Combined damper
By designing a combined damper and utilizing the vertical arrangement and triangular structure of the first and second dampers, the problems of single-directional energy consumption and post-earthquake residual deformation of traditional metal dampers are solved, and the effects of multi-directional energy consumption and easy recovery are achieved.
Patent Information
- Application Number
- CN202511093703.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-05
- Publication Date
- 2025-10-10
AI Technical Summary
Traditional metal dampers can only achieve energy dissipation and shock absorption in a single direction. The residual deformation after the earthquake is difficult to recover, and the structure is easily damaged by multiple aftershocks.
A combined damper is designed, including a first damper and a second damper, which are arranged vertically in their damping directions. The first damper dissipates vertical energy, while the second damper dissipates lateral energy. A connecting rod composed of a triangular structure and a spring is used to improve recoverability and multi-stage yield capacity.
It achieves multi-directional energy dissipation and shock absorption, reduces post-earthquake residual deformation, and improves the structure's seismic resistance and maintenance convenience.
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Figure CN120759356A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of structural energy dissipation and vibration reduction, in particular to a combined damper. Background Art
[0002] Vibrations of turbines and power plant buildings, as well as earthquakes, pose a significant threat to the safety of hydraulic structures. Therefore, how to reduce damage to engineering buildings by controlling the energy consumption of structural facilities has become a common consensus in the field of structural engineering.
[0003] With the rapid advancement of science and technology, dampers are often used in construction engineering to dissipate structural energy and reduce vibration. Based on their operating principles, dampers can be broadly categorized into: viscous fluid dampers, friction dampers, metal dampers, and magnetorheological dampers. Traditional dampers have numerous drawbacks. For example, due to the inherent properties of the liquid material, viscous fluid dampers can experience internal fluid leakage and aging over time. Friction dampers can also experience high ambient temperatures due to friction, leading to structural degradation. Magnetorheological dampers, which control resistance by varying current, can also leak internally over time, resulting in high costs. Metal dampers, among others, leverage the excellent mechanical properties of metal materials, their high yield strength, good plasticity, and ductility, along with their scientifically designed, to rapidly dissipate energy.
[0004] However, current metal dampers also have some shortcomings:
[0005] (1) Traditional metal dampers usually have only one energy dissipation unit and can only achieve energy dissipation and vibration reduction in a single direction, not in multiple directions. At the same time, after encountering a small earthquake, the energy dissipation unit will undergo elastic deformation and yield. Therefore, the metal damper energy dissipation unit must be replaced after the earthquake.
[0006] (2) The residual deformation of traditional metal dampers after an earthquake is difficult to recover. They are subjected to multiple reciprocating motions, which damages the structure. Therefore, they are unable to withstand multiple aftershocks during an earthquake. Summary of the Invention
[0007] An object of the present invention is to provide a combined damper for solving the problems in the background technology.
[0008] The purpose of the present invention can be achieved through the following technical solutions:
[0009] A combined damper includes a first damper, a second damper, a connecting and fixing rod and a connecting piece. The first damper and the second damper are both triangular. The triangular sides of the first damper can be elastically extended and contracted. The triangular sides of the second damper are fixed in length. The second damper is arranged in the triangle of the first damper. One end of the connecting and fixing rod is connected to the triangular side of the first damper, and the other end is connected to the triangular vertex of the second damper through the connecting piece. The distance between the triangular vertex of the first damper and the adjacent triangular vertex of the second damper is fixed. The damping direction of the second damper is perpendicular to that of the first damper.
[0010] In a further solution, each triangular side of the first damper is composed of a first connecting rod, a second connecting rod, a third connecting rod and a spring, wherein the spring is elastically connected between one end of the first connecting rod and one end of the second connecting rod and between one end of the third connecting rod and the other end of the second connecting rod, and the other end of the first connecting rod and the other end of the third connecting rod are respectively connected to one end of the first connecting rod and / or one end of the third connecting rod on the adjacent side.
[0011] In a further solution, the first connecting rod and the third connecting rod are of equal length, and two adjacent sides of the first damper triangle are connected by a connecting piece.
[0012] In a further embodiment, the spring stiffness is 1000 kN / mm to 2000 kN / mm, so that the spring has a certain anti-seismic stiffness when installed with anti-seismic structural members such as the main structure.
[0013] In a further solution, the second damper includes a first triangular fixing plate, a second triangular fixing plate and an energy-absorbing component, the energy-absorbing component is connected between the first triangular fixing plate and the second triangular fixing plate, and the triangular vertices of the first triangular fixing plate and the second triangular fixing plate are connected to the other end of the connecting fixing rod through the connecting component.
[0014] In a further solution, the energy absorbing component is a waist-shaped tube, and there are multiple of them. The installation center lines of the multiple energy absorbing components form multiple triangles, and an energy absorbing component is arranged at the vertex of each triangle.
[0015] In a further embodiment, the plurality of triangles form at least one inner triangle and one outer triangle, and the inner triangle is arranged inside the outer triangle, and the waist-shaped tubes at adjacent vertices of the inner triangle and the outer triangle are arranged in directions perpendicular to each other.
[0016] In a further solution, the energy dissipation component is connected to the first triangular fixing plate and / or the second triangular fixing plate via a connecting member.
[0017] In a further solution, the connecting member is a bolt, and the connection method of the bolt is detachable.
[0018] In a further solution, the triangular base of the first damper is arranged horizontally, so that when the first damper is installed with a seismic-resistant structural member such as a main structure, the first damper can better support the main structure.
[0019] Beneficial effects of the present invention:
[0020] The present invention arranges a second damper inside the first damper through structural design and scientific and reasonable arrangement and arrangement of various unit components. The damping directions of the two are perpendicular, and energy dissipation in the vertical and transverse planes can be achieved simultaneously. For example, the energy in the vertical plane is dissipated by the first damper, and the energy in the transverse plane is dissipated by the second damper, thereby improving the recoverability after an earthquake. When encountering large external loads and earthquakes, multi-level yield is formed to dissipate energy, which can effectively reduce the post-earthquake residual deformation of the structure. At the same time, the structure is easy to install, replace and maintain.
[0021] The second damper is arranged inside the first damper of the present invention in a triangular design, which has good stability, is not easy to deform, and has strong anti-seismic ability. BRIEF DESCRIPTION OF THE DRAWINGS
[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.
[0023] Figure 1 This is a schematic diagram of the installation of a combined damper in an embodiment of the present invention;
[0024] Figure 2 This is a schematic diagram of a combined damper according to an embodiment of the present invention;
[0025] Figure 3 for Figure 2 Explosion diagram of
[0026] Figure 4 Schematic diagram of a second damper in an embodiment of the present invention;
[0027] Figure 5 for Figure 4 Explosion diagram of
[0028] Figure 6 Schematic diagram of the connection of one side of the triangle of the first damper in an embodiment of the present invention;
[0029] Figure 7for Figure 6 Explosion diagram of
[0030] In the figure: 1. base support; 2. H-shaped steel frame; 3. No. 1 nut; 4. No. 1 bolt; 5. No. 2 bolt; 6. first connecting rod; 7. fixing block; 8. first positioning hole; 9. first triangular fixing plate; 10. second connecting rod; 11. third connecting rod; 12. connecting fixing rod; 13. limiting step; 14. first limiting circular hole member; 15. second limiting circular hole member; 16. third limiting circular hole member; 17. No. 2 nut; 18. second triangular fixing plate; 19. No. 3 bolt; 20. No. 3 nut; 21. first metal energy dissipation part; 22. second metal energy dissipation part; 23. third metal energy dissipation part; 24. fourth metal energy dissipation part; 25. fifth metal energy dissipation part; 26. sixth metal energy dissipation part; 27. second positioning hole; 28. spring; 29. first damper; 30. second damper; 31. limiting mounting groove DETAILED DESCRIPTION
[0031] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.
[0032] like Figure 1 As shown, a combined damper includes a first damper 29, a connecting and fixing rod 12 and a second damper 30, which are connected and fixed to the inner side of a main structure such as a steel structure through connecting parts such as No. 2 bolts 5, No. 2 nuts 17, No. 3 bolts 19 and No. 3 nuts 20.
[0033] The main structure can be composed of a base support 1, three H-shaped steel frames 2, No. 1 nut 3, No. 1 bolt 4 and a limit installation circular groove 31. The first damper 29 is installed in the limit installation circular groove 31 at the triangular vertex and is installed and fixed by No. 2 bolt 5 and No. 2 nut 17.
[0034] like Figure 4 As shown, the second damper 30 includes a first triangular fixing plate 9 and a second triangular fixing plate 18 coaxially arranged in an upper and lower structure. The first metal energy dissipation member 21, the second metal energy dissipation member 22, the third metal energy dissipation member 23, the fourth metal energy dissipation member 24, the fifth metal energy dissipation member 25, and the sixth metal energy dissipation member 26 placed between the first triangular fixing plate 9 and the second triangular fixing plate 18 are fixed and installed by connecting members such as No. 1 bolts 4 and No. 1 nuts 3, forming the second damper 30 as a whole.
[0035] like Figure 5As shown, the first triangular fixing plate 9 and the second triangular fixing plate 18 have the same structure and can be made of steel. The first triangular fixing plate 9 and the second triangular fixing plate 18 are triangular in structure, with three third retaining circular holes 16 welded and fixed at the three corners of the triangle, and second positioning holes 27 are provided for the installation and positioning of connecting parts such as bolts.
[0036] The first metal energy dissipation member 21, the second metal energy dissipation member 22, the third metal energy dissipation member 23, the fourth metal energy dissipation member 24, the fifth metal energy dissipation member 25 and the sixth metal energy dissipation member 26 have the same structure or different structures. They can be made of steel or alternative materials with equivalent strength. Four bolt holes are provided. The centers of the four bolt holes are their installation centers. The cross-section of the metal energy dissipation member is waist-shaped and hollow inside. The connection line of the installation centers of the first metal energy dissipation member 21, the second metal energy dissipation member 22 and the third metal energy dissipation member 23 forms an external triangle. The connection line of the installation centers of the fourth metal energy dissipation member 24, the fifth metal energy dissipation member 25 and the sixth metal energy dissipation member 26 forms an internal triangle. The first and fourth metal energy dissipation members 21 and 24 are arranged perpendicularly to each other within the outer triangle, respectively processing relative displacement in the transverse and longitudinal directions. The second and fifth metal energy dissipation members 22 and 25 are arranged perpendicularly to each other, respectively processing relative displacement in the transverse and longitudinal directions. The third and sixth metal energy dissipation members 23 and 26 are arranged perpendicularly to each other, respectively processing relative displacement in the transverse and longitudinal directions. This perpendicular arrangement enables deformation energy dissipation at multiple angles. It is conceivable that the above energy dissipation function can also be achieved by using three groups of energy dissipation members or by using three or more waist-shaped tubes in each group of energy dissipation members.
[0037] like Figure 6 As shown, the triangular side of the first damper 29 is composed of the first connecting rod 6, the second connecting rod 10, the third connecting rod 11 and the spring 28. In the initial state of the first damper 29, the spring 28 has a partial restoring force reserved. When the main structure is subjected to an earthquake and external loads, the first connecting rod 6, the third connecting rod 11 and the second connecting rod 10 will move relative to each other in the up and down directions along the first positioning hole 8, squeezing the spring 28 to generate a restoring force to achieve energy consumption. Sufficient internal space is reserved at both ends of the second connecting rod 10. After the earthquake and external loads, the restoring force generated by the spring 28 will restore the first damper 29 to its initial structural state. This allows the first damper 29 to be reused and reduces post-earthquake recovery costs.
[0038] like Figure 7As shown, the first connecting rod 6 and the third connecting rod 11 have the same structure, including a first limiting circular hole member 14, a limiting step 13 and a fixed block 7 arranged in sequence. The second connecting rod 10 includes a first positioning hole 8, and the fixed block 7 can move up and down in the first positioning hole 8. The upper end of the lower spring 28 of the two springs 28 contacts the lower end in the gap of the second connecting rod 10, and the lower end of the spring 28 contacts the upper end of the third connecting rod 11. The upper end of the upper spring 28 contacts the lower end of the first connecting rod 6, and the lower end of the spring 28 contacts the upper end in the gap of the second connecting rod 10. It can be imagined that in addition to limiting by the above-mentioned fixed block 7, step holes and step shafts that cooperate with each other can also be processed at the sliding connection ends of the two for limiting.
[0039] like Figure 2 As shown, a connecting rod 12 is fixed to one side of the middle of the first connecting rod 6 and the third connecting rod 11 by welding. Figure 3 As shown, a second limiting circular hole member 15 is welded and fixed to the side of the connecting and fixing rod 12 away from the first connecting rod 6 and the third connecting rod 11 .
[0040] like Figure 3 As shown, bolt holes are opened at the centers of the first limiting circular hole member 14 , the second limiting circular hole member 15 and the third limiting circular hole member 16 for fixing and connecting related parts.
[0041] like Figure 1 As shown, the first dampers 29 are arranged in a triangular shape and are secured to the main structure's limited mounting circular grooves 31 through the first limiting circular holes 14, using No. 2 bolts 5 and No. 2 nuts 17. This configuration transforms the main structure's rectangular unstable structure into three triangular stable structures, further increasing the main structure's safety and its ability to resist earthquakes and external loads.
[0042] like Figure 1 As shown, the second damper 30 is connected to the connecting and fixing rod 12 and fixedly connected via the second limiting circular hole 15 and the third limiting circular hole 16. Specifically, the second limiting circular hole 15 on the connecting and fixing rod 12 at the upper end of the first damper 29 on the left side is connected to the third limiting circular hole 16 on the upper portion of the first triangular fixing plate 9 via a No. 3 bolt 19 and a No. 3 nut 20 in a reserved bolt hole. The second limiting circular hole 15 on the connecting and fixing rod 12 at the lower end of the first damper 29 on the left side is connected to the third limiting circular hole 16 on the lower left side of the second triangular fixing plate 18 via a No. 3 bolt 19 and a No. 3 nut 20 in a reserved bolt hole. The second limiting circular hole 15 on the connecting and fixing rod 12 at the upper end of the first damper 29 on the right side is connected to the third limiting circular hole 16 on the upper portion of the second triangular fixing plate 18 via a No. 3 bolt 19 and a No. 3 nut 20 in a reserved bolt hole.
[0043] The second limiting round hole piece 15 on the connecting fixed rod 12 of the lower end of the first damper 29 on the right side is connected with the third limiting round hole piece 16 on the lower right side of the second triangular fixed plate 18 through the third bolt 19 and the third nut 20 in the reserved bolt hole.
[0044] In some embodiments, referring to Figure 2 As shown, the upper part of the first connecting rod 6 is composed of the first limiting round hole piece 14, the middle connecting rod, and the lower connecting rod, and the lower connecting rod has four fixed clamping blocks 7 fixed on the four sides respectively.
[0045] The first limiting round hole piece 14 has a bolt hole in the center for fixed connection. The second limiting round hole piece 15 has a bolt hole in the center for fixed connection.
[0046] The second connecting rod 10 has a cuboid internal space at the upper and lower ends of the rod respectively, and one spring 28 is installed in each internal space. The second connecting rod 10 has four first positioning holes 8 on the four sides of the upper and lower ends respectively. The four first positioning holes 8 on the upper end of the second connecting rod 10 are fixedly connected with the four fixed clamping blocks 7 on the lower end of the first connecting rod 6. The upper end of the upper spring 28 of the two springs 28 contacts the connecting rod at the lower part of the first connecting rod 6, and the lower end of the spring 28 contacts the upper end in the gap of the second connecting rod 10. The four first positioning holes 8 on the lower end of the second connecting rod 10 are fixedly connected with the four fixed clamping blocks 7 on the upper end of the third connecting rod 11.
[0047] The third connecting rod 11 is composed of the upper connecting rod, the middle connecting rod, and the lower first limiting round hole piece 14, and the upper connecting rod has four fixed clamping blocks 7 fixed on the four sides respectively.
[0048] The third connecting rod 11 has a connecting fixed rod 12 fixed by welding in the middle.
[0049] The upper end of the lower spring 28 of the two springs 28 contacts the upper end in the gap of the second connecting rod 10, and the lower end of the spring 28 contacts the upper end of the third connecting rod 11.
[0050] The first limiting round hole piece 14 on the left side of the upper end of the first damper 29 is connected with the first limiting round hole piece 14 on the upper end of the right side of the first damper 29 through the second bolt 5 and the second nut 17 in the reserved bolt hole.
[0051] The first limiting circular hole member 14 at the lower left end of the first damper 29 and the first limiting circular hole member 14 at the left end of the lower horizontally placed first damper 29 are connected at the reserved bolt hole through the No. 2 bolt 5 and the No. 2 nut 17.
[0052] The first limiting circular hole member 14 at the lower right end of the first damper 29 and the first limiting circular hole member 14 at the right end of the lower horizontally placed first damper 29 are connected at the reserved bolt hole through the No. 2 bolt 5 and the No. 2 nut 17.
[0053] The first triangular fixing plate 9 is a triangle with three vertices respectively provided with three third limiting circular holes 16. The first triangular fixing plate 9 has two sets of triangular bolt holes evenly distributed along the center, with one triangle located inside the other triangle, forming a built-in triangle.
[0054] The second triangular fixing plate 18 is a triangle with three vertices respectively provided with three third limiting circular holes 16. The second triangular fixing plate 18 is provided with bolt holes corresponding to those of the first triangular fixing plate 9.
[0055] A bolt hole is formed at the center of the third limiting circular hole member 16 .
[0056] The second limiting circular hole member 15 on the connecting fixing rod 12 at the upper left end of the first damper 29 and the third limiting circular hole member 16 on the upper part of the first triangular fixing plate 9 are connected in the reserved bolt hole through the No. 3 bolt 19 and the No. 3 nut 20.
[0057] The second limiting circular hole member 15 on the connecting fixing rod 12 at the lower left end of the first damper 29 and the third limiting circular hole member 16 on the lower left side of the second triangular fixing plate 18 are connected in the reserved bolt hole through the No. 3 bolt 19 and the No. 3 nut 20.
[0058] The second limiting circular hole member 15 on the connecting fixing rod 12 at the upper right end of the first damper 29 and the third limiting circular hole member 16 on the upper part of the second triangular fixing plate 18 are connected in the reserved bolt hole through the No. 3 bolt 19 and the No. 3 nut 20.
[0059] The second limiting circular hole member 15 on the connecting fixing rod 12 at the lower right end of the first damper 29 and the third limiting circular hole member 16 on the lower right side of the second triangular fixing plate 18 are connected in the reserved bolt hole through the No. 3 bolt 19 and the No. 3 nut 20.
[0060] The second limiting circular hole member 15 on the connecting fixing rod 12 at the lower left end of the first damper 29 and the third limiting circular hole member 16 on the lower left side of the first triangular fixing plate 9 are connected in the reserved bolt hole through the No. 3 bolt 19 and the No. 3 nut 20.
[0061] The second limiting circular hole member 15 on the connecting fixing rod 12 at the lower right end of the first damper 29 and the third limiting circular hole member 16 on the lower right side of the first triangular fixing plate 9 are connected in the reserved bolt hole through the No. 3 bolt 19 and the No. 3 nut 20.
[0062] like Figure 1 As shown, when the combined damper encounters a large earthquake and external load, the first damper 29 is relatively displaced. The shear force is applied to the first metal energy dissipation member 21, the second metal energy dissipation member 22, the third metal energy dissipation member 23, the fourth metal energy dissipation member 24, the fifth metal energy dissipation member 25, and the sixth metal energy dissipation member 26 through the connecting fixing rod 12, thereby causing the first metal energy dissipation member 21, the second metal energy dissipation member 22, the third metal energy dissipation member 23, the fourth metal energy dissipation member 24, the fifth metal energy dissipation member 25, and the sixth metal energy dissipation member 26 to yield, thereby dissipating energy and ensuring further protection of the main structure.
[0063] It can be imagined that in addition to the structure of bolts, the above-mentioned connecting parts can also be replaced by structures such as optical shafts or sleeves, which can be connected to corresponding parts through welding and bonding. The function of this application can be achieved by only slightly changing the first damper 29, the second damper 30, the connecting fixing rod 12 and the connecting parts, which should all be covered within the scope of protection of this application.
[0064] It should be noted that the terms "first," "second," etc., in this application are used to distinguish similar objects, and are not necessarily used to describe a specific order or precedence. It should be understood that the terms used in this manner are interchangeable where appropriate, so as to facilitate the embodiments of the present application described herein.
[0065] Throughout this specification, references to terms such as "one embodiment," "example," or "specific example" indicate that the specific features, structures, materials, or characteristics described in conjunction with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, schematic representations of these terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
[0066] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention, and such changes and modifications fall within the scope of the invention as claimed.
Claims
1. A combined damper, characterized in that: The invention comprises a first damper (29), a second damper (30), a connecting and fixing rod (12) and a connecting piece. The first damper (29) and the second damper (30) are both triangular in shape. The triangular side of the first damper (29) can be elastically extended and retracted. The triangular side length of the second damper (30) is fixed. The second damper (30) is arranged in the first damper (29). One end of the connecting and fixing rod (12) is connected to the triangular side of the first damper (29), and the other end is connected to the triangular vertex of the second damper (30) through the connecting piece. The distance between the triangular vertex of the first damper (29) and the adjacent triangular vertex of the second damper (30) is fixed. The damping directions of the second damper (30) and the first damper (29) are perpendicular to each other.
2. A combined damper according to claim 1, characterized in that: Each side of the first damper (29) includes a first connecting rod (6), a second connecting rod (10), a third connecting rod (11) and a spring (28), wherein the spring (28) is elastically connected between one end of the first connecting rod (6) and one end of the second connecting rod (10) and between one end of the third connecting rod (11) and the other end of the second connecting rod (10), and the other end of the first connecting rod (6) and the other end of the third connecting rod (11) are respectively connected to one end of the first connecting rod (6) and / or one end of the third connecting rod (11) on the adjacent side.
3. A combined damper according to claim 2, characterized in that: The first connecting rod (6) and the third connecting rod (10) are of equal length, and two adjacent sides of the triangle of the first damper (29) are connected via a connecting piece.
4. A combined damper according to claim 2, characterized in that: The spring (28) has a stiffness of 1000 kN / mm to 2000 kN / mm.
5. A combined damper according to claim 1, characterized in that: The second damper (30) comprises a first triangular fixing plate (9), a second triangular fixing plate (18) and an energy dissipation component, wherein the energy dissipation component is connected between the first triangular fixing plate (9) and the second triangular fixing plate (18), and the triangular vertices of the first triangular fixing plate (9) and the second triangular fixing plate (18) are connected to the other end of the connecting fixing rod (12) through the connecting member.
6. A combined damper according to claim 5, characterized in that: The energy-absorbing parts are waist-shaped tubes, and there are multiple of them. The installation center lines of the multiple energy-absorbing parts form multiple triangles, and an energy-absorbing part is arranged at each vertex of the triangle.
7. A combined damper according to claim 6, characterized in that: The multiple triangles form at least one inner triangle and one outer triangle, and the inner triangle is arranged inside the outer triangle. The waist-shaped tubes at adjacent vertices of the inner triangle and the outer triangle are arranged in directions perpendicular to each other.
8. The combined damper according to claim 5, characterized in that: The energy dissipation component is connected to the first triangular fixing plate (9) and / or the second triangular fixing plate (18) via a connecting piece.
9. A combined damper according to claim 1, 3 or 8, characterized in that: The connecting piece is a bolt, and the connection mode of the bolt is detachable.
10. The combined damper according to claim 1, characterized in that: The triangular base of the first damper (29) is arranged horizontally.