Self-resetting variable-stiffness bidirectional sliding friction damper and design method and application thereof

Abstract

The invention discloses a self-resetting variable-rigidity bidirectional sliding friction damper and a design method and application thereof. The self-resetting variable-rigidity bidirectional sliding friction damper comprises an upper sliding plate located on the upper portion, a lower sliding plate located on the lower portion and a middle double-spherical-surface sliding block located between the upper sliding plate and the lower sliding plate. The lower surface of the upper sliding plate and the upper surface of the lower sliding block are spherical curved surfaces, an upper sliding block is arranged between the upper sliding plate and the middle double-spherical-surface sliding block, and a lower sliding block is arranged between the lower sliding plate and the middle double-spherical-surface sliding block; prestress applying devices are arranged on the periphery of the upper sliding plate and the periphery of the lower sliding plate. Bidirectional deformation and sliding self-resetting are realized through spherical design. Self-resetting capacity and seismic oscillation energy are provided for the structure in the two horizontal directions, and structure displacement is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical fields of construction engineering and bridge engineering, and particularly relates to a self-centering variable-stiffness bi-directional sliding friction damper, its design method and application. Background Art

[0002] Friction dampers are widely used in anti-seismic structures, which can dissipate seismic energy and effectively reduce the displacement of structures under earthquakes. However, the currently commonly used sliding friction dampers mainly focus on energy dissipation and do not have the self-centering ability. This results in residual deformation after earthquakes.

[0003] To improve the self-centering ability of friction dampers, some scholars have proposed dampers based on shape memory alloy (SMA) cables, disc springs or inclined friction surfaces. They utilize the superelasticity of SMA cables, the elasticity of disc springs and the horizontal component force on the inclined plane to achieve automatic reset after deformation. The disadvantages of SMA cable friction dampers, disc spring friction dampers and inclined friction surface dampers are that their deformation capacity is too small. In addition, these self-centering dampers are all unidirectional, and their self-centering ability in the other horizontal direction is poor or basically non-existent. Summary of the Invention

[0004] Aiming at the defects existing in the above-mentioned prior art, the present invention proposes a self-centering variable-stiffness bi-directional sliding friction damper, its design method and application. The damper realizes bi-directional deformation and sliding self-centering through a spherical surface design. The design goal is to provide self-centering ability for the structure in both horizontal directions, dissipate seismic energy and reduce the structural displacement.

[0005] The above object is achieved by the following technical solutions:

[0006] A self-centering variable-stiffness bi-directional sliding friction damper, comprising an upper sliding plate located above, a lower sliding plate located below, and an intermediate double-spherical sliding block located between the upper sliding plate and the lower sliding plate. The lower surface of the upper sliding plate and the upper surface of the lower sliding block are both spherical surfaces. An upper slider is arranged between the upper sliding plate and the intermediate double-spherical sliding block, and a lower slider is arranged between the lower sliding plate and the intermediate double-spherical sliding block. Prestressing devices are arranged around the upper sliding plate and the lower sliding plate.

[0007] Further, the prestressing device includes a plurality of strip-shaped shape memory alloy bundles around the upper sliding plate and the lower sliding plate. Both ends of each strip-shaped shape memory alloy bundle pass through the upper sliding plate and the lower sliding plate and are fixed by bolts. The prestress P provided by this prestressing device SNA = n SMA ·σ SMA ·A SMA, where: n SMA is the number of SMA strips in the strip-shaped shape memory alloy bundle, and σ SMA is the inherent stress of the SMA, and A SMA is the cross-sectional area of a single SMA strip.

[0008] Furthermore, the prestress applying device includes a plurality of screw rods located around the upper sliding plate and the lower sliding plate. Both ends of each screw rod pass through the upper sliding plate and the lower sliding plate and are fixed by disc springs and nuts. The disc spring is sleeved on the end of the screw rod and is located between the nut and the upper side of the upper sliding plate / the lower side of the lower sliding plate. The pre-tightening force P provided by this prestress applying device total = P bolt + P spring = n bolt ·σ bolt ·A bolt + k spring ·Δ, where: n bolt is the number of high-strength screw rods, σ bolt is the yield stress of the screw rod material, A bolt is the cross-sectional area of a single screw rod, k spring is the stiffness coefficient of the disc spring, and Δ is the compression amount of the disc spring.

[0009] Furthermore, the spherical surface on the lower surface of the upper sliding plate, the spherical surface on the upper surface of the lower sliding block, and the spherical surfaces on the upper and lower sides of the intermediate double-spherical sliding block have the same spherical surface structure. The expression of the spherical surface contour curve is as follows:

[0010]

[0011] In the formula, R is the radius of curvature of the spherical surface, and d s is the width of the spherical surface.

[0012] The present invention also provides a design method for the above self-resetting variable-stiffness bi-directional sliding friction damper. This method includes the following steps:

[0013] S1. Determine the design dimensions of the damper according to the construction requirements, determine the displacement range of the intermediate double-spherical sliding block according to the design dimensions, and determine the maximum displacement u d , the maximum displacement

[0014] S2. Obtain the vertical load P through the force analysis during the working process. P = {P SNA , P total}, and the relationship with the radius of curvature R, where the vertical load P comes from the prestress applying device. The following sliding block is used for illustration:

[0015] Taking the center of the spherical surface of the following sliding plate as the origin, a coordinate system is established, with the horizontal direction as the X-axis and the vertical direction as the Y-axis. Under the action of an earthquake, the lower slider overcomes the static friction and slides. The instantaneous force balance equation of the lower slider at any moment is:

[0016] Pcosθ + Fsinθ - N = 0 (2)

[0017] Psinθ - Fcosθ + f = 0 (3)

[0018] In the formula, P is the vertical load provided by the prestressing device. According to different prestressing devices, P = {P SNA , P totak}, F is the restoring force, N is the normal reaction force received by the lower slider on the spherical surface of the lower sliding plate, f is the tangential friction force received by the lower slider on the spherical surface, and θ is the swinging angle of the lower slider relative to the vertical direction;

[0019] The tangential friction force f received by both sides of the lower slider during the sliding process:

[0020]

[0021] In the formula, μ represents the friction coefficient inherent in the material properties of the spherical surface, represents the sign function of velocity;

[0022] The surface function of the spherical surface is continuous and second-order differentiable throughout the spherical surface. Let the surface function of the spherical surface be y = y(x), then the slope on the spherical surface is y'(x) = tanθ. Therefore:

[0023]

[0024] In the formula, x represents the displacement of the lower slider in the horizontal direction during the sliding process;

[0025] Based on Equation (2), Equation (3), Equation (4) and Equation (5), the restoring force formula F is obtained:

[0026]

[0027] After simplification and substitution, it becomes:

[0028]

[0029] Analyzing the displacement x of the lower slider in the horizontal direction during the sliding process through the restoring force formula F obtained by Equation (7), when the lower slider does not slide in the initial state, the initial restoring force F0 is only provided by the friction force, and at this time x = 0;

[0030] F0 = 2μP (8)

[0031] When the lower slider reaches the maximum displacement x = u d When the restoring force F at the maximum displacement d The sum of friction and horizontal force is:

[0032]

[0033] S3. According to the vertical load P provided by the prestressing device, the maximum displacement u determined in step S1 d , the friction coefficient μ inherent in the material properties and the maximum restoring force F required by the design max , let F d =F max , substitute into formula (9) to calculate R.

[0034] Furthermore, in the process of calculating R in step S3, multiple maximum restoring forces F required by different designs are substituted. max , calculate the curvature radius R of multiple different spherical surfaces, and finally select a set of F according to the project needs max The curvature radius R of the corresponding spherical surface is designed.

[0035] The present invention also provides an application of the above-mentioned self-resetting variable-rigidity bidirectional sliding friction damper, which is installed between the piers and beams of the main bridge of the bridge or in the building structure. Under the action of small and medium earthquakes, a small relative displacement is generated between the piers and beams, and the damper works in coordination with friction energy consumption and elastic reset. The spherical sliding plate and the spherical lower sliding plate serve as fixed support surfaces and form bidirectional sliding contact with the middle double spherical sliding block. The middle double spherical sliding block: driven by the displacement of the piers and beams, slides bidirectionally along the spherical sliding plate, generates friction energy consumption with the contact surface of the upper and lower sliding plates, and dissipates seismic energy; the prestressing device applies a constant normal pressure through the preload force to maintain friction contact; after the earthquake, the prestressing device is used to provide a self-resetting force to reduce residual displacement; the upper slider and the lower slider: work in conjunction with the middle double spherical sliding block, and symmetrical displacement occurs during the sliding process to ensure balanced bidirectional energy consumption; high-strength screws and bolts: fix the upper and lower sliding plates, transfer prestress, and ensure close contact of the friction surfaces;

[0036] When encountering a large earthquake, the relative displacement of the pier and beam increases significantly. The damper adapts to the greater deformation demand through a variable stiffness mechanism, that is, the middle double spherical sliding block: the sliding amplitude increases, and the friction energy dissipation efficiency is improved; the spherical design allows stable sliding under greater displacement to avoid jamming; the prestressing device deforms more with the increase of displacement, the preload force is dynamically adjusted, the friction contact pressure is enhanced, and the energy dissipation capacity is improved; at the same time, the reset force is continuously provided. The curved surface design of the double spherical sliding block: the curved surface curvature radius controls the sliding trajectory to ensure uniform pressure distribution and prevent local wear. The symmetrical structure design: the symmetrical movement of the upper and lower sliders and the middle slider ensures that the damping force is consistent under bidirectional displacement to avoid unidirectional overload;

[0037] Under rare earthquake actions, the damper avoids stress concentration through structural optimization, maintains functional integrity. The middle double spherical sliding block: the sliding limit is further increased, the spherical contact area is enlarged, the stress peak is dispersed, and the friction surface failure is prevented. After the prestressing device reaches the maximum deformation, it still maintains a stable pre-tightening force to avoid fracture due to overload; during the reset process of the prestressing device after the earthquake, energy is absorbed, and the screw provides rigid constraint to prevent the structure from disintegrating. The symmetric bidirectional sliding mechanism: the bidirectional sliding capabilities are balanced, adapting to multi-directional earthquake excitations and avoiding performance degradation caused by unilateral overload.

[0038] Beneficial effects:

[0039] 1. The present invention adopts the double-slider design theory. There are two schemes for applying prestress to the damper. The first is to apply prestress by using SMA (shape memory alloy) plus bolt connection to clamp the upper and lower sliding plates. The second is to connect the upper and lower sliding plates with high-strength screws, and place disc springs between the screws and bolts to apply prestress. Under three levels of earthquake ground motions, namely small and medium earthquakes, large earthquakes, and great earthquakes, it shows excellent seismic performance, effectively reducing structural displacement and dissipating earthquake ground motion energy.

[0040] 2. Through the design structure of variable stiffness bidirectional sliding friction, the present invention can avoid the phenomenon of stress concentration and increase the deformation capacity of the damper. Brief description of the drawings

[0041] Figure 1 is the front view structural schematic diagram of the present invention;

[0042] Figure 2 is the component structure diagram of the present invention;

[0043] Figure 3 is the front view structural schematic diagram of another embodiment of the present invention;

[0044] Figure 4 is the motion mechanism schematic diagram during the working process of the present invention;

[0045] Figure 5 is the free body force distribution diagram of the present invention in the initial position;

[0046] Figure 6 is the force schematic diagram of the lower slider of the present invention during the working process;

[0047] Figure 7 is the force-displacement diagram of the present invention during the working process;

[0048] Figure 8 is the force-displacement diagram of the present invention using spherical curved surfaces with different curvature radii during the working process;

[0049] Description of the reference numerals in the drawings: 1. Upper sliding plate; 2. Lower sliding plate; 3. Intermediate double-spherical sliding block; 4. Upper slider; 5. Lower slider; 6. Strip-shaped shape memory alloy bundle; 7. Screw; 8. Disc spring; 9. Nut. Detailed implementation mode

[0050] The present invention will be further described below in conjunction with the drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.

[0051] Embodiment 1:

[0052] As Figure 1-2 shown, the self-resetting variable stiffness bi-directional sliding friction damper of the present invention includes an upper sliding plate 1 located above, a lower sliding plate 2 located below, and an intermediate double-spherical sliding block 3 located between the upper sliding plate and the lower sliding plate. The lower surface of the upper sliding plate and the upper surface of the lower sliding block are both spherical surfaces. An upper slider 4 is arranged between the upper sliding plate and the intermediate double-spherical sliding block, a lower slider 5 is arranged between the lower sliding plate and the intermediate double-spherical sliding block, and a prestress applying device is arranged around the upper sliding plate and the lower sliding plate.

[0053] In this embodiment, the prestress applying device includes a plurality of strip-shaped shape memory alloy bundles 6 arranged around the upper sliding plate and the lower sliding plate. Both ends of each strip-shaped memory alloy bundle pass through the upper sliding plate and the lower sliding plate and are fixed by bolts 7. The prestress P provided by this prestress applying device SNA = n SMA ·σ SMA ·A SMA , where: n SMA is the number of SMA strips in the strip-shaped shape memory alloy bundle, σ SMA is the inherent stress of SMA, and A SMA is the cross-sectional area of a single SMA. For example: if the cross-sectional area A SMA of a single SMA = 0.001m 2 , the superelastic stress σ SMA = 500 MPa, and the total pre-tightening force P = 50 kN is required, then the required number of SMAs is:

[0054] In this embodiment, the spherical surface on the lower surface of the upper sliding plate, the spherical surface on the upper surface of the lower sliding block, and the spherical surfaces on the upper and lower sides of the intermediate double-spherical sliding block have the same spherical surface structure, and the expression of the spherical surface contour curve is as follows:

[0055]

[0056] In the formula, R is the radius of curvature of the spherical surface, and d s is the width of the spherical surface.

[0057] Example 2:

[0058] As Figure 3-4 shown, in this embodiment, the prestress application device includes a plurality of screw rods 8 located around the upper sliding plate and the lower sliding plate. Both ends of each screw rod pass through the upper sliding plate and the lower sliding plate and are fixed by a disc spring 9 and a nut 10. The disc spring is sleeved on the end of the screw rod and is located between the nut and the upper side of the upper sliding plate / the lower side of the lower sliding plate. The pre-tightening force P provided by this prestress application device total = P bolt + P spring = n bolt ·σ bolt ·A bolt + k spring ·Δ, where: n bolt is the number of high-strength screw rods, σ bolt is the yield stress of the screw rod material, A bolt is the cross-sectional area of a single screw rod, k spring is the stiffness coefficient of the disc spring, and Δ is the compression amount of the disc spring. For example: For the screw rod part: If the cross-sectional area A of a single screw rod bolt = 0.0005m 2 , the yield stress σ bolt = 800 MPa, and the number n bolt = 3, then: P bolt = 3·800×10 6 Pa·0.0005m 2 = 1200 kN; For the disc spring part: If the spring stiffness k spring = 100 kN / mm and the compression amount Δ = 2 mm, then: P spring = 100 kN / mm·2 mm = 200 kN; The total pre-tightening force: P total = P bolt + P spring = 1200 kN + 200 kN = 1400 kN.

[0059] Example 3:

[0060] This embodiment provides a design method for the above self-resetting variable stiffness bi-directional sliding friction damper, and this method includes the following steps:

[0061] S1. Determine the design dimensions of the damper according to the construction requirements, determine the displacement range of the intermediate double-spherical sliding block according to the design dimensions, and determine the maximum displacement u d , the maximum displacement

[0062] S2. Obtain the vertical load P through the force analysis during the working process, P = {P SNA , P total}, and the relationship with the radius of curvature R, where the vertical load P is derived from the prestressing application device. The following slider is described as follows: As Figure 6-7 shown, establish a coordinate system with the center of the spherical surface of the following sliding plate as the origin, the horizontal direction as the X-axis, and the vertical direction as the Y-axis. Under the action of an earthquake, the lower slider overcomes the static friction and slides. The instantaneous force balance equation of the lower slider at any moment is:

[0063] Pcosθ + Fsinθ - N = 0 (2)

[0064] Psinθ - Fcosθ + f = 0 (3)

[0065] In the formula, P is the vertical load provided by the prestressing application device. According to different prestressing application devices, P = {P SNA , P total}, F is the restoring force, N is the normal reaction force received by the lower slider on the spherical surface of the lower sliding plate, f is the tangential friction force received by the lower slider on the spherical surface, and θ is the swinging angle of the lower slider relative to the vertical direction;

[0066] The tangential friction forces f received on both sides during the sliding process of the lower slider are:

[0067]

[0068] In the formula, μ represents the friction coefficient inherent in the material properties of the spherical surface, represents the sign function of velocity;

[0069] The surface function of the spherical surface is continuous and second-order differentiable throughout the spherical surface. Let the surface function of the spherical surface be y = y(x), then the slope on the spherical surface is y′(x) = tanθ. Therefore:

[0070]

[0071] In the formula, x represents the displacement of the lower slider in the horizontal direction during the sliding process;

[0072] Based on equations (2), (3), (4), and (5), the restoring force formula F is obtained:

[0073]

[0074] After simplification and substitution, it becomes:

[0075]

[0076] Analyze the horizontal displacement \(x\) of the lower slider during the sliding process using the restoring force formula \(F\) obtained from Equation (7). When the lower slider does not slide in the initial state, the initial restoring force \(F_0\) is provided only by the frictional force, and at this time \(x = 0\).

[0077] \(F_0 = 2\mu P\) (8)

[0078] When the lower slider reaches the maximum displacement \(x = u\) d the restoring force \(F\) at the maximum displacement d is the sum of the frictional force and the horizontal force:

[0079]

[0080] S3. Apply the vertical load \(P\) according to the prestressing device, the maximum displacement \(u\) determined in step S1 d , the friction coefficient \(\mu\) inherent in the material properties, and the maximum restoring force \(F\) required by the design requirements max , let \(F\) d \(= F\) max , substitute into the formula (9) to calculate \(R\). For example, given the design target restoring force \(F\) max \(= 0.432\ kN\), the vertical load \(P = 1\ kN\), the friction coefficient \(\mu = 0.05\), and the maximum lateral displacement \(u\) d \(= 70\ mm\), substituting into the formula gives \(R\approx200\ mm\).

[0081] Furthermore, during the process of calculating \(R\) in step S3, substitute multiple different maximum restoring forces \(F\) required by the design requirements max , calculate multiple different curvature radii \(R\) of the spherical surface, and finally select a set of \(F\) according to the engineering needs max and its corresponding curvature radius \(R\) of the spherical surface to complete the design, as Figure 7-8 shown:

[0082] Substitute the specific data of the damper into the formula for calculation, where let \(P = 1\), the friction coefficient \(\mu = 0.05\), the curvature radius \(R\) of the spherical surface \(= 200\ mm\), and the maximum displacement \(u\) d \(= 70\ mm\).

[0083] Obtain the initial position restoring force \(F_0\): \(F_0 = 0.005\ N\cdot mm\); obtain the restoring force \(F\) at the maximum displacement position d : \(F\) d \(= 0.432\ N\cdot mm\). Substitute the spherical surface radii of \(100\ mm\), \(125\ mm\), \(150\ mm\), \(175\ mm\), and \(200\ mm\) into the restoring force model for calculation, and draw the force-displacement diagrams of different curvature radii as Figure 8 shown.

[0084] The present invention also provides an application of the above self - resetting variable - stiffness bi - directional sliding friction damper, which is installed between the pier and the beam of the main bridge of a bridge or in a building structure, such as Figure 5 as shown:

[0085] (1) Under minor and moderate earthquakes, a small relative displacement occurs between the pier and the beam. The damper works in coordination with friction energy dissipation and elastic reset.

[0086] The upper sliding plate on the spherical surface and the lower sliding plate on the spherical surface serve as fixed supporting surfaces, forming a bi - directional sliding contact with the intermediate double - spherical sliding block to ensure uniform pressure distribution and avoid local stress concentration. Intermediate double - spherical sliding block: Driven by the displacement between the pier and the beam, it slides bidirectionally along the spherical sliding plate, generating friction energy dissipation at the contact surface with the upper and lower sliding plates to dissipate seismic energy. SMA cable (shape memory alloy) or disc spring: Apply a constant normal pressure through pre - tightening force to maintain frictional contact; after an earthquake, use super - elasticity (SMA) or elastic deformation (disc spring) to provide a self - resetting force to reduce residual displacement. Upper slider and lower slider: Linked with the intermediate double - spherical sliding block, they undergo symmetric displacement during the sliding process to ensure balanced bi - directional energy dissipation. High - strength screw and bolt: Fix the upper and lower sliding plates, transfer prestress, and ensure tight contact of the friction surface.

[0087] Overall effect: Friction energy dissipation is dominant, and SMA or disc spring simultaneously provides a resetting force, effectively controlling the displacement of the bridge and maintaining the structural stability.

[0088] (2) When a major earthquake occurs, the relative displacement between the pier and the beam increases significantly. The damper adapts to the greater deformation requirement through a variable - stiffness mechanism.

[0089] Intermediate double - spherical sliding block: The sliding amplitude increases, and the friction energy dissipation efficiency improves; the spherical design allows stable sliding under larger displacements, avoiding jamming. SMA cable or disc spring: Undergo greater deformation as the displacement increases, dynamically adjust the pre - tightening force, enhance the frictional contact pressure, and improve the energy - dissipation capacity; at the same time, continuously provide a resetting force. The curved - surface design of the double - spherical sliding block: The radius of curvature of the curved surface controls the sliding trajectory, ensures uniform pressure distribution, and prevents local wear. Symmetric structure design: The symmetric movement of the upper and lower sliders and the intermediate slider ensures that the damping force is consistent under bi - directional displacements and avoids unidirectional overload.

[0090] Overall effect: The cooperation between friction energy dissipation and elastic reset is enhanced, the stiffness is adaptively adjusted with the displacement, and the energy - dissipation capacity under major earthquakes is significantly improved.

[0091] (3) Under rare - earthquake actions, the damper avoids stress concentration through structural optimization and maintains the functional integrity.

[0092] Intermediate double spherical sliding block: The sliding limit is further increased, the spherical contact area is enlarged, the stress peak value is dispersed, and the friction surface failure is prevented. SMA cable or disc spring: After reaching the maximum deformation, it still maintains a stable pre-tightening force to avoid fracture due to overload; it can be completely reset through superelasticity / elasticity after an earthquake. High-strength screw and disc spring combination (the second structural solution): The disc spring compresses and deforms to absorb energy under a huge earthquake, and the screw provides rigid restraint to prevent the structure from disintegrating. Symmetrical two-way sliding mechanism: The two-way sliding capabilities are balanced, adapting to multi-directional earthquake excitations and avoiding performance degradation caused by unilateral overload.

[0093] Overall effect: Through stress dispersion and symmetrical design, the damper can still consume energy efficiently under extreme earthquakes, and ensure rapid reset after an earthquake to protect the safety of the main structure.

[0094] The above embodiments are the preferred embodiments of the nodes of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A self-resetting variable stiffness bi-directional sliding friction damper, comprising an upper sliding plate located above, a lower sliding plate located below, and an intermediate double spherical sliding block located between the upper sliding plate and the lower sliding plate, characterized in that, The bottom of the upper sliding plate and the top of the lower sliding block are both spherical surfaces. An upper sliding block is arranged between the upper sliding plate and the middle double-spherical sliding block, a lower sliding block is arranged between the lower sliding plate and the middle double-spherical sliding block, and prestressing devices are arranged around the upper sliding plate and the lower sliding plate.

2. The self-resetting variable stiffness bi-directional sliding friction damper according to claim 1, wherein The prestress application device includes a number of strip-shaped shape memory alloy bundles located around the upper sliding plate and the lower sliding plate. Both ends of each strip-shaped shape memory alloy bundle pass through the upper sliding plate and the lower sliding plate and are fixed by bolts. The prestress P provided by this prestress application device SNA = n SMA ·σ SMA ·A SMA , where: n SMA is the number of SMA strips in the strip-shaped shape memory alloy bundle, σ SMA is the inherent stress of the SMA, and A SMA is the cross-sectional area of a single SMA.

3. The self-resetting variable stiffness bi-directional sliding friction damper according to claim 1, characterized in that, The prestress applying device includes a number of screw rods located around the upper sliding plate and the lower sliding plate. Both ends of each screw rod pass through the upper sliding plate and the lower sliding plate and are fixed by disc springs and nuts. The disc springs are sleeved on the ends of the screw rods and are located between the nuts and the upper side of the upper sliding plate / the lower side of the lower sliding plate. The pre-tightening force P provided by this prestress applying device total = P bolt + P spring = n bolt ·σ bolt ·A bolt + k spring ·Δ, where: n bolt is the number of high-strength screw rods, σ bolt is the yield stress of the screw rod material, A bolt is the cross-sectional area of a single screw rod, k spring is the stiffness coefficient of the disc spring, and Δ is the compression amount of the disc spring.

4. The self-resetting variable stiffness bi-directional sliding friction damper according to claim 1 or 2 or 3, characterized in that, The spherical surface below the upper sliding plate, the spherical surface above the lower sliding block, and the spherical surfaces on both sides of the middle double-spherical sliding block have the same spherical surface structure, and the spherical surface contour curve expression is as follows: where R is the radius of curvature of the spherical surface, and d s is the width of the spherical surface.

5. A design method of the self-resetting variable stiffness bi-directional sliding friction damper according to any one of claims 1-4, characterized in that The method comprises the following steps: S1. Determine the design dimensions of the damper according to the construction requirements, determine the displacement range of the intermediate double spherical sliding block according to the design dimensions, and determine the maximum displacement u d , the maximum displacement S2. Obtain the vertical load P through the force analysis during the working process, P = {P SNA , P total}, and the relationship with the radius of curvature R, where the vertical load P is derived from the prestressing application device, and the following slider is described: The center of the spherical surface of the lower sliding plate is used as the origin to establish a coordinate system, with the horizontal direction as the X-axis and the vertical direction as the Y-axis. Under the action of an earthquake, the lower slider overcomes the static friction and slides. The instantaneous force balance equation of the lower slider at any time is: Pcosθ+Fsinθ-N=0 (2) Psinθ-Fcosθ+f=0 (3) Wherein, P is the vertical load provided by the prestressing device, and according to different prestressing devices, P = {P SNA , P total}, F is the restoring force, N is the normal reaction force that the lower slider receives on the spherical surface of the lower sliding plate, f is the tangential frictional force that the lower slider receives on the spherical surface, and θ is the swing angle of the lower slider relative to the vertical direction; The tangential friction force f on both sides of the lower slider during sliding is: where μ represents the coefficient of friction inherent in the material properties of the spherical surface, is the sign function representing the velocity; The surface function of the spherical surface is continuous and second-order differentiable throughout the spherical surface. Let the surface function of the spherical surface be y=y(x), then the slope on the spherical surface is y′(x)=tanθ, so: In the formula, x represents the horizontal displacement of the lower slider during sliding; Based on equations (2), (3), (4) and (5), the restoring force formula F is obtained: Simplify and substitute: The restoring force formula F obtained by formula (7) is used to analyze the horizontal displacement x of the lower slider during sliding. When the lower slider does not slide in the initial state, the initial restoring force F0 is only provided by the friction force, and x = 0; F0=2μP (8) When the lower slider reaches the maximum displacement x = u d the restoring force F d at the maximum displacement is the sum of the frictional force and the horizontal force: S3. Apply a vertical load P according to the prestressing device, and the maximum displacement u determined in step S1 d , the friction coefficient μ inherent in the material properties, and the maximum restoring force F required by the design requirements max , let F d = F max , substitute it into formula (9) to calculate R.

6. The design method of the self-resetting variable stiffness bi-directional sliding friction damper according to claim 5, characterized in that, During the process of calculating R in step S3, substitute the maximum restoring force F with multiple different design requirements max , calculate multiple different curvature radii R of the spherical surface, and finally select a set of F according to engineering requirements max Complete the design with the corresponding curvature radius R of the spherical surface 7. Application of a self-resetting variable stiffness bi-directional sliding friction damper according to any one of claims 1-4, characterized in that The self-resetting variable stiffness bidirectional sliding friction damper is installed between the piers and beams of the main bridge of the bridge or in the building structure. Under the action of small and medium earthquakes, a small relative displacement is generated between the piers and beams. The damper works in coordination with friction energy dissipation and elastic reset. The upper spherical sliding plate and the lower spherical sliding plate serve as fixed support surfaces and form bidirectional sliding contact with the middle double spherical sliding block. The middle double spherical sliding block: driven by the displacement of the piers and beams, slides bidirectionally along the spherical sliding plate, generates friction energy dissipation with the contact surface of the upper and lower sliding plates, and dissipates seismic energy; the prestressing device applies a constant normal pressure through the preload force to maintain friction contact; after the earthquake, the prestressing device is used to provide a self-resetting force to reduce residual displacement; The upper and lower sliders are linked with the middle double spherical sliding blocks, and symmetrical displacement occurs during the sliding process to ensure balanced energy consumption in both directions. High-strength screws and bolts fix the upper and lower sliding plates, transfer prestress, and ensure close contact between the friction surfaces. When encountering a major earthquake, the relative displacement between the pier and the beam increases significantly. The damper adapts to the greater deformation requirements through a variable stiffness mechanism, that is, the intermediate double spherical sliding block: the sliding amplitude increases, and the friction energy dissipation efficiency is improved; the spherical design allows stable sliding under greater displacements, avoiding jamming; the prestressing device undergoes greater deformation as the displacement increases, the pre-tightening force is dynamically adjusted, the frictional contact pressure is enhanced, and the energy dissipation capacity is improved; at the same time, a restoring force is continuously provided. The curved surface design of the double spherical sliding block: the radius of curvature of the curved surface controls the sliding trajectory, ensures uniform pressure distribution, prevents local wear, and the symmetric structure design: the symmetric movement of the upper and lower sliding blocks and the intermediate sliding block ensures the consistency of the damping force under bidirectional displacements, avoiding unidirectional overload. Under rare earthquake actions, the damper avoids stress concentration through structural optimization and maintains functional integrity. The intermediate double spherical sliding block: the sliding limit is further increased, the spherical contact area is enlarged, the stress peak value is dispersed, and the friction surface failure is prevented. After the prestressing device reaches the maximum deformation, it still maintains a stable pre-tightening force, avoiding fracture due to overload; during the reset process of the prestressing device after the earthquake, energy is absorbed, and the screw provides rigid constraints to prevent the structure from disintegrating. The symmetric bidirectional sliding mechanism: the bidirectional sliding capabilities are balanced, adapting to multi-directional earthquake excitations, and avoiding performance degradation caused by unilateral overload.

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