Encapsuled friction damper design

Abstract

A friction damper for mitigating high-frequency torsional oscillations in a drill string includes first and second inertia masses radially disposed about a drill string, each having equal rotational inertia. First and second bearings extend axially from the inertia masses, while third and fourth bearings are affixed to the drill string. Axial springs between the inertia masses apply a normal force, urging them apart so that friction surfaces of the bearings interface. Optional centering elements may maintain alignment and prevent unwanted motion between the inertia masses. The normal force is adjusted to provide a transition from sticking to sliding friction within a predetermined amplitude range, dissipating energy and damping oscillations. The damper may have an open configuration allowing mud flow, with protective elements preventing blockage, or a closed configuration with coverings sealing the annulus to prevent pressure drop.

Description

[0001]

[0002] ENCAPSULED FRICTION DAMPER DESIGN

[0003] TECHNICAL FIELD

[0004] This disclosure relates to the field of downhole vibration mitigation in drilling operations, and more particularly to a high-frequency torsional oscillation (HFTO) damper designed for effectively attenuating harmful vibrations while maintaining a compact form factor within limited space available.

[0005] BACKGROUND

[0006] Boreholes are drilled deep into the earth for various applications, such as hydrocarbon exploration and production. These boreholes are designed to pass through or allow access to materials (e.g., gas or fluid) contained in formations located below the earth's surface.

[0007] In hydrocarbon exploration and production, drilling is performed using a drill string, which is a long column of connected pipes that extends from the surface to the bottom of the well. The drill string includes the drill pipe, the bottom hole assembly (BHA), and the drill bit at the end. Its main functions are to transmit rotary motion and drilling fluid to the drill bit, enabling it to crush and cut through rock formations.

[0008] During drilling operations, severe vibrations in drill strings and BHAs can be caused by cutting forces at the bit or mass imbalances in downhole tools such as drilling motors. These vibrations can result in reduced rates of penetration, diminished quality of measurements made by formation evaluation tools in the BHA, and increased wear, fatigue, and / or failure of downhole components. Different t pes of vibrations exist, including lateral, axial, and torsional vibrations. Stick / slip of the whole drilling system and high-frequency torsional oscillations (HFTO) are both types of torsional vibrations. The terms "vibration," "oscillation," and "fluctuation" are used interchangeably herein to describe repeated and / or periodic movements or deviations from a mean value, such as position, velocity, acceleration, force, and / or torque. These terms encompass all kinds of deviations, including periodic, harmonic, and statistical deviations.

[0009] Torsional vibrations may be excited by self-excitation mechanisms that occur due to the interaction between the drill bit or any other cutting structure (e.g., reamer bit) and the formation. The main difference between stick / slip and HFTO is the frequency and typical mode shapes. HFTO typically have frequencies above 50 Hz. while stick / slip torsional vibrations usually have frequencies below 1 Hz. Moreover, the excited mode shape of stick / slip is typically a first mode shape of the whole drilling system, whereas HFTO mode shapes can be of higher order and are commonly localized to smaller portions of the drilling system with comparably high amplitudes at the point of excitation, which may be the bit, any other cutting structure, or any contact between the drilling system and the formation (e.g., by a stabilizer).

[0010] Due to the high-frequency of HFTO vibrations, they correspond to high acceleration and torque values along the BHA. Torsional movements involve acceleration, force, and torque; none of these can occur without the other two. The loads of high-frequency vibrations can negatively impact the efficiency, reliability, and durability of electronic and mechanical parts of the BHA.

[0011] To mitigate these harmful vibrations, HFTO dampers are employed in the drill string. An HFTO damper is a type of friction damper designed to dissipate energy and reduce the amplitude of high-frequency torsional vibrations. It may be placed near the drill bit in the BHA to minimize the transmission of vibrations from the bit to the rest of the drill string.

[0012] A friction damper includes two surfaces in contact with each other. When relative motion occurs between these surfaces, the friction force opposes the motion, dissipating energy and reducing the amplitude of vibrations. The magnitude of the damping force depends on the mass moment of the inertia, the normal force (the force perpendicular to the contact surfaces), the radius, and the coefficient of friction between the surfaces.

[0013] In an HFTO damper, a normal force device is used to apply the necessary force to press the two friction surfaces together. This force is crucial for the proper functioning of the friction damper, as it determines the amount of friction and, consequently, the damping effect. Springs, hydraulic or pneumatic systems, or other mechanical means can be used to generate the normal force.

[0014] The placement of an HFTO damper within the drill string is done for its effectiveness in mitigating harmful vibrations. While HFTO dampers can be positioned at various locations along the drill string, placing them near the drill bit offers several advantages.

[0015] A near-bit HFTO damper is particularly effective because it is situated close to the primary source of high-frequency torsional vibrations - the interaction between the drill bit and the rock formation. By positioning the damper near the bit, the vibrations can be attenuated before they propagate and amplify along the rest of the drill string. Modes susceptible to HFTO typically exhibit high mode shape amplitudes at the bit, as the amplitude indicates the mode's vulnerability to HFTO. Correspondingly, the damping effect intensifies with the amplitude observed at the damper's location. Consequently, placing the damper near the bit. where HFTO amplitudes are high, allows it to target naturally susceptible modes more effectively. This localized damping minimizes the transmission of harmful vibrations to other components of the BHA and the drill string, protecting them from excessive wear, fatigue, and potential failure.

[0016] However, the limited space available near the drill bit presents a challenge for the design of HFTO dampers. The damper must be compact enough to fit within the confined space while still providing sufficient damping capacity to effectively mitigate the vibrations. Therefore, there is a need for a near-bit HFTO damper that can deliver enhanced damping performance within the same design space. As such, further development is needed.

[0017] SUMMARY

[0018] A friction damper for mitigating torsional oscillation in a drill string includes a drill string having a longitudinal axis. A first inertia mass and a second inertia mass are movably attached to the drill string. A first stiffness element is positioned between the first inertia mass and the second inertia mass. A first frictional contact is formed between an axial end of the first inertia mass and the drill string, and a second frictional contact is formed between an axial end of the second inertia mass and the drill string. The first stiffness element applies a force to the first frictional contact and the second frictional contact.

[0019] The force applied to the first frictional contact and the second frictional contact may be applied along the longitudinal axis.

[0020] The first frictional contact may include a first frictional surface and a second frictional surface. The force applied to the first frictional contact may act normal to the first frictional surface and the second frictional surface.

[0021] The first inertia mass and the second inertia mass may surround the drill string. The friction damper may further include a centering element disposed between the first inertia mass and the second inertia mass to prevent relative motion between the first inertia mass and the second inertia mass.

[0022] The first inertia mass and the second inertia mass may be configured to rotate around the drill string.

[0023] The first stiffness element may be a compression spring, and may be configured to compress and expand in a direction parallel to the longitudinal axis of the drill string.

[0024] The first stiffness element may include a plurality of stiffness elements.

[0025] The first frictional contact may include a first frictional surface and a second frictional surface, and the first frictional surface and the second frictional surface may incorporate a poly crystalline diamond (PCD) material.

[0026] The friction damper may further include a second stiffness element between one of (i) the first inertia mass and the first frictional contact and (ii) the drill string and the first frictional contact. The second stiffness element may act in series with the first frictional contact.

[0027] The friction damper may further include a third stiffness element between the first inertia mass and the drill string. The third stiffness element may act parallel to the first frictional contact.

[0028] The first frictional contact may further include a first frictional surface and a second frictional surface. The first frictional surface and the second frictional surface may form an angle with the longitudinal axis that is different from 90 degrees.

[0029] The first inertia mass may further include at least two pieces, each of said pieces partially surrounding the drill string.

[0030] The first stiffness element may be located at least partially in a pocket in the first inertia mass, and the first stiffness element may be prestressed.

[0031] The first stiffness element may be prestressed, and the friction damper may further include an adjustment element configured to adjust the prestress.

[0032] The first stiffness element may include two first stiffness elements positioned axially side by side in the first inertia mass.

[0033] The first inertia mass and the second inertia mass may be configured to move relative to the drill string with a velocity that is a sum of a periodic velocity fluctuation having an amplitude and a mean velocity. The mean velocity may be lower than the amplitude of the periodic velocity fluctuation.

[0034] Also disclosed herein is a method of mitigating torsional oscillation in a drill string that includes providing a drill string having a longitudinal axis. A first inertia mass and a second inertia mass are movably attached to the drill string. A first stiffness element is positioned between the first inertia mass and the second inertia mass. A first frictional contact is formed between an axial end of the first inertia mass and the drill string. A second frictional contact is formed between an axial end of the second inertia mass and the drill string. A force is applied to the first frictional contact and the second frictional contact using the first stiffness element.

[0035] The force may be applied to the first frictional contact and the second frictional contact along the longitudinal axis.

[0036] Forming the first frictional contact may include providing a first frictional surface and a second frictional surface. The force may be applied to the first frictional contact normal to the first frictional surface and the second frictional surface.

[0037] The method may include surrounding the drill string with the first inertia mass and the second inertia mass. A centering element may be disposed between the first inertia mass and the second inertia mass to prevent relative motion between the first inertia mass and the second inertia mass.

[0038] The first inertia mass and the second inertia mass may be configured to rotate around the drill string.

[0039] Positioning the first stiffness element may include using a compression spring configured to compress and expand in a direction parallel to the longitudinal axis of the drill string.

[0040] Positioning the first stiffness element may include using a plurality of stiffness elements.

[0041] Forming the first frictional contact may include providing a first frictional surface and a second frictional surface. The first frictional surface and the second frictional surface may be formed from a poly cry stalline diamond (PCD) material.

[0042] The method may include positioning a second stiffness element between one of (i) the first inertia mass and the first frictional contact and (ii) the drill string and the first frictional contact. The second stiffness element may be configured to act in series with the first frictional contact.

[0043] The method may include positioning a third stiffness element between the first inertia mass and the drill string. The third stiffness element may be configured to act parallel to the first frictional contact.

[0044] Creating the first frictional contact may include providing a first frictional surface and a second frictional surface. An angle may be formed between the first frictional surface and the second frictional surface with the longitudinal axis that is different from 90 degrees.

[0045] Providing the first inertia mass may include using at least two pieces, each of said pieces partially surrounding the drill string.

[0046] The method may include locating the first stiffness element at least partially in a pocket in the first inertia mass. The first stiffness element may be prestressed.

[0047] The method may include prestressing the first stiffness element. An adjustment element may be provided to adjust the prestress.

[0048] Positioning the first stiffness element may include positioning two first stiffness elements axially side by side in the first inertia mass.

[0049] The first inertia mass and the second inertia mass may be configured to move relative to the drill string with a velocity that is a sum of a periodic velocity fluctuation having an amplitude and a mean velocity. The mean velocity may be lower than the amplitude of the periodic velocity fluctuation.

[0050] A property of the first stiffness element may be selected based on a numerical simulation of the drill string.

[0051] BRIEF DESCRIPTION OF THE DRAWINGS

[0052] FIG. 1 is an example of a system for performing downhole operations that can employ embodiments of this disclosure.

[0053] FIG. 2 is a longitudinal cross-sectional view of an embodiment of the friction damper disclosed herein having angled frictional contacts, disposed about a drill string.

[0054] FIG. 2A is a transverse cross-sectional view of the friction damper of FIG. 2.

[0055] FIG. 2B is another longitudinal cross-sectional view of the friction damper of FIG. 2, here showing a centering element.

[0056] FIG. 2C is a longitudinal cross-sectional view of the friction damper of FIG. 2, modified to have a closed configuration as opposed to an open configuration.

[0057] FTG. 2D is a longitudinal cross-sectional view of a dual spring configuration for the friction damper with two springs positioned axially side by side.

[0058] FIG. 3 is a longitudinal cross-sectional view of an embodiment of the friction damper disclosed herein having frictional contacts perpendicular to a longitudinal axis of the drill string.

[0059] FIG. 3A is a transverse cross-sectional view of the friction damper of FIG. 3.

[0060] FIG. 3B is another longitudinal cross-sectional view of the friction damper of FIG. 3, here showing a centering element.

[0061] FIG. 4A is a cross-sectional view of a vibration damping device with springs adjacent to the raised shoulders of the drill string.

[0062] FIG. 4B is a cross-sectional view of a vibration damping device with springs adjacent to the inertia masses.

[0063] FIG. 5 A is a perspective view of a vibration damping device with bar-shaped springs and filler inserts.

[0064] FIG. 5B is a detailed view of the vibration damping device showing holes in the base and cavities formed by the springs.

[0065] FIG. 5C is a side view of the vibration damping device illustrating the layered structure of the friction damper.

[0066] FIG. 5D is an isometric view highlighting the inertia mass, base, and bar-shaped springs of the vibration damping device.

[0067] FIG. 5E is an alternative design of the vibration damping device featuring a monolithic spring element.

[0068] FIG. 5F is a side view cross-section of the vibration damping device with the monolithic spring element.

[0069] FIG. 5G is a refinement of the vibration damping device design showing holes in the monolithic spring element for tuning.

[0070] FIG. 5H is a side view cross-section of the vibration damping device corresponding to the configuration in FIG. 5G.

[0071] FIG. 51 is another variation of the vibration damping device focusing on the spring element with grooves and projections.

[0072] FIG. 5J is a further embodiment of the vibration damping device with an increased number of bar-shaped springs.

[0073] FTG. 5K is a detailed side view cross-section of the vibration damping device corresponding to the configuration in FIG. 5J.

[0074] DETAILED DESCRIPTION

[0075] The following disclosure enables a person skilled in the art to make and use the subject matter described herein. The general principles outlined in this disclosure can be applied to embodiments and applications other than those detailed above without departing from the spirit and scope of this disclosure. It is not intended to limit this disclosure to the embodiments shown, but to accord it the widest scope consistent with the principles and features disclosed or suggested herein.

[0076] FIG. 1 depicts a schematic of a drilling system 110 for performing downhole operations. The system includes a drill string 10 with a drilling assembly 190 (also known as a bottomhole assembly or BHA) conveyed in a borehole 126 penetrating an earth formation 160. A conventional derrick 111 is erected on a floor 112 supports a rotary table 114. rotated by a prime mover (e.g.. an electric motor, not shown) at a desired rotational speed. The drill string 10 includes a drilling tubular 122 (e g., drill pipe) extending downward from the rotary table 114 into the borehole 126. A disintegrating tool 150 (e.g., drill bit) attached to the BHA 190 disintegrates geological formations when rotated to drill the borehole 126. The drill string 10 connects to surface equipment for lifting, rotating, and pushing, such as a drawworks 130, via a kelly joint 121, swivel 128, and line 129 through a pulley 123. A top drive (not showm) may also be used. The drawworks 130 controls weight on bit, affecting rate of penetration.

[0077] During drilling, a suitable drilling fluid 131 ("mud") from amud pit 132 is circulated under pressure through the drill string 10 by a mud pump 134. The drilling fluid 131 enters the drill string 10 via a desurger 136, fluid line 138, and kelly joint 121, discharging at the borehole bottom 151 through the disintegrating tool 150. The drilling fluid 131 then circulates uphole through the annular space 127 between the drill string 10 and borehole 126. returning to the mud pit 132 via a return line 135. Sensors provide information about various drilling parameters, including fluid flow rate (sensor SI), drill string torque and rotational speed (sensors S2 and S3), hook load, and others. Downhole sensors 170 may be located on the drill string 10 and / or BHA 190.

[0078] The disintegrating tool 150 can be rotated by rotating the drill string 10 alone or by a drilling motor 155 (e.g., mud motor) in the drilling assembly 190. Rate of penetration (ROP) depends largely on weight on bit and bit rotational speed for a given formation and drilling assembly. The drilling motor 155 couples to the disintegrating tool 150 via a drive shaft in a bearing assembly 157, rotating the tool 150 when drilling fluid 131 passes through under pressure. The bearing assembly 157 supports radial and axial forces of the tool 150, motor down thrust, and reactive upward loading from applied weight on bit. Stabilizers 158 on the bearing assembly 157 or elsewhere act as centralizers for the drilling assembly 190 or portions thereof.

[0079] A surface control unit 140 receives signals from downhole sensors and devices via a transducer 143 in the fluid line 138 and other sensors, processing them according to programmed instructions. It displays desired drilling parameters and other information on a display / monitor 142 for the rig site operator and contains a computer, memory, programs, models, algorithms, recorder, and other peripherals. The control unit 140 may include simulation models and respond to user commands via a keyboard or other input device, activating alarms 144 when unsafe or undesirable conditions occur.

[0080] The drilling assembly 190 also contains sensors and devices for measuring the surrounding formation and drilling the borehole 126 along a desired path, including devices for determining drill string inclination, azimuth, and position. An inclinometer 174 and a gamma ray device 176 may determine BHA inclination and formation gamma ray intensity7, respectively, while an azimuth device (not shown) determines drill string azimuth. The drilling motor 155 transfers power (torque) to the disintegrating tool 150 via a shaft enabling drilling fluid to pass from motor to tool. The motor 155 may be coupled below a resistivity measuring device 164 or at another suitable location.

[0081] While the described drilling system utilizes a drill pipe to convey the drilling assembly 190 into the borehole 126 with weight on bit controlled from the surface by the drawworks, certain current systems, especially for highly deviated and horizontal boreholes, use coiled tubing instead. In such applications, a thruster may be deployed to provide the desired force on the drill bit. With coiled tubing, the tubing is not rotated by a rotary table but is injected into the borehole by an injector, while a downhole motor 155 rotates the disintegrating tool 150. Offshore drilling employs an offshore rig or vessel to support the drilling equipment, including the drill string.

[0082] This disclosure relates to a friction damper 12 designed for mitigating high- frequency torsional oscillations (HFTO) in a drill string 10. Enabling this friction damper design is the way the normal force is applied to the frictional contacts of the friction damper (described in detail below), which offers significant benefits compared to other designs. A significant property of the friction damper is that a damper element is configured to move relative to the drill string with a velocity that is a sum of a periodic velocity fluctuation having an amplitude and a mean velocity, wherein the mean velocity is lower than the amplitude of the periodic velocity.

[0083] In this friction damper 12 disclosed herein, the normal force is carefully adjusted to provide for a transition from sticking friction to sliding friction within a reasonable amplitude range. This transition occurs when the inertial forces overcome the frictional moment MR = q ■ Fn■ r where q is the coefficient of friction, Fnis the normal force in the frictional contact, and r is the radius of the frictional contact. The equation governing this transition is J • Aangular> u ■ Fn- r, where J is the moment of inertia of the inertia mass in the friction damper 12, Aangularis the angular acceleration experienced by the inertia mass which is corresponding to a vibration of a HFTO mode, where / J. is the coefficient of friction, Fnis the normal force in the frictional contact, and r is the radius of the frictional contact (measured from the rotational axis 19).

[0084] Sliding friction corresponds to the energy dissipation and damping. The amplitude at which this transition occurs is critical. If the transition amplitude is too low, the damping curves become narrow, and there is a risk that the amplitude "jumps" over the range with high damping. Conversely, if the transition amplitude (normal force) is too high, the amplitude experienced by the bottom hole assembly (BHA) may again enter the damaging range, rendering the damper ineffective in preventing damage. Notably, the damping requirement is higher at low amplitudes, which suggests that a higher normal force and a higher amplitude of transition to sliding friction are advantageous. This is particularly relevant because the maximum damping provided is not significantly dependent on the normal force. The upper limit of the normal force corresponds to one limiting the loads of HFTO to an amplitude that does not cause damage.

[0085] The friction damper 12 disclosed herein therefore utilizes a split inertia with axial springs that rotate with the inertia mass relative to the BHA. This configuration enables the implementation of an effective friction damper for mitigating HFTO in drill strings by ensuring the transition from sticking to sliding friction occurs within an optimal amplitude range to maximize damping and protect critical components in the BHA.

[0086] The friction damper 12 is now described in detail. As shown in the cross-sectional view of FIG. 2, showing a cross section of the drill string section taken along its longitudinal axis 18, the drill string section 10 includes a necked-down portion 13 of drill-pipe which extends between two raised shoulders 14a, 14b. The damper element 20 is installed within the necked-down portion 13, fitting securely between the raised shoulders 14a, 14b. The damper element 20 comprises a first inertia mass 20a and a second inertia mass 20b that are symmetric, having equal rotational inertia. The inertia masses 20a and 20b surround the drill string section 10. The inertia masses 20a, 20b are connected by axial springs 40 that fit in spring pockets 21a, 21b respectively formed in corresponding ends of the inertia masses 20a, 20b and urge the inertia masses apart to generate the normal force, or a force oriented parallel to the longitudinal axis 18, used to cause the damping, with the normal force being applied in the axial direction onto the bearings 24a, 28a and 24b, 28b. Note that the axial springs 40 and the bearings 24a, 24b rotate with the inertia masses 20a, 20b during operation, and that by allowing the springs 40 and bearings 24a, 24b to rotate with the inertia masses 20a, 20b. the design is simplified and more compact, eliminating the need for complex axial decoupling mechanisms (e.g., needed if the normal force were applied outside or on one side of the inertia masses), making it well-suited for placement near the drill bit where space is limited. In FIG. 2 the force F is not oriented normal to the bearings 24a, 28a, and 24b, 28b, because the bearings have an angle with respect to the longitudinal axis which is different to 90 degrees.

[0087] Moreover, by using two separated inertia masses 20a and 20b instead of a single large inertia mass, the total required normal force can be distributed between the two masses (as the total normal force required is divided by the number of inertia elements used, which in this case is two), and this distribution of normal force can make the design more feasible and reduce the stress on individual components. This configuration facilitates achieving the minimum required normal force more easily, as the force is applied to both friction contacts, a first frictional contact between friction surfaces 27a, 3 la of bearings 24a, 28a, and a second frictional contact between friction surfaces 27b, 31b of bearings 24b, 28b. This configuration eliminates the need for complex axial decoupling mechanisms, which would be necessary if the normal force were applied externally or on only one side of the inertia masses, instead of the normal force being applied at the opposite side of each external inertia mass from where the spring force is applied. This configuration also allows for adjusting the friction damper's response to different frequencies by changing the properties of the springs, which can broaden the amplitude range over which the friction damper 12 effectively operates. The optimal configuration of the properties of the spring can be determined by modeling the drill string or the BHA, including the friction damper, and the response of the BHA to an excited HFTO mode by using a numerical simulation. The properties of the springs (stiffness, type of spring, shape, geometric dimensions) are selected based on the numerical simulation result and based on the required normal force to achieve a desired vibration damping.

[0088] Each inertia mass 20a, 20b includes bearing pockets 23a, 23b formed therein at an end opposite to the end into which the spring pockets 21a, 21b are formed. Bearings 24a, 24b include bearing shafts 25a, 25b having their proximal ends positioned within the bearing pockets 23a, 23b. with bearing heads 26a, 26b affixed to the distal ends of corresponding bearing shafts 25a, 25b so that the bearing heads 26a, 26b face away from the axial spring 40. The bearing heads 26a, 26b have friction surfaces 27a, 27b at their distal ends that interface with corresponding friction surfaces 31a, 31b of bearings 28a, 28b affixed to raised shoulders 14a, 14b in the drill string section 10.

[0089] The bearings 28a, 28b include bearing shafts 29a, 29b having their proximal ends positioned within bearing pockets or bearing recesses 15a, 15b formed within the raised shoulders 14a, 14b. Each bearing 28a, 28b has a bearing head 30a, 30b affixed to the distal end of its bearing shaft 29a. 29b, with the friction surfaces 31a, 31b being at the distal ends of the bearing heads 30a. 30b to interface with, as stated, the friction surfaces 27a. 27b of the bearing heads 26a, 26b of bearings 24a, 24b.

[0090] The axial springs 40 apply a normal force to the inertia masses 20a, 20b, urging them axially in a direction away from one another, increasing the friction between the friction surfaces 27a, 27b of the bearings 24a, 24b of the inertia masses and the friction surfaces 31a, 31b of the bearings 28a, 28b. The spring 40, as stated, is axially supported in the spring pockets 21a, 21b of the two separate inertia masses 20a, 20b and is prestressed in a defined way during the assembly process. Adjustment elements like shims or rings can be used to optimize the prestress. The prestress of the springs 40 and the number of springs 40 determines the normal forces acting on each frictional surface 27a, 27b, and consequently the frictional damping force provided by the friction damper 12.

[0091] In an alternative embodiment, each inertia mass 20a, 20b may incorporate multiple axial springs 40 arranged in series within its structure. For example, two or more springs 40 (FIG. 2D) may be positioned behind each other and concealed within a single inertia mass 20a or 20b. This configuration, where multiple springs 40 are hidden within one inertia element 20a or 20b, allows for greater flexibility in tuning the damping characteristics of the system. The series arrangement of springs 40 can provide a more nuanced response to torsional oscillations, potentially offering improved damping performance across a wider range of torsional vibration frequencies of HFTO. Additionally, this design can enhance force distnbution within the inertia mass 20a. 20b and may allow for more compact packaging of the damping elements. The number, type, and arrangement of these internal springs 40 can be optimized based on specific drilling conditions and desired damping properties. The spring pockets 21a, 21b in each inertia mass 20a, 20b may be modified to accommodate this series spring arrangement. Various types of axial springs 40 can be used, including spiral springs as shown in the concept design, cub springs, plate springs, or disk springs, and a compression spring configured to compress and expand in a direction parallel to the longitudinal axis 18. Other options include axial springs that are assembled from the inertia itself, any beam-like elements that can act like a spring, or 3D-printed springs (additive manufacturing) with optimized shape and geometry. Adjustment elements like shims or rings can be used to optimize or adjust the prestress of the axial springs 40. The prestress of each single axial spring 40 and the number of such axial springs 40 determine the normal forces acting on each frictional contact between friction surfaces 27a, 27b and 31a. 31b, and consequently the frictional damping force.

[0092] The friction surfaces 27a, 27b of both inertia masses 20a, 20b and their respective counterparts, friction surfaces 31a, 31b on the bearings 28a, 28b, have the same properties to provide for symmetric and consistent frictional damping. These properties include the radius of the friction surfaces, the surface properties of the friction surfaces (e.g. roughness), material forming the friction surface (e.g. polycrystalline diamonds, wolfram carbide, tungsten carbide), the dimension of the friction surface (surface area), and the coefficient of friction between the friction surfaces 27a, 27b and 31a, 31b. The frictional surfaces 27 a, 27b and 31a, 31b may be poly crystalline diamond (PCD), wolfram carbide inserts, wolfram carbide surface, or tungsten carbide surface.

[0093] Matching radii of the friction surfaces helps ensure that the frictional torque generated by each inertia mass and bearing pair is equal. While a symmetric design is optimal, an asymmetric configuration may offer advantages, particularly when additional inertia mass is needed at a specific position within the drilling system. For effective operation, it's beneficial if both inertia masses 20a, 20b transition from sticking to sliding friction at similar modal amplitudes of the HFTO vibration, ideally within a ±10% range. This similarity in transition amplitude can be achieved by matching the inertial forces and the friction forces on each side of the inertia.

[0094] There are multiple approaches to implementing such a design. One method involves using asymmetric inertia parts with similar mass moments of inertia while maintaining uniformity in other properties, such as friction radii. Alternatively, if the mass moments of inertia of the two parts differ, the friction moment MR can be adjusted accordingly, for example, by employing different radii (rl and r2) at the friction surfaces. The radius r of a friction surface is a representative of the distance of the friction surface from the rotational axis 19 of the bearing assemblies (27a, 31a and 27b, 31b) or the inertia masses 20a. 20b. A representative radius may be a minimum radius of the friction surface to the rotational axis, a maximum radius of the frictional surface, or a medium radius of the frictional surface to the rotational axis.

[0095] Ultimately, a design that satisfies the equation ^angular , sliding ,1 A angular, sliding, 2 is advantageous, where Aangular sliding lrepresents the angular acceleration at which the first inertia mass 20a transitions from sticking to sliding friction and Aanguiar, sliding ,2 represents the angular acceleration at which the second inertia mass 20b transitions from sticking to sliding friction, initiating the damping effect. This equation ensures that despite potential asymmetry, the friction damper maintains balanced and achieves effective performance.

[0096] In this design, as stated, the normal force acts in the axial direction, parallel to the longitudinal axis 18 of the drill string section 10. The axial springs 40 generates this normal force by pushing the inertia masses 20a, 20b apart, consequently pressing the friction surfaces 27a, 27b against the bearing surfaces 31a, 31b. The magnitude of the normal force depends on the stiffness (spring constant) of the axial springs 40 and the amount of compression (prestress) they undergo during assembly.

[0097] The coefficient of friction represents the ratio of the friction force to the normal force. It depends on the materials of the friction surfaces 27a, 27b and 31a, 31b, as well as factors such as surface roughness, temperature, the presence of lubricating fluids and the properties of those fluids. Matching coefficients of friction of the friction surfaces 27a, 31a and 27b, 31b helps ensure that the frictional damping provided by each inertia mass and bearing pair is equal.

[0098] By helping ensure that the radius, normal force, and coefficient of friction are the same for both sets of interacting friction surfaces 27a, 31a and 27b, 31b, or that the combination of these parameters leads to equivalent frictional damping, symmetric and predictable damping performance is achieved so as to provide for effective mitigation of high-frequency torsional oscillations in the drill string.

[0099] In the specific embodiment of FIG. 2, the heads 26a, 26b of bearings 24a, 24b have angled friction surfaces 27 a. 27b, meaning they are not perpendicular (90 degree) to the longitudinal axis 18 of the drill string 10. Similarly, the heads 30a, 30b of the bearings 28a, 28b have friction surfaces 3 la, 3 lb that are angled corresponding to the angles of the friction surfaces 27a, 27b of the heads 26a, 26b of bearings 24a, 24b. A benefit to this angled arrangement is that it provides for radial support as well as friction, eliminating the need for separate radial bearings between the inertia mass 20a, 20b and the necked-down portion 13 of the drill string 10. Also, due to this lack of a need for such separate radial bearings, more space is available radially for the inertia masses 20a, 20b. The angle with respect to the longitudinal axis 18 of the friction surfaces 27a, 27b may be between 89 degrees and 1 degree, or may be between 80 degrees and 10 degrees, or may be between 70 degrees and 20 degrees.

[0100] Note that the inertia masses 20a, 20b encircle the drill string section 10 within the necked-down portion 13. Refer now to FIG. 2A, showing a cross section of the drill string section 10 taken perpendicular to the longitudinal axis and along its diameter as opposed to along its longitudinal axis. From this view, it can be appreciated that there are multiple such springs 40 (twelve in the example shown in FIG. 2A) spaced azimuthally about the rotational axis 19 of the inertia masses 20a, 20b. To provide for proper alignment and prevent unwanted relative motion (radially and azimuthally to the longitudinal axis) between the two inertia masses 20a, 20b, centering elements 50, such as pins, are incorporated into the design. These centering elements 50 (ten in the example shown in FIG. 2A) are also spaced azimuthally about the rotational axis 19 of the inertia masses 20a, 20b. Refer additionally to FIG. 2B for additional details, where it can be observed that the centering elements 50 are disposed within passageways 51a, 51b formed in the inertia masses 20a, 20b and maintain the azimuthal and radial alignment of the inertia masses to each other, providing for consistent frictional contact betw een the bearings 24a, 24b of the inertia masses and the PCD bearings 28a, 28b of the drill string section 10. Note that while the centering elements 50 maintain azimuthal and radial alignment, they allow for axial movement of the inertia masses 20a, 20b. This axial freedom enables the axial springs 40 to effectively urge the inertia masses towards their respective frictional contacts.

[0101] The friction damper 12 design may be open or closed. In the examples shown in FIGS. 2 and 2B, it can be observed that paths exist from the exterior of the drill string section 10 to the interfaces between friction surfaces 27a, 27b and 31a, 31b, and into the annulus 32 between the friction damper 12 and the drill string section 10. This allows for mud flow from the borehole into these interfaces for cleaning or cooling purposes, as the pressure in the borehole is higher than the pressure in the annulus. In these open configurations, the drill string section 10 may include protection elements 60 to protect the bearings 24a, 24b and 28a, 28b from cuttings or mud cake that could otherwise block movement of the inertia masses 20a, 20b. These protection elements 60, as illustrated, may take the shape of a crushing element such as a sawtooth, and may be located on the outer surface 62 of the inertia masses and may run about the interface between the inertia masses 20a, 20b, for example.

[0102] As a result of the mud flow into the annulus 32 between the friction damper 12 and the drill stnng section 10, the inertia masses, the drill string section and the bearings may be impacted by abrasion due to abrasive components in the drilling mud and may successively degrade. Also, particles in the drilling mud (e.g. drill cuttings) may lead to blockages of the relative rotation of the inertia masses 20a, 20b to the drill string section 10. As such, instead of friction damper 12 design being open as in the examples of FIGS. 2 and 2B, the friction damper 12 may instead be closed, as shown in the example of FIG. 2C. To effectuate this, coverings 61a, 61b may extend over the interfaces between friction surfaces 27a and 31a, 27b and 31b, and the inertia masses 20a, 20b as shown to seal the annulus between the friction damper 12 and the drill string 10. This prevents the aforementioned abrasion or blockage effects. Given this closed design, the protection elements 60 may be removed, as shown. In an alternative embodiment only one covering is used instead of two coverings. The only one covering would be used to protect the inertia masses 20a, 20b and the bearings 28a, 24a, and 24b, 28b at both axial sides of the inertia masses from the drilling fluid. To still facilitate the relative movement of the inertia masses to the drill string section and the relative motion of the bearings to each other a lubrication fluid inside the covering(s) is deployed.

[0103] In FIG. 2D is shown an embodiment with two springs associated with the first inertia mass 20a (FIG. 2). The two springs are positioned axially (longitudinal axis 18) side by side. To place two springs axially side by side in a pocket in the inertia mass 21a, the inertia mass 20a is split into two parts, inertia mass 20al and inertia mass 20a2. A first spring 41 is positioned in a first spring pocket 2 lai in inertia mass 20al and a second spring 43 is positioned in a second spring pocket 21a2 in the inertia mass 20a2. The first spring 41 is applying a first spring force onto a plunger 44 through a spring plate 45. The plunger 44 is moved axially towards the second inertia mass 20b, so that the first spring force is transferred to the second inertia mass 20b (FIG. 2) not shown in FIG. 2D. The second spring 43 applies a second spring force onto the plunger 44, which is moved further towards the second inertia mass 20b. This way the first spring 41 and the second spring 43 work together to increase the force applied to the second inertia mass 20b to apply force on the bearings 24b and 28b (FIG. 2). To adjust the operation of the first spring 41 and the second spring 43 shim elements 46 and 47 are used to create prestress on the first spring 41 and the second spring 43. Shim element 47 comprises a guide bore 48 for the plunger to reach through so that the first spring 41 can move the plunger independently of the second spring 43. The spring plate 45 and the plunger 44 comprise radially extending flanges 52 and 53 configured to make contact with stops 54 and 55. The dimension of the first spnng 41 and the second spring 43, the dimensions of the shim elements 46 and 47, the dimension of the spring plate 45, and the dimension of the plunger 44 are adjusted to achieve optimized cooperation of the first spring 41 and the second spring 43 and to allow the first spring and the second spring to move the plunger 44 in a determined way before the flanges 52 and 53 of the spring plate 45 and the plunger 44 make contact with the stops 54 and 55 to limit the axial movement of the plunger.

[0104] As an alternative to the angled friction surfaces 27a, 27b and 31a, 31b of the friction damper 12 of FIG. 2. in the embodiment shown in FIG. 3, the heads 26a, 26b of bearings 24a, 24b have friction surfaces 27a, 27b perpendicular to the longitudinal axis of the drill string section 10’. Similarly, the heads 30a, 30b of the bearings 28a, 28b have friction surfaces 31a, 31b that are perpendicular to the longitudinal axis of the drill string section 10’. Here, grooves 22a. 22b are defined in the interior radial surfaces of the inertia masses 20a’, 20b’, with radial bearings 35a, 35b being disposed within the grooves 22a. 22b. These radial bearings 35a, 35b may be sealed conventional bearings, such as sliding bearings or friction bearings, and serve to provide radial support for the inertia masses 20a, 20b while permiting axial movement of the inertia masses 20a’, 20b’. In greater detail, these radial bearings 35a, 35b are made of steel to effectively transfer radial forces and provide structural integrity. This design allows the radial forces to be transferred through the steel radial bearings rather than through the high-inertia material of the inertia masses, which enhances the overall mechanical integrity of the system.

[0105] In an alternative embodiment, a parallel tuning spring or parallel tuning springs may be incorporated into the friction damper 12 design. These parallel tuning spring(s) 33 can be connected directly between the drill string section 10' (such as the raised shoulders 14a, 14b) and the inertia masses 20a’, 20b’, parallel to the existing friction surfaces 27a, 30a and / or 27b, 30b. A first parallel tuning spring 33a is located between the first inertia mass 20a and the drill string section 10’, wherein the first parallel tuning spring is connected at a first end at the first inertia mass and at a second end at the drill string section 10’. A second parallel tuning spring 33b is located between the second inertia mass 20b and the drill string section 10’, wherein the second tuning spring is connected at a first end at the second inertia mass and at a second end at the drill string section 10’. The parallel tuning spring(s) can optionally by a torsion spring element. The parallel tuning spring(s) 33 are designed to adjust the natural frequency of the vibration damping device, allowing it to more effectively mitigate high-frequency torsional oscillations (HFTOs) across a wider range of drilling conditions. The stiffness of the parallel tuning spring(s) can be selected to ensure that the natural frequency of the vibration damping device is tuned to the frequency of the HFTO acting on the drill sting 10’. This addition would enhance the capabilities of the friction damper 12, improving its overall performance in reducing harmful vibrations in the drill string. In one embodiment only one tuning spring (33a or 33b) is connected to either between the first inertia mass 20a or the second inertia mass 20b and the drill string section 10’.

[0106] In another alternative embodiment, the friction damper 12 may incorporate tuning springs arranged in series with the friction surfaces. These tuning springs can be positioned either between the inertia masses 20a’, 20b’ and their respective friction surfaces 27a, 27b, or between the drill string section 10 (such as the raised shoulders 14a, 14b) and the friction surfaces of their atached bearing surfaces 31a, 31b. This in-series tuning spring would be implemented symmetrically on both axial sides of the damper element 20. The stiffness of these in-series tuning springs could be adjusted to tune the natural frequency of the friction damper to be close or equal to the frequency of the HFTO.

[0107] In yet another configuration, both the parallel tuning spring (as described above) and the in-series tuning springs can be used simultaneously in the friction damper 12. This combined approach would create a dual-spring setup (parallel tuning spring(s) combined with in-series tuning spring(s)). where the overall frequency response of the friction damper incorporates the effects of both spring embodiments (parallel and in series). Such an arrangement could provide for a self-tuning friction damper configuration. This approach could potentially offer superior adaptability to varying drilling conditions and HFTO modes. The inertia masses 20a', 20b' are constructed from high-density materials to maximize their mass moment of inertia, which linearly increases the damping effect of the system. However, these high-density materials may have lower mechanical strength compared to steel. By using steel radial bearings to cany' the radial loads, the design effectively separates the force-bearing and damping functions. This configuration allows the high-density inertia masses to focus on providing optimal damping performance without compromising the structural integrity of the system. The combination of steel structural elements and high- density inertia masses results in a friction damper that balances robust mechanical performance with highly effective damping capabilities.

[0108] Do note that alternatives for the radial bearings 35a, 35b are available. For example, the radial bearings could be replaced by rubber elements or steel beam elements having a stiffness intended to tune the inertia masses 20a’, 20b’ (parallel tuning stiffness). As another example, the inertia masses 20a’, 20b’ may include projections extending from their interior radial surfaces, with the projections providing this radial support while permitting axial movement.

[0109] Refer now- to FIG. 3A, showing a cross section of the damping element 20‘ taken along its diameter as opposed to along its longitudinal axis, showing that there are multiple springs 40 (twelve in the example shown in FIG. 3A) spaced azimuthally about the rotational axis 19 of the inertia masses 20a’ (similar in 20b’). To provide for proper alignment and prevent unwanted relative motion between the two inertia masses 20a’, 20b’, centering elements 50, such as pins, are incorporated into the design. These centering elements 50 (ten in the example shown in FIG. 3A) are also spaced azimuthally about the rotational axis 19 of the inertia masses 20a', 20b'. Additional details are shown in FIG. 3B, where it can be observed that the centering elements 50 are disposed within passageways 51a, 51b formed in the inertia masses 20a’, 20b’ and maintain the axial and radial alignment of the inertia masses, providing for consistent frictional contact between the bearings 24a, 24b of the inertia masses and the bearings 28a, 28b of the drill string section 10’.

[0110] The outer shape of the inertia masses 20a’, 20b' may be optimized for flow and hole cleaning and wear. Since the location near the drill bit can be critical for various hole cleaning issues, a device can be added to the inertia masses 20a’, 20b’ that leads to better cleaning of the borehole with respect to cuttings and other formation parts or any material expected in the borehole. Such features may include protection elements 60 or wear bands (not shown). Wear bands are typically adjusted like a spiral on the exterior surfaces of the inertia masses 20a, 20b. Alternatively, the inertia masses 20a’. 20b’ themselves may have a geometry that is similar to a spiral. In general, the outer shape of the inertia masses 20a’, 20b' can be optimized for hole cleaning as determined by modeling the interaction of the drilling fluid with the structure of the inertia masses 20a’, 20b’.

[0111] The friction damper 12 may include a mechanism (not shown) for limiting the amplitude of the relative rotational movement between the inertia masses 20a’, 20b’ and the drill string section 10’ or components of the BHA. This amplitude limitation can be beneficial in controlling the heat generated at the friction surfaces 27a, 27b and 31a. 31b, for example. A mechanical limiter (not shown) may be provided to restrict the amplitude of the relative rotational movement between the inertia masses 20a’, 20b’ and the underlying structure of the drilling system near the drill bit (drill string section 10’). The allowed amplitude corresponds to the desired damping and the relative amplitude utilized to provide it. It can also be optimized or adjusted to provide shocks that enhance the overall relative velocity as described in U. S. Patent No. 12.091 ,921 , the contents of which are incorporated by reference in their entirety.

[0112] The axial springs 40 could be designed to allow start sliding of the friction surfaces 27a, 31a and 27b, 31b relative to each other from a pre-defined modal amplitude of the HFTO acting on either the BHA or the inertia masses 20a’, 20b’. This would reduce the possible relative axial movement of the two inertia masses relative to each other provided by the force the pre-stressed axial springs apply on the inertia masses 20a’ , 20b’ . This would also reduce the normal force applied on the friction surfaces 27a, 31a and 27b, 31b. Alternatively, the pre-stress of the axial springs 40 could be selected to allow sliding of the friction surfaces 27a. 31a and 27b, 31b relative to each other from a certain relative modal amplitude of the HFTO acting on the inertia masses 20a, 20b and the BHA.

[0113] Due to the necked-down portion 13 of the drill string section 10, the friction damper 12 is designed to be split into two c-shaped pieces 20(1) and 20(2), as shown in FIGS. 2A and 3 A. This split design allows the friction damper 12 to be easily installed around the drill string 10 at the necked-down portion 13. As there are two inertia masses the c-shaped pieces 20(1) and 20(2) include four pieces. Two pieces in the inertia mass 20a (20a(l) and 20a(2)) and two in inertia mass 20b (20b(l) and 20b(2)). The c-shaped pieces 20(1), 20(2) surround the drill string section 10 partially.

[0114] Each c-shaped piece, 20a(l), 20a(2) and 20b(l), 20b(2), comprises a quarter of the overall damper element 20 of the friction damper 12. When the four pieces are brought together around the drill string 10, they form the complete damper element assembly. The c-shaped pieces 20a(l), 20a(2) and 20b(l), 20b’2) are designed to securely fit together, encircling the necked-down portion 13 of the drill string section 10 or 10’.

[0115] As illustrated in FIG. 2A, the c-shaped pieces 20(1) and 20(2) each contain corresponding halves of the inertia masses 20a and 20b, as well as the spring pockets 21a and 21b that house the axial springs 40. The centering elements 50, which maintain the alignment and prevent unwanted relative motion between the inertia masses 20a and 20b, are also split between the two c-shaped pieces 20(1) and 20(2). When the c-shaped pieces 20(1) and 20(2) are assembled around the necked-down portion 13 of the drill string 10, they form a complete and functional friction damper 12. This split design facilitates easy installation and removal of the friction damper 12 without the need to disconnect or disassemble the drill string 10.

[0116] The friction damper 12 disclosed herein offers significant versatility in its application within a drill string 10. While the embodiments described above envision placement in or near the BHA 190, the friction damper can be effectively employed at any location along the drill string 10 where mitigation of high-frequency torsional oscillations is desired. This flexibility in positioning allows for strategic placement of the friction damper to optimize its performance based on the specific dynamics and characteristics of the drill string determined in a modal analysis of the drill string and / or the BHA which is performed by a simulation as described in U.S. Patent No. 11,692,404, the contents of which are incorporated by reference in their entirety. Moreover, the design of the friction damper 12 enables it to be used for various purposes beyond mitigating torsional oscillations. For example, it can be utilized to reduce longitudinal vibrations, lateral vibrations, or any combination thereof. The friction damper can also be employed to enhance the overall stability and performance of the drill string 10, improving drilling efficiency and reducing wear on critical components.

[0117] Finally, it is evident that modifications and variations can be made to what has been described and illustrated herein without departing from the scope of this disclosure.

[0118] For example, the design disclosed herein can be readily adapted to serve as a viscous damper. By replacing the friction surfaces 27a, 27b and 30a, 30b of the bearings 24a, 24b and 28a, 28b with suitable sealing elements and filling the spaces between the inertia masses 20a, 2b and the drill string section 10 with a viscous fluid, the friction damper 12 can provide viscous damping to mitigate vibrations and oscillations. The sealing elements, such as elastomeric seals or metal-to-metal seals, would be designed to contain the viscous fluid while allowing for relative motion between the inertia masses and the drill string section. The viscous fluid would dissipate energy through shear forces as the inertia masses 20a, 20b move relative to the drill string section 10. The viscosity of the fluid can be selected based on the specific application and operating conditions to optimize the damping performance. Additionally, the use of a viscous damper eliminates the need for precise control of the normal force between friction surfaces 27a, 27b and 30a, 30b, as the damping force is primarily governed by the viscosity of the fluid and the relative velocity between the inertia masses and the drill string section.

[0119] Also, while axial springs 40 have been described as the primary means of applying normal force to the inertia masses 20a, 20b, note that other functional elements could be employed to achieve the same purpose. These alternative elements could include, but are not limited to, hydraulic systems, pneumatic systems, or electromechanical actuators. For instance, a hydraulic system could use fluid pressure to push the inertia masses apart, while a pneumatic system could use compressed air. Electromechanical actuators, such as piezoelectric elements or linear motors, could also be used to generate the required normal force. Each of these alternatives offers unique advantages in terms of force control, response time, and adaptability to different operating conditions. The choice of force-generating element would depend on factors such as the specific drilling environment, space constraints, and the desired damping characteristics. Regardless of the specific mechanism used, the fundamental principle remains the same: to generate a controlled normal force that creates the necessary friction for effective damping of high-frequency’ torsional oscillations.

[0120] In the illustrated embodiments described hereinabove, the friction damper 12 includes bearings 24a, 24b with bearing heads 26a, 26b that have friction surfaces 27a, 27b at their distal ends that interface with corresponding friction surfaces 31a, 31b of bearing heads 30a, 30b of bearings 28a, 28b affixed to raised shoulders 14a, 14b of the string section 10. However, other configurations are possible.

[0121] For example, the bearings 24a, 24b and 28a. 28b may be replaced with a friction-stiffness element 212a, 212b as shown in FIG. 4A and as first disclosed in U.S. Provisional Application for Patent No. 63 / 589,123. The friction-stiffness element 212a encircles the string section 10 and lies betw een the inertia mass 20a and the raised shoulder 14a, and the friction-stiffness elements 212b encircles lhe string section 10 and lies between the inertia mass 20b and the raised shoulder 14b. The friction-stiffness element 212a, 212b may be designed to form a continuous ring around the string section, allowing for even distribution of the stiffness and frictional forces and providing for consistent performance regardless of the rotational position of the drill string or string section 10.

[0122] The friction-stiffness elements 212a, 212b are making the friction damper to become a self-tuning friction damper, as HFTOs are propagating through the friction damper and frictionstiffness elements 212a, 212b. The friction damper w ith the friction-stiffness elements 212a, 212b included, tunes to the frequency of the HFTOs, thereby dissipating the energy of the HFTO and damping or reducing the amplitude of the HFTOs in the drill string. The self-tuning capability is achieved through the careful selection of spring stiffness and frictional properties in the frictionstiffness elements 212a and 212b, allowing the friction damper to adjust its response to the frequency of the HFTO or to varying frequencies of HFTOs.

[0123] The friction-stiffness elements 212a, 212b each include a frictional element 302a, 302b and a stiffness element 304a, 304b. The stiffness element may be a spring. The frictional elements 302a, 302b provide a frictional resistance to motion (rotation) of the first and second inertia masses 20a, 20b with respect to the drill string and drill string section 10. The springs 304a, 304b provide the ability of the inertia masses 20a, 20b to oscillate (rotationally) with respect to the drill string section 10 while the friction elements 302a. 302b are still sticking. The springs 304a. 304b may be designed with a specific spring rate (spring constant or stiffness coefficient) that allows them to store and release energy efficiently at the frequencies typical of HFTOs, enhancing the overall damping effect.

[0124] The frictional elements 302a, 302b and the springs 304a, 304b are coupled to each other in series between the first and second inertia masses 20a. 20b and the raised shoulders 14a, 14b. with the springs 304a, 304b adjacent to the raised shoulders 14a, 14b and the frictional elements 302a, 302b adjacent to the respective first and second inertia masses 20a, 20b. The frictional elements 302a, 302b include surfaces which are oriented to cause friction during a relative rotation between raised shoulders 14a, 14b and the first and second inertia masses 20a, 20b. The springs 304a, 304b may be torsional springs. The series arrangement of the frictional elements and springs allows for a controlled transfer of energy from the drill string to an oscillation of the first and second inertia masses, where in a first stage the springs absorb the vibrational energy until the HFTO modal amplitude is large enough to overcome the sticking forces of the friction surfaces 27a, 30a and 27b, 30b in the frictional elements 302a, 302b and the first and second inertia masses start to slide relative to the drill string section 10. The frictional elements 212a and 212b dissipate kinetic energy as heat.

[0125] The first and second inertia masses 20a, 20b together have mass moment of inertia Ji. The springs 304a, 304b have a mass moment of inertia J . The mass moment of inertia of the first and second inertia masses may be much greater than the mass moment of inertia of the springs (i.e.. Ji »J2). Thus, acombined moment of inertia Jis equal to:

[0126] J = J1+J2 ~Ji.

[0127] For an HFTO having a low modal amplitude, the frictional elements 302a, 302b cause the springs 304a, 304b to stick to the raised shoulders 14a, 14b, thus transferring the HFTO to the spring 304a. 304b. The springs 304a, 304b therefore experience oscillation amplitudes when absorbing the HFTO. The moment or force between the inertia mass and the string section is then equal to the relative displacement between inertia and BHA times the spring constant. A springmass system defined by the mass moment of inertia of the inertia masses 20a, 20b, the mass moment of inertia of the springs 304a, 304b and a spring constant of the spring is excited and energy excited due to the HFTO is transferred into an oscillation of the spring-mass system. As the amplitude of the HFTO increases, the frictional elements 302a, 302b begin to slide, thereby reducing the amount of energy' transferred into the oscillation of the spring-mass system. At a high enough amplitude of the HFTO, the frictional elements 302a, 302b slide completely so that no energy is transferred into the spring-mass system. The springs 304a, 304b experience no oscillations. The progressive response of the system to increasing HFTO amplitudes ensures that the damping mechanism remains effective across a wide range of operating conditions (HFTO modes), providing optimal protection to the drill string.

[0128] The coefficient of friction of the frictional elements 302a, 302b and the spring constant of the springs 304a, 304b can be selected to make the natural frequency of the friction damper approach the frequency of the HFTO, thus providing increasing the damping of the HFTO mode in comparison to a purely frictional contact. The carefill tuning of the spring constants of the springs 304a, 304b and the coefficients of friction of the friction elements 302a, 302b allows the system to tune the natural frequency of the friction damper to the frequency of the HFTO, maximizing energy absorption and dissipation. This resonance-based damping approach significantly enhances the ability of the friction-stiffness elements 212a, 212b to mitigate harmful vibrations compared to conventional friction damping methods. The tuning effect is a self-tuning effect. When spring constants and coefficient of friction are selected accordingly the friction damper will self-tune its natural frequency to the frequency7of the HFTO when the modal amplitude of the HFTO mode increases.

[0129] Other configurations of the friction-stiffness elements 212a, 212b are possible. As shown in FIG. 4B, the frictional elements 302a, 302b and the springs 304a, 304b are coupled to each other in series between the inertia masses 20a, 20b and the raised shoulders 14a, 14b (string section 10), with the springs 304a, 304b adjacent to the inertia masses 20a, 20b and the frictional elements 302a, 302b adjacent to the raised shoulders 14a, 14b. This reversed configuration provides a similar dynamic response including the self-tuning effect of the natural frequency of friction damper to the frequency of the HFTO.

[0130] Various embodiments showing potential configurations of the friction-stiffness elements 212a, 212b are now described. Refer first to FIG. 5 A, showing a configuration of the frictionstiffness elements 212a, 212b in which a first frictional element portion 302al of the frictional element 302a, a first frictional element portion 302bl of frictional element 302b and the springs 304a, 304b are coupled to each other in series between the inertia masses 20a, 20b and the raised shoulders 14a, 14b, with the springs 304a, 304b adjacent to the inertia masses 20a, 20b and the frictional elements 302a, 302b adjacent to the raised shoulders 14a, 14b (corresponding generally to FIG. 4B). The frictional elements 302a, 302b each include a first frictional element portion 302al and 302bl, and a second frictional element portion 302a2 and 302b2. FIG. 5A shows the first frictional element portions 302al, 302bl connected to the stiffness elements 304a and 304b, while the second frictional element portions 302a2. 302b2 are connected to the raised shoulders 14a, 14b and are not shown. The frictional elements 302a, 302b may be bearings wherein one bearing surface may be part of the first frictional element portions 302al , 302bl and the respective other bearing surface may be part of the second frictional element portions 302a2, 302b2.

[0131] In this embodiment, the springs 304a, 304b take the form of multiple bar-shaped springs extending between frictional elements 302a, 302b (302al, 302b 1) and bases 64a, 64b, with the bases 64a, 64b being affixed to the inertia masses 20a, 20b. These multiple bar-shaped springs 304a, 304b may be equally spaced about the axis of the drill string section. The bar-shaped springs may provide a unique combination of torsional stiffness, allowing the friction-stiffness elements 212a, 212b to respond effectively to torsional vibrations. The equal spacing provides for uniform load distribution and consistent damping performance.

[0132] Cavities are defined by the arrangement of the bar-shaped springs 304a, 304b, bases 64a, 64b, and frictional elements 302a, 302b, or frictional element portions 302al, 302bl, forming the sides of the cavities, and filler inserts 70a, 70b are disposed within these cavities. The mass moment of inertia of the filler inserts 70a, 70b add to the mass moment of inertia of the inertia masses 20a, 20b. Through selection of the stiffness (spring constant) of the bar-shaped springs 304a, 304b and selection of the coefficient of friction of the frictional element 302a, 30b the vibration damping of the friction damper 12 can be tuned. The filler inserts 70a, 70b can be made from a material that has a high density to achieve a large inertia mass to further enhance the overall damping characteristics of the friction damper. These inserts can also serve to protect the springs and frictional elements from debris and drilling fluids, prolonging the operational life of the damping devices.

[0133] Note that the first frictional element portions 302al, 302bl have multiple frictional contacts 24a. 24b extending therefrom to make contact with the frictional contacts on the second frictional element portions 302a2, 302b2 connected to the raised shoulders 14a, 14b. In this specific example, the frictional contacts 24a, 24b are in groups of three, with a respective screwhole 60a, 60b being defined in the first frictional element portions 302al, 302b 1 between each group of three frictional contacts 24a, 24b. A screw or bolt (not shown) may extend through the screw-holes 60a, 60b, through corresponding holes defined in the filler inserts 70a, 70b, and into corresponding holes defined in the bases 64a, 64b. In fact, these screws or bolts may extend through the holes defined in the bases 64a, 64b and into corresponding holes define in the distal ends of the inertia masses 20a, 20b; this w ay, bar-shaped springs 304a, 304b and the respective first the frictional element portions 302al. 302bl of the friction-stiffness elements 212a, 212b are connected to the inertia masses 20a, 20b. The second friction element portions 302a2. 302b2 of the friction-stiffness elements 212a, 212b are connected to the raised shoulder 14a, 14b (not shown). The grouping of frictional contacts in threes may provide a stable contact pattern, providing for even pressure distribution and consistent frictional behavior. The screw or bolt arrangement may allow for easy assembly and disassembly of the friction-stiffness elements, facilitating maintenance and replacement of individual components as needed.

[0134] FIG. 5B provides a detailed view of the friction-stiffness element 212b and the inertia mass 20b. This figure illustrates the holes 68b in the base 64b, which serve as mounting points for the assembly. The cavities 69b, formed by the arrangement of the bar-shaped springs 304b, base 64b, and first frictional element portion 302bl, are clearly visible in this view. These cavities 69b play a role in the friction damper, housing filler inserts (as shown in FIG. 5A) that can further modify the damping characteristics. Notably, the bar-shaped springs 304b feature holes 67b along their length. These holes 67b serve to tune (such as decrease) the stiffness of the bar-shaped springs 304b, allowing for fine-tuning of the spring's response to vibrations. This design element provides an additional way of optimizing damping performance, enabling it to be tailored to specific operational requirements or drilling conditions.

[0135] FIG. 5C presents a side view of the inertia mass 20b and the connected friction-stiffness element 212b, including the spring 304b and the first frictional element portion 302bl, offering a different perspective on the arrangement of components previously seen in FIG. 5B. This cross- sectional view illustrates the layered structure of the friction damper. The inertia mass 20b has the base 64b attached to its outer surface. The bar-shaped springs 304b extend outward from the base 64b, with their holes 67b visible along their length. These holes 67b, as mentioned earlier, serve to decrease the stiffness of the springs 304b, allowing for fine-tuning of the self-tuning damping response. The cavities 69b, formed between the bar-shaped springs 304b, are clearly defined in this view, showcasing the spaces where filler inserts can be placed to further modify the damping characteristics (e.g., increase inertia mass). At the outermost layer, the first frictional element portion 302bl, which interfaces with the drill string via the second frictional element portion 302b2 (not shown), can be observed. The frictional contacts 24b are visible protruding from the first frictional element portion 302bl, arranged in groups to provide balanced contact with the second frictional element portion.

[0136] FIG. 5D provides a detailed isometric view of the components of the friction-stiffness element 212b, specifically highlighting the inertia mass 20b, the base 64b, and the bar-shaped springs 304b. This figure offers a clear perspective on how' these elements are integrated to form the foundation of the friction damper. The inertia mass 20b has the base 64b securely attached to an annular shoulder on the inertia mass. Extending axially (longitudinal axis 18, FIG. 2) from the base 64b are the bar-shaped springs 304b, which are evenly distributed azimuthally along the base 64b and around the longitudinal axis. This arrangement provides for an azimuthally symmetric spring constant. The bar-shaped springs 304b are shown, designed to provide the desired stiffness in series with the frictional element 302b for achieving the self-tuning vibration damping while maintaining structural integrity. The holes 68b in the base 64b are clearly visible, serving as mounting points for the assembly and potentially for attaching additional components (filler inserts). This view emphasizes the design of the system, showing how the bar-shaped springs 304b are anchored to the base 64b and positioned to effectively absorb and dissipate vibrational energy from the drill string.

[0137] FIG. 5E illustrates an alternative design of the friction-stiffness element 212b, featuring a modification to the stiffness element. In this configuration, instead of individual bar-shaped springs, a single monolithic piece of material serves as the stiffness element 304b. The monolithic piece of material may be made from rubber or an elastomer. This continuous ring-shaped structure is positioned between the base 64b and the first frictional element portion 302b 1. The monolithic spring 304b performs the same function as the previously described bar-shaped springs, but with a different structural approach. This design may offer more uniform stress distribution and simplified manufacturing. The frictional element 302b and the first frictional element portion 302bl retains its structure with multiple frictional contacts 24b arranged azimuthally along the first frictional element portion 302b 1, maintaining the ability to provide friction-based damping. Screw holes 60b are visible at regular intervals and reaching through the monolithic spring 304b, serving as attachment points. This monolithic spring design demonstrates the versatility of the friction damper, demonstrating how different spring configurations can be implemented to achieve the desired self-tuning vibration damping characteristics while potentially improving durability and ease of assembly. The monolithic material may be connected to the base 64b and the first friction element portion 302bl by gluing or vulcanization.

[0138] FIG. 5F shows a side view cross-section of the friction-stiffness element 212b, corresponding to the configuration illustrated in FIG. 5E. This perspective clearly shows the layered structure of the device. The inertia mass 20b provides the primary mass for the friction damper. Adjacent to the inertia mass 20b is the base 64b, serving as an interface between the inertia mass 20b and the stiffness element. The monolithic spring 304b, replacing the individual bar-shaped springs seen in earlier configurations, is visible as a continuous layer extending from the base 64b to the first frictional element portion 302bl. This single-piece spring design potentially offers more uniform stress distribution and simplified assembly.

[0139] FIG. 5G illustrates a further refinement of the friction-stiffness element 212b, building upon the design shown in FIG. 5E. The structure remains similar, with the inertia mass 20b at the center affixed to the base 64b and the monolithic spring 304b being capped by the first frictional element portion 302bl with its protruding frictional contacts 24b. Note here the introduction of holes or slits 71b placed throughout the monolithic spring 304b. These holes 71b serve as atuning mechanism for the monolithic spring 304b, allowing for precise adjustment of its stiffness and damping characteristics. By varying the size, shape, and distribution of these holes 71b, the monothetic spring's 304b response to different frequencies and amplitudes of vibration can be finely tuned, potentially enhancing effectiveness in mitigating high-frequency torsional oscillations. The screw holes 60b remain present, providing for secure assembly of the components.

[0140] FIG. 5H shows a side view cross-section (along the longitudinal axis) of the frictionstiffness element 212b, corresponding to the configuration illustrated in FIG. 5G. The inertia mass 20b provides the primary mass for the friction damper. Adjacent to the inertia mass 20b is the base 64b, serving as an interface between the inertia mass 20b and the spring. The monolithic spring 304b is visible as a continuous layer extending from the base 64b to the first frictional element portion 302bl. This view shows the holes 71b cut into the monolithic spring 304b. These holes 71b are suitably placed along the axial length of the spring 304b to allow for precise tuning of its stiffness and damping characteristics. The outermost layer includes the first frictional element portion 302b 1, from which the frictional contacts 24b protrude. The holes or slits may be substantially oriented axially. In an alternative embodiment the holes or slits are angled with respect to the longitudinal axis 18.

[0141] FIG. 51 shows another cross-sectional view (perpendicular to the longitudinal axis) of the friction-stiffness element 212b, focusing on the monolithic spring 304b and its interface with the base 64b. In this configuration, the first frictional element portion 302bl is not shown, allowing for a clearer view of the monolithic spring’s structure. The inertia mass 20b is affixed to the base 64b. The holes or slits 71b are cut into the monolithic spring 304b. These holes or slits 71b are extending radially through the monolithic spring 304b and define multiple projections 72b that extend outward from the base 64b. The projections 72b are evenly distributed azimuthally along the base 64b, forming a comb-like structure. This allows for a more complex and potentially more tunable spring response. The holes or slits 71b can be varied in depth, width, and azimuthal spacing to each other to adjust the stiffness and damping characteristics of the monolithic spring 304b. Additionally, this structure may provide improved (e.g., greater) flexibility in certain directions (torsional) while maintaining larger rigidity in others (axially), potentially offering more sophisticated vibration control. The projections 72b may also serve as mounting points for additional components or allow for easier integration with the first frictional element portion 302b 1.

[0142] FIG. 5J shows a further embodiment of the friction-stiffness element 212b, building upon the concepts seen in previous figures, particularly FIG. 5B. This configuration maintains the structure with the inertia mass 20b at the center, affixed to the base 64b. Observe the increased number and modified arrangement of bar-shaped springs 304b. These springs 304b extend axially (longitudinal axis 19, FIG. 2) from the base 64b, creating a more densely packed spring system compared to earlier versions. The bar-shaped springs 304b are interspersed with cavities 71b, which serve to fine-tune the overall stiffness and damping characteristics. These cavities 7 lb may also provide space for additional components or filler materials to further optimize performance. The outer layer includes the first frictional element portion 302bl, which incorporates multiple frictional contacts 24b arranged azimuthally.

[0143] FIG. 5K shows a detailed side view cross-section (along the longitudinal axis) of the friction-stiffiiess element 212b, corresponding to the configuration illustrated in FIG. 5 J. The inertia mass 20b provides the primary mass for the friction damper. Adjacent to the inertia mass 20b is the base 64b, serving as an interface between the mass 20b and the spring elements. The spring system includes multiple bar-shaped springs 304b extending from the base 64b along the longitudinal axis and radially along the radial extension of the base 64b. These springs 304b create a series of cavities 71b between them. The outermost layer includes the first frictional element portion 302bl, from which the frictional contacts 24b protrude. These contacts 24b are arranged in groups, providing balanced frictional interaction with the second frictional element portion 302b2 on the raised shoulder 14b (drill string). Instead of a hole in the bar-shaped springs, connecting areas 80 between the bar-shaped spring 304b and the base 64b and betw een the barshaped spring and the first friction element portion 302bl is modified to tune the stiffness of the bar-shaped spring 304b. The stiffness can be tuned or determined by shaping the connecting areas 80, such as making the connecting areas smaller or larger. Making the connecting areas smaller, leads to a smaller stiffness. Making the connecting areas larger, leads to a larger stiffness of the bar-shaped spring 304b.

[0144] It should be noted that while FIGS. 5B-5K illustrate various configurations and arrangements of the friction-stiffness element 212b, these designs are equally applicable to the friction-stiffiiess element 212a. Although only 212b is explicitly shown in these figures, the same structural elements, configurations, and design principles would be employed for 212a The mirrored design of 212a would feature the same components - including the inertia mass, base, spring (whether bar-shaped or monolithic), and frictional elements - arranged in the same manner as shown for 212b.

[0145] Copending application PCT Application No. PCT / USXX / XXXXX, filed October 10, 2024 and claiming priority to U.S. Provisional Application for Patent No. 63 / 589,123 filed

[0146] October 10, 2023, is incorporated herein by reference in its entirety, and includes further details that may be utilized w ith the embodiments described herein.

[0147] Although this disclosure has been described with a limited number of embodiments, those skilled in the art, having the benefit of this disclosure, can envision other embodiments that do not deviate from the disclosed scope. Furthermore, skilled persons can envision embodiments that represent various combinations of the embodiments disclosed herein made in various ways.

Claims

CLAIMS1. A friction damper for mitigating torsional oscillation in a drill string, comprising: a drill string having a longitudinal axis; a first inertia mass and a second inertia mass movably attached to the drill string; a first stiffness element between the first inertia mass and the second inertia mass; and a first frictional contact between an axial end of the first inertia mass and the drill string, and a second frictional contact between an axial end of the second inertia mass and the drill string; wherein the first stiffness element applies a force to the first frictional contact and the second frictional contact.

2. The friction damper of claim 1, wherein the force applied to the first frictional contact and the second frictional contact is applied along the longitudinal axis.

3. The friction damper of claim 1, wherein the first frictional contact includes a first frictional surface and a second frictional surface, wherein the force applied to the first frictional contact acts normal to the first frictional surface and the second frictional surface.

4. The friction damper of claim 1, wherein the first inertia mass and the second inertia mass surround the drill string, and the friction damper further comprises a centering element disposed between the first inertia mass and the second inertia mass to prevent relative motion between the first inertia mass and the second inertia mass.

5. The friction damper of claim 4, wherein the first inertia mass and the second inertia mass are configured to rotate around the drill string.

6. The friction damper of claim 1. wherein the first stiffness element is a compression spring, and is configured to compress and expand in a direction parallel to the longitudinal axis of the drill string.

7. The friction damper of claim 1 , wherein the first stiffness element includes a plurality7of stiffness elements.

8. The friction damper of claim 1, wherein the first frictional contact includes a first frictional surface and a second frictional surface, and the first frictional surface and the second frictional surface comprise a poly crystalline diamond (PCD) material.

9. The friction damper of claim 1 , further comprising a second stiffness element between one of (i) the first inertia mass and the first frictional contact and (ii) the drill string and the first frictional contact; wherein the second stiffness element acts in series with the first frictional contact.

10. The friction damper of claim 1 , further comprising a second stiffness element between the first inertia mass and the drill string, and wherein the second stiffness element acts parallel to the first frictional contact.

11. The friction damper of claim 1, wherein the first frictional contact further comprises a first frictional surface and a second frictional surface, and wherein the first frictional surface and the second frictional surface form an angle with the longitudinal axis that is different from 90 degrees.

12. The friction damper of claim 1, wherein the first inertia mass further comprises at least two pieces, each of said pieces partially surrounding the drill string.

13. The friction damper of claim 1, wherein the first stiffness element is located at least partially in a pocket in the first inertia mass, and the first stiffness element is prestressed.

14. The friction damper of claim 1, wherein the first stiffness element is prestressed, and the friction damper further comprises an adjustment element configured to adjust the prestress.

15. The friction damper of claim 1, wherein the first stiffness element comprises two first stiffness elements positioned axially side by side in the first inertia mass.

16. The friction damper of claim 1, wherein the first inertia mass and the second inertia mass are configured to move relative to the drill string with a velocity that is a sum of a periodic velocity fluctuation having an amplitude and a mean velocity, wherein the mean velocity is lower than the amplitude of the periodic velocity fluctuation.

17. A method of mitigating torsional oscillation in a drill string, the method comprising: providing a drill string having a longitudinal axis; movably attaching a first inertia mass and a second inertia mass to the drill string; positioning a stiffness element between the first inertia mass and the second inertia mass; forming a first frictional contact between an axial end of the first inertia mass and the drill string; forming a second frictional contact between an axial end of the second inertia mass and the drill string; and applying a force to the first frictional contact and the second frictional contact using the stiffness element.

18. The method of claim 17, wherein applying the force to the first frictional contact and the second frictional contact comprises applying the force along the longitudinal axis.

19. The method of claim 17, further comprising: locating the stiffness element at least partially in a pocket in the first inertia mass; and prestressing the stiffness element.

20. The method of claim 17, wherein a property of the stiffness element is selected based on a numerical simulation of the drill string.

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