Patent Publication Number: US-9410573-B1

Title: Bearing assemblies

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 14/489,027 filed on 17 Sep. 2014, the disclosure of which is incorporated herein, in its entirety, by this reference. 
    
    
     BACKGROUND 
     Bearing apparatuses exhibit a number of configurations including ball bearings, roller bearings, thrust bearings, radial bearings, journal bearings, and roller bearings. Depending on the application, the bearing apparatus may operate as a plain bearing, a roller bearing, a fluid bearing, or other any other mode of operation of a bearing. 
     Bearing apparatuses have found particular use as radial, thrust, and journal bearings. Each bearing apparatus may include a stator that does not rotate and a rotor that is attached to an output shaft and rotates with the output shaft. The stator and rotor may each include one or more bearing elements or inserts thereon. Each bearing element may be fabricated to provide an upper bearing surface that bears against other bearing surfaces during use. 
     In a conventional polycrystalline diamond compact (“PDC”) bearing apparatus, a bearing assembly may include a support ring that may be configured to accept a number of superhard bearing elements. The superhard bearing elements may be made from a polycrystalline diamond (“PCD”) layer formed on a cemented tungsten carbide substrate that forms a PDC. 
     Despite the availability of a number of different bearing assembly designs, manufacturers and users of bearing apparatuses continue to seek improved bearing apparatus designs and manufacturing techniques. 
     SUMMARY 
     Embodiments of the invention relate a bearing assembly, which may be operated at least partially hydrodynamically, and includes a support ring having reduced-thickness portions configured to elastically deflect for promoting hydrodynamic fluid film formation between opposing bearings of the bearing assembly incorporated in a bearing apparatus. The disclosed bearing assemblies and apparatuses may be employed in downhole motors of a subterranean drilling system or other mechanical systems. 
     In an embodiment, a bearing assembly includes a plurality of superhard bearing elements distributed circumferentially about an axis. Each of the plurality of superhard bearing elements includes a leading side and a trailing side. The bearing assembly further includes a support ring having the plurality of superhard bearing elements mounted thereto. The support ring including a first surface, a second surface spaced from the first surface, and a plurality of reduced-thickness portions. Each of the reduced-thickness portions exhibits a reduced-thickness dimension relative and is defined between the first and second surfaces of the support ring. Each of the plurality of reduced-thickness portions may be selectively located proximate to the leading side of a respective one of the plurality of superhard bearing elements. 
     In an embodiment, a bearing apparatus includes two opposing bearing assemblies, one of which may be configured as a rotor and the other as a stator. At least one of the rotor or stator may be configured as any of the embodiments of bearing assemblies disclosed herein. 
     Features from any of the disclosed embodiments may be used in combination with one another, without limitation. In addition, other features and advantages of the present disclosure will become apparent to those of ordinary skill in the art through consideration of the following detailed description and the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The drawings illustrate several embodiments of the invention, wherein identical reference numerals refer to identical or similar elements or features in different views or embodiments shown in the drawings. 
         FIG. 1A  is an isometric view of a thrust-bearing assembly according to an embodiment. 
         FIG. 1B  is a partial, cross-sectional side view of the thrust-bearing assembly of  FIG. 1A . 
         FIG. 1C  is an exaggerated, partial, cross-sectional side view of the thrust-bearing assembly of  FIG. 1A  during use. 
         FIG. 1D  is a partial, cross-sectional side view of a thrust-bearing assembly according to an embodiment. 
         FIG. 1E  is an isometric cutaway view of the thrust-bearing assembly of  FIG. 1A . 
         FIG. 1F  is an exploded isometric view of the thrust-bearing assembly of according to an embodiment. 
         FIG. 2A  is an isometric view of a thrust-bearing assembly according to an embodiment. 
         FIG. 2B  is a partial, cross-sectional side view of the thrust-bearing assembly of  FIG. 2A . 
         FIG. 3  is an exploded isometric view of two thrust-bearing assemblies that form a thrust-bearing apparatus according to an embodiment. 
         FIG. 4A  is an isometric view of the thrust-bearing apparatus of  FIG. 3  assembled. 
         FIG. 4B  is an isometric view of a thrust-bearing apparatus according to an embodiment. 
         FIG. 4C  is an isometric view of a thrust-bearing apparatus according to an embodiment. 
         FIG. 5A  is a top plan view of a radial bearing assembly according to an embodiment. 
         FIG. 5B  is an isometric view of the radial bearing assembly of  FIG. 5A . 
         FIG. 5C  is a partial, isometric cutaway view of a radial bearing assembly according to an embodiment. 
         FIG. 5D  is a partial, cross-sectional view of the radial bearing assembly of  FIG. 5A . 
         FIG. 5E  is an isometric cutaway view of a radial bearing assembly according to an embodiment. 
         FIG. 5F  is a partial, cross-sectional side view of the radial bearing assembly of  FIG. 5A . 
         FIG. 5G  is an exaggerated, partial, cross-sectional side view of the radial bearing assembly of  FIG. 5A  during use. 
         FIG. 6  is an isometric cutaway view of a radial bearing assembly according to an embodiment. 
         FIG. 7  is a top plan view of a radial bearing assembly according to an embodiment. 
         FIG. 8A  is an isometric cutaway view of a radial bearing apparatus according to an embodiment. 
         FIG. 8B  is an isometric cutaway view of a radial bearing apparatus according to an embodiment. 
         FIG. 9  is a schematic isometric cutaway view of a subterranean drilling system according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the invention relate a bearing assembly, which may be operated at least partially hydrodynamically, and includes a support ring having reduced-thickness portions configured to elastically deflect for promoting hydrodynamic fluid film formation between opposing bearings of the bearing assembly incorporated in a bearing apparatus. The disclosed bearing assemblies and apparatuses may be employed in downhole motors of a subterranean drilling system or other mechanical systems. 
     While the description herein provides examples relative to a subterranean drilling and a motor assembly, the bearing assembly and apparatus embodiments disclosed herein may be used in any number of applications. For instance, the bearing assemblies and apparatuses may be used in pumps, motors, compressors, turbines, generators, gearboxes, and other systems and apparatuses, or in any combination of the foregoing. Furthermore, while the embodiments disclosed herein are described as being operated hydrodynamically, the bearing assemblies and apparatuses may also be operated partially hydrodynamically or not hydrodynamically, if desired or needed, without limitation. 
       FIG. 1A  is an isometric view of a thrust-bearing assembly  102  according to an embodiment. The thrust-bearing assembly  102  may form a stator or a rotor of a thrust-bearing apparatus. The thrust-bearing assembly  102  includes a support ring  104  that carries a plurality of superhard bearing elements  120  circumferentially spaced about a thrust/rotation axis “R.” The support ring  104  may exhibit a nominal thickness “M” and a plurality of (or one or more) reduced-thickness portions  110  (i.e., portions of the support ring  104  exhibiting a reduced thickness relative to adjacent portions of the support ring  104  and/or the nominal thickness M of the support ring  104 ) at a lower surface thereof sufficient to allow deformation (e.g., temporary elastic deflection or bending) of the support ring  104  to create hydrodynamic fluid film formation or adjust hydrodynamic flow between the plurality of superhard bearing elements  120  and an opposing surface (e.g., opposing superhard bearing elements, journal, or shaft) when fluid forces a leading side of a superhard bearing element  120  to deflect away from an opposing surface or superhard bearing element  120 . Each of the plurality of reduced-thickness portions  110  is selectively positioned proximate to a leading side of at least one of the plurality of superhard bearing elements  120 , with the leading side determined by the direction of rotation of the support ring  104 . The plurality of reduced-thickness portions  110  may include a recessed surface  112  (e.g., sloped or angled surface) and/or a gap  116 . 
     The support ring  104  may include an upper surface  105  and a lower surface  106  spaced from each other by a radial (e.g., lateral surface) surface defining the thickness of the support ring  104 . The upper surface  105  may be substantially planar except for the superhard bearing elements  120  attached (e.g., mounted or affixed) thereto or any bearing recesses formed therein. The lower surface  106  may partially define the plurality of reduced-thickness portions  110 . For example, the reduced-thickness portion  110  may include a portion of the support ring  104  exhibiting the reduced-thickness dimension between the upper surface  105  and the lower surface  106  of the support ring  104  in relation to an adjacent portion of the support ring  104  and/or to the thickness M of the support ring  104 . The reduced-thickness dimension may be formed by removing (e.g., by machining) a portion of material from the support ring  104  or forming the support ring  104  to near net shape such as by powder metallurgy or casting. 
     The support ring  104  may be made from a variety of different materials. For example, the support ring  104  may comprise carbon steel, stainless steel, tungsten carbide, or another suitable material. Although described as upper and lower surfaces herein, the terms upper and lower surfaces are merely used for differentiation between a surface of the support ring having superhard bearing elements bonded thereto or therein—the upper surface—and a surface separated therefrom—the lower surface. 
     As shown in  FIGS. 1A and 1B , the support ring  104  may carry the plurality of superhard bearing elements  120  thereon. Each or at least some of the plurality of superhard bearing elements  120  may include a substrate  122  and a bearing body  124  bonded to the substrate  122 , with the bearing body  124  including an optional chamfer  125 . Optionally, at least some of the plurality of superhard bearing elements  120  may not include the substrate  122  and may only include the bearing body  124 , such as the bearing body  124  bonded directly to or mechanically attached to the support ring  104 . Examples of bearing assemblies having thermally-stable polycrystalline diamond bearing elements secured with a support ring by use of a retention ring are disclosed in U.S. Pat. No. 8,496,075, the disclosure of which is incorporated herein, in its entirety, by this reference. 
     Each of the plurality of superhard bearing elements  120  may include a leading side  140 , a trailing side  141 , and a bearing surface  128  (i.e., upper working surface) therebetween. The leading side  140  and trailing side  141  may be determined from the relative rotation of the support ring  104 . In some embodiments, each of the bearing surfaces  128  may be substantially planar and substantially coplanar with each other. In some embodiments, a fluid used to cool and/or lubricate the superhard bearing elements  120  rotating in a direction R may encounter the leading side  140  first and the trailing side  141  second. The fluid may be forced or allowed in between the bearing surface  128  and an opposing bearing surface by deformation (e.g., a temporary deflection or bending) of the support ring  104  proximate to the leading side  140  due to the increased compliance/flexibility of the reduced-thickness portion  110 . Each of the plurality of superhard bearing elements disclosed herein may be circumferentially spaced from each other a selected distance to allow deformation (e.g., deflection or bending) of the support ring  104  between adjacent superhard bearing elements  120  to thereby allow more fluid and/or a fluid film to develop between the superhard bearing elements  120  and the opposing superhard bearing elements or surface, resulting in greater hydrodynamic force between opposing superhard bearing elements and the ability to respond to varying or fluctuating thrust loads during operation. Such spacing between the plurality of superhard bearing elements  120  may be about 250 μm or greater, such as about 1 mm to about 2 cm, or about 2 mm to about 1 cm. 
     In any of the embodiments disclosed herein, at least one, at least some, or each of the plurality of superhard bearing elements (e.g., the superhard bearing elements  120 ) may be made from one or more superhard materials, such as polycrystalline diamond, polycrystalline cubic boron nitride, silicon carbide, tungsten carbide, or any combination of the foregoing superhard materials. As used herein a “superhard material” is a material exhibiting a hardness that is greater tungsten carbide and a “superhard bearing element” includes a superhard material therein. For example, the superhard bearing element may include a body or table formed from polycrystalline diamond and the substrate may be formed from cobalt-cemented tungsten carbide. Furthermore, in any of the embodiments disclosed herein, the polycrystalline diamond body or table may be leached to at least partially or substantially completely remove a metal-solvent catalyst (e.g., cobalt, iron, nickel, or alloys thereof) that was used to initially sinter precursor diamond particles that form the polycrystalline diamond. In another embodiment, an infiltrant used to re-infiltrate a preformed leached polycrystalline diamond table may be leached or otherwise removed to a selected depth from a bearing surface inward. Moreover, in any of the embodiments disclosed herein, the polycrystalline diamond may be unleached and include a metal-solvent catalyst (e.g., cobalt, iron, nickel, or alloys thereof) that was used to initially sinter the precursor diamond particles that form the polycrystalline diamond or an infiltrant used to re-infiltrate a preformed leached polycrystalline diamond table. Other examples of methods for fabricating the superhard bearing elements are disclosed in U.S. Pat. Nos. 7,866,418, 7,842,111, 8,236,074, the disclosure of each of which is incorporated herein, in its entirety, by this reference. 
     The diamond particles that may form the polycrystalline diamond in the bearing body  124  may also exhibit a larger average particle size and at least one relatively smaller average particle size (i.e., a bimodal diamond powder). According to various embodiments, the diamond particles may include a portion exhibiting a relatively larger size of about 8 μm and larger (e.g., 30 μm, 20 μm, 15 μm, 12 μm, 10 μm, 8 μm) and another portion exhibiting at least one relatively smaller size of about 6 μm and smaller (e.g., 6 μm, 5 μm, 4 μm, 3 μm, 2 μm, 1 μm, 0.5 μm, less than 0.5 μm, 0.1 μm, less than 0.1 μm). In an embodiment, the diamond particles may include a portion exhibiting a relatively larger size between about 10 μm and about 40 μm and another portion exhibiting a relatively smaller size between about 1 μm and 4 μm. In some embodiments, the diamond particles may comprise three or more (i.e., trimodal or greater diamond powders) different average particle sizes (e.g., one relatively larger size and two or more relatively smaller sizes, or vice versa), without limitation. 
     Additionally, as discussed in more detail below, in any of the embodiments disclosed herein, the superhard bearing elements  120  may be free-standing (e.g., substrateless) and formed from a polycrystalline diamond body that is at least partially or fully leached to remove a metal-solvent catalyst initially used to sinter the polycrystalline diamond body. 
     The support ring  104  may exhibit the thickness M (e.g., a greater thickness or even maximum thickness) and at least one (e.g., one or more, or a plurality of) portion having a smaller thickness S (e.g., a reduced thickness or even a minimum thickness). The reduced-thickness portion  110  may allow the support ring  104  and the superhard bearing element  120  thereon to deflect or bend away from an opposing superhard bearing element or surface when fluid is encountered by the leading side  140  to thereby allow more fluid between the superhard bearing element  120  and the opposing superhard bearing element or surface, resulting in greater hydrodynamic force/behavior between opposing superhard bearing elements and the ability to respond to varying or fluctuating thrust loads. 
     Each of the plurality of reduced-thickness portions  110  includes a discrete portion or region of the lower surface  106  of the support ring  104  exhibiting some thickness less than the thickness M (e.g., greater thickness or maximum thickness). Each of the plurality of reduced-thickness portions  110  may be selectively located proximate to corresponding leading sides  140  of the plurality of superhard bearing elements  120 . Put another way, each of the plurality of reduced-thickness portions  110  may exhibit the thickness S (e.g., reduced thickness or minimum thickness) at a point circumferentially between two adjacent bearing elements  120  of the plurality of superhard bearing elements  120 . In the illustrated embodiment, the reduced-thickness portion  110  may include a recessed surface  112  and/or at least one gap  116 . The recessed surface  112  may extend along a portion of the circumferential length L of the lower surface  106  of the support ring  104 , with the thickness S selectively located proximate to the leading side  140  of one of the plurality of superhard bearing elements  120 . The recessed surface  112  may extend to the thickness M at a location nearer the trailing side  141  of the same one of the plurality of superhard bearing elements  120 . The recessed surface  112  of the reduced-thickness portion  110  may terminate at the thickness M (e.g., maximum thickness) of the support ring  104 , which may extend for a portion of the length L, thereby forming a support surface  121  (e.g., a land or flat portion of the lower surface) exhibiting the thickness M between adjacent reduced-thickness portions  110 . The recessed surface  112  may be at least partially non-planar, at least partially planar, or combinations of planar and non-planar, without limitation. The circumferential length L of the recessed surface  112  may be same as, less than, or greater than the overall lateral dimension (e.g., diameter, width, or length as measured with respect to the circumference of the support ring  104 ) of the corresponding superhard bearing element  120  proximate to the recessed surface  112 , such that the recessed surface  112  (e.g., sloped surface) allows the reduced-thickness portion  110  and the superhard bearing element  120  thereon to deflect away from an opposing bearing surface when the leading side  140  encounters the fluid, thereby creating and/or enhancing hydrodynamic lift between opposing superhard bearing elements. For example, the circumferential length L of the recessed surface  112  may be equal to or greater than the greatest lateral dimension (e.g., diameter, width, or length) of the corresponding superhard bearing element  120  proximate to the recessed surface  112 , such as about 40% or more, about 40% to about 120%, about 50% to about 110%, about 60% to about 100%, about 75% to about 90%, about 80% to about 100%, about 90% to about 110%, about 50%, about 90%, or about 100% of the greatest lateral dimension (e.g., diameter, width, or length) of the corresponding superhard bearing element proximate to the recessed surface  112 . In such embodiments, the remainder or portions of the remainder of the lower surface  106  of the support ring  104  may be substantially parallel to the upper surface  105  of the support ring  104  or the superhard bearing element  120  and may exhibit the nominal thickness M, thereby forming a land or flat portion of the lower surface  106 . In some embodiments, the circumferential length L of the recessed surface  112  may be between about 50% and less than 100% of the greatest lateral dimension of the corresponding superhard bearing element  120  proximate to the recessed surface  112 . In such embodiments, the recessed surface  112  may exhibit a portion having the thickness S proximate to the leading side  140  and increase in thickness to a point closer to the trailing side  141 , with the thickness again decreasing as it approaches the trailing side  141  to thereby allowing the support ring  104  to deflect the one of the plurality of superhard bearing elements  120  away from an opposing superhard bearing elements regardless of the direction of rotation. Put another way, the lower surface  106  of the support ring  104  may include reduced-thickness portions at both the leading side and the trailing side to allow or improve hydrodynamic flow between superhard bearing elements  120  no matter the direction of rotation of the support ring  104  (e.g., a double tapered reduced-thickness portion or portions). 
     The recessed surface  112  may form an angle θ (e.g., a constant angle defining a planar surface) with respect to the bearing surface  128  of a corresponding individual one of the superhard bearing elements  120 . The angle θ may be more than zero degrees, such as an angle greater than zero degrees to about 70 degrees or less, about 1 degree to about 60 degrees, about 5 degrees to about 45 degrees, about 15 degrees to about 30 degrees, about 30 degrees to about 60 degrees, about 5 degrees to about 45 degrees, about 10 degrees, about 20 degrees, about 30 degrees, about 45 degrees, about 60 degrees, or about 70 degrees. In some embodiments, the recessed surface  112  may have a changing angle θ across at least a portion of the circumferential length L of the recessed surface  112 , thereby at least partially defining the reduced-thickness portion  110  exhibiting an increasing or decreasing in slope (e.g., a non-planar surface) along its circumferential length L. In some embodiments, the angle θ may increase along the circumferential length L from the leading side to the trailing side, resulting in a concave recessed surface  112 . In some embodiments, the angle θ may decrease along the circumferential length L from the leading side to the trailing side, resulting in a convex recessed surface  112 . In some embodiments, convex or concave recessed surfaces may begin or terminate on any angle θ described above. 
     As previously discussed, in some embodiments, the reduced-thickness portion  110  may include the gap  116 . The gap  116  may exhibit a gap width or distance G extending between a gap wall surface  117  and a second gap wall surface  119 . The support ring  104  may exhibit a reduced-thickness in the gap  116  that is smaller than any thickness along the recessed surface  112  (e.g., the thickness S). The gap  116  may exhibit a gap width or distance G less than, equal to, or greater than the distance between adjacent superhard bearing elements  120 . The gap  116  may have a gap width or distance G of about 0.01 inches or more, such as about 0.01 inches to about 1 inch, about 0.05 inches to about 0.750 inches, about 0.10 inches to about 0.50 inches, about 0.01 inches to about 0.40 inches, about 0.20 inches to about 0.25 inches, about 0.10 inches to about 0.50 inches, about 0.020 inches, about 0.1 inches, or about 0.25 inches. The gap width or distance G may be about 10% or more of the distance between adjacent superhard bearing elements  120 , such as about 10% to about 200%, about 25% to about 175%, about 50% to about 150%, about 75% to about 125%, about 90% to about 110%, about 110% to about 200%, about 10% to about 90%, about 100%, about 50%, or about 150% the distance between adjacent superhard bearing elements  120 . The gap width or distance G may be selected based on any of a number of factors including, the desired amount of flex in the support ring  104 , the desired tilt of the bearing elements during use, the diameter of the support ring  104 , a radial width W of the support ring  104 , the size (e.g., diameter, length, and/or width) of the superhard bearing elements  120  in relation to the support ring  104 , the distance between the bearing elements  120 , the thickness S of the support ring  104 , or combinations of any of the foregoing. The thickness S of the support ring  104  may be configured to allow for temporary elastic deformation of the support ring in order to create or adjust hydrodynamic fluid flow (e.g., by allowing tilt and/or rotation of one or more bearing elements) between opposing superhard bearing elements and a return to the original shape of the support ring. In some embodiments, the thickness S (e.g., minimum thickness), as found in the gap  116  or the thickness of the recessed surface  112 , may be a proportion of the thickness M (e.g., maximum thickness) of the support ring  104 , such as about 10% of the thickness M of the support ring  104 , such as about 10% to about 95%, about 20% to less than 100%, about 30% to about 90%, about 40% to about 80%, about 50% to about 75%, about 25%, about 50%, about 75% or about 90% of the thickness M of the support ring  104 . 
     In some embodiments, the gap  116  may be at least partially defined by substantially parallel gap wall surfaces  117  and  119 . The gap wall surfaces  117  and  119  may be positioned at or near the leading side of the recessed surface  112  and the trailing side of an adjacent support surface  121 , and may extend radially through the width W of the support ring  104 . The gap wall surfaces  117  and  119  may be substantially perpendicular to the upper surface  105  of the support ring  104 , or may be formed at an angle with respect to the upper surface  105  of the support ring  104  and may be separated by a uniform or non-uniform gap width G substantially similar to any described herein. The gaps  116  may be positioned generally circumferentially between adjacent superhard bearing elements  120  or may be positioned such that a portion of the gap  116  is below (e.g., directly below) a portion of one or both proximate superhard bearing elements  120 . 
       FIG. 1C  depicts an exaggerated, partial, cross-sectional view of the bearing assembly of  FIGS. 1A and 1B  during use (e.g., while deflection of the bearing surface  128  is taking place). As the leading side  140  of one of the bearing elements  120  encounters an oncoming fluid (e.g., a lubricating fluid), the pressure P of the fluid between the bearing surface  128  and an opposing surface exerts a force on the bearing surface  128  away from the opposing bearing surface (e.g., opposing bearing element). The pressure P exerted on the bearing surface  128  at the leading side  140  may cause the bearing surface  128  and proximate portion of the support ring  104  to deflect away responsive to the pressure. The reduced-thickness portion  110  may provide an empty space for the support ring to deflect into between the lower surface of the support ring  104  and the support  175  on which the support ring  104  rests. The amount of displacement/deflection depicted in  FIG. 1C  is exaggerated to illustrate displacement during use. In some embodiments, the support surface  121  may remain substantially or completely in contact with support  175  during use. The distance of displacement/deflection may vary based on the size of the support ring, size of the bearing elements, thickness of the support ring (both in an out of the reduced thickness portion), amount of pressure exerted by the fluid, and other characteristics of the bearing apparatus without limitation. In an embodiment, the leading side  140  of one of the bearing surfaces  128  of the bearing element  120  may deflect 0.00001 inches or more away from an opposing bearing surface during use, such as about 0.00001 inches to about 0.003 inches, about 0.00002 inches to about 0.002 inches, about 0.00005 inches to about 0.001 inches, about 0.00045 inches, about 0.0007 inches about 0.001 inches, or about 0.002 inches. 
     As shown in  FIG. 1D , in some embodiments, the reduced-thickness portion  110  may be formed solely by the recessed surface  112 . In such embodiments, the recessed surfaces  112  may be distinct from one another as shown in  FIG. 1D . 
     Referring again to  FIG. 1A , in some embodiments, the support ring  104  may have a radial width W. In one embodiment, the radial width W may be sufficient to allow for a single superhard bearing element  120  to fit within the width of the support ring  104  (e.g., to provide an excess of width relative to the width of the superhard bearing element  120 ). In one embodiment, the radial width W may be sufficient to allow for more than one row of superhard bearing elements  120  thereon. For example, the radial width W may allow for 2 or more rows (e.g., staggered or radially spaced from one another) of superhard bearing elements  120 . In some embodiments, the plurality of reduced-thickness portions  110  may extend radially across the entire width of the support ring  104 . The reduced-thickness portion  110  (e.g., the recessed surface and/or gaps) may exhibit substantially consistent geometry or varying geometry across the width W of the support ring  104 . For example, the angle θ may be the same at the inner radial surface and the outer radial surface, or the gap width G may have the same circumferential length L across the entire width of the support ring. In some embodiments, the reduced-thickness portion  110  (e.g., a recessed surface and/or gaps) may exhibit substantially non-uniform or varying geometry across the width W of the support ring  104 , without limitation. For example, the reduced-thickness portion  110  may have a greater angle θ near the outer radial surface than near the inner radial surface or vice versa; may have a greater thickness S (e.g., reduced thickness) near the outer surface than near the inner radial surface or vice-versa; may have a proportionally larger gap width G near the inner surface than near the outer radial surface or vice versa; or combinations of any of the foregoing. 
     In some embodiments, the reduced-thickness portion  110  may exclude the recessed surface  112 . Put another way, the reduced-thickness portion  110  may solely comprise a gap  116  or a plurality of gaps  116  (e.g., forming a stepped lower surface of the support ring  104 ). In such embodiments, the gap  116  or plurality of gaps may be positioned proximate to the leading side  140  of a corresponding superhard bearing element  120 , and may extend along the circumferential length L of the support ring sufficient to allow the support ring to flex when the leading side  140  of a superhard bearing element  120  deflects during use (e.g., from hydrodynamic fluid during film development between the opposing superhard bearing elements). For example, the gap width or distance G or sum of gap widths G may extend laterally a circumferential length L of about half or more of the greatest lateral dimension of the corresponding superhard bearing element  120 . 
     In some embodiments, the support ring  104  may include a common channel formed in the upper surface  105  in which the superhard bearing elements  120  may be placed or affixed to the support ring  104 . In other embodiments, such as that shown in  FIG. 1E , the support ring  104  may define multiple pockets or recesses  109  into which the superhard bearing elements  120  may be placed or affixed. In some embodiments, the upper surface  105  of the support ring  104  may be substantially planar thereacross (i.e., having no pockets or channels therein), and the plurality of superhard bearing elements  120  may be attached or otherwise mounted thereto. The superhard bearing elements  120  may then be supported or secured to or within the support ring  104  in any suitable manner. At least a portion of or all of the superhard bearing elements  120  may be partially secured at least partially in the recesses  109  via brazing, welding, soldering, press-fitting, fastening with a fastener, or another suitable technique. The support ring  104  may also include an inner radial surface  107  defining an aperture  118 . The aperture  118  may be generally centered about the thrust/rotation axis R, and may be adapted to receive a shaft (e.g., a downhole drilling motor shaft). 
       FIG. 1F  illustrates a bearing assembly  102 ′ including a plurality of freestanding superhard bearing bodies  124 ′ (e.g., a polycrystalline diamond body without a substrate) which may be secured thereto by a retention ring  150  and fasteners  155 . Any suitable superhard bearing element may be secured to the support ring  104 ′ by the retention ring  150  and fasteners  155 , in a similar or identical manner as shown in U.S. Pat. No. 8,496,075. The support ring  104 ′ may be substantially similar to any support ring  104 ,  204 , or  304  described herein, including some or all if the features associated therewith. The support ring  104 ′ may have a plurality of recessed  109  formed therein. The recesses  109  may be sized and configured to allow a superhard bearing element  120 ′ to fit therein. Each of the plurality of freestanding superhard bearing bodies  124 ′ may have an upper surface  128 ′, a lower surface  127  and a lateral surface therebetween. In some embodiments, the plurality of freestanding superhard bearing bodies  124 ′ may be generally cylindrical, frustoconical, cuboid, combinations of the foregoing, or exhibit any other suitable shape without limitation. The freestanding superhard bearing bodies  124 ′ shown in  FIG. 1F  exhibit a frustoconical configuration wherein the upper surface  128 ′ is smaller than the lower surface  127 . When positioned on the support ring (e.g., in one of the recesses  109  or on the upper surface  105 ), the bearing bodies may be secured in place by the retention ring  150 . The retention ring  150  may be placed over and/or around the free standing superhard bearing bodies  124 ′ and be affixed to the support ring  104 ′ by fasteners  155  (e.g., bolts, screws, rivets, or any other suitable fastener, without limitation). The fasteners  155  may be aligned and inserted through the holes  157  in the retention ring  150  and into the receiving holes  153  located in the support ring. In an embodiment, the receiving holes  153  may be threaded and the fasteners  155  may be bolts having a complementary thread inserted therein. The fasteners  155  may be secured to the support ring (e.g., tightened into the receiving holes  153 ) to hold the retention ring  150  down with sufficient force to secure the plurality of free standing superhard bearing bodies  124 ′ in place during use of the bearing assembly  102 ′. The retention ring  150  may be configured to flex and/or otherwise allow deflection of the free standing superhard bearing bodies  124 ′ therein during use. The retention ring  150  may define a pattern (e.g., circumferentially spaced pattern) of bearing body holes  152  configured to allow the free standing superhard bearing bodies  124 ′ to fit partially through the bearing body holes  152  but not pass entirely through. The bearing body holes  152  may include an upper aperture  152   a  and a lower aperture  152   b , wherein the lower aperture  152   b  is wider than the upper aperture  152   a . The circumferentially-spaced pattern may correspond to the recesses  109  in the support ring  104 ′. The retention ring  150  may also include a plurality of holes  157  spaced about the bearing body holes  152  and correspond to the receiving holes  153  in the support ring  104 ′. 
     In an embodiment, a plurality of superhard bearing elements or superhard bearing bodies may be affixed directly to the support ring using any one of an adhesive, brazing, integral formation (e.g., sintering), any other suitable attachment means, or combinations of any of the foregoing. In an embodiment, the support ring  104 ′ may exhibit a substantially flat upper surface  105 ′ (e.g., having no recesses therein). The retention ring  150  may define the spacing for the superhard bearing elements or bodies placed on the upper surface  105 ′. 
     In some embodiments, differing superhard bearing element shapes or constructions (PCD or other) may be used to form any of the bearing assemblies described herein. For example, the thrust-bearing assemblies of  FIGS. 1A-1F  depict substantially cylindrical superhard bearing elements  120 . In other embodiments, the plurality of superhard bearing elements  120  may be non-cylindrical, such as generally cuboid (e.g., a cuboid with rounded corners), pyramidal, a frustum, arbitrary shapes, or combinations of the foregoing. For example, the plurality of superhard bearing elements  220  shown in  FIGS. 2A and 2B  exhibit a generally trapezoidal bearing surface having a leading side  240 , a trailing side  241 , a first end  243  proximate to an interior portion of a support ring  204 , and a second end  244  proximate to an exterior portion of the support ring  204 . The circumferential length L of the first end  243  is smaller than the circumferential length L of the second end  244 . Further, reduced-thickness portions  210  may extend radially across the width W of the support ring  204 . The support ring  204  includes an upper surface  205 , a lower surface  206 , and a plurality of superhard bearing elements  220  circumferentially spaced about a thrust/rotation axis. At least one or at least some of the plurality of superhard bearing elements  220  may include a substrate  222  and a bearing body (or table)  224  bonded to the substrate  222 . The substrate  222  and the bearing body  224  may be formed according to any process described herein, and may comprise any suitable substrate and bearing body materials described herein. The support ring  204  may include a plurality of recesses  209 , into which superhard bearing elements may be at least partially positioned, mounted, and/or affixed. The support ring  204  may further include reduced-thickness portions  210 . The reduced-thickness portions  210  may be substantially similar to those described above. For example, as shown in  FIGS. 2A and 2B , each or at least some of the reduced-thickness portions  210  may include a recessed surface  212  and a gap  216 . The reduced-thickness portions  210  may have a thickness S (e.g., minimum thickness) at the gap  216  and the plurality of recessed surfaces  212  may have a more reduced thickness at a location proximate to the leading side  240  of a corresponding one the plurality of superhard bearing elements  220 , the thickness of the support ring  204  tapering to a thickness M (e.g., a greater thickness or maximum thickness) at a point closer to the trailing side  241  of the corresponding one the plurality of superhard bearing elements  220 . Additionally, the properties of the reduced-thickness portion  210  may be substantially consistent across the width W of the support ring  204 , or the properties may vary across the width W. 
     In some embodiments, such as that shown in  FIGS. 3 and 4A , a thrust-bearing apparatus  300  may include two opposing thrust-bearing assemblies that may be positioned such that the bearing surfaces thereof face each other and substantially contact each other absent a fluid film therebetween. In some embodiments, each of the opposing bearing assemblies  302  and  352  may be configured the same or similarly to the bearing assembly  102 . In other embodiments, only one of the bearing assemblies  302  or  352  may be configured the same or similarly as the bearing assembly  102 . For example, the thrust-bearing assembly  302  may include a support ring  304  having an upper surface  305 , a lower surface  306 , an inner radial surface  307 , an outer radial surface  308 , a plurality of superhard bearing elements  320  distributed circumferentially about a thrust/rotation axis “R,” and a plurality of reduced-thickness portions  310 . The plurality of reduced-thickness portions  310  may include one or more of a recessed surface  312  and a gap  316 . Each of the plurality of superhard bearing elements  320  may include a leading side  340 , a trailing side  341 , and a bearing surface  328  therebetween. The leading side  340  and trailing side  341  being determined by the relative rotation of the support ring  304 . Each of the plurality of superhard bearing elements  320  may include a substrate  322  and a bearing body or table  324  including any suitable shapes or materials described herein for the substrate and the bearing body, or may be configured according to any other type of bearing element disclosed herein. The reduced-thickness portion  310  exhibits a thickness S (e.g., reduced thickness or minimum thickness) proximate to the leading side of rotation of the corresponding superhard bearing element  320 . The reduced-thickness portion  310  may taper or step from a thickness S to a greater thickness or even nominal thickness M (e.g., maximum thickness) at a location nearer to the trailing side of the corresponding superhard bearing element  320 . The positions, angles, sizes, and configurations of the reduced-thickness portions  310  may resemble any described herein. 
     In some embodiments, an opposing thrust-bearing assembly  352  may include a support ring  354  having an upper surface  355 , a lower surface  356 , an inner radial surface  357 , an outer radial surface  358 , a plurality of superhard bearing elements  370  distributed about an axis (e.g., circumferentially distributed about a thrust axis), and a plurality of reduced-thickness portions  360 . The plurality of reduced-thickness portions  360  may include a recessed surface  362  and/or a gap  366 . Each of the plurality of superhard bearing elements  370  may include a leading side, a trailing side, and a bearing surface  378  therebetween. The leading side and trailing side being determined by the relative rotation of the support ring  354 . Each of the plurality of superhard bearing elements  370  may include a substrate  372  and a bearing body or table  376  including any suitable shapes or materials described herein for a substrate and a bearing body. The reduced-thickness portions  360  may include one or more of a recessed surface  362  and a gap  366 . The reduced-thickness portion having a smallest thickness proximate to the leading side of rotation of the corresponding superhard bearing element  370 . The reduced-thickness portion  360 , may taper, step, or otherwise transition from a thickness S (e.g., reduced or minimum thickness) up to the thickness M (e.g., greater thickness or maximum thickness) at a location nearer to the trailing side of the corresponding superhard bearing element  370 . The positions, angles, sizes, and configurations of the reduced-thickness portions  360  may resemble any described herein. Either of the bearing assemblies  302  and  352  may be configured as a rotor or a stator. 
     As shown in  FIG. 4A , the thrust-bearing assemblies  302  and  352  may be assembled such that the bearing surfaces  328  and  378  generally oppose each other. One of the thrust-bearing assemblies  302  or  352  may configured as a stator and the other one of the thrust-bearing assemblies  302  or  352  may be configured as a rotor. The resulting bearing apparatus  400  may function as a thrust bearing. In some embodiments, each superhard bearing element  320  and  370  may have a corresponding reduced-thickness portion  310  or  360  ( FIG. 3 ) proximate thereto on the support ring  304  or  354 . In such embodiments, each of the support rings  304  and  354  may elastically deflect or deform at the plurality of reduced-thickness portions  310 ,  360  ( FIG. 3 ) such that fluid at the leading side of rotation may form or adjust hydrodynamic lift between the opposing bearing surfaces  328  and  378  to enable complete or partial hydrodynamic operation under certain thrust loads and rotational speeds. 
     In some embodiments, the support rings  304  and  354  of the bearing assemblies  302  and  352  may include the plurality of reduced-thickness portions  310  or  360  corresponding to every other superhard bearing element  320  or  370 . In some orientations, in such a configuration when the bearing assemblies  302  and  352  are positioned to oppose each other, the superhard bearing element  320  or  370  having the corresponding reduced-thickness portion  310  or  360  opposite thereto on one support ring  304  or  354  opposes the superhard bearing element  370  or  320  that may not have the corresponding reduced-thickness portion  360  or  310  proximate thereto. In such an embodiment, the support rings  304  and  354  may exhibit more rigidity (e.g., undergoes less deformation) than support rings including reduced-thickness portions  310  or  360  corresponding to every superhard bearing element thereon, while still allowing some of the superhard bearing elements  320  and  370  on the support rings  304  and  354  to deflect away from the opposing bearing surface  328  or  378  to allow or adjust hydrodynamic fluid flow between opposing sets of superhard bearing elements  320  and  370 . In some embodiments, such as illustrated in  FIG. 4A , the reduced-thickness portions  310  and  360  may be oriented in the same direction (e.g., having recessed surfaces  312  and  362  tapering to a greater thickness along the same circumferential direction) such as both clockwise or counterclockwise. 
     In an embodiment, such as illustrated in  FIG. 4B , the bearing assemblies  302  and  352  may be substantially as described above with respect to  FIG. 4A , but exhibit an opposing orientation (e.g., having recessed surfaces  312  and  362  tapering to a greater thickness in different circumferential directions). Such a configuration would allow for both opposing bearing surfaces and support rings  304  and  354  to be displaced or deflected away from one another substantially simultaneously as the leading sides of the opposing superhard bearings elements  320  and  370  rotate past one another. Such dual deflection may produce and/or increase hydrodynamic flow between the opposing superhard bearing elements  320  and  370  as compared to a bearing apparatus only including one support ring having reduced thickness portions. 
     In some embodiments, a thrust-bearing apparatus may include one thrust-bearing assembly  302  comprising the support ring  304  including the plurality of superhard bearing elements  320  each having the bearing surface  328  thereon opposed to another surface (e.g., continuous ring, thrust face, or collar). 
     In an embodiment, a bearing assembly  302  may oppose a conventional bearing assembly (e.g., a bearing assembly not having reduced thickness portions). As illustrated in  FIG. 4C , the bearing assembly  302  may be substantially identical to the bearing assemblies described above with respect to  FIGS. 3-4B . The bearing assembly  302  may oppose a bearing assembly  352 ′ including bearing elements  370  disposed about a support ring  354 ′. The support ring  354 ′ may include an upper surface  355 ′, a lower surface  356 ′, and an inner surface  357 ′ and outer surface  358 ′ both extending therebetween. The lower surface  356 ′ of the support ring  354 ′ may be substantially planar (e.g., a conventional support ring having no reduced-thickness portions). In such an embodiment, the support ring  304  may be configured to displace or deflect away from the support ring  354 ′. The plurality of reduced-thickness portions  310 , such as any described herein, may correspond to the plurality of superhard bearing elements  320  on the opposite surface of the support ring  304  such that the reduced-thickness portion exhibiting the thickness S may be selectively located proximate to the leading side of the corresponding superhard bearing element. In such embodiments, the support ring  304  may deflect or deform away from the opposing surface at or near the location where the support ring  304  exhibits the reduced-thickness portion  310 . The bearing assembly  302  may be configured as a stator or a rotor (as shown). 
     In some embodiments, such as those shown in  FIGS. 5A-5E , a bearing assembly comprising a support ring including reduced-thickness portions may be configured to function as a radial bearing.  FIG. 5A  is top plan view of a radial bearing assembly  502  including a support ring  504  according to an embodiment. The support ring  504  may include a substantially radially uniform inner surface  505  (with the exception of the superhard bearing elements attached thereto) facing inward toward a center point about which an axis of rotation is centered, an outer surface  506  generally opposite the inner surface  505 , and outer surfaces  508  between the inner surface  505  and the outer surface  506  on either side of the support ring  504 . The support ring  504  may include a plurality of superhard bearing elements  520  distributed circumferentially about the axis of rotation. Each superhard bearing element includes a leading side  540 , a trailing side  541 , and a bearing surface  528  therebetween. The leading side  540  and trailing side  541  may be determined from the relative direction of rotation R of the support ring  504 . The support ring  504  may include a plurality of reduced-thickness portions  510 . Each of the plurality of reduced-thickness portions  510  may be defined by a reduced-thickness dimension between the inner surface  505  and the outer surface  506  of the support ring  504  relative to an adjacent portion of the support ring  504  and/or the thickness M (e.g., greater thickness or maximum thickness) of the support ring  504 . The reduced-thickness portions  510  includes a portion having a thickness S (e.g., reduced thickness or minimum thickness) selectively positioned proximate to the leading side  540  of the corresponding superhard bearing element  520  on the opposite surface of the support ring  504 , and tapering or stepping to the thickness M at a location on the support ring  504  closer to the trailing side  541 . In some embodiments, the reduced-thickness portions  510  are configured to allow and promote deformation of the support ring  504  in a radially outward direction (i.e., away the center of the axis of rotation) to promote or adjust hydrodynamic fluid flow or behavior. 
     In some embodiments, the plurality of reduced-thickness portions  510  may include a recessed surface  512  and/or a gap  516 . The recessed surface  512  may be extend along circumferential length L of the support ring  504 , providing the support ring  504  with the reduced-thickness dimension that tapers to the thickness M along the length L from a location proximate to the leading side  540  of the corresponding superhard bearing element to a location closer to the trailing side  541  of the corresponding superhard bearing element, thereby at least partially defining the recessed surface  512 . The recessed surface  512  may exhibit an angle θ with respect to an adjacent portion of the support ring  504 . The recessed surface  512  may terminate at a gap wall surface  517  or  519  and/or at a support surface  521  (e.g., a flat or land of the lower surface of the support ring). For example, the support surface  521  may be substantially planar, curved (e.g., substantially match a concave or convex cylindrical geometry of an underlying support), irregularly shaped surfaces, or combinations thereof. The gap wall surfaces  517  and  519  may be substantially parallel to one another or may be radially varying (e.g., increasing or decreasing radially at an angle perpendicular to the upper surface of the support ring). The recessed surface  512  may exhibit any of the configurations, angles, positions, or thicknesses described above with respect to recessed surfaces  112 ,  212 ,  312 , and  512 . 
     In some embodiments, the plurality of reduced-thickness portions  510  may include the gap  516 . The gap  516  may exhibit a gap width G extending from the gap wall surface  517  (e.g., on the leading side of one recessed surface  112 ) to the gap wall surface  519  (e.g., on the trailing side of the preceding recessed surface  512  or portion of the support ring exhibiting a greater thickness), thereby at least partially defining the gap  516 . The support ring  504  may exhibit the reduced-thickness dimension in the gap  516  that is smaller than the reduced-thickness dimension of the recessed surface  512  thereby defining a thickness S (e.g., minimum thickness) of the support ring  504 . The gap width G may be less than, equal to, or greater than the distance between adjacent superhard bearing elements, such as any of those gap distances G described above. 
     In some embodiments, the plurality of reduced-thickness portions  510  may only include the recessed surfaces  512 . In some embodiments, the plurality of reduced-thickness portions  510  may only include gaps  516 . For example, a reduced-thickness portion may include one or more gaps  516 , thereby at least partially defining a stepped lower surface proximate to a corresponding superhard bearing element in a manner substantially similar to any of those described above. In such embodiments, the gap  516  or plurality of gaps  516  may be selectively positioned proximate to the leading side  540  of the corresponding superhard bearing element  520 , and may extend along the circumferential length L of the support ring sufficient to allow the support ring to flex when the leading side  540  of the superhard bearing element  520  deflects away from another surface or superhard bearing element to create, adjust, or allow hydrodynamic fluid flow/behavior between the opposing bearing surfaces. For example, the gap widths G or sum of gap widths G may extend a circumferential length L of about half or more of the greatest lateral dimension (e.g., circumferential diameter, width, or length) of the corresponding superhard bearing element. 
     In some embodiments, the plurality of superhard bearing elements  520  may be substantially similar to any of those described herein, including but not limited to geometric configuration (e.g., shape or height), material composition, use of a substrate or lack thereof, positioning and/or amount used, or combinations of the any of the foregoing. In some embodiments including a radial or journal bearing assembly, the bearing surface  528  may be concave (e.g., generally cylindrical or generally spherical) or convex (e.g., generally cylindrical or generally spherical) to accommodate or complement, the opposing surface (e.g., a journal, or opposing radial bearing assembly). 
     As shown in  FIG. 5B , the outer surface  506  may partially define the plurality of reduced-thickness portions  510 , including the plurality of recessed surfaces  512  and/or gaps  516  that extend across the width W of the support ring  504 . In some embodiments including the gaps  516 , the gaps  516  may be at least partially defined by a first portion of the lower surface proximate to the leading side of the superhard bearing element  520  and a second portion of the lower surface proximate to the trailing side of the preceding superhard bearing element  520 , wherein the first and second portions of the outer surface  506  may be substantially perpendicular to the inner surface  505  and further define the gap  516  between therebetween. The inner surface  505  may have any shape or configuration including, but not limited to cylindrical, a plurality of planar surfaces, a plurality of non-planar surfaces, and combinations of the foregoing. In some embodiments, the width W of the support ring  504  may be sufficient to allow one or more of the plurality of superhard bearing elements  520  across the width W at a circumferential position on the support ring. For example, the width W may be sufficient to allow a single row of superhard bearing elements  520  on the support ring  504 , a staggered configuration of superhard bearing elements  520  (i.e., one superhard bearing element fitting at a point lateral and subsequent to another superhard bearing element), or more than one row of superhard bearing elements extending around the support ring. 
     According to an embodiment shown in  FIG. 5C , the support ring  504  may include a plurality of reduced-thickness portions  510   c  each of which includes a recessed surface  512   c  sloping at an angle that varies along the circumferential length L of the recessed surface  512   c . For example, the reduced-thickness portions  510   c  exhibits a smaller thickness at a location nearest the leading side of the corresponding one of the plurality superhard bearing elements  520  and increase in thickness along the circumferential length L as the reduced-thickness portion  510   c  approaches a point nearer the trailing surface of the corresponding one of the plurality superhard bearing elements  520 , until the reduced-thickness portion  510   c  reaches the thickness M. The reduced-thickness portion  510   c  may form an angle θ with respect to an adjacent portion of the support ring  504 , or the angle θ may change and/or change at different positions along recessed surface  512   c . For example, the recessed surface  512   c  may be arcuate (e.g., a convex recessed surface  512   c ). In some embodiments, recessed surface  512   c  may form a concave recessed surface (not shown). The recessed surface  512   c  may terminate at a location along the length L where the reduced-thickness portion  510   c  reaches the thickness M. In some embodiments, the support surface  521  may exhibit a nominal thickness M over the remainder of the circumferential length L until the subsequent reduced-thickness portion. As noted above, each of the plurality of reduced-thickness portions  510  may extend circumferentially along a proportion of the outer surface  506  of the support ring  504  in relation to the greatest circumferential diameter, width, or length of the corresponding superhard bearing element  520  proximate to the recessed surface  512 . For example, the circumferential length L of the recessed surface  512   c  may be about 40% or more of the greatest lateral dimension (e.g., circumferential diameter, width, or length) of the corresponding superhard bearing element  520 , such as about 40% to about 200%, about 50% to about 150%, about 75% to about 125%, about 100%, or any of the percentages or ranges of percentages of the greatest lateral dimension of the corresponding superhard bearing element  520  disclosed herein. 
     In some embodiments, such as that shown in  FIG. 5D , the reduced-thickness portion  510   d  may increase in thickness over portion of the circumferential length L from a reduced thickness at a location nearest the leading side of the corresponding one of the plurality of superhard bearing elements until the support ring  504  reaches the thickness M at a point nearer the trailing side of the corresponding superhard bearing element (e.g., the endpoint, midpoint or some other intermediate point, or after the endpoint of the corresponding superhard bearing element), thereby at least partially defining the recessed surface  512   d . The reduced-thickness portion  510   d  may then decrease in thickness from the nominal thickness M over the remaining portion of the circumferential length L of the reduced-thickness portion  510   d  to a reduced thickness at a location proximate to the trailing end of the corresponding superhard bearing element to form a second recessed surface  512   dd . The recessed surface  512   dd  may exhibit any feature, any angle θ, or any configuration for any recessed surface described herein, irrespective of the angle θ or configuration of the recessed surface  512   d . Such embodiments may function to allow the support ring and associated superhard bearing elements thereon to deform (e.g., deflect or dip) away from an opposing surface to accommodate (e.g., create or adjust) hydrodynamic fluid flow therebetween regardless of the direction of the rotation of the support ring. Such embodiments may be operated in either a clockwise rotation or a counterclockwise rotation. Embodiments such as that described immediately above, may also include a gap  516 , such as any described herein, in combination with the recessed surfaces  512   d  and  512   dd  to form the reduced-thickness portion  510   d . In some embodiments, the recessed surfaces  512   d  and  512   dd  may be convex slopes such as any described herein in which the resulting reduced-thickness portion may exhibit a generally rounded outer surface along the circumferential length L of the reduced-thickness portion. In some embodiments, the recessed surfaces  512   d  and  512   dd  may be concave slopes such as any described herein in which the resulting reduced-thickness portion may be defined by a lower surface converging in a cusp or point along the circumferential length L of the reduced-thickness portion. 
     In some embodiments, the plurality of superhard bearing elements  520  may be attached to or otherwise mounted on the support ring using any one of a number of means such as welding, soldering, brazing, mechanical attachment, press-fitting, or any other suitable means of attachment. 
     As shown in  FIG. 5E , a radial or journal bearing assembly may include the support ring  504  having a plurality of pockets or recesses  509  formed therein to at least partially accommodate and affix the plurality of superhard bearing elements  520  therein. In some embodiments, the plurality of recesses  509 , plurality of superhard bearing elements  520 , and plurality of reduced-thickness portions  510  may be configured to ensure that the plurality of superhard bearing elements do not extend to or through the outer surface  506  of the support ring  504  (i.e., the reduced-thickness portions  510  leave a thickness sufficient to form the recess  509  in the support ring  504  proximate to the reduced-thickness portion without protruding therethrough). The depth of the recesses  509  may be less than the thickness S of the support ring  504 . For example, the depth of the recesses  509  in the support ring  504  as measured from the inner surface  505  may be 250 μm or more, such as about 250 μm to about 3 cm, about 500 μm to about 2 cm, about 1 μm to about 1 cm, about 2 mm to about 8 mm, about 3 mm to about 6 mm, about 1.5 cm, about 1 cm, or about 5 mm. In some embodiments, the depth of the recess  509  in the support ring  504  as measured from the inner surface  505  may be a proportion of the thickness of the support ring at the location in which the recess is formed, such as about 95% or less of the thickness of the support ring at the location in which the recess  509  is formed, about 95% to about 5%, about 90% to about 10%, about 80% to about 20%, about 60% to about 40%, about 50%, about 75%, or about 25% of the thickness of the support ring at the location in which the recess  509  is formed. 
       FIGS. 5F and 5G  depict the bearing assembly  502  including the support ring  504 , as described above, before and during use (in an exaggerated view), respectively. As shown in  FIG. 5F , a portion of the outer (e.g., lower) surface  506  (e.g., the support surface  521 ), may be in contact with a support  575  (e.g., a wall, housing, etc.). There may be a distance between the support  575  and the reduced thickness portions  510 . During operation, as shown in  FIG. 5G , the pressure P may be exerted on the bearing surface  528  near the leading side  540 . Responsive to the pressure P, the bearing surface  528  and underlying support ring  504  may deflect away from an opposing surface (not shown) into the empty space between the support  575  and the support ring  504  created by the reduced-thickness portion  510 . The amount of displacement/deflection depicted in  FIG. 5G  is exaggerated to illustrate displacement during use. In some embodiments, the support surface  521  may remain substantially or completely in contact with support  575  during use. The distance of displacement/deflection may vary based on the size of the support ring, size of the bearing elements, thickness of the support ring (both inside and outside of the reduced thickness portion), amount of pressure P exerted by the fluid, and other characteristics of the bearing apparatus without limitation. In an embodiment, the leading side  540  of a bearing surface  528  of a bearing element  120  may deflect 0.00001 inches or more away from an opposing surface during use, such as about 0.00001 inches to about 0.003 inches, about 0.00002 inches to about 0.002 inches, about 0.00005 inches to about 0.001 inches, about 0.00045 inches, about 0.0007 inches about 0.001 inches, or about 0.002 inches. 
     While shown as having a plurality of cylindrical superhard bearing elements in  FIGS. 5A-5G , a radial or journal bearing assembly may include a plurality of superhard bearing elements having a different shape, such as any superhard bearing element shapes described herein. For example, in some embodiments such as that shown in  FIG. 6 , a radial or journal bearing assembly  602  may comprise a support ring  604  including an upper surface  605  having a plurality of superhard bearing elements  620  with a bearing surface  628  exhibiting a substantially rectangular shape (e.g., generally rectangular with rounded corners) attached thereto, and a lower surface  606 , and a plurality of reduced-thickness portions  610  thereon. The plurality of superhard bearing elements  620  exhibiting a rectangular bearing surface geometry may be configured to create a selected amount of bearing surface area on the bearing assembly  602 . The plurality of superhard bearing elements  620  exhibiting a rectangular bearing surface geometry may include any of the features described for a superhard bearing element described herein, including but not limited to, use of a substrate, composition of materials therein, size, spacing, or combinations of the foregoing. Each of the plurality of superhard bearing elements  620  exhibiting a rectangular geometry may have a leading side  640 , a trailing side  641 , a first end  643 , and a second end  644 . Each of plurality of reduced-thickness portions  610  being disposed proximate to and on the opposite (e.g., lower surface) a corresponding one of the plurality of superhard bearing elements  620 . The reduced thickness portions  610  may include one or more of a recessed portion  612  and a gap  616 . The support ring  604  and each of the plurality of reduced-thickness portions  610 , including a recessed portion  612  and/or gap  616 , may be configured substantially identical to any of the embodiments of a support ring and reduced-thickness portions described herein. 
     In some embodiments such as that shown in  FIG. 7 , a radial bearing assembly  702  may comprise a support ring  704  including an outer surface  705  facing away from the center point of the bearing assembly (e.g., the axis of rotation) and having a plurality of superhard bearing elements  720  distributed circumferentially thereon, an inner surface  706  facing inwardly toward a center point/rotation axis of the radial bearing assembly  702 , and peripheral surfaces  708  therebetween. The superhard bearing elements  720  may have a leading side  740  and a trailing side  741 , depending on the direction of rotation R of the support ring  704 . The support ring  704  may include a plurality of reduced-thickness portions  710  at last partially defined by the inner surface  706 . The reduced-thickness portions may include a recessed portion  712  and/or a gap  716 . In some embodiments, the reduced-thickness portions  710  are configured to allow and promote deformation of the support ring  704  in a radially inward direction (i.e., toward the center of the axis of rotation) to promote or adjust hydrodynamic fluid flow. The plurality of reduced-thickness portions  710 , including any recessed portion  712  and/or gap  716  therein, may be substantially similar to, identical to, or exhibit substantially similar features, configurations or combinations thereof as any of the plurality of reduced-thickness portions disclosed herein. In some embodiments, the bearing surfaces  728  of the plurality of the superhard bearing elements  720  may be convex such as generally cylindrical or generally spherical. Such a convex configuration may allow for use of the bearing assembly  702  with a complementary surface (e.g., inner bearing surface of another superhard bearing element). 
       FIG. 8A  depicts an embodiment of a radial bearing apparatus  800  including a first or outer radial bearing assembly  502  (e.g., race) that receives a second or inner radial bearing assembly  702 . In some embodiments, the inner radial bearing assembly  702  may be configured as a rotor or a stator and the outer radial bearing assembly  502  may be configured as the other of a rotor or a stator. In an embodiment, the reduced thickness portions  510  and  710  may increase in thickness in the same circumferential direction, or in different circumferential directions. 
     Similar to the thrust-bearing apparatus  400  described above, the radial bearing apparatus  800  may include reduced-thickness portion  510  or  710  opposite each of the plurality of superhard bearing elements  520  or  720  on the respective support rings  504  and  704  on the bearing assemblies  502  and  702  substantially as described above. In some embodiments similar to those described above with respect to thrust-bearing apparatus  400 , the radial bearing apparatus  800  may include the reduced-thickness portion  510  or  710  opposite every other one of the plurality of superhard bearing elements  520  or  720  on the respective support rings  504  and  704 . In other embodiments, the support rings may only include reduced-thickness portions proximate to only one or more of the superhard bearing elements thereon, without limitation. In some embodiments, a bearing apparatus such as any described herein may only include reduced-thickness portions only on one support ring, wherein the opposing support ring has a substantially uniform thickness therethrough or is structured in another conventional manner. For example, as illustrated in  FIG. 8B , the bearing apparatus  800 ′ may include the support ring  504 , substantially identical to the support ring  504  described above. The support ring  504  may oppose a bearing assembly  702 ′ having a conventional support ring  704 ′ including an upper surface  705 ′, a lower surface  706 ′, and peripheral surfaces  708 ′ therebetween. The upper surface  705 ′ of the support ring  704 ′ may face radially outward and include a plurality of bearing elements  720  distributed circumferentially thereon. The bearing surfaces  728  may oppose the bearing surfaces  528 . The lower surface  706 ′ may be substantially smooth (e.g., having no recessed surfaces and/or gaps therein) and the support ring  704 ′ may have a uniform thickness therethrough. In such an embodiment, the support ring  504  may be configured to be displaced or deflect way from the opposing surface when pressure is applied to the leading side  540  of the bearing elements  520 . In  FIG. 8B , the support ring  504  is depicted as a rotor, however, in other embodiments the support ring  504  may be a stator wherein the recessed surfaces (portions)  512  are oriented in the opposite direction to provide for deflection of the bearing surfaces and support ring  504 . In an embodiment, the support ring  504  may exhibit a substantially uniform thickness (e.g., smooth lower surface) and the support ring  704  may be configured with reduced-thickness portions  710  to allow for deflection of the support ring to develop/enhance hydrodynamic flow between the bearing surfaces of the opposing bearing elements. In some embodiments, the radial bearing assembly  502  may be used with a shaft or journal to form a journal bearing without the inner bearing assembly  702 . 
     Any feature described with respect to a thrust-bearing assembly may be used on a radial bearing assembly, and any feature described with respect to radial bearing assembly may be used on a thrust-bearing assembly, including without limitation, features, orientations, or configurations of the support rings and superhard bearing elements. 
       FIG. 9  is a schematic isometric cutaway view of a subterranean drilling system  901  according to an embodiment. The subterranean drilling system  901  may include a housing  961  enclosing a downhole drilling motor  963  (i.e., a motor, turbine, or any other device capable of rotating an output shaft) that may be operably connected to an output shaft  915 . A thrust-bearing apparatus  900  may be operably coupled to the downhole drilling motor  963 . The thrust-bearing apparatus  900  may be configured as any of the previously described thrust-bearing apparatus embodiments including reduced-thickness portions therein. A rotary drill bit  917  may be configured to engage a subterranean formation and drill a borehole and may be connected to the output shaft  915 . The rotary drill bit  917  is shown as a fixed cutter rotary bit including a plurality of superabrasive cutting elements  919 . However, other embodiments may utilize different types of rotary drill bits, such as core bits, roller cone bits, eccentric bits, bicenter bits, reamers, reamer wings, or any other downhole tool including superabrasive cutting elements, such as PDCs. As the borehole is drilled, pipe sections may be connected to the subterranean drilling system  901  to form a drill string capable of progressively drilling the borehole to a greater size or depth within the earth. U.S. Pat. Nos. 4,410,054; 4,560,014; 5,364,192; 5,368,398; and 5,480,233, the disclosure of each of which is incorporated herein, in its entirety, by this reference, disclose subterranean drilling systems within which bearing apparatuses utilizing the PCD elements and/or PDCs disclosed herein may be incorporated. 
     The thrust-bearing apparatus  900  may include a stator  902  that does not rotate and a rotor  952  that may be attached to the output shaft  915  and rotates with the output shaft  915 . As discussed above, the thrust-bearing apparatus  900  may be configured as any of the embodiments disclosed herein having a plurality of reduced-thickness portions. For example, the stator  902  and/or rotor the 952 may include a plurality of circumferentially-distributed superhard bearing elements  920  such as any described herein, and the support ring  904  and/or  954  may include a plurality of reduced-thickness portions substantially similar to any of those described herein. 
     The downhole drilling apparatus may include a radial bearing assembly such as any described herein. The radial bearing assembly may also be configured to be operably connected to the output shaft. Optionally, a radial bearing apparatus may be used, with one radial bearing assembly is operably connected to the output shaft and is positioned to oppose another radial bearing assembly operably connected to the inner surface of the housing. The opposing bearing assemblies being configured substantially similar to any described herein. 
     In operation, drilling fluid may be circulated through the downhole drilling motor  963  to generate torque and effect rotation of the output shaft  915  and the rotary drill bit  917  attached thereto so that a borehole may be drilled. A portion of the drilling fluid may also be used to lubricate opposing bearing surfaces of the stator and the rotor to provide hydrodynamic lift between the bearing surfaces of the stator and the rotor. When the rotor is rotated or the on the bearing assembly changes, the plurality of reduced-thickness portions or may deflect away from an opposing bearing assembly creating or adjusting hydrodynamic fluid flow between the bearing surfaces of the stator and/or the rotor, as disclosed herein. 
     In some embodiments, a method of using any of the bearing apparatuses or assemblies described herein may include forming one or more support rings such as any of those described herein, out of any of the materials described herein; forming a plurality of reduced-thickness portions thereon substantially similar to any of those described herein; affixing superhard bearing elements thereto, optionally including forming the superhard bearing elements according to any of the embodiments described herein; positioning and/or aligning the bearing assembly or opposing bearing assemblies such that the bearing surfaces thereon are aligned with an opposing surface or bearing surfaces; and operating the bearing apparatus in an at least partially hydrodynamic mode sufficient to create or adjust hydrodynamic fluid flow between the opposing bearing surfaces. The support ring may be made by casting the general shape thereof and any of the features thereon, or by forming a substantially cylindrical or round ring and then machining (e.g., milling, turning, lasing, electrical discharge machining (“EDM”), grinding, lapping, or combinations thereof). 
     While various aspects and embodiments have been disclosed herein, other aspects and embodiments are contemplated. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting. Additionally, the words “including,” “having,” and variants thereof (e.g., “includes” and “has”) as used herein, including the claims, shall be open ended and have the same meaning as the word “comprising” and variants thereof (e.g., “comprise” and “comprises”).