Damping amplification type friction pendulum tuned mass damper and design method thereof

Abstract

The invention provides a damping amplification type friction pendulum tuned mass damper and a design method thereof, and belongs to the technical field of energy dissipation and vibration reduction. Comprising a multi-dimensional concave curved surface guide rail, a mass unit, a displacement amplification rod, a viscous liquid damper, a universal fisheye bearing, a universal ball bearing, a supporting bottom plate and a supporting column. The mass unit and a universal ball bearing installed at the bottom of the mass unit are located in the multi-dimensional concave curved surface guide rail and can slide in the multi-dimensional concave curved surface guide rail, and a circular hole is formed in the center of the multi-dimensional concave curved surface guide rail and used for installing a universal fisheye bearing. The displacement amplification rod penetrates through the lower end of the universal fisheye bearing and is connected with a viscous liquid damper, one end of the viscous liquid damper is hinged to the displacement amplification rod, the other end of the viscous liquid damper is hinged to a supporting bottom plate, and the supporting bottom plate is connected with the multi-dimensional concave curved surface guide rail through a supporting column; and the control curve of the sliding surface of the multi-dimensional concave curved surface guide rail is a cycloid. The sensitivity under small and medium earthquakes is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of structural energy dissipation and vibration reduction, and particularly relates to a damping amplified friction pendulum tuned mass damper and its design method. Background Art

[0002] Since the structural vibration control technology was proposed in 1972, remarkable progress has been made in the past more than 30 years. According to whether external energy is required, the current structural vibration control is mainly divided into passive control, semi-active control and active control. Because passive control does not rely on external energy, has a simple structure, low cost and convenient maintenance, it has become a hot field in current engineering applications.

[0003] The tuned mass damper (TMD), as an effective passive control means, is widely used in the seismic and wind resistance control of high-rise and tall structures. At present, many buildings have adopted single pendulum type TMD to control structural vibration. However, these TMDs usually require long cables, resulting in a large amount of internal building space occupation and affecting the actual use function of the building. For the friction pendulum type TMD, although it reduces the occupation of the internal building space, there are problems of poor sensitivity and unsatisfactory shock absorption effect under medium and small earthquakes.

[0004] Therefore, researching and developing a sensitive, efficient and small-space-occupying TMD is of great significance for structural vibration control, release of the internal space of building structures and optimization of building function layout. Summary of the Invention

[0005] The purpose of the present invention is to provide a damping amplified friction pendulum tuned mass damper and its design method for the above existing problems to improve the shock absorption effect.

[0006] To achieve the above purpose, the present invention provides the following solutions:

[0007] A damping amplified friction pendulum tuned mass damper of the present invention includes a multi-dimensional concave curved surface guiding track, a mass unit, a displacement amplification rod, a viscous liquid damper, a universal fish-eye bearing, a universal ball bearing, a support bottom plate, and a support column; the mass unit and the universal ball bearing installed at its bottom are located in the multi-dimensional concave curved surface guiding track and can slide in the multi-dimensional concave curved surface guiding track. A circular opening is provided at the central position of the multi-dimensional concave curved surface guiding track for installing the universal fish-eye bearing. The displacement amplification rod passes through the universal fish-eye bearing and is connected with a viscous liquid damper at the lower end. One end of the viscous liquid damper is hinged to the displacement amplification rod, and the other end is hinged to the support bottom plate. The support bottom plate is connected to the multi-dimensional concave curved surface guiding track through the support column; the control curve of the sliding surface of the multi-dimensional concave curved surface guiding track is a cycloid, and the parametric equation of the cycloid is:

[0008]

[0009] Wherein, r is the radius of the rolling circle, and θ is the angle of the rolling circle.

[0010] Furthermore, the number of the viscous dampers is n, which are evenly arranged within 2π. Therefore, the viscous coefficient C of a single viscous damper needs to satisfy the following conditions:

[0011]

[0012] Wherein, C m is the viscous coefficient of the resistance acting on the mass unit. During design, after determining the mass ratio μ, frequency ratio f, and damping ratio ζ of the tuned mass damper, the calculated mass m (TMD) , stiffness k (TMD) , then the value of C m is:

[0013]

[0014] β is the amplification coefficient of the displacement amplification rod, β = B / b, where B is the distance from the lower end of the displacement amplification rod to the universal fish-eye bearing, and b is the distance from the universal fish-eye bearing to the center point of the mass unit.

[0015] Furthermore, the number n of the viscous dampers is taken as 4 - 8.

[0016] The present invention also provides a design method for the above-mentioned damping amplified friction pendulum tuned mass damper, and the method includes the following steps:

[0017] After determining that the mass ratio μ of the tuned mass damper is taken as 1% - 5%, the frequency ratio f is taken as 0.9 - 1, and the damping ratio ζ is taken as 5% - 15% according to empirical values, calculate the mass m of the mass unit (TMD) , stiffness k (TMD) , then the damping coefficient C of the damping required for the tuned mass damper m is:

[0018]

[0019] The amplification coefficient of the displacement amplification rod is set as β. Set the distance from the lower end of the displacement amplification rod to the universal fish-eye bearing as B, and the distance from the universal fish-eye bearing to the center point of the mass unit as w, β = B / w. According to empirical values, the value range of β is 1.5 - 2;

[0021] Taking the derivative of the displacement element Δd of the mass unit at any moment with respect to time t gives the velocity Δd′ at this moment. According to the similarity ratio, the velocity of the lower end of the lever at this moment is βΔd′. Then the viscous damping force F received by the lower part of the displacement amplification rod is F = C eq V = 0.6Cn·Δd′β, where C eq represents the damping coefficients C of all single viscous dampers connected to the displacement amplification rod synthesized into 1 total equivalent damping coefficient, and n represents the number of viscous dampers; although the output force of the viscous damper does not directly act on the mass unit, through the transmission of the lever, the essence of the resistance received by the mass unit from the displacement amplification rod is still the viscous damping force. Define the viscous coefficient of the resistance acting on the mass unit as C m , according to the lever balance: power × power arm = resistance × resistance arm, we have

[0022] C m ·Δd′·1 = C eq ·Δd′β·β

[0023] C m ·Δd′ = 0.6Cn·Δd′β·β

[0024] C m = 0.6Cnβ 2

[0025] Therefore, the viscous coefficient C of a single viscous damper is:

[0026]

[0027] According to the viscous coefficient C, the required model of a single viscous damper can be determined.

[0028] Compared with the prior art, the beneficial effects of the present invention include the following aspects:

[0029] For the friction pendulum type tuned mass damper with a damping amplification function proposed by the present invention, since the shape of the track is a cycloid, the isochronism of the mass block during movement is ensured, and the detuning problem caused by the nonlinear phenomenon during large-amplitude swinging of the traditional pendulum type TMD is greatly improved, effectively enhancing the robustness of the tuned mass damper.

[0030] Since a ball bearing is installed at the bottom of the mass unit, compared with the friction pendulum type TMD, the sensitivity of this tuned mass damper under medium and small earthquakes is significantly improved, and it can also play a role under medium and small earthquakes, effectively avoiding the problem of poor vibration control effect of the friction pendulum type TMD under medium and small earthquakes due to the large starting slip force.

[0031] The displacement of the mass unit is amplified by a displacement amplification rod, which can achieve more efficient energy dissipation under medium and small earthquakes, further improving the seismic reduction effect of the tuned mass damper under medium and small earthquakes. Description of the Drawings

[0032] Figure 1 It is a schematic structural diagram of a friction pendulum tuned mass damper with a damping amplification function in an embodiment of the present invention.

[0033] Figure 2 It is a front view of a friction pendulum tuned mass damper with a damping amplification function in an embodiment of the present invention.

[0034] Figure 3 It is a top view of a friction pendulum tuned mass damper with a damping amplification function in an embodiment of the present invention.

[0035] Figure 4 It is a sectional view of the 1-1 section in an embodiment of the present invention.

[0036] Figure 5 It is a schematic structural diagram of a viscous liquid damper in an embodiment of the present invention.

[0037] Figure 6 It is a schematic structural diagram of a universal fish-eye bearing in an embodiment of the present invention.

[0038] Figure 7 It is a schematic structural diagram of a universal ball bearing.

[0039] Figure 8 It is a schematic structural diagram of a displacement amplification rod in an embodiment of the present invention.

[0040] Figure 9 It is a schematic diagram of the movement of a viscous damper in an embodiment of the present invention.

[0041] Figure 10 It is a schematic diagram of the amplification function of a displacement amplification rod in an embodiment of the present invention.

[0042] Wherein: 1 - multi-dimensional concave surface guiding track, 2 - mass unit, 3 - displacement amplification rod, 4 - viscous liquid damper, 5 - universal fish-eye bearing, 6 - universal ball bearing, 10 - support base plate, 11 - support column. Detailed Embodiments

[0043] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0044] The object of the present invention is to provide a friction pendulum tuned mass damper with a damping amplification function, so as to solve the problems existing in the above-mentioned prior art and improve the damping effect.

[0045] In order to make the above objects, features and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] As Figures 1-10 shown, the damping amplified friction pendulum tuned mass damper of the present invention includes a multi-dimensional concave curved surface guiding track 1, a mass unit 2, a displacement amplification rod 3, a viscous liquid damper 4, a universal fish-eye bearing 5, a universal ball bearing 6, a support base plate 10, and a support column 11; the mass unit 2 and the universal ball bearing 6 installed at its bottom are located in the multi-dimensional concave curved surface guiding track 1 and can slide in the multi-dimensional concave curved surface guiding track 1. A circular opening is provided at the central position of the multi-dimensional concave curved surface guiding track 1 for installing the universal fish-eye bearing 5. The displacement amplification rod 3 passes through the lower end of the universal fish-eye bearing 5 and is connected to a viscous liquid damper 4. The displacement amplification rod 3 can move freely in the opening, realizing the self-adaptation when the mass unit 2 drives the displacement amplification rod 3 to move, and effectively avoiding the occurrence of jamming. One end of the viscous liquid damper 4 is hinged to the displacement amplification rod 3, and the other end is hinged to the support base plate 10. The support base plate 10 is connected to the multi-dimensional concave curved surface guiding track 1 through the support column 11; the control curve of the sliding surface of the multi-dimensional concave curved surface guiding track 1 is a cycloid, and the parametric equation of the cycloid is:

[0047]

[0048] In the formula, r is the radius of the rolling circle, and θ is the angle of the rolling circle.

[0049] In this embodiment, the number of the viscous dampers 4 is n, which are uniformly arranged within 2π. Therefore, the viscous coefficient C of a single viscous damper 4 needs to satisfy the following conditions:

[0050]

[0051] In the formula, C m is the viscous coefficient of the resistance acting on the mass unit 2. During design, after determining the mass ratio μ, frequency ratio f, and damping ratio ζ of the tuned mass damper, the calculated mass m (TMD) , stiffness k (TMD) , then the value of C m is:

[0052]

[0053] β is the amplification factor of the displacement amplification rod 7, β = B / b, where B is the distance from the lower end of the displacement amplification rod 7 to the universal spherical bearing 5, and b is the distance from the universal spherical bearing 5 to the center point of the mass unit 2.

[0054] In this embodiment, the number n of the viscous dampers 4 is taken as 4 - 8.

[0055] Working process:

[0056] During an earthquake, the main structure vibrates first due to earthquake excitation, and the mass unit will also move within the multi-dimensional concave surface guiding track. Since the movement of the mass block is synchronous but out-of-phase with the main structure, the mass block will exert a reverse inertial force on the structure to control the vibration of the main structure. Thanks to the use of a cycloid as the control curve for the multi-dimensional concave surface guiding track, the period remains unchanged during the movement of the mass unit, effectively avoiding the risk of detuning of the tuned mass damper when the movement amplitude of the mass unit is large. The motion equation of the mass unit 2 oscillating along the multi-dimensional concave surface guiding track 1 only under the action of gravity is:

[0057]

[0058] In the above formula, s is the arc length from the mass unit 2 to the lowest point of the cycloid at a certain moment, g is the acceleration due to gravity, r is the radius of the rolling circle, and t is the time.

[0059] Therefore, the motion of the mass unit 2 within the multi-dimensional concave surface guiding track 1 with simple harmonic motion is simple harmonic motion, thus proving the isochronism of its motion; Motion period

[0060] During the movement of the mass unit, it will drive the displacement amplification rod to move together, and then drive the viscous damper connected to the lower part of the displacement amplification rod to move together. While amplifying the displacement of the mass unit, the displacement amplification rod will also amplify its motion speed. Since the viscous damper is a velocity-dependent damper, the amplification of the motion speed effectively increases the energy dissipation of the viscous damper, can more efficiently consume the externally input energy, and significantly improves the vibration control effect of the tuned mass damper on the main structure.

[0061] The design method of the above damping amplification type friction pendulum tuned mass damper includes the following steps:

[0062] After determining the mass ratio μ of the tuned mass damper to be 1% - 5%, the frequency ratio f to be 0.9 - 1, and the damping ratio ζ to be 5% - 15% according to empirical values, calculate the mass m of the mass unit 2 (TMD) , stiffness k (TMD) , then the damping coefficient C of the damping required for the tuned mass damper m The value of is:

[0063]

[0064] The magnification coefficient of the displacement amplification rod 7 is set to β. Let the distance from the lower end of the displacement amplification rod 7 to the universal fish-eye bearing 5 be B, and the distance from the universal fish-eye bearing to the center point of the mass unit 2 be w. Then β = B / w. According to empirical values, the value range of β is 1.5 to 2;

[0065] Taking the derivative of the displacement element Δd of the mass unit 2 at any time with respect to time t to obtain the velocity Δd' at this moment. According to the similarity ratio, the velocity of the lower end of the lever at this moment is βΔd'. Then the viscous damping force F received by the lower part of the displacement amplification rod 7 at this moment is F = C eq V = 0.6Cn·Δd'β, where C eq represents the damping coefficients C of all single viscous dampers 4 connected to the displacement amplification rod 7 synthesized into one total equivalent damping coefficient. n represents the number of viscous dampers 4. Although the output force of the viscous damper does not directly act on the mass unit 2, through the transmission of the lever, the essence of the resistance received by the mass unit 2 at this time is still the viscous damping force. Define the viscous coefficient of the resistance acting on the mass unit (2) as C m According to the lever balance: power × power arm = resistance × resistance arm, we have

[0066] C m ·Δd'·1 = C eq ·Δd'β·β

[0067] C m ·Δd' = 0.6Cn·Δd'β·β

[0068] C m = 0.6Cnβ 2

[0069] Therefore, the viscous coefficient C of a single viscous damper is:

[0070]

[0071] According to the viscous coefficient C, the required model of a single viscous damper can be determined.

[0072] To simplify the calculation and provide convenience for the design, the damping coefficients C of all single viscous dampers 4 connected to the displacement amplification rod (7) are synthesized into one total equivalent damping coefficient C eq , and its derivation is as follows:

[0073] Assume that the lower end of the displacement amplification rod (7) undergoes displacement under the action of a known force F. The initial length of the viscous damper is l. Let C eq (unknown quantity) be the total equivalent damping coefficient, and we have:

[0074]

[0075] Wherein, V is the velocity of the center point (known), x is the length of the line connecting the center points before and after the change (known), and t is the time (known).

[0076] Select a certain direction as the reference direction. The angle between the moving direction of the center point and the reference direction is γ, the number of viscous dampers is n, the damping coefficient of all viscous dampers is C, the velocity exponent α is taken as 1, and they are evenly arranged within 2π. The angle between the damper i and the reference direction The angle between the moving direction of the center point and the damper i is γ - θ i . The length of the damper after the change Then the change in the damper length G i = |a - b|. The damping force of the damper i The energy dissipation W of the damper i i = F i ·G i , and the formula is obtained:

[0077]

[0078] Here it is assumed that the magnitude of the piston movement speed of each damper is the same as that of the center point, and there is:

[0079]

[0080] Find C eq The mean value within the range of 0 - 2π is:

[0081]

[0082] Also It is assumed that at a certain moment l = x, there is:

[0083]

[0084] The viscous dampers are evenly arranged within 0 - 2π. Therefore, when integrating within 0 - 2π, the contribution of each damper is the same. Therefore, the average contribution of the sum can be approximated by the integration result of a certain angle. The integration can be regarded as the contribution of the "average angle". θ i = 0 can be used as a representative angle to calculate the entire integration, and the result is multiplied by n. Therefore, C eq can be simplified to:

[0085]

[0086] When

[0087]

[0088] When the mass unit (2) drives the displacement amplification rod (7) to move, the total damping force F = C eq ·V = 0.6Cn·V.

Claims

1. A damped amplified friction pendulum tuned mass damper, characterized in that, It includes a multi-dimensional concave curved surface guiding track (1), a mass unit (2), a displacement amplification rod (3), a viscous liquid damper (4), a universal fish-eye bearing (5), a universal ball bearing (6), a support base plate (10), and a support column (11); the mass unit (2) and the universal ball bearing (6) installed at its bottom are located within the multi-dimensional concave curved surface guiding track (1) and can slide within the multi-dimensional concave curved surface guiding track (1). A circular opening is provided at the central position of the multi-dimensional concave curved surface guiding track (1) for installing the universal fish-eye bearing (5). The displacement amplification rod (3) passes through the universal fish-eye bearing (5), and a viscous liquid damper (4) is connected to the lower end. One end of the viscous liquid damper (4) is hinged to the displacement amplification rod (3), and the other end is hinged to the support base plate (10). The support base plate (10) is connected to the multi-dimensional concave curved surface guiding track (1) through the support column (11); the control curve of the sliding surface of the multi-dimensional concave curved surface guiding track (1) is a cycloid, and the parametric equation of the cycloid is: In the formula, r is the radius of the rolling circle, and θ is the angle of the rolling circle.

2. The damped amplification type friction pendulum tuned mass damper according to claim 1, wherein The number of the viscous dampers (4) is n, and they are evenly arranged within 2π. Therefore, the viscous coefficient C of a single viscous damper (4) needs to meet the following conditions: Where C m is the viscous coefficient of the resistance acting on the mass unit (2). During the design, after determining the mass ratio μ, frequency ratio f, and damping ratio ζ of the tuned mass damper, the calculated mass m (TMD) , stiffness k (TMD) , then the value of C m is as follows: β is the amplification coefficient of the displacement amplification rod (7), β = B / b, where B is the distance from the lower end of the displacement amplification rod (7) to the universal fish-eye bearing (5), and b is the distance from the universal fish-eye bearing to the center point of the mass unit (2).

3. The damped amplified friction pendulum tuned mass damper according to claim 1, wherein The number n of the viscous dampers (4) is taken as 4 - 8.

4. The design method of the damped amplified friction pendulum tuned mass damper according to any one of claims 1-3, characterized in that, The method includes the following steps: After determining that the mass ratio μ of the tuned mass damper is 1% - 5%, the frequency ratio f is 0.9 - 1, and the damping ratio ζ is 5% - 15% according to the empirical values, the mass m of the mass unit (2) is calculated (TMD) , the stiffness k (TMD) , then the damping coefficient C of the damping required for the tuned mass damper m takes the value of: The amplification coefficient of the displacement amplification rod (7) is set to β. Let the distance from the lower end of the displacement amplification rod (7) to the universal fish-eye bearing (5) be B, and the distance from the universal fish-eye bearing to the center point of the mass unit (2) be w. β = B / w. According to empirical values, the value range of β is 1.5 - 2; The derivative of the displacement element Δd of the mass unit (2) at any moment with respect to time t is taken to obtain the velocity Δd' at this moment. According to the similarity ratio, the velocity at the lower end of the lever at this moment is βΔd'. Then the viscous damping force F received by the lower part of the displacement amplification rod (7) at this moment is F = C eq V = 0.6Cn·Δd'β, where C eq represents the combination of the damping coefficients C of all single viscous dampers (4) connected to the displacement amplification rod (7) into 1 total equivalent damping coefficient, and n represents the number of viscous dampers (4); although the output force of the viscous damper does not directly act on the mass unit (2), but through the transmission of the lever, the essence of the resistance received by the mass unit (2) from the displacement amplification rod (7) at this time is still the viscous damping force. The viscous coefficient of the resistance acting on the mass unit (2) is defined as C m , according to the lever balance: power × power arm = resistance × resistance arm, there is C m ·Δd′·1 = C eq ·Δd′β·β C m ·Δd′ = 0.6Cn·Δd′β·β C m = 0.6Cbβ 2 Therefore, the viscous coefficient C of a single viscous damper is: According to the viscous coefficient C, the required model of a single viscous damper can be determined.

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