Patent Publication Number: US-2023142360-A1

Title: Inertia damping systems and methods

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to, and the benefit of, U.S. Patent Application No. 63/002,039 filed Mar. 30, 2020, and U.S. Patent Application No. 63/022,825 filed May 11, 2020, both of which are incorporated herein by reference in their entirety. 
    
    
     BACKGROUND 
     Downhole drilling systems may include one or more rotating components. During operation, the rotating components may perform a variety of operations, including power generation, drilling, reaming, casing cutting, milling, steering, and other rotary operations. When rotating, the components may experience various types of vibrations, including axial, lateral, and torsional vibrations. Vibrations or oscillations in the tool may fatigue the downhole tool components (e.g., housings, shafts, etc.), increase wear, decrease tool effectiveness, or otherwise damage downhole tools. 
     SUMMARY 
     In some embodiments, a downhole inertia damping system include a collar having an inner surface. A plurality of dampers includes a housing. An inertia ring is rotatably installed inside the housing and a torsion fluid is located between the housing and the inertia ring. 
     In some embodiments, an inertia damping system includes a collar located between a downhole motor and a bit. A plurality of dampers is located between the downhole motor and the bit. The dampers include a housing and an inertia ring positioned inside the housing. The inertia ring is rotatable within the housing. A torsion fluid is located between the housing and the inertia ring. 
     In some embodiments, a method for damping oscillations includes securing a plurality of dampers to a collar. The method includes rotating an inertia ring inside of the housing of each damper independent of and in response to movement of the collar. 
     This summary is provided to introduce a selection of concepts that are further described in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter. Additional features and aspects of embodiments of the disclosure will be set forth herein, and in part will be obvious from the description, or may be learned by the practice of such embodiments. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In order to describe the manner in which the above-recited and other features of the disclosure can be obtained, a more particular description will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. For better understanding, the like elements have been designated by like reference numbers throughout the various accompanying figures. While some of the drawings may be schematic or exaggerated representations of concepts, at least some of the drawings may be drawn to scale. Understanding that the drawings depict some example embodiments, the embodiments will be described and explained with additional specificity and detail through the use of the accompanying drawings in which: 
         FIG.  1    is schematic view of a drilling system, according to at least one embodiment of the present disclosure; 
         FIG.  2    is a longitudinal cross-sectional view of an inertia damping system, according to at least one embodiment of the present disclosure; 
         FIG.  3 - 1    is a cross-sectional view of an inertia damping system, and  FIG.  3 - 2    is a representation of an oscillation profile of the inertia damping system of  FIG.  3 - 1   , according to at least one embodiment of the present disclosure; 
         FIG.  4 - 1    through  FIG.  4 - 7    are transverse cross-sectional views of dampers at different oscillation states, according to at least one embodiment of the present disclosure; 
         FIG.  5 - 1    through  FIG.  5 - 4    are further transverse cross-sectional views of dampers at different oscillation states, according to at least one embodiment of the present disclosure; 
         FIG.  6    is a longitudinal cross-sectional view of another inertia damping system, according to at least one embodiment of the present disclosure; 
         FIG.  7    is a longitudinal cross-sectional view of yet another inertia damping system, according to at least one embodiment of the present disclosure; 
         FIG.  8 - 1    is a longitudinal cross-sectional view of another inertia damping system, according to at least one embodiment of the present disclosure; 
         FIG.  8 - 2    is an enlarged view of a bearing and damper divider assembly within the inertia damping system of  FIG.  8 - 1   ; 
         FIG.  8 - 3    is an end view of a bearing within the inertia damping system of  FIGS.  8 - 1  and  8 - 2   ; 
         FIG.  9 - 1    is a transverse cross-sectional view of still another inertia damping system, according to at least one embodiment of the present disclosure; 
         FIG.  9 - 2    is a longitudinal cross-sectional view of the inertia damping system of  FIG.  9 - 1   , according to at least one embodiment of the present disclosure; 
         FIG.  9 - 3    is another longitudinal cross-sectional view of the inertia damping system of  FIG.  9 - 1   , according to at least one embodiment of the present disclosure; 
         FIG.  10 - 1    is a transverse cross-sectional view of a further inertia damping system, according to at least one embodiment of the present disclosure; 
         FIG.  10 - 2    is a transverse cross-sectional view of the inertia damping system of  FIG.  10 - 1   ; and 
         FIG.  11    is a flowchart of a method for damping vibrations, according to at least one embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present disclosure relate to devices, systems, and methods for damping vibrations/oscillations in downhole tools. For instance, downhole systems may experience a variety of motions, vibrations, and oscillations. In some embodiments, the movements may be associated with drilling activities. For example, a downhole tool may rotate to degrade a formation or other downhole materials by using a rotating bit, mill, or reamer. The engagement of the downhole tool and/or drill string with downhole materials, the flow of drilling or production fluids against or through the tool, or other conditions may cause vibrations, torsional oscillations, and other motions. For the purposes of this disclosure, the terms vibrations, oscillations, and other motions may be used interchangeably, unless otherwise stated. Left unchecked, these torsional oscillations may increase wear on the downhole tool, damage the downhole tool, increase fatigue on materials in the downhole tool, and combinations thereof. A damper may be installed on the downhole tool to reduce the effect of the torsional oscillations or axial vibrations. For example, an inertial damper may reduce the amplitude or frequency of the torsional oscillations. Of course, vibrations and oscillations may be a concern in other downhole contexts apart from drilling (e.g., testing, perforating, production, artificial lift, etc.), so a downhole environment should not be limited to drilling systems. 
       FIG.  1    shows one example of a drilling system  100  for drilling an earth formation  101  to form a wellbore  102 . The drilling system  100  includes a drill rig  103  used to turn a drilling tool assembly  104  which extends downward into the wellbore  102 . The drilling tool assembly  104  may include a drill string  105 , a bottomhole assembly (BHA)  106 , and a bit  110 , attached to the downhole end of drill string  105 . 
     The drill string  105  may include several joints of drill pipe  108  connected end-to-end through tool joints  109 . The drill string  105  transmits drilling fluid through a central bore and transmits rotational power from the drill rig  103  to the BHA  106 . In some embodiments, the drill string  105  may further include additional components such as subs, pup joints, etc. The drill pipe  108  provides a hydraulic passage through which drilling fluid is pumped from the surface. The drilling fluid discharges through nozzles, jets, or other orifices in the bit  110  for the purposes of cooling the bit  110  and cutting structures thereon, and for lifting cuttings out of the wellbore  102  as it is being drilled. 
     The BHA  106  may include the bit  110  or other components. An example BHA  106  may include additional or other components (e.g., coupled between to the drill string  105  and the bit  110 ). Examples of additional BHA components include drill collars, stabilizers, measurement-while-drilling (MWD) tools, logging-while-drilling (LWD) tools, downhole motors, underreamers, section mills, hydraulic disconnects, jars, vibration or damping tools, other components, or combinations of the foregoing. The BHA  106  may further include a rotary steerable system (RSS). The RSS may include directional drilling tools that change a direction of the bit  110 , and thereby the trajectory of the wellbore. In some cases, at least a portion of the RSS may maintain a geostationary position relative to an absolute reference frame, such as gravity, magnetic north, or true north. Using measurements obtained with the geostationary position, the RSS may locate the bit  110 , change the course of the bit  110 , and direct the directional drilling tools on a projected trajectory. 
     In general, the drilling system  100  may include additional or other drilling components and accessories, such as special valves (e.g., kelly cocks, blowout preventers, and safety valves). Additional components included in the drilling system  100  may be considered a part of the drilling tool assembly  104 , the drill string  105 , or a part of the BHA  106  depending on their locations in the drilling system  100 . 
     In some embodiments, a downhole motor  111  in the BHA  106  may generate power for downhole systems and/or provide rotational energy for downhole components (e.g., rotate the bit  110 ). The downhole motor  111  may be any type of downhole motor  111 , including a positive displacement pump (such as a progressive cavity motor) or a turbine. In some embodiments, the downhole motor  111  may be powered by the drilling fluid. In other words, the drilling fluid pumped downhole from the surface may provide the energy to rotate a rotor in the downhole motor  111 . The downhole motor  111  may operate with an optimal pressure differential or pressure differential range. The optimal pressure differential may be the pressure differential at which the downhole motor  111  may not stall, burn out, overspin, or otherwise be damaged. In some cases, the downhole motor  111  may rotate the bit such that the drill string  105  may not be rotated at the surface. 
     The bit  110  in the BHA  106  may be any type of bit suitable for degrading downhole materials. For instance, the bit  110  may be a drill bit suitable for drilling the earth formation  101 . Example types of drill bits used for drilling earth formations are fixed cutter or drag bits (or PDC bits), roller cone bits, coring bits, and combinations thereof (e.g., hybrid roller cone and fixed cutter bits). In other embodiments, the bit  110  may be a mill used for removing metal, composite, elastomer, other downhole materials, or combinations thereof. For instance, the bit  110  may be used with a whipstock to mill into casing  107  lining the wellbore  102 . The bit  110  may also be a junk mill used to mill away tools, plugs, cement, other materials within the wellbore  102 , or combinations thereof. Swarf or other cuttings formed by use of a mill may be lifted to surface or may be allowed to fall downhole. In still other embodiments, the bit  110  may include a reamer. For instance, an underreamer may be used in connection with a drill bit and the drill bit may bore into the formation while the underreamer enlarges the size of the bore. 
     Rotating the drill string  105  and/or operation of the downhole motor  111  may wholly or partially cause oscillations in the drill string  105  and/or the BHA  106 . The oscillations can have various effects. For instance, the oscillations are a generated by taking energy input into the system. Accordingly, that energy used by the oscillations is not input into the bit, and reduces the efficient transfer of energy to the bit. The vibrations/oscillations may also damage one or more components of the BHA  106 . In some embodiments, the oscillations may be at least partially damped using a downhole inertia damping system  112 . In some implementations, the downhole inertia damping system  112  may be located between the downhole motor  111  and the bit  110 . Using the downhole inertia damping system  112  to reduce the oscillations between the downhole motor  111  and the BHA  106  may reduce damage to components of the BHA  106  and/or more efficiently transfer power/energy to the bit, thereby increasing system efficiency, reducing downtime, or decreasing costs. In other embodiments, the inertia damping system  112  may be within the BHA  107  but above the downhole motor  111 . In other embodiments, the inertia damping system may be outside of the BHA  106 . Further still, in some embodiments, a downhole motor  111  may not be present and the inertia damping system  112  may be used. In at least some embodiments, the downhole motor  111  may include or be replaced by a steering tool (e.g., a RSS), and the inertia damping system  112  may be positioned above, below, or within the steering tool. 
       FIG.  2    is a cross-sectional view of an example downhole inertia damping system  212 , according to at least one embodiment of the present disclosure. The downhole inertia damping system  212  includes a collar  214  having an inner surface  216 . In some embodiments, the collar  214  may be any collar. For example, the collar  214  may be a drill collar, an MWD collar or housing, and LWD collar or housing, a housing or body of a steering tool (e.g., an RSS), the housing or body of a downhole tool (e.g., a stabilizer, reamer, casing cutter, mill), the collar or housing of any other downhole tool, sub, any other downhole element, and combinations thereof. One or a plurality of dampers  218  may be coupled to the inner surface  216  of the collar  214 . While the embodiments of the present disclosure illustrate and discuss the dampers  218  as being coupled to the inner surface  216  of the collar  214 , it should be understood that the one or more dampers  218  may be coupled to an outer surface  217  of the collar  214  (shown in phantom), between components, or to other components that may experience oscillations. 
     The damper(s)  218  may be torsional dampers that reduce or limit torsional oscillations of the collar  214 , or downhole tools coupled to the collar  214 , or other components. In  FIG.  2   , the dampers  218  (e.g., viscous dampers) are located between a downhole motor  211  and a bit  210 . In some embodiments, the oscillation of the BHA may be greatest, most intense, or may cause the most damage between the downhole motor  211  and the bit  210 . For instance, even if the oscillations are not the largest magnitude, they may resonate and thus increase damage, or may be at a high frequency and thus cycle rapidly and thereby lead to fatigue failures. Thus, by locating the plurality of dampers  218  between the downhole motor  211  and the bit  210 , the dampers  218  may be placed in a location where they may dampen the potentially damaging oscillations in the BHA. One or more of the plurality of dampers  218  are configured to dampen high-frequency torsional oscillations (HFTO). Whereas some systems are configured to reduce or mitigate relatively low-frequency oscillations (e.g., less than approximately 1 Hz, less than approximately 5 Hz) or mid-frequency oscillations (e.g., between approximately 5 Hz to approximately 40 Hz), embodiments of the dampers  218  discussed below having a torsional fluid and/or granular material may be configured to dampen HFTO. It is appreciated that HFTO may include torsional oscillations greater than approximately 40 Hz, or greater than approximately 50 Hz. Moreover, the dampers  218  discussed below may be configured to dampen HFTO up to approximately 250 Hz, approximately 300 Hz, or approximately 350 Hz. Furthermore, systems described herein may have one or more dampers  218  configured to dampen one or more HFTO frequencies in the BHA. 
     The dampers  218  of  FIG.  2    include a housing  220 . The housing  220  may the portion of the dampers  218  that is connected to the collar  214 . Some or each damper  218  of the plurality of dampers  218  may share a housing  220 , although in other embodiments one or more dampers  218  has an individual housing  220 . The housing  220  may be coupled to the collar  214 , and in some embodiments is rotationally, longitudinally, or radially fixed to the collar  214 . Thus, the housing  220  may not move relative to the collar  214  in at least some embodiments. In some embodiments, the housing  220  is integrally formed as part of the collar  214 . 
     The collar  214  may be positioned axially between, and potentially extend a full length between, the downhole motor  211  and the bit  210 . In some embodiments, the collar  214  includes multiple segments/collars connected end-to-end between the downhole motor  211  and the bit  210 . Thus, vibrations, oscillations, and other motions of the collar  214  between the downhole motor  211  and the bit  210  may be transmitted along the collar  214 . One or more dampers  218  installed between the downhole motor  211  and the bit  210  may reduce the oscillations not only at the location of the damper  218 , but along the collar  214  between the downhole motor  211  and the bit  210 , within the bit  210 , and above the downhole motor  211 . 
     The housing  220  in  FIG.  2    defines an interior space  222 . The interior space  222  may be defined by an inner wall  228 , an outer wall  230 , a lower wall  232  and an upper wall  233 . In FIG.  2 , the housing  220  is shown as having an annular construction around an axis of the collar  214 . An inertia element  224  may be located in (e.g., placed in) the interior space  222 . In some cases, the inertial element is a ring having an annular shape, although in other cases the inertia element may be a rod or partial ring. Thus, although the description refers to an inertia ring  224 , it will be appreciated the inertia element  224  may have other constructions. The inertia ring  224  may be rotatably installed inside the housing in the interior space  222 , and thus free to rotate within the interior space  222 . With such construction, as the housing  220  or the collar  214  rotates or oscillates, the inertia ring  224  may be able to move or rotate at a different rotational rate or potentially in a different manner or direction. 
     A torsion fluid  226  can be located in the interior space  222 , and can at least partially fill the gap between the inertia ring  224  and the walls defining the interior space  222  (e.g., the inner wall  228 , the outer wall  230 , the lower wall  232 , and the upper wall  233 ) of the housing  220 . The torsion fluid  226  may resist rotation of the inertia ring  224  inside the interior space  222 . For example, the viscosity and density of the torsion fluid  226  may affect the resistance to rotation of the inertia ring  224 , and therefore different torsion fluids  226  can change the damping effect of the dampers  218 . A higher viscosity or density fluid may have higher resistance to rotation/movement of the inertia ring  224 , and a lower viscosity or density may have lower resistance to rotation/movement of the inertia ring  224 . In some embodiments, the torsion fluid  226  may include a silicone-based fluid, an oil-based fluid, a water-based fluid, a magnetorheological fluid, an electrorheological fluid, have other components, or include a combination of the foregoing. In some embodiments, the torsion fluid  226  includes or is replaced by a granular material, such as ceramic or graphite beads or flakes. In some embodiments, the torsion fluid  226  may include a combination of fluids and solids. In some embodiments, different dampers  218  in the same drill string may include different torsion fluids  226 , or each damper  218  may include the same torsion fluid  226 . 
     The inertia ring  224  can have various constructions and in some implementations includes one or more bores, cavities, channels, or other passages. For example, the inertia ring  224  may include one or more cavities and the torsion fluid  226  may be located in and/or flow into and out of the one or more cavities in the inertia ring  226 . This flow may reduce the torsional oscillations or reduce/dissipate heat generated by the inertia ring  226 . 
     In some embodiments, the inertia ring  224  rotates out of sync with the collar  214 , by rotating at a different rotational rate or in a different rotational direction than the collar  214 , relative to a common reference frame. Thus, the rotation or other movement of the inertia ring  224  may not be synchronized with the collar  214 . During oscillation of the collar  214 , the collar  214  may rotate in a first direction and a second direction (or rotate in the first direction at first and second speeds). When rotating in the first direction (or first speed), the collar  214  may cause the housing  220  to rotate with it. The torsion fluid  226  and the inertia ring  224  can be rotationally independent of the housing  220  (which includes being rotationally out of sync with the housing  220 ). As the housing  220  rotates, the walls of the housing  220  may exert a frictional shear force on the torsion fluid  226  and/or the inertia ring  224 , or the torsion fluid  226  may exert a frictional/shear force on the inertia ring  224 , thereby applying a torque on the inertia ring  224 . This may urge the inertia ring  224  to rotate in the first direction. The collar  214  and the housing  220  may then oscillate and thereby move in a second direction (or in the first direction at a different speed). This may cause an opposite or reduced rotational force on the torsion fluid  226  and the inertia ring  224 , or a reduced or increased rotational force. However, because the inertia ring  224  is rotating in the first direction at a given speed, the inertia ring  224  may resist rotation in the second direction or resist an increase/decrease in speed. This resistance to rotational change may exert a counter-torque on the housing  220  and the collar  214 . This counter torque may reduce the amplitude or frequency of the oscillation of the collar  214 , which may reduce fatigue on components connected to the collar  214 , reduce damage and wear, extend the life of components connected to the collar  214 , or more efficiently transfer energy through the collar  214  to the bit  210 . 
     In some embodiments, the mass of the inertia ring  224  may affect the resistance to rotation of the inertia ring  224  and the damping effect of the inertia ring  224 . The mass of the inertia ring  224  may be affected by its physical size and construction or the density. For example, a larger inertia ring  224  has greater mass than a smaller inertia ring  224  of the same material, which can change the damping effect of the inertia ring  224 . In  FIG.  2   , the inertia ring  224  has a height  234 , which is the distance between axially lower surface  235  and axially upper surface  236  of the inertia ring  224 . In some embodiments, the height  234  may be in a range having a lower value, an upper value, or lower and upper values including any of 1 in. (2.54 cm), 2 in. (5.01 cm), 3 in. (7.62 cm), 5 in. (12.7 cm), 7.5 in. (19.05 cm), 10 in. (25.4 cm), 12 in. (30.48 cm), 2 ft. (0.61 m), 5 ft. (1.52 m), 10 ft. (3.05 m), 20 ft. (6.10 m), 30 ft. (9.14 m), or any value therebetween. For example, the height  234  may be greater than 1 in. (2.54 cm). In another example, the height  234  may be less than 30 ft. (9.14 m). In yet other examples, the height  234  may be any value in a range between 1 in. (2.54 cm) and 30 ft. (9.14 m), such as between 2 in. (5.01 cm) and 10 in. (25.4 cm) or between 2 in. (5.01 cm) and 7.5 in. (19.05 cm). In other examples, the height  234  may be greater than 30 ft. (9.14 m) or less than 1 in. (2.54 cm). 
     The inertia ring  224  also has a cross-sectional width which is the difference between an inner radius  238  and an outer radius  240  of the inertia ring  224 . In some embodiments, the inner radius  238  may be in a range having a lower value, an upper value, or lower and upper values including any of 1.0 in (2.54 cm), 1.5 in. (3.81 cm), 2.0 in. (5.08 cm), 2.5 in. (6.35 cm), 3.0 in. (7.62 cm), 3.5 in. (8.89 cm), 4.0 in. (10.16 cm), 5.0 in. (12.7 cm), 5.5 in. (13.97 cm), 6.0 in. (15.24 cm), 10 in. (25.4 cm), 15 in. (38.1 cm), or any value therebetween. For example, the inner radius  238  may be greater than 1.5 in. (3.81 cm). In another example, the inner radius  238  may be less than 15 in. (38.1 cm). In yet other examples, the inner radius  238  may be any value in a range between 1.0 in. (2.54 cm) and 15 in. (38.1 cm), and may be between 2.0 in. (5.8 cm) and 6.0 in. (15.24 cm), or between 2.5 in. (6.35 cm) and 5.0 in. (12.7 cm). In some examples, the inner radius  238  may be less than 1.0 in. (2.54 cm) or greater than 15 in. (38.1 cm). 
     In some embodiments, the outer radius  240  may be in a range having a lower value, an upper value, or lower and upper values including any of 1.5 in. (3.81 cm), 2.0 in. (5.08 cm), 2.5 in. (6.35 cm), 3.0 in. (7.62 cm), 3.5 in. (8.89 cm), 4.0 in. (10.16 cm), 5.0 in. (12.7 cm), 6.0 in. (15.24 cm), 10 in. (25.4 cm), 15 in. (38.1 cm), 20 in. (50.8 cm), or any value therebetween. For example, the outer diameter  240  may be greater than 1.5 in. (3.81 cm). In another example, the outer diameter  240  may be less than 20 in. (50.8 cm). In yet other examples, the outer diameter  240  may be any value in a range between 1.5 in. (3.81 cm) and 20 in. (50.8 cm), such as between 1.5 in. (3.81 cm) and 12.5 in. (31.75 cm), or between 3.5 in. (8.98 cm) and 10 in. (25.4 cm). In some examples, the outer diameter  240  may be less than 1.5 in. (3.81 cm) or greater than 20 in. (50.8 cm). 
     The mass of the inertia ring  224  is determined by the shape, size, and density of the material of the inertia ring  224 . In some embodiments, the inertia ring  224  includes or is made from tungsten alloys, steel alloys, aluminum alloys, any other metal alloy, ceramics, carbides, other non-metallic materials, or combinations of the foregoing. In some embodiments, the inertia ring  224  is a unitary component. 
     In the embodiment shown, the inertia ring  224  may passively rotate, that is to say the inertia ring  224  rotates in response to the motion of the collar  214  or the housing  220 . For instance, frictional or shear forces on the fluid  226  may cause the inertia ring  224  to rotate. In some embodiments, passively rotated inertia rings  224  may reduce the overall length of the inertia damping system  212 , and may be relatively easy to install with reduced cost. This may increase the locations in which the inertia damping system  212  may be used. Furthermore, because the inertia rings  224  may be passively rotated, individual inertia rings  224  may be placed in or on different downhole tools without lengthening the tool or BHA. In other embodiments, active or energized inertia rings  224  can rotate even without movement of the collar  214  or the housing  220 . 
     In some embodiments, the interior space  222  may be larger than the inertia ring  224 . The torsion fluid  226  may fill the space, or gap  242 , between the walls of the interior space  222  and the inertia ring  224 . In some embodiments, the gap  242  may help to determine the amount of oscillation damping provided by the torsion fluid  226 . The gap  242  is shown as a radial gap and as being relatively constant between the inertia ring  224  and the inner wall  228  and the outer wall  230 . In some embodiments, however, the gap  242  may not be constant. For instance, as a BHA (e.g., BHA  106 ) bends during a directional application, the gap  242  may change and cause some portions of the inertia ring  224  to become closer to the outer wall  230 . Thus, the gap  242  should be considered an average gap, or half the difference between the width of the inertia ring  224  and the width of the interior space  222 . Additionally, while the inertia ring  224  and interior space  222  are schematically shown as having linear surfaces in cross-section as when the inertia ring  224  is formed as a rectangular toroid, any or all of such surfaces may be curved or contoured in other embodiments (e.g., the inertia ring  224  may be a torus). 
     In some embodiments, the gap  242  may be in a range having a lower value, an upper value, or lower and upper values including any of 0.0001 in. (2.54 μm), 0.0005 in. (12.7 μm), 0.001 in. (25.4 μm), 0.002 in. (50.8 μm), 0.003 in. (76.2 μm), 0.004 in. (101.6 μm), 0.005 in. (127.0 μm), 0.006 in. (152.4 μm), 0.007 in. (177.8 μm), 0.008 in. (203.2 μm), 0.009 in. (228.6 μm), 0.010 in. (254.0 μm), 0.050 in. (0.127 cm), 0.10 in. (0.25 cm), 0.5 in. (1.27 cm), 1 in. (2.54 cm), 2 in. (5.08 cm), 3 in. (7.62 cm), 4 in. (10.2 cm), 5 in. (12.7 cm), or any value therebetween. For example, the gap  242  may be greater than 0.0001 in. (2.54 μm). In another example, the gap  242  may be less than 5 in. (12.7 cm). In yet other examples, the gap  242  may be any value in a range between 0.0001 in. (2.54 μm) and 5 in. (12.7 cm), such as between 0.0005 in. (12.7 μm) and 0.25 in. (6.35 mm). 
     As discussed herein, the inertia element  224  may help to damp torsional oscillations of the housing  214 . The damping of torsional oscillations may be modeled as energy dissipated in a single vibration cycle. The energy dissipated in a single vibration (E loss ) may be modeled according to Eq. 1: 
     
       
         
           
             
               
                 
                   
                     
                       E 
                       loss 
                     
                     = 
                     
                       
                         π 
                         ⁢ 
                         
                           C 
                           
                             t 
                             ⁢ 
                             o 
                             ⁢ 
                             r 
                           
                         
                         ⁢ 
                         
                           v 
                           
                             h 
                             ⁢ 
                             s 
                             ⁢ 
                             g 
                           
                           2 
                         
                         ⁢ 
                         
                           J 
                           r 
                           2 
                         
                         ⁢ 
                         ω 
                       
                       
                         
                           
                             
                               J 
                               r 
                               2 
                             
                             ⁢ 
                             
                               ω 
                               2 
                             
                           
                           + 
                           
                             C 
                             
                               t 
                               ⁢ 
                               o 
                               ⁢ 
                               r 
                             
                             2 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   Eq 
                   . 
                       
                   1 
                 
               
             
           
         
       
     
     where C tor  is the torsional damping coefficient, V hsg  is the rotational velocity of the housing, ω is the angular velocity, and J r  is the rotational inertia of the inertia element  224 . The torsional damping coefficient (C tor ) may be determined according to Eq. 2: 
     
       
         
           
             
               
                 
                   
                     
                       C 
                       tor 
                     
                     = 
                     
                       
                         
                           2 
                           ⁢ 
                           πμ 
                           ⁢ 
                           
                             D 
                             ⁡ 
                             ( 
                             
                               
                                 r 
                                 2 
                                 3 
                               
                               + 
                               
                                 r 
                                 1 
                                 3 
                               
                             
                             ) 
                           
                         
                         h 
                       
                       + 
                       
                         
                           πμ 
                           ⁡ 
                           ( 
                           
                             
                               r 
                               2 
                               4 
                             
                             - 
                             
                               r 
                               1 
                               4 
                             
                           
                           ) 
                         
                         h 
                       
                     
                   
                   , 
                 
               
               
                 
                   Eq 
                   . 
                       
                   2 
                 
               
             
           
         
       
     
     where μ is the viscosity of the torsion fluid  226 , D is the height  234 , r 1  is the inner radius  238 , r 2  is the outer radius  240 , and h is the gap  242 . The rotational inertia (e.g., J r ) may be determined according to Eq. 3: 
     
       
         
           
             
               
                 
                   
                     
                       J 
                       r 
                     
                     = 
                     
                       
                         m 
                         ⁡ 
                         ( 
                         
                           
                             r 
                             1 
                             2 
                           
                           + 
                           
                             r 
                             2 
                             2 
                           
                         
                         ) 
                       
                       2 
                     
                   
                   , 
                 
               
               
                 
                   Eq 
                   . 
                       
                   3 
                 
               
             
           
         
       
     
     where m is the mass of the inertia element  224 . As may be seen through an analysis of Eq. 2 and Eq. 3, changing the size of the inertia element  224  may change the inertial properties of the inertia element  224 . For example, increasing r 2  may increase C tor  and J r . In some embodiments, m may be changed without affecting C tor . For example, the density of the inertia element  224  may be increased. For the same size inertia element  224 , this would increase m, thereby increasing J r , while C tor  remains the same. Furthermore, changing the properties of the inertia fluid  226  may change C tor  while J r  remains unchanged. For example, increasing p may increase C tor . 
     An analysis of Eq. 1 shows that E loss  may be changed by changing one or both of C tor  and J r . If the energy of the oscillations is known or predictable, then the energy loss from the inertia damping system  212  may be optimized to the oscillation energy. In this manner, an operator may change the properties of the inertia damping system  212  (e.g., size and/or density of the inertia element  224 , properties of the inertia fluid  226 ) to optimize boss for a given application. 
     In at least one embodiment, the inertia element  224  has a D of 6 in. (15.2 cm), r 1  of 1.3 in. (3.3 cm), r 2  of 2 in. (5.1 cm), h of 0.005 in. (0.127 mm), and μ of 2,400 cSt. Inserting these values into Eq. 1, Eq. 2, and Eq. 3 provides result in an E loss  of about 0.25 lbf-ft.s/rad. If μ is changed to 12,000 cSt, then E loss  of about 1.25 lbf-ft.s/rad. 
     The bit has a bit energy (e.g., W bit ), which is the amount of energy that the bit adds to the oscillation system. The bit energy may be determined according to Eq. 4: 
     
       
         
           
             
               
                 
                   
                     
                       W 
                       
                         b 
                         ⁢ 
                         i 
                         ⁢ 
                         t 
                       
                     
                     = 
                     
                       
                         
                           T 
                           amp 
                         
                         ⁢ 
                         
                           v 
                           
                             b 
                             ⁢ 
                             i 
                             ⁢ 
                             t 
                           
                         
                         ⁢ 
                         π 
                       
                       ω 
                     
                   
                   , 
                 
               
               
                 
                   Eq 
                   . 
                       
                   4 
                 
               
             
           
         
       
     
     where T amp  is the amplitude of the oscillation torque and v bit  is the oscillation velocity amplitude of the bit. Based on the E loss  and the W bit , the system has an energy dissipation ratio, which may be determined according to Eq. 5: 
     
       
         
           
             
               
                 
                   
                     Energy 
                     ⁢ 
                         
                     Dissipation 
                     ⁢ 
                         
                     Ratio 
                   
                   = 
                   
                     
                       
                         E 
                         
                           l 
                           ⁢ 
                           o 
                           ⁢ 
                           s 
                           ⁢ 
                           s 
                         
                       
                       
                         W 
                         
                           b 
                           ⁢ 
                           i 
                           ⁢ 
                           t 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   Eq 
                   . 
                       
                   5 
                 
               
             
           
         
       
     
     In some embodiments, the energy dissipation ratio may be a representation of the amount of torsional oscillation energy damped by the inertia damping system  212 . In some embodiments, the energy dissipation ratio may be in a range having a lower value, an upper value, or lower and upper values including any of 1%, 5%, 10%, 15%, 20%, 25%, 50%, 75%, 95%, or any value therebetween. For example, the energy dissipation ratio may greater than 1%. In some examples, the energy dissipation ratio may be less than 95%. In some examples, the energy dissipation ratio may be any value in a range between 1% and 95%, such as between 1% and 10%, or between 5% and 20%. In other embodiments, the energy dissipation ratio may be less than 1% or greater than 95%. 
     In the embodiment shown, the inertia damping system  212  includes two dampers  218 . However, it should be understood that the inertia damping system  212  may include more or fewer than three dampers. For example, the inertia damping system  212  may include one, two, three, four, five, six, seven, eight, nine, ten, or more dampers  218 . 
     In the embodiment shown, each damper  218  is immediately longitudinally adjacent to another damper  218 . In other words, the upper wall  233  of a first damper  218  is contacting the lower surface  232  of a second damper. In some embodiments, the wall  233  of the first damper  218  may be the lower surface  232  of the second damper  218 . In other embodiments, there may be a space or gap between dampers  218  (see  FIG.  3   ). 
       FIG.  3    (composed of  FIGS.  3 - 1  and  3 - 2   ) includes a cross-sectional view of a torsional damping system  312  ( FIG.  3 - 1   ), along with a representation of a torsional oscillation profile  350  of a downhole tool ( FIG.  3 - 2   ), according to at least one embodiment of the present disclosure. The oscillation profile  350  shows the rotational speed oscillation magnitude  352  increasing along the x-axis and the distance  354  from the bit  310  increasing along the y-axis. An undamped oscillation profile  356  may represent the oscillation profile of a sample collar. The undamped oscillation profile  356  may have an oscillation peak  358 , which may represent the maximum oscillation magnitude of the undamped oscillation profile  356 . A damped oscillation profile  364  may represent the oscillation profile of the sample collar after damping. As the damped oscillation profile  364  shows when compared to the undamped oscillation profile  356 , by utilizing one or more dampers, the oscillations of the collar may be reduced across the length of the profile. 
     The oscillation peak  358  of the undamped profile may occur at a peak distance  361  from the bit  310 . The location of the bit is represented as point  362  in the profile  350 . The peak distance  361  can be represented as a percentage of the motor distance  363 , which is the distance between the bit location  362  and a downhole motor location  360 . The percentage of the motor distance can be determined by dividing the peak distance  361  by the motor distance  363 . In some embodiments, the peak location percentage may be in a range having a lower value, an upper value, or lower and upper values including any of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, or any value therebetween. For example, the peak percentage may greater than 10%. In some examples, the peak percentage may be less than 90%. In some examples, the peak percentage may be any value in a range between 10% and 90%, such as between 20% and 80%, or between 50% and 70%. In some embodiments, the peak percentage may be 0% (i.e., the oscillation peak  358  is located at the bit location  362 ). In some embodiments, the peak percentage may be 100% (i.e., the oscillation peak  358  is located at the downhole motor location  360 ). In some embodiments, the undamped oscillation profile  356  may include more than one oscillation peak  358 . 
     The torsional damping system  312  of  FIG.  3 - 1    is shown to the left of the oscillation profile  350  in  FIG.  3 - 2    and has the same longitudinal scale as the oscillation profile  350 . While the torsional damping system  312  shown includes a downhole motor  311 , a bit  310 , and three dampers  318 - 1 ,  318 - 2 ,  318 - 3  (collectively dampers  318 ), it should be understood that the torsional damping system  312  may include additional or different downhole tools that may be found in a BHA or drill string, different numbers of dampers, and the like. 
     In the embodiment shown, the first damper  318 - 1  is placed between the bit  310  and the motor  311 . For instance, the first damper  318 - 1  may be placed at or near the location of the oscillation peak  358  on the oscillation profile  350 . When placed near the location of the oscillation peak  358 , the distance between the axial center of the first damper  318 - 1  and the oscillation peak  358  may be less than 2%, less than 5%, or less than 10% of the motor distance  363 . Placing the first damper  318 - 1  at (or near) the oscillation peak  358  may provide the greatest reduction in the frequency or amplitude of the oscillations in some embodiments. As seen in the oscillation profile  356 , the oscillation peak  358  in this embodiment is located nearer the downhole motor location  360  of the downhole motor  311  than the bit location  362  of the bit  310 . Thus, the first damper  318 - 1  may be placed closer to the downhole motor  311  than the bit  310 . To further reduce the oscillations near the oscillation peak  358 , a second damper  318 - 2  may be placed between the first damper  318 - 1  and the downhole motor  311  (and thus also nearer the downhole motor  311  than the bit  310 ). By clustering the dampers  318  at or near the oscillation peak  358 , the magnitude or frequency of the oscillations may be further reduced. In some embodiments, a third damper  318 - 3  may be placed at a location between the downhole motor  311  and the bit  310 . For example, the third damper  318 - 3  may be placed closer to the bit  310  than to the downhole motor  311 , or even closer to the bit  310  than to the first damper  318 - 1 . Furthermore, in some embodiments, any number of dampers  318  may be placed between the bit  310  and the downhole motor  311 . Spacing between the dampers  318  may be irregular as shown in  FIG.  3   , or there may be regular intervals/spacing between dampers. In some embodiments, irregular spacing between dampers  318  may generally reflect the oscillation profile  350 . For instance, the greater the distance  354  and magnitude  352  between points on the oscillation profile  350 , the greater the separation distance in the torsional damping system  312 . 
     As discussed herein, in some embodiments, the first damper  318 - 1  may be placed near the oscillation peak  358  with a peak damper placement defined as a percentage of the motor distance  363 . In some embodiments, the peak damper placement may be in a range having a lower value, an upper value, or lower and upper values including any of 0.5%, 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 15%, 20%, 25%, or any value therebetween. For example, the peak percentage may greater than 0.5%. In some examples, the peak damper placement may be less than 25%. In some examples, the peak damper placement be may be any value in a range between 0.5% and 25%, such as between 0.5% and 10%, or between 1% and 7%. In some embodiments, the peak damper placement may be 0% (i.e., the first damper  318 - 1  is located at oscillation peak  358 ). In some embodiments, it can be critical to performance of the torsional damping system  312  that the peak damper placement is within 10% to dampen the oscillation peak  358 . In some embodiments, a single damper  318  may be placed within the peak damper placement. In other embodiments, a plurality of dampers  318  may be placed within the peak damper placement to further dampen the oscillation peak  358 . 
     In some embodiments, placing dampers  318  at or near the oscillation peak  358  may cause the oscillation peak  358  to change locations, and to potentially change magnitude. For example, the dampers  318  may reduce the oscillations at the location of the oscillation peak  358  such that a different location may experience the highest oscillations on the BHA or drill string. In some embodiments, an oscillation peak  358  may be identified during downhole drilling operations or through simulation. The dampers  318  located at or near the peak may include a magnetorheological torsion fluid, an electrorheological torsion fluid, or any other suitable fluid. In some embodiments, by applying a magnetic field to a magnetorheological fluid (or an electrical field to an electrorheological fluid), the density of the torsion fluid may be changed, which may change (and potentially increase) the oscillation damping. 
     In some embodiments, the dampers  318  may be evenly placed between the bit  310  and the downhole motor  311 , or evenly spaced along a portion of the distance between the bit  310  and the motor  311 . Evenly spaced dampers  318  may help to damp oscillations across an entirety of the distance between the downhole motor  311  and the bit  310 , or an entirety of the distance covered. In some embodiments, evenly spaced dampers  318  may be used for oscillation profiles  356  that change depending on the downhole tools being used or the drilling conditions. 
     In some embodiments, the oscillation peak  358  may be located above the downhole motor  311 . In some embodiments, dampers  318  may be placed at any location along the drill string, including above the downhole motor  311 . Of course, in some embodiments, a damper  318  may be used in a BHA or drill string that does not include a downhole motor. In such case, the position of the damper relative to an oscillation peak may be measured in relation to other components (e.g., distance between bit and LWD, between bit and reamer, between bit and RSS, etc.). 
       FIG.  4 - 1    is a transverse cross-sectional view of a first damper  418 - 1  and a second damper  418 - 2  according to some embodiments. As may be seen, the collars  414 - 1 ,  414 - 2  (collectively  414 ), the housing  420 , and the inertia rings  424 - 1 ,  424 - 2  (collectively  424 ) can have annular cross-sectional shapes. In this manner, the inertia ring  424  may freely rotate within the housing  420 . Of course, the inertia ring  424  may have different shapes, including partial rings as discussed herein. 
     The housing  420  can define or otherwise include a central bore  444 . Drilling fluid may flow through the central bore  444 . In some embodiments, as the inertia ring  424  rotates, heat is generated in the torsion fluid  426 , the housing  420 , or the inertia ring  424 . The drilling fluid flowing through the central bore  444  may cool the housing  420 , the inertia ring  424 , and the torsion fluid  426 , and may act as a heat sink for the torsional damping system  412 . 
     The first damper  418 - 1  may be located at a different longitudinal location than the second damper  418 - 2 . For example, the first damper  418 - 1  may be located at or near an oscillation peak (e.g., oscillation peak  358  of  FIG.  3   ). The collar  414  may oscillate in response to downhole conditions and operations, and the first damper  418 - 1  and the second damper  418 - 2  may be connected to the same collar  414 ; however, the position of collar  414 - 1  may oscillate with a different oscillation energy, including amplitude, frequency, or direction, than the position at collar  414 - 2 . In some embodiments, the first damper  418 - 1  and the second damper  418 - 2  may have identical construction (e.g., same mass, fluid, size, density, etc.), although they may have different constructions in other embodiments. 
     During operation, the collar  414  may oscillate and rotate in a first collar direction  437 . First collar direction  427  is shown in a reference frame relative to the surrounding formation. The inertia ring  424  in  FIG.  4 - 1    is not rotationally fixed to the housing  420  or the collar  414  and may therefore not rotate in sync with the collar  414 . As the collar  414  and housing  420  rotate, the housing  420  can exert a frictional/shear torque in the first collar direction  437  on the torsion fluid  426 , which may transfer the frictional torque in the first collar direction  437  to the inertia ring  424 . The inertia ring  424  may, however, initially resist rotation such that the collar  414  rotates while the inertia ring  424  remains rotationally stationary or has a relative stationary position. 
     In some embodiments, the first inertia ring  424 - 1  may rotate or otherwise move with a different rotational energy than the second inertia ring  424 - 2 . This may be a result of different oscillation energy of the collar  414 - 1  at the first inertia ring  424 - 1  than of the collar  414 - 2  at the second inertia ring  424 - 2 . For example, in the embodiment shown in  FIG.  4 - 1   , oscillation and movement of the collar  414 - 1  has caused the first inertia ring  424 - 1  to rotate in the first ring direction  439  relative to the surrounding formation, by imparting at least some energy to the first inertia ring  424 - 1  through the housing  420  and torsion fluid  426 . This may reduce the amplitude and/or the frequency of the oscillation of the collar  414 - 1 . In the embodiment shown, the collar  414 - 2  is rotating in the first collar direction  437  at the second damper  418 - 2 , but the second inertia ring  424 - 2  has not been caused to rotate by the collar  414 - 2 . Thus, the first inertia ring  424 - 1  may be rotating while the second inertia ring  424 - 2  may not rotate, may rotate at a different magnitude, or may rotate in a different direction. It should be understood that, in some embodiments, the first inertia ring  424 - 1  may not rotate/move, and the second inertia ring  424 - 2  may rotate/move. 
     In  FIG.  4 - 2   , the oscillation of the collar  414 - 2  at the second damper  418 - 2  has caused the second inertia ring  424 - 2  to rotate in the first collar direction  439 . The collar  414 - 1  at the first damper  418 - 1  may still be rotating in the first collar direction  439  and imparting at least a portion of its energy to the first inertia ring  424 - 1 , which may rotate in the first collar direction  439  at the same or different rate of rotation as the second inertia ring  424 - 2 . 
     In  FIG.  4 - 3   , the oscillation of the collar  414  at the first damper  418 - 1  and the second damper  418 - 2  has stopped. For example, the oscillation of the collar  414  may be at a point between rotational directions. However, the mass of the first inertia ring  424 - 1  and the second inertia ring  424 - 2  may cause the first inertia ring  424 - 1  and the second inertia ring  424 - 2  to continue to rotate in the first collar direction  439 . In this manner, the first inertia ring  424 - 1  and the second inertia ring  424 - 2  may continue to impart energy to the collar  414  for a time, even after the collar  414  has stopped rotating. 
     In  FIG.  4 - 4   , the second inertia ring  424 - 2  has stopped rotating and the first inertia ring  424 - 1  is still rotating. This may result from the amount of energy imparted to the first inertia ring  424 - 1  by the collar  414 - 1  being greater than the amount of energy imparted to the second inertia ring  424 - 2  by the collar  414 - 2 . In this manner, including a plurality of dampers  418  may allow the dampers  418  to damp different oscillation energies at different locations. This may help to damp oscillation across the length of the collar, drill string, or BHA. 
     In  FIG.  4 - 5   , the collar  414  at both the first damper  418 - 1  and the second damper  418 - 2  is oscillating in a second collar direction  441 , which is opposite the direction of the first collar direction  437  of  FIGS.  4 - 1  and  4 - 2   . The first inertia ring  424 - 1  may retain at least a portion of the rotational energy imparted to it by the collar  414 - 1  before the collar  414 - 1  oscillation causes rotation in the second collar direction  441 . Thus, the collar  414 - 1  may impart at least a portion of its rotational energy to the first inertia ring  424 - 1  and the first inertia ring  424 - 1  may impart at least a portion of its rotational energy to the collar  414 - 1 . This may reduce the oscillation energy of the collar  414 - 1 , thereby reducing the amplitude or the frequency of the oscillation of the collar  414 - 1 . In  FIG.  4 - 5   , the collar  414 - 2  at the second damper  418 - 2  may not have caused the second inertia ring  424 - 2  to yet rotate. Thus, the collar  414 - 2  may impart at least a portion of its rotational energy to cause the second inertia ring  424 - 2  to rotate, thereby damping at least a portion of the oscillation of the collar  414 - 2 . 
     In  FIG.  4 - 6   , the collar  414 - 2  has imparted enough oscillation energy to the second inertia ring  424 - 2  to cause the second inertia ring  424 - 2  to rotate in the second ring direction  243 . The first inertia ring  424 - 1  may still be rotating in the first ring direction  439 . Thus, depending on the different oscillation energy of the collar  414  at the first damper  418 - 1  and the second damper  418 - 2 , the first inertia ring  424 - 1  and the second inertia ring  424 - 2  may rotate in different directions. 
     In  FIG.  4 - 7   , the collar  414 - 1  at the position of the first damper  418 - 1  may oscillate in a different rotational direction than the collar  414 - 2  at the position of the second damper  418 - 2 . In other words, the collar  414 - 1  may vibrate in a manner causing rotation in the first collar direction  437  and the collar  414 - 2  may vibrate in a manner causing rotation in the second collar direction  441 . As described herein, the collar  414 - 1  and the first inertia ring  424 - 1  may impart at least a portion of their energy to each other, thereby at least partially reducing the oscillation of the collar  414 - 1 . Similarly, the collar  414 - 2  and the second inertia ring  424 - 2  may impart at least a portion of their energy to each other, thereby at least partially reducing the oscillation of the collar  414 - 2 . Because the first damper  418 - 1  and the second damper  418 - 2  are separate dampers  418 , then each damper  418  may damp oscillations of the collar  414  in a manner unique to the damper&#39;s  418  location. In this manner, including a plurality of dampers  418  may reduce the oscillation of the collar  414  along the length of the collar  414 . The collar  414 - 1  and collar  414 - 2  may also be the same collar, but can reflect different axial/longitudinal positions along the collar. 
     Referring now to  FIG.  5 - 1   , in some embodiments, a first inertia ring  524 - 1  of a first damper  518 - 1  may have a different mass than a second inertia ring  524 - 1  of a second damper  518 - 2 . For example, the first inertia ring  524 - 1  may have a greater mass than the second damper  518 - 2  on account of use of a material having different density, or having a different size or shape. Thus, when the collar  514  rotates in the first collar direction  537  within a torsion fluid  526 , the first inertia ring  524 - 1  may take longer to begin rotating than the second inertia ring  524 - 2 . Accordingly, the second inertia ring  524 - 2  may begin to rotate in the first ring direction  539  before the first inertia ring  524 - 1 . This may be because the first inertia ring  524 - 1  may take more energy to start rotating than the second inertia ring. 
     As may be seen in  FIG.  5 - 2   , the collar  514  may impart sufficient rotational energy to the first inertia ring  524 - 1  to cause the first inertia ring  524 - 1  to begin rotating in the first ring direction  539 . Because the first inertia ring  524 - 1  is more massive than the second inertia ring, the collar  514  may impart more energy to the first inertia ring  524 - 1  (or more energy may be used to cause movement of the first inertia ring  524 - 1 ), and therefore the first inertia ring  524 - 1  may damp the oscillations of the collar  514  to a greater extent than the second inertia ring  524 - 2 . 
     In  FIG.  5 - 3   , the rotation of the collar  514  has stopped and the second inertia ring  524 - 2  has transferred all of its energy to the collar  514  and stopped rotating as well. In some embodiments, because the first inertia ring  524 - 1  is more massive than the second inertia ring, the first inertia ring  524 - 1  may take longer to stop rotating in the first ring direction  539 . In this manner, the first inertia ring  524 - 1  may continue to transfer its rotational energy to the collar  514 . 
     In  FIG.  5 - 4   , the collar  514  is oscillating in the second collar direction  541 . The first inertia ring  524 - 1  may continue to rotate in the first ring direction  539 . In some embodiments, the collar  514  may cause the second inertia ring  524 - 2  to rotate in the second ring direction  543 . The first inertia ring  524 - 1  and the second inertia ring  524 - 2  may impart their respective rotational energy to the collar  514  to damp the oscillations of the collar. Because the first inertia ring  524 - 1  has a different mass than the second inertia ring  524 - 2 , the first inertia ring  524 - 1  may rotate in a different direction than the second inertia ring  524 - 2  at a particular moment in time, even if undergoing the same oscillation. This may increase the damping of the magnitude or frequency of oscillations of the collar. This may reduce damage to downhole tools, thereby saving time and money associated with tool repair. 
     It should be understood that an oscillation may include any change in rotational energy. Changes in rotational energy may include changes in rotational direction, changes in rotational rate, changes in oscillation frequency, changes in oscillation amplitude, and combinations thereof. Thus, embodiments of the present disclosure may include oscillations from the first collar direction to the first collar direction with a different rotational rate, oscillations from the first collar direction to no rotation, oscillations from the first collar direction to the second collar direction, oscillations from the second collar direction to the second collar direction with a different rotational rate, oscillations from the second collar direction to no rotation, and oscillations from the second collar direction to the first collar direction. Similarly, these varied oscillations in the collar may cause the inertia ring to change direction from the first ring direction to the second ring direction, to change the rotational rate of the inertia ring in the first ring direction, to change the rotation of the inertia ring from the first ring direction to no rotation, to change the rotational rate of the inertia ring in the second ring direction, to change the rotation of the inertia ring from the second ring direction to no rotation, or to change the rotation of the inertia ring from the second ring direction to the first ring direction. 
       FIG.  6    is a representation of a torsional damping system  612 , according to at least one additional embodiment of the present disclosure. In the embodiment shown, the plurality of dampers  618  are longitudinally separated from each other. In other words, there is a damper spacing  646  between a first damper  618 - 1  and a second damper  618 - 2  (collectively dampers  618 ), which may be a percentage of the total inertia damper height  648 . In some embodiments, the damper spacing  246  may be in a range having a lower value, an upper value, or lower and upper values including any of 0%, 2.5%, 5%, 10%, 25%, 50%, 75%, 100%, 150%, 200%, 300%, or any value therebetween. For example, the damper spacing  646  may be less than 300% of the damper height  648 . In some examples, the damper spacing  646  may be greater than 0%, 5%, 10%, or 300% of the damper height  648 . Where the dampers  618  have different heights  648 , the damper spacing  646  may be determined as a function of the damper  618  having a lesser height  648 . 
     In some embodiments, the damper spacing  646  may be determined based on the location(s) of the maximum oscillations. In some embodiments, at least three dampers  618  may be evenly spaced (e.g., have the same damper spacing  646 ) along the collar  614 . In some embodiments, the dampers  618  may be unevenly spaced (e.g., have different damper spacing  646 ). In some embodiments, the dampers  618  may be spaced based on an oscillation profile of the collar  614  to place the dampers  618  where the oscillation is the highest or where peaks are observed or expected. 
       FIG.  7    is a representation of a torsional damping system  712  according to at least one additional embodiment of the present disclosure. In the embodiment shown, a single housing  714  includes a plurality of inertia rings  724 - 1 ,  724 - 2  (collectively  724 ). The housing  714  includes an interior space  722 . A plurality of inertia rings  724  may be installed in the interior space  722 . For example, the first inertia ring  724 - 1  may be located longitudinally uphole of the second inertia ring  724 - 2  inside the interior space  722 . A torsion fluid  726  may be located in the interior space  722  between the housing  714  and the inertia rings  724 . In some embodiments, the torsion fluid  726  may be located between the first inertia ring  724 - 1  and the second inertia ring  724 - 2 . Optionally, one or more spacers  729  may be used to separate the first and second inertia rings  724 - 1 ,  724 - 2 . Including a plurality of inertia rings  724  in a single housing  714  may simplify the torsional damping system  712 , which may simplify installation and maintenance. Of course, there may also be multiple interior spaces  722  defined by a single housing  714 , and each interior space  722  may include one or more inertia rings  724 . 
     In some embodiments, the first inertia ring  724 - 1  and the second inertia ring  724 - 2  may rotate independently relative to each other, with a different rotational rate or direction. The first inertia ring  724 - 1  and the second inertia ring  724 - 2  may have the same or different mass, shape/construction, or the like. For example, the first inertia ring  724 - 1  may be larger than the second inertia ring  724 - 2  or include a more dense material. In some examples, the first inertia ring  724 - 1  may be smaller than the second inertia ring  724 - 2  or include a less dense material. 
     In some embodiments, the inertia rings  724  may include one or more slots or channels  731  on the surfaces of the inertia rings  724 - 1 ,  724 - 2 . These slots or channels may facilitate movement of the torsion fluid  726  throughout the space between the housing  714  and the inertia rings  724 , and between the first inertia ring  724 - 1  and the second inertia ring  724 - 2 . Including slots or channels on the inertia rings  724  may further facilitate heat transfer in the torsion fluid  726  and in the inertia rings  724 . In some embodiments, a pressure differential may exist between portions of the interior space  722 . Slots or channels  731  in the inertia rings  724  or spacers  729  may facilitate pressure compensation throughout the interior space  722 . 
       FIG.  8 - 1    is a cross-sectional view of another torsional damping system  812  according to at least one additional embodiment of the present disclosure. In the embodiment shown, the torsional damping system  812  includes a collar  814  and six inertia elements  824 , which are optionally formed as rings as discussed herein. The number of inertia elements  824  is merely illustrative, and may include more or fewer than six inertia elements  824 . 
     The torsional damping system  812  is conceptually similar to the torsional damping system  712  schematically shown in  FIG.  7    in that multiple inertia elements  824  are included within a housing, but additional features and various alternative aspects are also shown. For instance, rather than using a single, integral element for a housing of the multiple inertia elements  824 , the housing may be formed by multiple components that collectively define an interior space for the torsion fluid and the inertia elements  824 . In particular, in this embodiment, an interior space is defined radially between an inner shaft or mandrel  853  and the inner surface of the collar  814 . 
     The interior space depicted in  FIG.  8 - 1    also extends axially between a locking element  857  and a fluid filling fixture  861 . The example locking element  857  may a locking nut or other element that can couple the mandrel  853  or other portions of a housing to the collar  814 . For instance, the locking element  857  may couple to the mandrel  853  and load the inner assembly— including the mandrel  853  and inertia elements  824 —onto a shoulder of the outer collar  814 . 
     An optional fluid filling fixture  861  can define the upper end of the interior space in  FIG.  8 - 1   , and can also be used for filling the interior space with torsion fluid  826  (see  FIG.  8 - 2   ). This may be done with one or more fluid ports  879 . Additionally, or alternatively, one or more other ports may be used. For instance, one or more ports  880  in the collar  814  may be used to assist in filling or removing torsion fluid  826 . 
     The torsion fluid  826  contained in the interior space within the housing (or in this embodiment, the inner assembly that with the collar  814  defines a housing) may be separated from other fluid within the torsional damping system  812 . For instance, drilling fluid may flow through the bore in the mandrel  853  for delivery to a drill bit or other downhole tool, while the torsion fluid  826  (which is optionally different than the drilling fluid) is contained in the space around the inertia elements  824 . One or more plugs, valves, or the like may be used in the ports  879 ,  880  to maintain separation between the inertia fluid  826 , drilling fluid, production fluids, or other fluids. 
     The plurality of inertia elements  824  positioned in the annular space between the mandrel  853  and the collar  814 , and may rotate within the housing and collar  814 . In particular, and as discussed herein, as the collar  814  rotates and oscillates, torsion fluid  826  (see  FIG.  8 - 2   ) around the inertia elements  824  may exert frictional, shear forces on the inertia elements to cause rotation of the inertia elements  824 . As the collar  814  undergoes various changes to its rotational speed or direction (e.g., during torsional oscillations), the inertia elements  824  may rotate out of sync with the collar  814 . Due to the coupling of the mandrel  853  to the collar  814  (e.g., via the between a locking element  857 , the fluid filling fixture  861 , or both), the mandrel  853  may rotate in sync with the collar  814 . 
     To facilitate rotation of the inertia elements  824 , one or more friction reducing elements may be used within the inner assembly and housing of the torsional damping system  812 . In  FIG.  8 - 1   , for instance, an end bearing  851 - 1  is positioned axially between the uppermost inertia element  824  and the fluid filling fixture  861 . Similarly, another end bearing  851 - 2  is positioned axially between the lowermost inertia element  824  and the locking element  857 . 
     While a single inertia element  824  may be located within the housing—and in this embodiment between the end bearings  852 - 1 ,  851 - 2 —multiple inertia elements  824  are included in some embodiments. In such embodiments, one or more divider bearings  849  are optionally placed axially between adjacent inertia elements  824 . The divider bearings  849  can act as thrust bearings, radial bearings, or as both thrust and radial bearings. 
       FIG.  8 - 2    provides an enlarged view of an example divider bearing  849  in a position between two inertia elements  824 . As shown, the divider bearing  849  has a T-shaped cross-section although other shapes can be used. For instance, end bearings  851 - 1  and  851 - 2  of  FIG.  8 - 1    may have an L-shaped cross-section. In  FIG.  8 - 2   , the head of the T extends axially along the inner radial surfaces of the adjacent inertia elements  824 , while the post of the T extends radially between the collar  814  and the mandrel  853 , and along axial ends of the adjacent inertia elements  824  that are separated by the divider bearing  849 . 
     In the illustrated embodiment, a bushing  847  is fitted to the inner surface of each axial end of the inertia element  824 , and cooperates with the head of the divider bearing  849  to reduce friction as the inertia element  824  rotates relative to the collar  814 , mandrel  852 , and divider bearing  849 . The bushing  847  may be press-fit, mechanically attached, or otherwise fixed to the inertia element  824 . The bushing  847  may be formed of any suitable material, and the bushing  847  and the inertia element  824  may be formed of the same or different materials. For instance, if the inertia element  824  is formed of steel, the bushing may be or include steel, brass, bronze, titanium, tungsten, a composite, an alloy, a polymer, or the like. Of course, the inertia element  824  may be formed of other materials as discussed herein. 
     A design of the bushing  847  (or the inertia element  824  itself when there is no bushing  847 ) and the divider bearing  849  may include one or more predefined bearing clearances. Such clearances may define gaps, and can include a radial clearance  845 - 1  between an inner surface of the bushing  857  (or inner surface of the inertia element  824 ) and an outer surface of the head of the divider bearing  849 . Additionally, or alternatively, an axial clearance  845 - 2  may be formed between an axial end of the bushing  847  (or axial end of the inertia element  824 ) and a radially extending surface of the head or post of the divider bearing  849 . 
     In some embodiments, the clearances  845 - 1 ,  845 - 2  (collectively bearing clearance  845 ) may be in a range having a lower value, an upper value, or lower and upper values including any of 0.0001 in. (2.54 μm), 0.0005 in. (12.7 μm), 0.001 in. (25.4 μm), 0.002 in. (50.8 μm), 0.0025 in. (63.5 μm), 0.003 in. (76.2 μm), 0.004 in. (101.6 μm), 0.005 in. (127.0 μm), 0.006 in. (152.4 μm), 0.007 in. (177.8 μm), 0.008 in. (203.2 μm), 0.009 in. (228.6 μm), 0.010 in. (254.0 μm), 0.050 in. (0.13 cm), 0.10 in. (0.25 cm), 0.25 in. (0.64 cm), or any value therebetween. For example, the bearing clearances  845  may be greater than 0.0001 in. (2.54 μm). In another example, the bearing clearances  845  are less than 0.25 in. (0.64 cm). In yet other examples, the gap  242  may be any value in a range between 0.0001 in. (2.54 μm) and 0.25 in. (0.64 cm), such as between 0.001 in. (25.4 μm) and 0.005 in. (127.0 μm), or between 0.002 in. (50.8 μm) and 0.010 in. (254.0 μm). Additionally, while the radial clearance  845 - 1  may be the same as the axial clearance  845 - 2 , in other embodiments they may be different. For instance, the radial clearance  845 - 1  may be more or less than the axial clearance  845 - 2 . 
     An inertia element  824  may have a width (e.g., measured radially) that is less than the width of the interior space. In  FIG.  8 - 2   , the interior space is defined between the collar  814  and the outer surface of a spacer  855  coupled to the outer surface of the mandrel  853 . As shown, the spacer  855  is mounted to the divider bearing  849  (e.g., using pins). This may be used to restrict rotation of the spacers  855 , and thereby couple rotation of the spacers  855  and divider bearings  849 , which may also be rotationally coupled to one or both of the mandrel  853  or the collar  814 . In other embodiments, the spacer  855  may be removed or may be integral with the mandrel  853  or divider bearing  849 , and the mandrel  853  or the divider bearing  849  may define the interior space. 
     The reduced width of the inertia element  824  relative to the interior space may allow for various radial gaps  842 - 1 ,  842 - 2  to be formed on the inner and outer surfaces of the inertia elements  824 . At the same time, the length of the inertia elements  824  may be less than the length of the interior space between opposing divider bearings  842  (or between a divider bearing  842  and an end bearing  851 - 1 ,  851 - 2  or between other components defining an interior space). In this way, axial gaps  842 - 3 ,  842 - 4  may be formed on the upper and lower ends of the inertia elements  824 . 
     The radial gaps  842 - 1 ,  842 - 2  and axial gaps  842 - 3 ,  842 - 4  collectively define fluid gaps  842  that may be used to define the frequency response of the torsional damping system  812 . For instance, by changing the size of the fluid gaps  842 , the frequency response can be targeted for different vibration ranges. Moreover, the fluid gaps  842  can provide at least four surfaces over which the torsion fluid  826  can exert frictional/shear forces on each inertia element  824  in order to change the rotational speed or direction of the inertia element  824 . Similar to the bearing clearances  845 , the fluid gaps  842  can be varied. For instance, the radial gaps  842 - 1 ,  842 - 2  may be equal to, less than, or greater than the axial gaps  842 - 3 ,  842 - 4 . 
     In some embodiments, different inertia elements  824  may provide different frequency responses for different vibration ranges. For instance, an inertia element  824  may have a different shape, size, or material, or different fluid gaps  842  or bearing clearances  845  than another inertia element  824  within the same torsional damping system  812 —or even within the same housing. Moreover, the fluid gaps  842  and the bearing clearances  845  may not only be different, but may be different so that either or both may be changed to suit a customized set of frequency or vibration ranges. Different configurations may be arranged in any suitable manner. For instance, a dampening stage (e.g., inertia elements  824  and corresponding bearing clearance and fluid gap configuration) at one or both axial ends of the torsional damping system  812  may be different than one or each dampening stage between the end stages. In other embodiments, stages may alternate configurations. Of course, other configurations are possible, including as described herein with respect to  FIGS.  3 - 1  and  3 - 2    to target expected oscillation profiles at different locations. The various changes to inertia element and bearing materials, fluid gaps, bearing gaps, torsion fluid composition, and the like can allow the torsional dampening device to be tuned for specific oscillation profiles, downhole conditions, and operations 
     The bearings (including divider bearings  849  and end bearings  851 - 1 ,  851 - 2 ), can also have any number of other features or configurations.  FIG.  8 - 3   , for instance, is an end view of an example divider bearing  849  that is configured to allow torsion fluid  826  to flow between different stages, and optionally to push out trapped air. In particular, the divider bearing  849  includes one or more openings  881  that allow torsion fluid  826  or air to flow from the space around one inertia element  824 , through the divider bearing  849 , and into the space around an adjacent inertia element  824 . Optionally, channels  883  in one or more axial or radial surfaces of the divider bearing  849  may also facilitate fluid flow between stages. This may facilitate, for instance, filling the interior chamber using a fluid filling fixture  861  or collar port  880 , so that the torsion fluid  826  may flow along a full interior chamber within the housing of the torsional damping system  812 . 
     In other embodiments, each stage may be separated and self-contained so that fluid is contained around one inertia element  824  and does not flow to the space around another inertia element  824 . This may allow, for instance, different torsion fluids  826  to be used in different stages to target different vibration frequencies. 
     Although  FIGS.  8 - 2  and  8 - 3    shows a divider bearing  849 , one skilled in the art should appreciate that end bearings  851 - 1 ,  851 - 2  can be similarly configured. For instance, end bearings  851 - 1  and  851 - 2  can include bearing clearances, fluid gaps, and the like to allow rotation of the inertia element  824  while providing a desired frequency response. Similarly, openings, channels, or other fluid flow passages may be provided to allow fluid flow within a single dampener stage, or between different stages. 
       FIG.  9 - 1    is a representation of a transverse cross-sectional view of a torsional damping system  912 , according to at least one additional embodiment of the present disclosure. The torsional damping system  912  includes a housing  914  having one or more housing extensions  978 - 1 ,  978 - 2  (collectively housing extensions  978 ). A torsion shaft  971  is located inside the housing  914 . The torsion shaft  971  is rotatable relative to the housing  914 . The torsion shaft  971  includes one or more damping members  973 . The torsion damping members  973  may extend (e.g., protrude) from a central shaft  975  of the torsion shaft  971 . In the embodiment shown, the torsion shaft  971  includes four torsion damping members  973 . However, it should be understood that the torsion shaft  971  may include more or fewer than four torsion damping member  973 . For example, the torsion shaft  971  may include one, two, three, four, five, six, seven, eight, nine, ten, or more torsion damping members  973 . Additionally, the torsion members  973  may be spaced at equal or unequal angular intervals around the circumference of the torsion shaft  971 . 
     A resilient member  977 - 1 ,  977 - 2  (collectively  977 ) extends between adjacent housing extensions  978  and the torsion damping members  973 . In some embodiments, a first resilient member  977 - 1  may extend from a first side  980 - 1  of the torsion damping member  973  to a first housing extension  978 - 1  and a second resilient member  977 - 2  may extend from a second side  980 - 2  of the damping member  973  to a second housing extension  978 - 2 . In some embodiments, the torsional damping system  912  may include a single resilient member  977  connected to the torsion damping member  973  (or multiple resilient members  977  coupled to a single side of the damping member  973 ). In some embodiments, the resilient members  977  may cause the torsion damping member  973  to be biased toward a centered or other defined position between the first housing extension  978 - 1  and the second housing extension  978 - 2 . 
     As the torsional damping system  912  experiences torsional oscillations/vibrations, the housing  914  may rotate (e.g., in the first housing direction  937 ). This may cause the second resilient member  977 - 2  to compress, and the first resilient member  977 - 1  to expand. The compression and extension of the resilient members  977  may cause the torsion shaft  971  to rotate in the same direction as the housing  914  (e.g., in the first housing direction  937 ), and may transfer at least a portion of the energy of the housing  914  to the torsion shaft  971 . During oscillation, the housing  914  may change the rotational rate and/or the rotational direction. However, the torsion shaft  971  may continue to rotate in the first housing direction  937  until the opposing forces on the torsion damping member  973  cause the torsion shaft  971  to stop rotating and/or rotate in the opposite direction. This movement may transfer at least a portion of the energy of the torsion shaft  971  to the housing  914 . In this manner, extension and contraction of the resilient members  977  may reduce the energy of the housing  914 , thereby damping the magnitude and/or frequency of the oscillations. 
     In some embodiments, the resilient members  977  may be any resilient or biasing member. For example, the resilient members  977  may be made from one or more springs, such as coil springs, wave springs, leaf springs, Belville springs, and the like. In some examples, the resilient members  977  may be made from an elastically deformable and/or compressible material, such as rubber, silicone, plastic, and the like. In some examples, the resilient members  977  may be made from a combination of springs and elastically deformable/compressible materials. 
       FIG.  9 - 2    is a representation of a longitudinal cross-sectional view of the torsional damping system  912  of  FIG.  9 - 1    along A-A′. The depicted torsional damping system  912 - 1  includes a housing  914  that defines a torsion cavity  982  (e.g., the space between the first housing extension  978 - 1  and the second housing extension  978 - 2  in  FIG.  9 - 1   ). The torsion damping member  973 - 1  extends into the torsion cavity  982 . The resilient member  977 - 1  is connected to the torsion damping member  973  along the longitudinal length of the torsion damping member  973 . In some embodiments, the resilient member  977 - 1  extends along the entirety of the longitudinal length of the torsion damping member  973 - 1 . In some embodiments, the resilient member extends along an extension percentage of the torsion damping member  973 - 1 . In some embodiments, the extension percentage may be in a range having a lower value, an upper value, or lower and upper values including any of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% 100%, or any value therebetween. For example, the extension percentage may be greater than 10%. In another example, the extension percentage may be less than 100%. In yet other examples, the extension percentage may be any value in a range between 10% and 100%. In the embodiment shown in  FIG.  9 - 2   , the resilient member  977 - 1  is made from an elastically deformable block of material, such as rubber or silicone. However, the resilient member  977 - 1  may be made from a wave spring, a leaf spring, or any other resilient or biasing member. 
       FIG.  9 - 3    is a representation of another longitudinal cross-sectional view of another embodiment of a torsional damping system  912 - 2  taken along A-A′ of  FIG.  9 - 1   . In the embodiment shown, the torsion damping member  973 - 2  includes a plurality of resilient members  977 - 4  along the illustrated height of the torsion damping member  973 - 2 . In the embodiment shown, the torsion damping member  973 - 2  includes three resilient members  977 - 4 ; however, it should be understood that the torsion damping member  973 - 2  may include more or less than three resilient members  977 - 4 . For example, the torsion damping member  977 - 4  may include one, two, three, four, five, six, seven, eight, nine, ten, or more resilient members longitudinally aligned or otherwise positioned along the torsion damping member  973 - 2 . 
     In the embodiment shown, the torsion damping member  973 - 2  includes a plurality of torsion fluid pathways  984 . The torsion fluid pathways  984  include, in this embodiment, small holes or openings through which a torsion fluid in the cavity  982  may travel. Torsion fluid traveling through the torsion fluid pathways  984  may change the inertial properties of the torsion damping member  973 . For example, a larger number of torsion fluid pathways  984  may decrease the resistance to rotation of the torsion damping member  973 . A smaller number of torsion fluid pathways  984  may increase the resistance to rotation of the torsion damping member  973 . The torsion fluid pathways  984  can include through holes or blind holes, or may include slots or channels in a surface of the torsion shaft  971   
     FIG. 10 - 1  is a representation of a torsional damping system  1012 , according to at least one additional embodiment of the present disclosure. The torsional damping system  1012  shown includes a housing  1020  coupled to the inner surface  1016  of a collar  1014 . Although the housing  1020  is shown as extending along the inner surface  1016 , in some embodiments, the collar  1014  may itself define a housing for the torsional damping system, as described herein with reference to  FIGS.  8 - 1  and  8 - 2   . 
     In some embodiments, an interior space  1022  of the housing  1020  may be partially or fully filled with a granular material, such as a plurality of inertia beads  1066 . As the collar  1014  or the housing  1020  rotates in a first direction, the inertia beads  1066  in the interior space  1022  may be caused to rotate in the first direction. When the collar  1014  or the housing  1020  oscillate and rotate in a second direction (or at a different rate in the first direction), some or all of the inertia beads  1066  may continue to rotate in the first direction (or at a first rate). Furthermore, the inertia beads  1066  may include move uphole and downhole in response to axial vibrations in the collar  1014 . In some embodiments, the inertia beads  1066  may not move in concert (e.g., at the same time, with the same velocity). Individual inertia beads  1066  may impact, contact, bump, and jostle each other. The impact and friction between individual inertia beads  1066  with each other may dissipate energy from torsional oscillations and axial or lateral vibrations. This energy dissipation may reduce the amplitude or the frequency of the oscillations of the collar  1014 . 
     In some embodiments, the inertia beads  1066  may be fabricated from a metal alloy, including tungsten alloys, steel alloys, aluminum alloys, lead, any other metal, ceramics, carbides, sand (e.g., silica or quartz sand), other non-metal materials, or combinations thereof. 
     In some embodiments, a gas such as atmospheric air fully or partially fills the space between the inertia beads  1066 . In some embodiments, a liquid such as a torsion fluid, water, oil, drilling mud, or other fluid fully or partially fills the space between the inertia beads  1066 . The liquid may be a Newtonian fluid or a non-Newtonian fluid. In some embodiments, the liquid may partially fill the space between the inertia beads  1066 , and a gas or a different liquid may fill the remainder of the space between the inertia beads  1066 . The material filling the space between the inertia beads  1066  may help to determine the damping effect of the inertia beads  1066 . For example, a less dense fluid (gas or liquid) between the inertia beads  1066  may result in a larger damping effect, and a denser fluid between the inertia beads  1066  may result in a smaller damping effect. 
       FIG.  10 - 2    is a cross-sectional view of the torsional damping system  1012  of  FIG.  10 - 1    along the line B-B′ of  FIG.  10 - 1   . In some embodiments, the interior space  1022  of the housing may include one or more chambers  1069 . The chambers may include one or more radial or axial features, including walls or baffles  1069 . The inertia beads  1066  may engage or contact the radial or axial walls, which may help to further damp rotational oscillations and/or vibrations. In some embodiments, the walls  1069  may be longitudinal (e.g., extend in a direction parallel to the longitudinal axis). Longitudinal walls  1069  may help to damp rotational vibrations and oscillations. In some embodiments, the walls  1069  may be radial (e.g., extending radially from a central bore to the collar  1014 ). Radial walls  1069  may help to damp vertical vibrations and oscillations. 
       FIG.  11    is a flowchart depicting a method  1168  for damping torsional oscillations. The method  1168  includes coupling a first damper a collar at  1170 . As discussed herein, this may include coupling a damper to the collar. In some embodiments, this includes coupling a housing of the damper to the collar so that the housing and collar move in synchronization. The damper may be coupled to an inner or outer surface of the collar, or may be coupled to an uphole or downhole portion of the collar. 
     A second damper is optionally coupled to the collar at  1172 . The second damper may be coupled in the same or a different manner as compared to the first collar. The collar may be rotated in a downhole environment at  1174 . In some embodiments, rotating the collar downhole may include or result in vibrations/oscillations of the collar. For example, the collar may oscillate in response to downhole drilling or production activities, such as drilling, generating power with a downhole motor, reaming, fracturing, lifting production fluids, or performing other downhole activities. 
     In response to rotating the collar, one or more inertia elements of the first or second damper may move at  1176 . The inertia elements may be located inside or outside the interior space of a housing of each damper, and may be moved out of sync with the collar. For example, inertia rings may rotate with a different rotational rate or in a different rotational direction than the collar. Similarly, inertia beads may rotate within the housing at a different rotational speed or direction as compared to the oscillating collar. Moving the inertia element(s) in response to the collar rotation may include rotating the inertia elements based on the rotation of the collar. For example, rotating the collar may include transferring a frictional/shear torque or force to a torsion fluid in the interior space of the housing. The torsion fluid may transfer at least a portion of the frictional/shear force to the inertia elements, which may cause the inertia element to rotate. 
     The inertia elements may rotate or otherwise move out of sync with the collar. This may cause the inertia elements to transfer at least a portion of their energy to the collar or for the collar to transfer at least a portion of its rotational energy to the inertia elements. In this manner, the inertia elements may reduce the rotational energy of the oscillating collar, which may reduce the torsional oscillations of the collar. This may help to reduce damage to downhole components caused by torsional oscillations. In some embodiments, rotating the inertia ring out of sync with the collar is the result of torsional oscillations. For instance, as torsional oscillations (i.e., changes in direction or magnitude of rotation experienced by the collar) occur, the first and/or second damper may not respond at the same time as the corresponding location on the collar, resulting in inertia elements in the first and second dampers rotating at a different speed or direction as compared to the corresponding locations of the collar. 
     Accordingly, the method  1168  may include moving a first inertia element (e.g., a ring or granular material in a first housing of the first damper) with a first rotational rate or direction. A second inertia element (e.g., a ring or granular material in a second housing of the second damper, or in a second location in the same housing) is moved with a second rotational rate or direction. In some embodiments, the first rotational rate is different than the second rotational rate. In some embodiments, the first rotational direction is different than the second rotational direction. Thus, the method  1168  may include moving the first inertia element at a different rotational rate or direction than the second inertia element (and optionally compared to the collar). This may be due to the placement of the inertia elements at different locations along the length of a BHA (e.g., between the downhole motor and the bit), different structures of the inertia elements, and the like. 
     In some embodiments, the method  1168  may further include flowing a fluid flow through a central bore in the housing and cooling the plurality of dampers with the fluid flow. Moving the inertia elements inside the housing may cause the housing, the inertia elements, or a torsion fluid to increase temperature, which could damage such components. In some embodiments, heating the torsion fluid may decrease the fluid viscosity and change the torsional damping properties of the dampers. Cooling the plurality of dampers may therefore improve the torsional damping characteristics of the plurality of dampers, or at least improve the consistency of the dampers. 
     INDUSTRIAL APPLICABILITY 
     Embodiments of the present disclosure relate to devices, systems, and methods for inertia damping in downhole tools. Downhole systems may include many motions, vibrations, oscillations, and other movements. In some embodiments, the movements may be associated with drilling, remedial, or production activities. For example, a downhole tool may rotate to degrade a formation during a drilling operation. The engagement of the downhole tool with the formation may cause vibrations, torsional oscillations, and other motions. For the purposes of this disclosure, the terms vibrations, oscillations, and other motions may be used interchangeably, unless otherwise stated. Left unchecked, these torsional oscillations may increase wear on the downhole tool, damage the downhole tool, increase fatigue on materials in the downhole tool, and combinations thereof. A damper may be installed on the downhole tool to reduce the effect of the torsional oscillations. For example, a damper may reduce the amplitude and/or frequency of the torsional oscillations. 
     In some embodiments, the properties and structure of the inertia damping systems discussed above may be combined, changed, and/or modified to optimize an inertia damping system for a particular application. In some embodiments, changing the properties and/or structure of the inertia damping system may widen or narrow the range of magnitude and/or frequency of inertia damping provided by the inertia damping system. 
     In some embodiments, the material from which the inertia ring is fabricated may be changed to change the magnitude and/or frequency of the torsional oscillation damping. Changing the inertia ring material may include changing the density of the inertia ring, which may change the mass of the inertia ring, thereby changing its oscillation damping properties. 
     In some embodiments, the torsion fluid may be changed to reduce the magnitude and/or frequency of the torsion oscillation damping. For example, the viscosity of the torsion fluid may be changed to change the resistance to rotation of the inertia ring by the torsion fluid. This may change the frequency and/or magnitude of the inertia damping provided by the inertia ring. In some embodiments, the torsion fluid may be changed to a granular material, such as a plurality of small torsion beads as discussed herein. 
     In some embodiments, the gap between the inner walls of the housing or collar and the inertia ring may be changed to change the magnitude and/or frequency of the inertia damping system. This may include increasing the gap, decreasing the gap, and adding variations in the gap (such as by modifying the texture and/or profile of the surface of the inner wall of the housing). 
     In some embodiments, an inertia damping system may allow for different mechanisms of oscillation damping at different locations of oscillation. For example, the material and/or the dimensions of an inertia ring may be changed either along the length of the inertia ring, or different inertia rings within the same housing or in different dampers may have different materials and/or dimensions. This may help to change the range of the magnitude and/or frequency bandwidth of the damped oscillations. 
     In some embodiments, a damper may be separated and/or segmented to have one or more inertia rings at any or each location of oscillation. In some embodiments, an inertia ring may be split within the same interior space of a housing to allow for independent rotation of the inertia rings within the housing. In some embodiments, the properties of the separated and/or segmented dampers and/or inertia rings may be different. For example, a first inertia ring may be made from a first material, and a second inertia ring may be made from a second material. In another example, a first inertia dampener may be used with a torsion fluid of a first type, while another inertia dampener uses a torsion fluid of a different type. Other variations may also be made, including fluid frictional/shear gaps around a torsion ring, bearing clearances, torsion ring shapes, and the like. These options may allow the inertia damping system to provide differing magnitudes and/or frequencies (or magnitude and frequency ranges) of damping based on oscillation profile of a downhole tool. In this manner, the downhole drilling system may experience reduced oscillation and/or vibrations along a length of the downhole drilling system (or its entirety). In some cases, differing components can be interchangeable so as to easily change the tool at the surface to be suitable for different conditions expected during separate operations. 
     In some embodiments, separating and/or segmenting damping systems and/or inertia rings may allow for differing levels of rigidity of a downhole tool. For example, a downhole tool may need to bend to complete a dogleg, such as through directional drilling, using a whipstock, or other dogleg mechanism. By segmenting the dampers and/or inertia rings into multiple pieces, the bendability of the inertia damping system may be matched to the flexibility of the downhole drilling system. 
     The embodiments of the torsional oscillation system have been primarily described with reference to wellbore drilling operations; however, the torsional oscillation systems described herein may be used in applications other than the drilling of a wellbore, including in producing or remediating a wellbore. In other embodiments, torsional oscillation systems according to the present disclosure may be used outside a wellbore or other downhole environment used for the exploration or production of natural resources. For instance, torsional oscillation systems of the present disclosure may be used in a borehole used for placement of utility lines. Accordingly, the terms “wellbore,” “borehole” and the like should not be interpreted to limit tools, systems, assemblies, or methods of the present disclosure to any particular industry, field, or environment. 
     One or more specific embodiments of the present disclosure are described herein. These described embodiments are examples of the presently disclosed techniques. Additionally, in an effort to provide a concise description of these embodiments, not all features of an actual embodiment may be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous embodiment-specific decisions will be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which may vary from one embodiment to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. 
     Additionally, it should be understood that references to “one embodiment” or “an embodiment” of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. For example, any element described in relation to an embodiment herein may be combinable with any element of any other embodiment described herein. Numbers, percentages, ratios, or other values stated herein are intended to include that value, and also other values that are “about” or “approximately” the stated value, as would be appreciated by one of ordinary skill in the art encompassed by embodiments of the present disclosure. A stated value should therefore be interpreted broadly enough to encompass values that are at least close enough to the stated value to perform a desired function or achieve a desired result. The stated values include at least the variation to be expected in a suitable manufacturing or production process, and may include values that are within 5%, within 1%, within 0.1%, or within 0.01% of a stated value. 
     A person having ordinary skill in the art should realize in view of the present disclosure that equivalent constructions do not depart from the spirit and scope of the present disclosure, and that various changes, substitutions, and alterations may be made to embodiments disclosed herein without departing from the spirit and scope of the present disclosure. Equivalent constructions, including functional “means-plus-function” clauses are intended to cover the structures described herein as performing the recited function, including both structural equivalents that operate in the same manner, and equivalent structures that provide the same function. It is the express intention of the applicant not to invoke means-plus-function or other functional claiming for any claim except for those in which the words ‘means for’ appear together with an associated function. Each addition, deletion, and modification to the embodiments that falls within the meaning and scope of the claims is to be embraced by the claims. 
     The terms “approximately,” “about,” and “substantially” as used herein represent an amount close to the stated amount that is within standard manufacturing or process tolerances, or which still performs a desired function or achieves a desired result. For example, the terms “approximately,” “about,” and “substantially” may refer to an amount that is within less than 5% of, within less than 1% of, within less than 0.1% of, and within less than 0.01% of a stated amount. Further, it should be understood that any directions or reference frames in the preceding description are merely relative directions or movements. For example, any references to “up” and “down” or “above” or “below” are merely descriptive of the relative position or movement of the related elements. As used herein, the term “axial” refers to directions measured along an axis (e.g., a longitudinal axis of a tool), while the term “radial” refers to a direction perpendicular to such an axis (e.g., extending from the longitudinal axis toward an outer housing, collar, etc.). 
     Various features are described herein in alternative format in order to emphasize that features may be combined in any number of combinations. Each feature should be considered to be combinable with each other feature unless such features are mutually exclusive. The term “or” as used herein is not exclusive unless the contrary is clearly expressed. For instance, having A or B encompasses A alone, B alone, or the combination of A and B. In contrast, having only A or B encompasses A alone or B alone, but not the combination of A or B. Even if not expressly recited in multiple independent form, the claims should be considered combinable with each other claim (or any combination of other claims). 
     The present disclosure may be embodied in other specific forms without departing from its spirit or characteristics. The described embodiments are to be considered as illustrative and not restrictive. The scope of the disclosure is, therefore, indicated by the appended claims rather than by the foregoing description. Changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope.