Self-tuning friction damper

Abstract

A drill string (102) includes a downhole vibration damping system (122). The drill string (102) comprises: an inertial mass (208) configured to move relative to the drill string (102); a friction element (302) between the inertial mass (208) and the drill string (102); and a first stiffness element (304) in series with the friction element (302) and between the friction element (302) and one of the inertial mass (208).

Description

Background Technology

[0001] This application claims the benefit of an earlier filing date of U.S. Provisional Application Serial No. 63 / 589,123, filed on October 10, 2023, the entire disclosure of which is incorporated herein by reference.

[0002] In the resource recovery industry, a drill string is delivered downhole to drill a borehole. For drilling purposes, the drill string includes a drill bit attached to a bottom hole assembly (BHA), which connects to the drill pipe extending to the surface. During downhole drilling, severe vibrations or oscillations can occur, affecting the reliability and durability of the tools within the BHA. These vibrations, such as high-frequency torsional oscillations (HFTO), can cause premature damage to the tools or their sub-components. Therefore, a system and method are desired to reduce or mitigate the effects of vibration and HFTO on the BHA during drilling operations. Summary of the Invention

[0003] This document discloses a downhole vibration damping system in a drill string. The system includes: an inertial mass configured to move relative to the drill string; a friction element between the inertial mass and the drill string; and a first stiffness element connected in series with the friction element and between a damper element and the drill string; wherein a first stiffness of the first stiffness element is less than the stiffness of the inertial mass.

[0004] This document also discloses a method for operating a drill string. Vibrations are received at the drill string. The drill string includes: an inertial mass configured to move relative to the drill string; a friction element between the inertial mass and the drill string; and a first stiffness element connected in series with the friction element and between a damper element and the drill string. During drilling, vibrations are absorbed by the movement of the inertial mass relative to the drill string, and the first stiffness element and the friction element absorb vibrations, wherein the first stiffness of the first stiffness element is less than the stiffness of the inertial mass. Attached Figure Description

[0005] The following description should not be considered as limiting in any way. Referring to the accompanying drawings, similar element numbers are similar:

[0006] Figure 1 A drilling system in an exemplary embodiment is shown;

[0007] Figure 2 A side view of the vibration damping section of the drill string in the embodiment is shown;

[0008] Figure 3 A side view of the vibration damping section of the drill string in the first embodiment is shown, which illustrates the details of the vibration damping system;

[0009] Figure 4 A drill string with a vibration damping system is shown in the second embodiment;

[0010] Figure 5 A schematic model is shown, which illustrates, as Figure 3 and Figure 4 The arrangement of components in the vibration damping system shown;

[0011] Figure 6 A schematic model of a vibration damping system in another embodiment is shown;

[0012] Figure 7 A schematic model of the vibration damping system in yet another implementation scheme is shown;

[0013] Figure 8 A schematic model of the vibration damping system in yet another implementation scheme is shown;

[0014] Figure 9 A schematic model of the vibration damping system in yet another implementation scheme is shown;

[0015] Figure 10 A schematic model of the vibration damping system in yet another implementation scheme is shown;

[0016] Figure 11 A schematic model of the vibration damping system in yet another implementation scheme is shown;

[0017] Figure 12 It shows things like Figure 5 The figure shows the damping coefficient curve of a vibration damping system that includes friction elements and stiffening elements connected in series.

[0018] Figure 13 A graph showing the effective stiffness of the vibration damping system is presented.

[0019] Figure 14 A graph showing the natural frequency of the vibration damping system is provided.

[0020] Figure 15 The damping of the HFTO mode caused by the vibration damping system is shown.

[0021] Figure 16 Friction connected to an inertial mass is shown. A cross-section of a portion of a stiffening element;

[0022] Figure 17 It shows Figure 16 The indicated friction Perspective view of a portion of a stiffening element;

[0023] Figure 18 It shows Figure 16 and Figure 17 The indicated friction Perspective view of the stiffening element, the friction The stiffening element includes additional inertial mass disposed in a cavity within the stiffening element;

[0024] Figure 19 It shows Figure 16 and Figure 17 The indicated friction Cross-sectional view of a stiffening element;

[0025] Figure 20 The stiffness-limiting section is shown to be constructed from a ring-shaped element made of an elastic material, such as rubber or an elastomer.

[0026] Figure 21 As shown Figure 20 The indicated rubber or elastomer material, which optionally includes cuts;

[0027] Figure 22 It shows Figure 21 A cross-sectional view of the stiffness-limiting section in the stiffness element and the first friction element portion of the embodiment shown;

[0028] Figure 23 As shown Figure 22 The indicated sectional view;

[0029] Figure 24 An alternative shape combination is shown. Figures 16 to 19 The described implementation scheme of the rod-shaped spring structure; and

[0030] Figure 25 It shows Figure 24 A cross-sectional view of the indicated implementation scheme. Detailed Implementation

[0031] Specific embodiments of one or more implementations of the devices and methods disclosed herein are presented by way of example rather than limitation, with reference to the accompanying drawings.

[0032] refer to Figure 1A drilling system 100 is shown in an exemplary embodiment. The drilling system 100 includes a drill string 102 extending from a platform 106 at a surface location 108 into a borehole 104. The drill string 102 includes a drill bit 110 disposed at its bottom end and a bottom drill string assembly (BHA) 112 in the surface direction of the drill bit 110. Drilling fluid is pumped through the inner bore of the drill string 102 and exits the drill string through nozzles in the drill bit 110. The drilling fluid travels back to the surface in the annulus between the drill string and the borehole wall, and delivers drill cuttings from the borehole to the surface. The BHA 112 includes a downhole telemetry device 114 that communicates with a surface decoder device 116 at the platform 106. The downhole telemetry device 114 transmits pressure pulse signals through the drilling fluid within the drill string 102 for reception at the surface decoder device 116. Pressure pulses are generated by an electrical device 120 housed within the downhole telemetry unit 114. During drilling, drilling fluid is pumped downhole through the drill string 102 to exit at the drill bit 110. The fluid then returns to the surface through the borehole 104 within the annulus formed between the drill string 102 and the borehole wall. Thus, the drill string 102 and the borehole 104 are generally filled with drilling fluid. The drill string 102 may also include the electrical device 120, which performs various operations downhole. The BHA optionally includes a mud motor that rotates the drill bit 110.

[0033] A controller 118 at ground location 108 can be used to control the operation of drill string 102 by changing drilling parameters of drill string 102, such as the rotational speed of drill string 102 (revolutions per minute (RPM)) and the weight applied to the drill bit (WOB) . Operating drill bit 110 to drill hole 104 generates torsional oscillations at drill string 102, which are referred to as high-frequency torsional oscillations (HFTO). Drill string 102 includes a vibration damping system 122 that includes a self-tuning damping device that reduces HFTO and thus mitigates any damage to drill string 102 that would otherwise be caused by HFTO, as disclosed herein.

[0034] The vibration damping system 122 may be placed at selected locations along the drill string 102, such as at the drill bit 110 or in the uphole direction of the drill bit. An example of a configuration having the vibration damping system 122 at the drill bit 110 is shown and described in commonly owned U.S. Patent No. 11,448,015, the entire contents of which are incorporated herein by reference. An example of a configuration having the vibration damping system 122 in the uphole direction of the drill bit is shown and described in commonly owned U.S. Patent No. 11,199,242, the entire contents of which are incorporated herein by reference. Optimizations of the placement of the vibration damping system 122 are shown and described in commonly owned U.S. Patent No. 11,692,404.

[0035] Figure 2 A side view 200 of a vibration damping system 122 for a drill string 102 in one embodiment is shown. The vibration damping system 122 includes a tubular element 202 defining a longitudinal axis 205. In various embodiments, the tubular element 202 may be a section of the drill string 102 or the BHA 112. A drill bit 110 is located at the bottom end of the tubular element 202. The tubular element 202 includes a support 204 that extends radially beyond the radius of the tubular element 202. The support 204 may be a flange of the tubular element 202 or a mass coupled to the outer surface of the tubular element 202. The support 204 is fixedly connected to the tubular element 202 and rotates with the drill string 102 and the BHA 112. Alternatively, the support 204 may be an integral part of the tubular element or the drill string 102. The support cannot rotate relative to the tubular element or the drill string 102. The support member 204 includes a first surface 206 (support surface) located in a transverse plane perpendicular to the longitudinal axis 205. The inertial mass 208 of the vibration damping system 122 is transmitted downhole along with the drill string 102. The inertial mass 208 may be an annular ring or annular sleeve surrounding the tubular element 202. The inertial mass 208 is not directly coupled to the tubular element 202 and moves freely about the tubular element 202. Optionally, a radial bearing is present between the inertial mass 208 and the tubular element 202 to facilitate rotational movement of the inertial mass about the tubular element 202. The inertial mass 208 includes a second surface 210 (mass surface) located in a transverse plane perpendicular to the longitudinal axis 205. The second surface 210 of the inertial mass 208 and the first surface 206 of the support member 204 face each other. A friction-stiffness element 212 includes a friction element and a stiffness element and is located between the support member 204 and the inertial mass 208. The friction-stiffness element 212 enables the vibration damping system 122 to be a self-tuning damping device. As the HFTO is transmitted to the vibration damping system 122 through the drill string 102, the friction-stiffness element 212 tunes the vibration damping system to the frequency of the HFTO, thereby dissipating the energy of the HFTO and damping or reducing the amplitude of the HFTO. The HFTO typically has a frequency higher than 50 Hz, while the viscous / slip torsional vibration typically has a frequency lower than 1 Hz. The inertial mass is optionally formed of a material with high density to achieve a large inertial mass within a given volume. The material of the inertial mass can be, for example, steel, tungsten, nickel, copper, iron, or cobalt. The vibration damping system 122 includes a friction damper. The nature of the friction damper is that the damper element (inertial mass) 208 is configured to move relative to the drill string 102 at a speed equal to the sum of a periodic velocity fluctuation with amplitude and an average velocity, wherein the average velocity is lower than the amplitude of the periodic velocity fluctuation.

[0036] Figure 3A side view 300 of the vibration damping system 122 of the drill string 102 in the first embodiment is shown, illustrating details of the friction-stiffness element 212. The friction-stiffness element 212 includes a friction element 302 and a stiffness element 304. The friction element 302 is an element that provides frictional resistance to the motion (rotation) of the inertial mass 208 relative to the drill string 102. The stiffness element 304 provides the ability of the inertial mass 208 to oscillate (rotatably) relative to the drill string 102. The oscillation is excited by a force acting on the inertial mass 208 (corresponding to the amplitude of the HFTO mode) that is too small to cause the friction element 302 to begin sliding in frictional contact.

[0037] In one embodiment, the stiffness element 304 may be a spring. The friction element 302 and the spring 304 are connected in series in the friction-stiffness element 212. The friction element 302 includes a surface oriented to induce friction during relative rotation between the support 204 and the inertial mass 208. Figure 3 In one embodiment, the friction-stiffness element 212 is mechanically coupled to the inertial mass 208. The friction element 302 in the friction-stiffness element 212 includes a first friction surface 201. A second friction surface 203 is coupled to a support 204. The first friction surface 201 and the second friction surface 203 may be parallel to each other and lie in a plane transverse to the longitudinal axis 205. The spring 304 has two ends, with a first end fixed to the first friction surface 201 and a second end fixed to the inertial mass 208. Figure 3 In this embodiment, the stiffness element 304 is therefore connected to the inertial mass 208. The spring 304 is connected in series with the friction element 302. In this embodiment, the spring 304 is a torsion spring.

[0038] The inertial mass 208 has a moment of inertia J1. The spring 304 has a moment of inertia J2. In various embodiments, the moment of inertia J1 of the inertial mass is much larger than the moment of inertia J2 of the spring (i.e., J1 >> J2). Therefore, the combined moment of inertia J is equal to J = J1 + J2 ~ J1.

[0039] For an HFTO with low modal amplitude, when the frictional contact between the first friction surface 201 and the second friction surface 203 is viscous (neither suddenly loosening nor sliding), the friction element 302 causes the spring 304 to adhere to the support 204 via the first end of the spring 304, the first friction surface 201, and the second friction surface 203. The spring-mass system, defined by the mass of the inertial mass 208, the mass of the spring 304, and the spring constant (stiffness coefficient or spring stiffness), is excited, and the energy excited by the HFTO is converted into oscillations of the spring-mass system. The spring 304 experiences a high oscillation amplitude. The torque between the inertial mass 208 and the drill string 102 is equal to the relative displacement between the inertial mass 208 and the drill string multiplied by the spring constant. As the amplitude of the HFTO increases, the friction element 302 suddenly loosens, and the first friction surface 201 begins to slide relative to the second friction surface 203, and vice versa, thereby reducing the amount of energy stored in the spring-mass system. Therefore, the spring 304 experiences a smaller or reduced oscillation amplitude. At a sufficiently high amplitude of HFTO, the spring-mass system contains no energy, and deformation of spring 304 ceases. The spring-mass system no longer experiences oscillations. The coefficient of friction of friction element 302 and the spring constant of spring 304 can be selected to make the natural frequency of the vibration damping system close to the frequency of HFTO, thus providing increased damping of the HFTO mode compared to pure frictional contact. The normal force F on the frictional contact between the first friction surface 201 and the second friction surface 203... N Provided by bias element 207. Bias element 207 is optionally a spring between inertial mass 208 and block 209 connected to and axially fixed to drill string 102.

[0040] Figure 4 A drill string 102 with a friction-stiffness element 212 is shown in a second embodiment. The friction-stiffness element 212 includes a friction element 302 connected in series with a spring 304. The spring 304 has two ends, one end of which is connected to a support 204, and the other end is connected to a second friction surface 203 included in the friction element 302. A first friction surface 201 is coupled to an inertial mass 208. Thus, in this embodiment, the spring 304 is coupled to the tubular element 202 and the drill string 102 via the support.

[0041] Although the vibration damping system 122 is shown in a tubular design, other designs are contemplated in other embodiments. Different exemplary configurations of the vibration damping system are shown and described in commonly owned U.S. Patent No. 11,136,834, the entire contents of which are incorporated herein by reference.

[0042] Figure 5 A schematic model 500 is shown, which illustrates, as Figure 3The arrangement of components in a vibration damping system, including a friction-stiffness element 212, is shown. A friction element 502 (symbolically represented as friction element 302) and a spring 504 (symbolically represented as spring 304) are shown between a support 204 and an inertial mass 208. The friction element 502 is connected to the support 204 at a first contact 506, and the spring 504 is connected to the inertial mass 208 at a second contact 510. The friction element 502 is characterized by a coefficient of friction μ and a normal force F. N This indicates that the stiffness of spring 504 is determined by the coefficient c. k (Spring stiffness) is expressed as force F. J This represents the force acting on the drill string due to HFTO.

[0043] Figure 6 It shows Figure 3 A schematic model 600 of an alternative embodiment of the vibration damping system is shown. The friction-stiffness element 612 shown between the inertial mass 208 and the support member 204 is represented by a friction element 602 and a spring 604. In this embodiment, the spring 604 serves as a first stiffness element. A second spring 607 is shown between the support member 204 and the inertial mass 208, and this second spring is connected in parallel with the friction-stiffness element 612 and, in particular, with the friction element 602. The second spring 607 has a second stiffness and is connected to the support member 204 at a first end and to the inertial mass 208 at a second end.

[0044] The natural frequency f of the vibration damping system 600 VDS It is a function of the first spring 604, the second spring 607, and the inertial mass 208. The first spring 604, inside the friction-stiffness element 612, is composed of c... k (its limited stiffness c) 串联 The second spring 607, which is connected in parallel with the friction element 602, is defined by c (whose stiffness c is defined by c). 并联 (This is represented by the symbol ) . Due to the nonlinearity of frictional contact, the stiffness c 串联 It is a function of the amplitude of the HFTO. Typically, the effective stiffness decreases with the amount of slip during one oscillation cycle.

[0045] When no slippage occurs at the friction element 602 (i.e., low HFTO amplitude), the natural frequency f of the vibration damping system 600 is... VDS Equal to the viscous frequency f 粘滞 It is shown in equation (1):

[0046] Equation (1)

[0047] Where c 串联 The stiffness is due to the first spring 604, and c 并联is the stiffness due to the second spring 607, and J is the moment of inertia of the inertial mass 208.

[0048] As the amplitude of the HFTO increases, the friction element 602 allows sliding between the first end of the first spring 604 and the support 204. The amount of sliding under vibration at a given amplitude depends on the normal force on the friction surface of the friction element 602, the coefficient of friction μ of the friction surface, the radius r of the friction surface, and the inertia of the inertial mass 208 . When the friction element 602 begins to allow sliding, the natural frequency f of the vibration damping system 600 VDS changes to the effective frequency f 有效 , as shown in Equation (2):

[0049] Equation (2)

[0050] where c 有效 is the spring stiffness c of the first spring 604 k and the properties of the friction element 602 (μ, F N , r, and the moment of inertia J and the amplitude A of the vibration occurring at the friction element 602 where sliding is now allowed). In other words:

[0051] Equation (3)

[0052] At higher amplitudes of the HFTO, the friction element 602 allows sufficient sliding in the friction element 602 and between the first end of the first spring 604 and the support 204 such that the contribution of the first spring 604 to the natural frequency f of the vibration damping system 600 VDS is close to zero. Thus, the natural frequency f VDS is close to the frequency limit f 极限 , as shown in Equation (4):

[0053] Equation (4)

[0054] The value of the spring stiffness c of the first spring 604 in the friction - stiffness element 612 k can be selected to provide natural oscillations at the HFTO mode frequency. Specifically, these values can be selected such that f 粘滞 > the highest expected frequency of the HFTO, and f 极限 < the lowest expected frequency of the HFTO.

[0055] Figure 7A schematic model 700 of a vibration damping system 122 in yet another embodiment is shown. A friction-stiffness element 712, shown between the inertial mass 208 and the support member 204, is represented by a friction element 702 and a first spring 704. A fluid damping element 709 (viscous damping element) is shown in parallel with the first spring 704 and in series with the friction element 702. The fluid damping element 709 is positioned between the friction element 702 and the inertial mass 208. The first spring 704 serves as a first stiffness element. A second spring 707 is shown between the support member 204 and the inertial mass 208, and in parallel with the friction-stiffness element 712. The second spring 707 serves as a second stiffness element. The second spring 707 is connected in parallel with the friction element 702, the stiffness element 704, and the viscous damping element 709. The second spring 707 is connected to the support member 204 at a first end and to the inertial mass 208 at a second end.

[0056] Figure 8 A schematic model 800 of a vibration damping system 122 in yet another embodiment is shown. A friction-stiffness element 812 is shown between the support 204 and the fluid damping element 809. The friction-stiffness element 812 is represented by a friction element 802 and a first spring 804. The fluid damping element 809 is between the friction element 802 and the inertial mass 208. The fluid damping element 809 is shown in series with the friction element 802 and the first spring 804. The friction element 802 is located between the first spring 804 and the fluid damping element 809. The first spring 804 serves as a first stiffness element. A second spring 807 is shown between the support 204 and the inertial mass 208, and in parallel with the friction element 802, the spring 804, and the fluid damping element 809. The second spring 807 serves as a second stiffness element. The second spring 807 is connected to the support 204 at a first end and to the inertial mass 208 at a second end.

[0057] Figure 9A schematic model 900 of a vibration damping system 122 in yet another embodiment is shown. A friction-stiffness element 912 is shown between a support 204 and an inertial mass 208. The friction-stiffness element 912 is represented by a first friction element 902 and a spring 904. A first portion of the first friction element 902 is connected to the support 204. A first end of the spring 904 is connected to a second portion of the first friction element 902. A second end of the spring 904 is connected to the inertial mass 208. A fluid damping element 909 is shown in series with a second friction element 911. The fluid damping element 909 and the second friction element 911 are shown between the support 204 and the inertial mass 208. A first portion of the second friction element 911 is connected to the support 204. A first end of the fluid damping element 909 is connected to a second portion of the second friction element 911. A second end of the fluid damping element 909 is connected to the inertial mass 208. The fluid damping element 909 and the second friction element 911, connected in series, are shown in parallel with the friction-stiffness element 912, which includes the first friction element 902 and the spring 904.

[0058] Figures 3 to 9 A common feature of vibration damping systems is that they all include frictional contacts connected in series with a stiffening element (e.g., a spring). In embodiments that include fluid damping elements, the viscosity of the fluid in the fluid damping element is selected to optimize the self-tuning effect of the friction-stiffness element included in the vibration damping system. When the vibration damping system restricts the movement of the spring in the friction damping element, too much fluid damping reduces the vibration damping system's ability to self-tune to the HFTO frequency.

[0059] Figure 10 A schematic model 1000 of a vibration damping system 122 according to yet another embodiment is shown. The vibration damping system 122 includes a friction-stiffness element 1012, represented by a friction element 1002 connected in series with a spring 1004. The friction element 1002 is connected at a first portion to a support 204 and at a second portion to a first end of the spring 1004. The spring 1004 is connected at its second end to an inertial mass 208. A fluid damping element 1009 is connected in parallel with the friction-stiffness element 1012. The fluid damping element 1009 is connected at a first end to the support 204 and at a second end to the inertial mass 208.

[0060] Figure 11A schematic model 1100 of a vibration damping system 122 in yet another embodiment is shown. The vibration damping system 122 includes a friction-stiffness element 1112, represented by a friction element 1102 connected in series with a first spring 1104. The friction element 1102 is connected at a first portion to a support 204 and at a second portion to a first end of the first spring 1104. The first spring 1104 is connected at a second end to an inertial mass 208. A fluid damping element 1109 is connected in parallel with the friction-stiffness element 1112. The fluid damping element 1109 is connected at a first end to the support 204 and at a second end to the inertial mass 208. A second spring 1107 is connected at a first end to the support 204 and at a second end to the inertial mass 208. The second spring 1107 is connected in parallel with the friction-stiffness element 1112 and in parallel with the fluid damping element 1109.

[0061] Figure 12 A graph 1200 shows the damping coefficient at one modal amplitude of the HFTO vibration damping system, which includes a friction-stiffness element 212 having a friction element 602 and a spring 604 connected in series with the friction element 602, such as Figure 6 As shown. The combined moment of inertia J is equal to 0.03 kg-m. 2 The drill bit rotational speed is shown on the horizontal axis in revolutions per minute (RPM), and the damping coefficient D of the vibration damping system 600 is shown on the vertical axis. Percentages (%) are scaled only by multiplying the damping value of the self-tuning device (by multiplying by 100). Curve 1202 shows the maximum damping coefficient achievable with an untuned friction damper placed at the drill bit. Curve 1204 shows the damping coefficient achievable with a vibration damping system including friction-stiffness elements that make the vibration damping system a self-tuned resonant vibration damping device. The damping coefficient of the self-tuned resonant vibration damping device exceeds the maximum damping coefficient of the friction damper at approximately 32 RPM.

[0062] Figure 13 A graph 1300 showing the effective stiffness of the vibration damping system 600 is presented. The drill bit rotational speed is shown along the horizontal axis in revolutions per minute (RPM), and the effective stiffness is shown along the vertical axis in Newton-meters per radian (Nm / rad). At rotational speeds less than approximately 20 RPM, the friction element 602 is viscous. There is no slippage in the friction element 602. Therefore, the effective stiffness of the vibration damping system 600 is equal to the stiffness of the first spring 604 connected in series with the friction element 602 (first stiffness) plus the stiffness of the second spring 607 acting in parallel with the friction-stiffness element 612 (second stiffness) (i.e., c 串联 +c 并联The stiffening element 607 is fixedly connected to the inertial mass 208 and the support 204, and is positioned between the inertial mass and the support. At rotational speeds greater than approximately 20 RPM, the friction element 602 begins to allow slippage, resulting in a decrease in the initial stiffness of the stiffening element 604 connected in series at higher RPMs.

[0063] Figure 14 A graph 1400 shows the natural frequencies of the vibration damping system 600. The drill bit rotational speed is shown on the horizontal axis in revolutions per minute (RPM), and the natural frequencies are shown on the vertical axis in Hertz (Hz). The dashed line 1402 corresponds to the maximum natural frequency of the vibration damping system (i.e., f). 粘滞 The dashed line 1404 corresponds to the minimum natural frequency (i.e., f) of the vibration damping system. 极限 And it depends on the amplitude of the rotational speed fluctuation present at the drill bit. Curve 1406 is Figure 6 The effective tuning natural frequency of the vibration damping system 600 is shown in curve 1408, which illustrates the frequency of the HFTO-related mode considered in the simulation. The natural frequency of the vibration damping system 600 (curve 1406) decreases with increasing modal amplitude (i.e., with increasing rotational speed). Therefore, the vibration damping system is tuned to an HFTO mode for a specific modal amplitude that provides high damping for that HFTO mode. Tuning of the frequency of that mode can be achieved if the natural frequency is close to the frequency of the HFTO mode. If the frequency of the expected HFTO mode to be damped is within the maximum natural frequency (f) of the vibration damping system... 粘滞 ) and minimum natural frequency (f 极限 This is the case when the natural frequency of the vibration damping system is between 612 and 712. In this case, the friction-stiffness element 612 will self-tune the vibration damping system to the frequency of the HFTO mode, thereby achieving high damping, which is significantly higher than the damping achieved by a vibration damping system using a frequency not tuned to the HFTO mode. The highest damping is achieved when the natural frequency of the vibration damping system is equal to the frequency of the HFTO mode. However, as... Figure 12 It is evident that the damping coefficient increases when the natural frequency of the vibration damping system approaches the natural frequency of the HFTO mode. The natural frequency can also be slightly lower or higher than the HFTO mode frequency (20Hz or 40Hz, or relatively 5% or 10% lower than the HFTO frequency) while still achieving a high damping coefficient.

[0064] Figure 15 The damping of the HFTO mode caused by the vibration damping system 600 is shown. (Reference) Figure 14 and Figure 15As the modal amplitude increases, the frequency of the vibration damping system 600 approaches the natural frequency of the HFTO mode (curve 1408), increasing the damping of the HFTO mode as shown in curve 1502. This damping significantly exceeds that achievable by a non-self-tuning resonant vibration damper (such as a friction damper that does not include a stiffness element 602 connected in series with the friction element 602). A tuned friction damper is a friction damper that includes a stiffness element 607 connected in parallel with the friction element 602, as described in U.S. Patent No. 9,476,261 or U.S. Patent No. 11,136,834. A self-tuning friction damper includes a stiffness element 604 connected in series with the friction element 602, as first disclosed in this application. In addition to the stiffness element 604 connected in series with the friction element 602, a self-tuning friction damper may also include a stiffness element 697 connected in parallel with the friction element 602 to further optimize the self-tuning effect.

[0065] Figure 16 Vibration damping systems (such as) are shown. Figure 3 A detailed embodiment of the friction-stiffness element 1612 in a vibration damping system. The friction-stiffness element 1612 includes a stiffness element 1604 and a friction element 1602. The friction-stiffness element 1612 is connected to a support 204 at a first axial end 1611 and to an inertial mass 208 at a second axial end 1613 opposite to the first axial end. The axial end refers to the longitudinal axis 205. The support 204 is connected to the drill string (such as...). Figure 3 A tubular element (not shown) is depicted. In this embodiment, a stiffening element 1604 is positioned between an inertial mass 208 and a friction element 1602, and the friction element 1602 is positioned between the stiffening element 1604 and a support 204. The friction element 1602 includes a first friction element portion 1602a and a second friction element portion 1602b. The first friction element portion 1602a is part of or fixedly connected to a first base 1614 of the stiffening element 1604, and the second portion 1602b is part of or fixedly connected to the support 204. The friction element 1602 includes a first friction surface 1601 on the first friction element portion 1602a and a second friction surface 1603 on the second friction element portion 1602b. The friction element 1602 is optionally a bearing. The bearing surface is optionally defined by a bearing insert 1619, such as, for example, a diamond insert (polycrystalline diamond composite (PDC)). Friction-stiffening element 1612 is formed as a ring and surrounds the drill string. Figure 2The system comprises a tubular element, which is part of the drill string, and a support 204 connected to the tubular element. The support 204 rotates together with the drill string 102, while the inertial mass 208 is configured to rotate relative to the drill string. The stiffness element 1604 is a segment of the friction-stiffness element 1612 that is more flexible or has less stiffness than the support 204 or the drill string 102 and / or has less stiffness than the inertial mass 208, and is adjusted to a desired stiffness, which is also referred to herein as the predetermined stiffness. Figure 16 The stiffening element 1604 shown in the embodiment is a torsional stiffening element. For example... Figure 16 As shown, the desired stiffness is achieved through a specific geometric configuration of stiffness element 1604. In the illustrated embodiment, a rod spring 1618 is fabricated in stiffness element 1604. The geometry and number of rod springs 1618 (such as azimuth thickness, axial length, annular extension, and the number of rod springs) define the stiffness of stiffness element 1604 in friction-stiffness element 1612. To produce the rod spring in stiffness element 1604, material is removed from annular friction stiffness element 1612. A plurality of rod springs connect the inertial mass 208 and friction element 1602 or first friction element portion 1602a. Each of the plurality of rod springs covers only a small portion of the entire circle (360°) of the ring. The rod spring terminates at a first axial side at a first base 1614 of stiffness element 1604, to which the first friction element portion 1602a is connected. Multiple rod-shaped springs terminate at a second base 1616 connected to an inertial mass 208 on a second axial side opposite to the first axial side. The second base 1616 is connected to a second surface 210. Figure 3 The rod spring 1618 is formed integrally with the second surface 210. It provides flexibility to the stiffness element 1604 and defines a stiffness-defining section of the stiffness element 1604. The stiffness-defining section has a smaller stiffness than the first and second bases. The rod spring is optionally formed by additive manufacturing. Additive manufacturing allows for the formation of more complex structures in the stiffness element 1604 and allows for precise tuning of the desired stiffness (stiffness coefficient). Multiple rod springs may be spaced at a fixed distance from each other along the entire 360° extension about the longitudinal axis 205 of the drill string. In the illustrated embodiment, six rod springs are present at an angular distance of 60° from each other. Alternatively, the rod springs may be placed at non-uniform distances from each other along the entire circle of the ring. A hole 1620 is formed in each rod spring to increase the flexibility of the stiffness element 1604 or decrease its stiffness, depending on the properties that the friction-stiffness element 1612 should possess, to provide efficient damping capability to the vibration damping system. Multiple rod springs 1618 may have all the same size and shape, or their size and shape may vary. The rod springs 1618 are like... Figures 3 to 5The spring shown in the illustrated embodiment functions similarly to the spring. The desired stiffness can optionally be achieved through a design different from that of a rod-shaped spring, such as (i) placing a screw of a specific diameter and length between the first and second bases and configuring it to mechanically connect the first base 1614 and the second base 1616 to the inertial mass 208, or (ii) a flexible material (e.g., rubber or elastomer) between the inertial mass 208 and a first portion of the friction element 1602a or between the first base 1614 and the second base 1616. In embodiments, the stiffness element 1604 may have a complex structure to achieve the desired stiffness required to tune the vibration damping system to a specific natural frequency. Numerical structural modeling (e.g., finite element analysis) can be used to define the geometry of the stiffness element. Figure 16 The geometry shown (bar spring) is just one possible geometry among many optional structures. As an example, the torsional stiffness of the stiffening element 1604 can be between 0.1E+06 N-m / rad and 2.0E+06 N-m / rad.

[0066] Figure 17 A perspective view of a portion of the friction-stiffness element 1612 connected to the mass of inertia 208 is shown. This perspective view shows a through-hole 1630 along the azimuth angle in the first friction element portion 1602a and the first base 1614. The through-hole 1630 is oriented along the longitudinal axis 205 and provides a path for a fixing element (not shown) to pass through and enter a fixing hole 1631 in the second base 1616. The fixing element may be a screw that engages with a thread in the mass of inertia 208 and connects the friction-stiffness element 1612 to the mass of inertia 208. Figure 17 In the illustrated embodiment, the first base 1614 has six through holes 1630, and the second base 1616 has six fixing holes 1631. The second base 1616 is fixedly connected to a shoulder on the inertial mass 208. The shoulder is located on the second surface 210. Figure 3 A rod-shaped spring 1618 is positioned between the first base 1614 and the second base 1616, which provides stiffness to the stiffness element 1604 in the friction-stiffness element 1612. Figure 16In this embodiment, each of the rod springs 1618 includes at least one hole 1620. An azimuth distance from one rod spring to an adjacent rod spring optionally forms a cavity 1619. The dimensions of the cavity between the rod springs, the dimensions and shape of the rod springs 1618 (rectangular, triangular, or curved cross-section perpendicular to the longitudinal axis), the dimensions of the hole 1620 in the rod spring, the axial length of the rod spring, and the material of the rod spring (such as metal), the first base 1614, and the second base 1616 define the stiffness or flexibility (stiffness coefficient) of the stiffness element 1604. The first base 1614 forms a first friction element portion 1602a and includes a first friction surface 1601 of the friction element 1602. Figure 16 The first friction surface 1601 is oriented perpendicular to the longitudinal axis 205 and away from the inertial mass 208. Optionally, the first friction surface 1601 includes a cutting edge with an ultrahard surface, such as a PDC cutting edge 1619. In an alternative embodiment, the first friction surface 1601 may be configured differently and may not include a cutting edge, but may include a continuous surface, such as a tungsten carbide surface or a surface formed of a material that allows tuning the coefficient of friction of the first friction surface 1601. Figure 17 The second friction element 1602b, not shown in the perspective view, complements the friction-stiffness element 1612 to become as follows: Figure 16 The complete friction-stiffness element 1612 is shown. The second friction element portion 1602b is fixedly connected to the support 204. Figure 16 The friction element 1602a is constructed similarly to the first friction element 1602a, thereby including a second friction surface 1603, which correspondingly includes a blade. In one embodiment, the inertial mass 208 is isolated from the downhole environment and drilling fluid by a capping sleeve (not shown) that surrounds and encloses the inertial mass 208 and the friction-stiffness element 1612. In another embodiment, the inertial mass 208 and the friction-stiffness element 1612 are not enclosed by a capping sleeve, but are exposed to the downhole environment and drilling fluid.

[0067] Figure 18 The image shows cavity 1619 placed in stiffness element 1604. Figure 17 The supplementary inertial mass 1632 is added to the initial mass 208 and increases the inertial mass. The supplementary inertial mass 1632 is optionally formed of the same material as the inertial mass 208. In one embodiment, the supplementary inertial mass 1632 is formed of a different material than the inertial mass 208. Figure 18The diagram shows multiple supplementary masses 1632 placed in cavities between rod springs 1618. The supplementary inertial masses 1632 are held within cavities 1619 by a fixing element (not shown) passing through a path through-hole 1630 in the first base 1614 and a hole (not shown) in the supplementary inertial masses, mechanically connecting the supplementary masses 1632 to the friction-stiffness element 1612 and the inertial mass 208. The larger inertial mass 208 plus 1632 has a beneficial effect and increases the damping effect. A gap exists between the rod springs 1618 and the adjacent supplementary inertial masses 1632 to provide space for deformation of the rod springs when torsional oscillations begin to occur, in the event of torsional oscillations acting on the drill string 102 and transmitted through the support 204 and viscous frictional contact in the friction element 1602 to the inertial masses 208 and the supplementary inertial masses 1632.

[0068] Figure 19 It shows Figure 17 The indicated cross-sectional view. This cross-section extends through the rod spring 1618 within the stiffness-defined section of the stiffness element 1604. The cross-section also extends through the hole 1620 in the rod spring 1618. The inertial mass 208 has an inner diameter 1634 and an outer diameter 1635. The inner diameter 1634 extends through the section of the drill string (not shown) surrounded by the inertial mass 208. The inner diameter of the second base 1616 optionally has the same inner diameter 1634 and the same outer diameter 1635 as the inertial mass 208. The second base 1616 is connected to the inertial mass 208 by a fixing element (not shown) passing through the fixing hole 1631. The mass moment of inertia (J2) of the stiffness element 1604 is defined by the materials and geometry of the first base 1614, the second base 1616, and the rod spring 1618. The moment of inertia (J2) of the inertial mass 208 is defined by the material and geometry (inner and outer diameters, axial length) of the inertial mass 208.

[0069] exist Figure 20 In another embodiment shown, the stiffness-defining section is constructed of an annular element 1740, which is made of an elastic material, such as rubber or an elastomer. The rubber material is positioned in the stiffness element 1704 between a first base 1714 and a second base 1716. The rubber or elastomer material is optionally vulcanized to the first and second bases. The rubber material optionally includes, for example, […]. Figure 21 The cut 1741 is shown. The dimensions of the cut 1741 are set to achieve the desired stiffness of the stiffness element 1704. The cut may optionally have different shapes, such as curved cuts or holes. The axial length of the cut 1741 is shorter than the axial length of the rubber material between the first base 1614 and the second base 1616. Figure 22 It shows Figure 21The side view of the stiffness element 1704 and the first friction element portion 1702a of the embodiment shown. Figure 23 As shown in Figure 22 The indicated cross-sectional view. The cross-section is perpendicular to the longitudinal axis 205 of the drill string and extends through the elastic material of the stiffness-defined section of the stiffness element 1704. The cross-section also extends through cutout 1741. A through-hole 1742 in the elastic material is shown, allowing a fixing element (not shown) to pass through. The fixing element connects a friction-stiffness element, including the stiffness element, to the inertial mass 208.

[0070] Figure 24 and Figure 25 The image shows a combination with alternative shapes. Figures 16 to 19 An embodiment of the described rod-spring structure. An optional method to achieve the desired stiffness of the stiffening element 2404 is to use a modified rod-spring geometry. Instead of holes in the rod spring, the connection region 2450 between the rod spring 2418 and the first base 2414 and the second base 2416 is modified to tune the stiffness of the stiffening element 2404. The connection region 2450 in... Figure 25 The image is shown in a side sectional view. Stiffness can be tuned or determined by shaping the connection region 2450 (e.g., making the connection region smaller or larger). Making the connection region smaller results in lower stiffness. Making the connection region larger results in higher stiffness of the stiffness element 2404. Figure 24 and Figure 25 The text shows the relationship with... Figures 16 to 19 The illustrated embodiment uses a greater number of rod springs along the azimuth angle compared to stiffness element 2404. A greater number of rod springs results in a greater number of cavities between them. Both the number of rod springs and the number of cavities contribute to the stiffness value.

[0071] Figures 16 to 25 All the implementation schemes shown correspond to Figure 3 The configuration of the vibration damping system is schematically shown in the diagram. In an alternative embodiment, the friction element 302 (1602) is positioned between the inertial mass 208 and the stiffness elements 304 (1604, 1704, 2504), as... Figure 4 As shown schematically. In this embodiment, stiffness elements 304, 1604, 1704, or 2404 are mechanically coupled to support 204 instead of inertial mass 208. The second base 1616 of the stiffness element is connected to the first surface 206. Figure 3 The second friction element 1602b is either integrally formed with or connected to the inertial mass 208.

[0072] The following are some of the aforementioned publicly disclosed implementation schemes:

[0073] Implementation Scheme 1. A downhole vibration damping system in a drill string. The system includes: an inertial mass configured to move relative to the drill string; a friction element between the inertial mass and the drill string; and a first stiffness element connected in series with the friction element and between the inertial mass and the drill string; wherein a first stiffness of the first stiffness element is less than the stiffness of the inertial mass.

[0074] Implementation Scheme 2. A downhole vibration damping system according to any of the previous embodiments, wherein the friction element includes a first friction surface and a second friction surface, the first friction surface being coupled to a first stiffness element, and the second friction surface being coupled to one of the drill string and the inertial mass.

[0075] Implementation Scheme 3. A downhole vibration damping system according to any of the previous embodiments, wherein the first stiffness is a predetermined stiffness determined by simulation, and the natural frequency of the vibration damping system is tuned to the frequency of torsional vibration of the drill string caused by drilling operations.

[0076] Implementation Scheme 4. A downhole vibration damping system according to any of the previous embodiments, wherein the drill string includes a longitudinal axis, and the first stiffness element includes a first base at a first axial end and a second base at a second axial end opposite to the first axial end, and a stiffness defining section between the first base and the second base.

[0077] Implementation Scheme 5. A downhole vibration damping system according to any of the previous embodiments, wherein the first base is coupled to the friction element and the second base is coupled to one of the inertial mass and the drill string.

[0078] Implementation Scheme 6. A downhole vibration damping system according to any of the previous embodiments, wherein the stiffness limiting section comprises one of a plurality of rod springs, a rubber element, and a plurality of screws.

[0079] Implementation Scheme 7. A downhole vibration damping system according to any of the previous embodiments, wherein the drill string includes a longitudinal axis, and the damper element is rotatably movable relative to the drill string about the longitudinal axis, and the first stiffness element is a torsional stiffness element.

[0080] Implementation Scheme 8. A downhole vibration damping system according to any of the previous embodiments, wherein the inertial mass is configured to move relative to the drill string at a speed that is the sum of a periodic velocity fluctuation with amplitude and an average speed, wherein the average speed is lower than the amplitude of the periodic velocity fluctuation.

[0081] Implementation Scheme 9. A downhole vibration damping system according to any of the previous embodiments, the downhole vibration damping system further comprising a second stiffness element positioned in parallel with the friction element, wherein one end of the second stiffness element is fixedly connected to the inertial mass, and a second end of the second stiffness element is fixedly connected to the drill string.

[0082] Implementation Scheme 10. The downhole vibration damping system according to any of the previous embodiments further includes a fluid damping element.

[0083] Implementation Scheme 11. The downhole vibration damping system according to any of the previous embodiments, wherein the downhole vibration damping system further includes a fluid damping element.

[0084] Implementation Scheme 12. The downhole vibration damping system according to any of the previous embodiments further includes a biasing element configured to force the inertial mass to apply a normal force to the frictional contact between the first and second friction surfaces in the friction element.

[0085] Implementation Scheme 13. A downhole vibration damping system according to any of the previous embodiments, wherein the inertial mass is a sleeve that surrounds a section of the drill string.

[0086] Implementation Scheme 14. A method for damping torsional vibrations in a drill string. Vibrations are received at a vibration damping system in the drill string. The vibration damping system includes: an inertial mass configured to move relative to the drill string; a friction element between the inertial mass and the drill string; and a first stiffness element connected in series with the friction element and between the inertial mass and the drill string. The torsional vibrations are damped at the vibration damping system via the movement of the inertial mass relative to the drill string, wherein a first stiffness of the first stiffness element is less than the stiffness of the inertial mass.

[0087] Implementation Scheme 15. The method according to any prior embodiment, wherein the friction element includes a first friction surface and a second friction surface, the first friction surface being coupled to the first stiffness element, and the second friction surface being coupled to one of the drill string and the inertial mass.

[0088] Implementation Scheme 16. The method according to any prior embodiment, the method further comprising determining the first stiffness by simulation to tune the natural frequency of the vibration damping system to the frequency of torsional vibration of the drill string caused by drilling operations.

[0089] Implementation Scheme 17. The method according to any prior embodiment, wherein the drill string includes a longitudinal axis, and the first stiffening element includes a first base at a first axial end and a second base at a second axial end opposite to the first axial end, and a stiffening defining section between the first base and the second base.

[0090] Implementation Scheme 18. The method according to any previous embodiment, wherein the first base is coupled to the friction element and the second base is coupled to one of the inertial mass and the drill string.

[0091] Implementation Scheme 19. The method according to any prior embodiment, wherein the stiffness limiting section comprises one of a plurality of rod springs, a rubber element, and a plurality of screws.

[0092] Implementation Scheme 20. The method according to any previous embodiment, wherein the drill string includes a longitudinal axis, and the inertial mass is rotatably movable about the longitudinal axis, and the first stiffness element is a torsional stiffness element.

[0093] Implementation Scheme 21. The method according to any prior embodiment, the method further comprising moving the inertial mass relative to the drill string at a speed equal to the sum of a periodic velocity fluctuation having an amplitude and an average speed, wherein the average speed is less than the amplitude of the periodic velocity fluctuation.

[0094] Implementation Scheme 22. According to any of the previous implementation schemes, the downhole vibration damping system further includes a second stiffness element positioned in parallel with the friction element, wherein one end of the second stiffness element is fixedly connected to the inertial mass, and a second end of the second stiffness element is fixedly connected to the drill string.

[0095] Implementation Scheme 23. The method according to any prior embodiment, the method further comprising absorbing the torsional vibration at a fluid damping element.

[0096] Implementation Scheme 24. The method according to any prior embodiment, the method further comprising absorbing the torsional vibration at a fluid damping element.

[0097] Implementation Scheme 25. The method according to any prior embodiment, the method further comprising forcing the inertial mass to apply a normal force to the frictional contact between the first friction surface and the second friction surface in the friction element via a biasing element.

[0098] Implementation Scheme 26. The method according to any previous implementation scheme, wherein the inertial mass is a sleeve that surrounds a section of the drill string.

[0099] In the context of describing the invention (particularly in the context of the appended claims), the terms “an” and “the”, and similar designations, should be interpreted to cover both singular and plural forms, unless otherwise specified herein or clearly contradicted by the context. Furthermore, it should be noted that the terms “first,” “second,” etc., used herein do not indicate any order, quantity, or importance, but are used to distinguish one element from another. The terms “about,” “substantially,” and “generally” are intended to include a degree of error associated with a specific number of measurements based on the equipment available at the time of filing. For example, “about” and / or “substantially” and / or “generally” can include a range of ±8% for a given value.

[0100] The teachings of this disclosure can be applied to a variety of well operations. These operations may involve treating a formation, fluids residing in the formation, the wellbore, and / or equipment within the wellbore, such as production tubing, with one or more treatment agents. Treatment agents can be in the form of liquids, gases, solids, semi-solids, and mixtures thereof. Exemplary treatment agents include, but are not limited to, fracturing fluids, acids, steam, water, brine, corrosion inhibitors, cementing agents, permeability modifiers, drilling mud, emulsifiers, demulsifiers, tracers, flow improvers, etc. Exemplary well operations include, but are not limited to, hydraulic fracturing, production enhancement, tracer injection, cleaning, acidizing, steam injection, water injection, cementing, etc.

[0101] Although the invention has been described with reference to one or more exemplary embodiments, those skilled in the art will understand that various changes can be made and equivalents can be substituted for elements therein without departing from the scope of the invention. Furthermore, many modifications can be made to adapt particular situations or materials to the teachings of the invention without departing from the basic scope of the invention. Therefore, it is contemplated that the invention is not limited to the specific embodiments disclosed as the best mode contemplated for carrying out the invention, but rather that the invention will encompass all embodiments falling within the scope of the claims. Additionally, exemplary embodiments of the invention have been disclosed in the drawings and detailed descriptions, and although specific terminology has been used, it is used in a general and descriptive sense only, and not for limiting purposes, unless otherwise specified; therefore, the scope of the invention is not limited thereto.

Claims

1. A downhole vibration damping system in a drill string, the downhole vibration damping system comprising: Inertial mass, which is configured to move relative to the drill string; A friction element, the friction element being located between the inertial mass and the drill string; and A first stiffness element, which is connected in series with the friction element and between the inertial mass and the drill string; The first stiffness of the first stiffness element is less than the stiffness of the inertial mass.

2. The downhole vibration damping system according to claim 1, wherein the friction element includes a first friction surface and a second friction surface, the first friction surface being connected to the first stiffness element, and the second friction surface being connected to one of the drill string and the inertial mass.

3. The downhole vibration damping system according to claim 1, wherein the first stiffness is a predetermined stiffness determined by simulation, and the natural frequency of the vibration damping system is tuned to the frequency of the torsional vibration of the drill string caused by drilling operations.

4. The downhole vibration damping system of claim 1, wherein the drill string includes a longitudinal axis, and the first stiffness element includes a first base at a first axial end and a second base at a second axial end opposite to the first axial end, and a stiffness-defining section between the first base and the second base.

5. The downhole vibration damping system of claim 4, wherein the first base is coupled to the friction element, and the second base is coupled to one of the inertial mass and the drill string.

6. The downhole vibration damping system according to claim 4, wherein the stiffness limiting section comprises one of a plurality of rod springs, a rubber element, and a plurality of screws.

7. The downhole vibration damping system of claim 1, wherein the drill string includes a longitudinal axis, and the damper element is rotatably movable relative to the drill string about the longitudinal axis, and the first stiffness element is a torsional stiffness element.

8. The downhole vibration damping system of claim 1, wherein the inertial mass is configured to move relative to the drill string at a speed that is the sum of a periodic velocity fluctuation with amplitude and an average speed, wherein the average speed is lower than the amplitude of the periodic velocity fluctuation.

9. The downhole vibration damping system according to claim 1, further comprising a second stiffness element, the second stiffness element being positioned in parallel with the friction element, wherein one end of the second stiffness element is fixedly connected to the inertial mass, and a second end of the second stiffness element is fixedly connected to the drill string.

10. The downhole vibration damping system according to claim 9, wherein the downhole vibration damping system further comprises a fluid damping element.

11. The downhole vibration damping system according to claim 1, wherein the downhole vibration damping system further comprises a fluid damping element.

12. The downhole vibration damping system of claim 1, further comprising a biasing element configured to force the inertial mass to apply a normal force to the frictional contact between the first and second friction surfaces of the friction element.

13. The downhole vibration damping system according to claim 1, wherein the inertial mass is a sleeve that surrounds a section of the drill string.

14. A method for damping torsional vibration in a drill string, the method comprising: Torsional vibrations are received at a vibration damping system in the drill string, the vibration damping system comprising: Inertial mass, which is configured to move relative to the drill string; A friction element, the friction element being located between the inertial mass and the drill string; A first stiffness element, connected in series with the friction element and between the inertial mass and the drill string; and The torsional vibration is damped at the vibration damping system by the movement of the inertial mass relative to the drill string, wherein the first stiffness of the first stiffness element is less than the stiffness of the inertial mass.

15. The method of claim 14, wherein the friction element comprises a first friction surface and a second friction surface, the first friction surface being coupled to the first stiffness element, and the second friction surface being coupled to one of the drill string and the inertial mass.

16. The method of claim 14, further comprising determining the first stiffness by simulation to tune the natural frequency of the vibration damping system to the frequency of torsional vibration of the drill string caused by drilling operations.

17. The method of claim 14, wherein the drill string includes a longitudinal axis, and the first stiffening element includes a first base at a first axial end and a second base at a second axial end opposite to the first axial end, and a stiffening defining section between the first base and the second base.

18. The method of claim 17, wherein the first base is coupled to the friction element, and the second base is coupled to one of the inertial mass and the drill string.

19. The method of claim 17, wherein the stiffness-limiting section comprises one of a plurality of rod springs, a rubber element, and a plurality of screws.

20. The method of claim 14, wherein the drill string includes a longitudinal axis, and the inertial mass is rotatably movable about the longitudinal axis, and the first stiffness element is a torsional stiffness element.

21. The method of claim 14, further comprising moving the inertial mass relative to the drill string at a speed equal to the sum of a periodic velocity fluctuation having an amplitude and an average speed, wherein the average speed is lower than the amplitude of the periodic velocity fluctuation.

22. The method of claim 14, wherein the downhole vibration damping system further comprises a second stiffness element, the second stiffness element being positioned in parallel with the friction element, wherein one end of the second stiffness element is fixedly connected to the inertial mass, and a second end of the second stiffness element is fixedly connected to the drill string.

23. The method of claim 22, further comprising absorbing the torsional vibration at a fluid damping element.

24. The method of claim 14, further comprising absorbing the torsional vibration at a fluid damping element.

25. The method of claim 14, further comprising forcing the inertial mass to apply a normal force to the frictional contact between the first and second friction surfaces in the friction element via a biasing element.

26. The method of claim 14, wherein the inertial mass is a sleeve that surrounds a section of the drill string.

Images