  720 ,  714  retains or captures the intermediate ring  706  in between the inner ring  702  and the outer ring  704 , still allowing the required tilting for the pitching and yawing movement between them. The curvature of the inserts  720  may be considered convex and curvatures of the inserts  714  may be considered concave. Further, it should be noted that the curvature is in three dimensions because the curvature  730  is spherical in shape. Thus, the term “complementary curvatures” refers to curvatures that allow surfaces defined by such curvatures to physically engage and slide against one another over an area, as opposed to slide against a point. In aspects, the area is substantially a majority of the bearing surface of the inserts  720 ,  714 . Thus, in the illustrated embodiment, the insert  720  has a surface with a curvature that is complementary to curvature defining the surface of the insert  714 . 
     In this illustrated embodiment, the complementary configuration is obtained by pairing a convex surface with a concave surface. In another embodiment not illustrated, the curvature of the inserts  720  may be concave and curvatures of the inserts  714  may be considered convex. It should be noted that where the convex surfaces are formed on the intermediate ring  706 , the intermediate ring  706  and/or the outer ring  704  comprise two single rings for assembly purposes. As a result, the two single rings would require retaining elements such as screws and clamps to hold the two single rings together during operation. 
     In contrast to the inserts  720 ,  724 , the inner set of inserts  710 ,  724  do not have a spheroid curvature. Instead, the inserts  710 ,  724  have surfaces  736 ,  738  that conform to a cylindrical surface  732  and are shaped cylindrically. In an un-tilted condition, the cylindrical surface  732  may have a rotational axis  741  that is concentric, or at least generally parallel, with the rotational axis  740  of the outer ring  704 . Thus,  FIG. 11  illustrates one non-limiting embodiment wherein an inner set of inserts has a geometric shape defining a surface that is different from a geometric shape defining a surface of an outer set of inserts. 
       FIGS. 12A-D  illustrate the operation of the bearing  700 . In  FIG. 12A , the bearing  700  is shown in a neutral alignment wherein the inserts, collectively  734 , of the bearing  700  are aligned. By aligned, it is meant that the intermediate ring  706  is centered relative to the inner and outer rings  702 ,  704  in axial direction. Further, there is no angular misalignment between the rotational axis  740  of the outer ring  704  and the rotational axis  742  of the inner ring  702 . In  FIG. 12B , the bearing  700  is shown in an axial misalignment. The axial misalignment is caused by the axial displacement of the inner ring  702  relative to the outer ring  704  and respectively to the inner surface of the intermediate ring  706 . This axial misalignment is accommodated by the cylindrical surfaces of the inserts  710 ,  724  that are parallel with the cylindrical surface  732  ( FIG. 11 ). In  FIG. 12C , the bearing  700  is shown with angular misalignment between the inner ring  702  relative the outer ring  704 . The angular misalignment is accommodated by the spheroid surface defined by the radii  730  ( FIG. 11 ) and the inserts  720 ,  714  respectively. In  FIG. 12D , the bearing  700  is shown with axial displacement and angular misalignment. The axial displacement is shown between the inner ring  702  relative the outer ring  704  and the intermediate ring  706 . Further, an angular misalignment exists between the rotational axis  740  of the outer ring  704  and the rotational axis  742  of the inner ring  702 . The axial and angular misalignment are accommodated by the spheroid surface defined by the radii  730  ( FIG. 11 ) and cylindrical surfaces parallel to the cylindrical surface  732  ( FIG. 11 ). Despite the misalignments, the bearing assembly  700  maintaining alignment between the contacting bearing surfaces; i.e., the surfaces contact one another over an area instead of at a line or a point while a drive shaft  218 / 512  is rotating relative to the drilling housing  220 / 504 . 
     Referring to  FIG. 13 , there is shown another self-aligning bearing  800  according to the present disclosure. In one embodiment, the alignment bearing  800  includes an inner ring  802 , an outer ring  804 , and an intermediate ring  806 . The rings  802 ,  804 ,  806  are telescopically arranged and can slide relative to one another when rotated. The mating surfaces of the rings  802 ,  804 , and  806  are bearing surfaces formed by inserts. The inner ring  802  includes inserts  810  circumferentially distributed on an outer surface  812  and the outer ring  804  has inserts  814  circumferentially distributed on an inner surface  816 . The intermediate ring  806  includes inserts  820  circumferentially on an outer surface  822  and inserts  824  circumferentially distributed on an inner surface  826 . The inserts  820  and  814  are arranged to slidingly engage one another and the inserts  824  and  810  are arranged to slidingly engage one another. While two rows of inserts are shown, other embodiments may include greater or fewer rows of inserts. 
     In one embodiment, the inner set of inserts  810 ,  824  share complementary curvatures. In one embodiment, the curvatures conform to a surface of a sphere, i.e., are spherically shaped. The radius of the sphere is selected to support radial loads for rotation of the drive shaft  218 / 512  within the drill string housing  220 / 504  about the rotational axis  115 / 224  of the drive shaft  218 / 512  while having sufficient curvature to allow pivoting (pitching and yawing) about an axis perpendicular to the rotational axis  222  of the drill string housing  220 / 504  and/or the rotational axis  115 / 224  of the drive shaft  218 / 512 . The inserts  810 ,  824  may have a curvature  830  such that a radius defining the surfaces of the inserts  810 ,  824  projects away from the rotational axis  222  of the drill string housing  220 / 504  and/or the rotational axis  115 / 224  of the drive shaft  218 / 512 . The curvature of the inserts  810  may be considered concave and curvatures of the inserts  824  may be considered convex. Further, it should be noted that the curvature is in three dimensions because the curvature  830  is spherical in shape. Thus, the term “complementary curvatures” refers to curvatures that allow surfaces defined by such curvatures to physically engage and slide against one another over an area, as opposed to a point. In aspects, the area is substantially a majority of the bearing surface of the inserts  810 ,  824 . Thus, in the illustrated embodiment, the insert  810  has a surface with a curvature that is complementary to curvature defining the surface of the insert  824 . 
     In this illustrated embodiment, the complementary configuration is obtained by pairing a convex surface with a concave surface. In an embodiment not illustrated, the curvature of the inserts  810  may be considered convex and curvatures of the inserts  824  may be considered concave. It should be noted that where the convex surfaces are formed on the intermediate ring  806 , the inner ring  802  would be split into two single rings for assembly purposes. As a result, two single rings would require retaining elements, such as screws or clamps to hold the two single rings together during operation. 
     In contrast to the inserts  810 ,  824 , the outer set of inserts  814 ,  820  do not have a curvature. Instead, the inserts  814 ,  820  have surfaces  836 ,  838  that conform to and are parallel with the surfaces of a cylindrical surface  832 . The cylindrical surface  832  may have a rotational axis  841  that is concentric, or at least generally parallel, with the rotational axis  840  of the outer ring  804 . Thus,  FIG. 13  illustrates another non-limiting embodiment wherein an inner set of inserts has a geometric shape defining a surface that is different from a geometric shape defining a surface of an outer set of inserts. 
       FIGS. 14A-D  illustrate the operation of the bearing  800 . In  FIG. 14A , the bearing  800  is shown in a neutral alignment wherein the inserts, collectively  834 , of the bearing  800  are aligned. By aligned, it is meant that the inserts  834  are centered relative to the inner and outer rings  802 ,  804  in axial direction. Further, there is no angular misalignment between the rotational axis  840  of the outer ring  804  and the rotational axis  842  of the inner ring  802 . In  FIG. 14B , the bearing  800  is shown in an axial misalignment. The axial misalignment is cause by the axial displacement of the inner ring  802  and the intermediate ring  806  relative to the outer ring  804 . This axial misalignment is accommodated by the cylindrical surfaces of the inserts  814 ,  820  ( FIG. 13 ) that are parallel with the cylindrical surface  832  ( FIG. 13 ). In  FIG. 14C , the bearing  800  is shown with angular misalignment between the inner ring  802  relative the outer ring  804 . The angular misalignment is between the rotational axis  840  of the outer ring  804  and the rotational axis  842  of the inner ring  802 . The angular misalignment is accommodated by the spheroid surface defined by the radii  830  ( FIG. 13 ). In  FIG. 14D , the bearing  800  is shown with axial displacement and angular misalignment. The axial displacement is between the inner ring  802  relative the outer ring  804 . Further, an angular misalignment exists between the rotational axis  840  of the outer ring  804  and the rotational axis  842  of the inner ring  802 . The axial and angular misalignment are accommodated by the spheroid surface defined by the radii  830  ( FIG. 13 ) and cylindrical surfaces parallel to the cylindrical surface  832  ( FIG. 13 ). Despite the misalignments, the bearing assembly  800  maintaining alignment between the contacting bearing surfaces; i.e., the surfaces contact one another over an area instead of at a point. 
     While the foregoing disclosure is directed to the one mode embodiments of the disclosure, various modifications will be apparent to those skilled in the art. It is intended that all variations within the scope of the appended claims be embraced by the foregoing disclosure.