CN108797311B - Eddy current tuned mass damper for ropeway bridge and design method - Google Patents
Eddy current tuned mass damper for ropeway bridge and design method Download PDFInfo
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Abstract
The invention relates to the technical field of structural shock absorption, in particular to an eddy current tuned mass damper for a cableway bridge, and discloses a design method of the eddy current tuned mass damper for the cableway bridge; the damping device comprises a frame and a damping element, wherein a plurality of guide rails are vertically arranged on the frame, the lower ends of the guide rails are fixedly connected with a bottom plate of the frame, and the upper ends of the guide rails are arranged on a top plate of the frame in a penetrating manner and are in matched connection with the top plate; the damping element can be assembled on the guide rails in a vertically movable manner, and a plurality of pressure springs are arranged between the two ends of the damping element and the top plate and between the two ends of the damping element and the bottom plate; conductor plates are arranged on the upper end surface and the lower end surface of the damping element, and permanent magnet arrays are arranged on the top plate and the bottom plate; the invention has reasonable structure, when the relative distance between the permanent magnet and the conductor plate is changed, damping force for blocking relative movement can be generated between the permanent magnet and the conductor plate, energy is finally dissipated in the conductor plate in the form of heat energy, the vibration of the ropeway bridge can be effectively reduced, and the invention has the advantages of easy adjustment of damping, no need of later maintenance, good durability, easy assembly and the like.
Description
Technical Field
The invention relates to the technical field of structural shock absorption, in particular to an eddy current tuned mass damper for a ropeway bridge, and discloses a design method of the eddy current tuned mass damper for the ropeway bridge.
Background
A cableway bridge is a bridge which takes high-strength steel wire ropes, steel strands or parallel steel wire bundles as main bearing components. The anchor is used as an important foundation to anchor the bearing cable of the whole bridge, the steel cross beam and the bridge deck are used as local stress members, and the anchor has the characteristics of small rigidity, high bearing capacity and the like. With the large-scale construction of mountain roads in China, cableway bridges are more and more widely applied, for example, temporary bridges for hydraulic and hydroelectric engineering construction are used for people and vehicles to pass through or conveying building engineering materials and the like; can also be used as an emergency bridge for military affairs, emergency relief and the like; can cross high and deep canyons, rivers with steep water flow on both sides and the like, and is used for people, tracked vehicles and wheeled vehicles to pass through; and is also used for a ropeway bridge in a scenic spot for tourists to walk and the like. Because the main bearing structure of the ropeway bridge is a flexible component, the flexibility of the bridge is high, and the ropeway bridge is easy to generate large-amplitude vibration when a vehicle runs on the bridge, so that the safety operation, the service life and the driving comfort of the bridge are greatly influenced, and the large-amplitude vibration of the ropeway bridge can be reduced by adding a vibration damper generally.
At present, a plurality of control means for the vibration of a bridge structure exist, but the vibration control method for the ropeway bridge is less, and the tuned mass damper is mainly adopted to control the vibration of the ropeway bridge. The tuned mass damper is a small vibration system, and consists of a mass, an elastic element and a damping element. The mechanism of vibration control of the structure is as follows: the dynamic characteristic of the original structure system is changed due to the addition of the tuned mass damper, when the original structure bears dynamic load and vibrates greatly, reverse acting force is applied to the original structure due to the inertia of the mass block of the tuned mass damper, the damping also plays a role in energy consumption, and therefore the vibration reaction of the original structure is obviously weakened.
Damping elements of the traditional tuned mass damper generally adopt high-rubber-grade damping materials and liquid viscous dampers. However, the rubber material has the defects of aging, difficulty in separating rigidity from damping and the like, the viscous damper has the problems of oil leakage, difficulty in maintaining and the like, and the damping coefficient of the traditional tuned mass damper is difficult to adjust in the later stage and the durability is poor.
Accordingly, the prior art is yet to be improved and developed.
Disclosure of Invention
The invention aims to provide an eddy current tuned mass damper for a ropeway bridge and a design method thereof, wherein the eddy current tuned mass damper has the advantages of reasonable structure, no direct contact, no need of subsequent maintenance, easy adjustment of damping force and long service life, and aims to overcome the defects and defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to an eddy current tuned mass damper for a ropeway bridge, which comprises a frame and a damping element, wherein a plurality of guide rails are vertically arranged on the frame, the lower ends of the guide rails are fixedly connected with a bottom plate of the frame, and the upper ends of the guide rails are arranged on a top plate of the frame in a penetrating manner and are in matched connection with the top plate; the damping element can be assembled on the guide rails in a vertically movable manner, and a plurality of pressure springs are arranged between the two ends of the damping element and the top plate and between the two ends of the damping element and the bottom plate; conductor plates are arranged on the upper end face and the lower end face of the damping element, and permanent magnet arrays are arranged on the top plate and the bottom plate.
According to above scheme, damping element includes the basis piece, be equipped with on the basis piece with a plurality of guide rail complex linear bearing, a plurality of pressure springs suit respectively on the guide rail and with basic piece conflict setting, the conductor board transversely sets up on the upper and lower terminal surface of basis piece.
According to the scheme, a plurality of adjustable mass blocks are arranged between the conductor plate and the foundation block, the foundation block is provided with the long rod bolt, and two ends of the long rod bolt are respectively connected with the conductor plates of the upper layer and the lower layer so as to connect the foundation block and the adjustable mass blocks into a whole.
According to above scheme, the frame is upper end open-ended closed structure, and the roof can be followed frame upper end mouth and moved from top to bottom, through right angle sign indicating number fixed connection between roof and the frame, guide rail lower extreme and bottom plate fixed connection are equipped with a plurality of through-holes that correspond with the guide rail on the roof.
A method for designing an eddy current tuned mass damper for a ropeway bridge comprises the following steps:
① establishing finite element model according to the design parameters of the cableway bridge, and determining the modal mass M of the cableway bridgebNatural frequency fbDamping ratio ξbAnd the first three vertical vibration modes;
② determining the mass m of the tuned mass damper of eddy currents according to the modal mass of the ropeway bridgetThe ratio of the mass of the eddy current tuned mass damper to the modal mass of the cableway bridge is 5-10%, so that m is equal tot＝μMb；
③ according to natural frequency f of cableway bridgebDetermining the natural frequency f of an eddy current tuned mass dampertHere, use is made of ft＝n×fbWherein n is generally 0.85-1.0;
④ tuning the mass m of a mass damper according to eddy currentstAnd natural frequency ftDetermining the stiffness coefficient k of the compression springt＝mt×(2πft)2；
⑤ calculating the damping coefficient of the mass damper, wherein the permanent magnet has a moving speed in the z direction when the conductor plate and the permanent magnet generate relative motion, the damping force generated in the z direction is generated by the magnetic flux in the y direction cut by the conductor plate, and the damping force and the damping coefficient can be expressed as
Wherein, ctFor the damping coefficient, δ and v are the vertical relative velocity between the thickness of the conductor plate and the permanent magnet, respectively;
⑥, calculating to obtain each parameter of the eddy current tuned mass damper according to ① - ⑤, and assembling each component in sequence to obtain the eddy current tuned mass damper for the ropeway bridge.
The invention has the beneficial effects that: the vibration reduction device is reasonable in structure, the radial magnetic flux generated by cutting the permanent magnet by the conductor plate is changed, when the relative distance between the permanent magnet and the conductor plate is changed, eddy current is generated in the conductor plate when the magnetic flux is changed, damping force for blocking relative motion can be generated between the permanent magnet and the conductor plate, the vibration of the structure gradually disappears, energy is finally dissipated in the conductor plate in a heat energy mode, and the optimal vibration reduction effect can be obtained by optimally setting parameters of all components according to the inherent dynamic characteristics of the ropeway bridge; the vibration of the ropeway bridge can be effectively reduced, and the damping device has the advantages of easiness in damping adjustment, no need of later maintenance, good durability, easiness in assembly and the like.
Drawings
FIG. 1 is a schematic view of the overall cross-sectional structure of the present invention;
FIG. 2 is a schematic diagram of the eddy current generation mechanism of the present invention;
FIG. 3 is a schematic diagram of the magnetic field strength generated by the circular magnetized strip of the present invention.
In the figure:
1. a frame; 2. a guide rail; 3. a base block; 11. a top plate; 12. a base plate; 13. a permanent magnet; 14. right-angle corner connectors; 21. a pressure spring; 31. a conductor plate; 32. an adjustable mass block; 33. a linear bearing; 34. a long rod bolt.
Detailed Description
The technical solution of the present invention is described below with reference to the accompanying drawings and examples.
As shown in fig. 1, the tuned mass damper of eddy current for a cableway bridge according to the present invention comprises a frame 1 and a damping element, wherein a plurality of guide rails 2 are vertically arranged on the frame 1, the lower ends of the guide rails 2 are fixedly connected with a bottom plate 12 of the frame 1, and the upper ends of the guide rails 2 are inserted into a top plate 11 of the frame 1 and are connected with the same in a matching manner; the damping elements can be assembled on the guide rails 2 in a vertically movable manner, and a plurality of pressure springs 21 are arranged between the two ends of each damping element and the top plate 11 and the bottom plate 12; conductor plates 31 are arranged on the upper end face and the lower end face of the damping element, and permanent magnet 13 arrays are arranged on the top plate 11 and the bottom plate 12; the guide rails 2 are symmetrically distributed in the frame 1 at equal intervals, the damping elements are suspended between the top plate 11 and the bottom plate 12 under the support of the upper and lower compression springs 21 and can move up and down along the guide rails 2, and the conductor plates 31 at the upper and lower ends of the damping elements are used for cutting magnetic lines of force of the permanent magnet 13 array; the conductor plate 31 is a red copper plate with relatively low resistivity, and the permanent magnet 13 is a neodymium iron boron magnet which has extremely high magnetic accumulation energy and coercive force and can provide enough magnetic field intensity; the working principle of the invention is as follows: the damper is installed at the maximum displacement of a vibration mode of the ropeway bridge, such as the midspan and the quarter span, and a damping element can move up and down along the guide rail 2 along with the vibration of the ropeway bridge, so that the relative distance between the conductor plate 31 and the permanent magnet 13 array in the frame 1 can be changed, the conductor plate 31 cuts the radial magnetic flux of the permanent magnet 13, so that an eddy current is generated in the conductor plate 31, and according to lenz's law, a force for blocking relative motion, namely a damping force, can be generated between the conductor plate 31 and the permanent magnet 13, the energy is finally consumed in the conductor plate 31 in the form of heat energy, and the vibration gradually disappears under the action of the damping force; the working mechanism of the device conforms to the inherent characteristics of the ropeway bridge, and the vibration of the ropeway bridge can be effectively reduced to ensure the safety of the bridge; the working parts of the damper are not in direct contact with the bridge, the decay period of the permanent magnet 13 is long, the durability is good, the whole sealing is slightly influenced by the external environment, the follow-up maintenance is not needed, and the service life is long.
The damping element comprises a base block 3, a linear bearing 33 matched with a plurality of guide rails 2 is arranged on the base block 3, a plurality of pressure springs 21 are respectively sleeved on the guide rails 2 and are abutted against the base block 3, a conductor plate 31 is transversely arranged on the upper end surface and the lower end surface of the base block 3, the base block 3 is used as a resonance component for absorbing the vibration of the ropeway bridge and is used as a balance weight, the base block 3 is suspended in a frame 1 under the support of the pressure springs 21 and enables the conductor plate 31 and a permanent magnet 13 array to keep relative interval, when the base block 3 moves up and down, the conductor plate 31 cuts the radial magnetic flux of the permanent magnet 13 to generate eddy current and damping force, the eddy current on the conductor plate 31 is converted into heat energy to be consumed, so that the vibration of the ropeway bridge is reduced in the repeated vibration of the base block 3, the pressure springs 21 are used as elastic elements to provide elastic restoring force for the base block 3, and, the damper is only installed on a ropeway bridge through the frame 1, so that the service life of the damper is in direct proportion to the magnetic decay period of the permanent magnet 13, and the service life is longer without subsequent maintenance.
A plurality of adjustable mass blocks 32 are arranged between the conductor plate 31 and the base block 3, a long rod bolt 34 is arranged on the base block 3, and two ends of the long rod bolt 34 are respectively connected with the conductor plates 31 on the upper layer and the lower layer so as to connect the base block 3 and the adjustable mass blocks 32 into a whole; the adjustable mass block 32 is used for being matched with the foundation block 3 to form a balance weight for absorbing the vibration of the ropeway bridge, so that the vibration of the ropeway bridge is better inhibited, the conductor plate 31, the adjustable mass block 32 and the foundation block 3 are connected into a whole through the long-rod bolt 34 to form a damping element, and the damping element is reasonably configured according to the vibration characteristic of the ropeway bridge so as to obtain the optimal vibration reduction effect.
The frame 1 is of a closed structure with an opening at the upper end, the top plate 11 can move up and down along the upper end opening of the frame 1, the top plate 11 is fixedly connected with the frame 1 through a right-angle corner brace 14, the lower end of the guide rail 2 is fixedly connected with the bottom plate 12, and the top plate 11 is provided with a plurality of through holes corresponding to the guide rail 2; the damping elements need to be set according to the vibration characteristics of the ropeway bridge, so that the weight of the damping elements needs to be reasonably set by adjusting the number of the adjustable mass blocks 32, the change of the number of the adjustable mass blocks 32 can cause the overall height of the damping elements to change, and the conductor plates 31 at the two ends of the damping elements and the permanent magnet 13 array keep a reasonable distance through the top plate 11 with adjustable height.
A method for designing an eddy current tuned mass damper for a ropeway bridge comprises the following steps:
① establishing finite element model according to the design parameters of the cableway bridge, and determining the modal mass M of the cableway bridgebNatural frequency fbDamping ratio ξbAnd the first three vertical vibration modes;
② determining the mass m of the tuned mass damper of eddy currents according to the modal mass of the ropeway bridgetThe ratio of the mass of the eddy current tuned mass damper to the modal mass of the cableway bridge is 5-10%, so that m is equal tot＝μMb；
③ according to natural frequency f of cableway bridgebDetermining the natural frequency f of an eddy current tuned mass dampertHere, use is made of ft＝n×fbWherein n is generally 0.85-1.0;
④ tuning the mass m of a mass damper according to eddy currentstAnd natural frequency ftDetermining the stiffness coefficient k of the compression spring 21t＝mt×(2πft)2；
⑤ calculating the damping coefficient of the mass damper, when the conductor plate 31 and the permanent magnet generate relative motion, the permanent magnet 13 has a moving speed in the z direction, the damping force generated in the z direction is generated by the conductor plate 31 cutting the magnetic flux in the y direction, the damping force and the damping coefficient can be expressed as
Wherein, ctTo be a damping coefficient, δ and v are the thickness of the conductor plate 31 and the vertical relative velocity between the permanent magnets, respectively;
as shown in fig. 2-3, the eddy current tuned mass damper used here is in the form of a conductor plate 31 cutting radial magnetic flux, i.e. the conductor plate 31 moves along the axis of a cylindrical magnet to cut the radial magnetic flux generated by the permanent magnet. When the conductor plate 31 and the permanent magnet are relatively moved, the eddy current I generated in the conductor plate 31 is calculated as follows
I＝σ(v×B) (G1)
Where σ is the electric conductivity of the conductor plate 31, v is the relative movement velocity vector, and B is the magnetic field strength vector.
According to electromagnetism, the direction of repulsion force generated by the eddy current I is opposite to the relative motion direction, and the magnitude can be obtained according to the Lorentz force law:
when the relative movement is repeated, the repulsive force generated by the eddy current is also repeatedly generated and dissipated, and the repulsive force is the damping force generated by the damper. Because the conductor plate 31 and the cylindrical magnet generate axial relative motion, radial magnetic induction lines are cut, the direction of the current vortex generated in the conductor plate 31 is rotated around the z-axis, and B is accordinglyzThe directional magnetic flux does not generate a damping force, and thus an expression for the damping force can be calculated:
where v is the relative moving speed of the conductor plate 31 and the permanent magnet 13, δ is the thickness of the conductor plate 31, and reIs the equivalent radius of the conductor plate 31,/dIs the gap between the conductor plate 31 and the permanent magnet.
The magnetic induction of the permanent magnet 13 at a point Q (t, α, z) is calculated in the form of a cylindrical coordinate the expression for calculating the magnetic induction of the loop circuit by using biot-savart law is as follows:
in the above formula,. mu.0、M0、T1And d ε are eachThe magnetic field comprises space permeability, the magnetization intensity of the permanent magnet in unit length, and distance vectors and infinitesimal body vectors of micro sections of the eddy current annular loop and space field points. Vector T1The definition of (1) is a distance vector from a micro element unit on a ring loop to a certain point of a y-z plane, and can be written as follows:
T1＝T-t (G5)
wherein T ═ yj + zk, T ═ rcos β i + rsin β j.
The vector d epsilon can be expressed as
dε＝-rsinβdβi+rcosβdβj (G6)
In the above formula, r is the radius of the cylindrical permanent magnet.
The y-direction magnetic induction intensity generated by the eddy current loop circuit obtained by substituting the formulas (G5) and (G6) into (G4) is as follows:
wherein, dByMagnetic induction in the y direction, H1Is an equation that includes an elliptic integral. The magnetic induction intensity generated by the cylindrical magnet can be calculated by integrating the equation (G7) according to the thickness h of the cylindrical permanent magnet 13
Wherein z is1And h are the distance in the z direction from the permanent magnet infinitesimal and the length of the cylindrical permanent magnet, respectively.
When the permanent magnet has a moving speed in the z direction, the magnetic induction intensity Bz(y,z,z1) No damping force is generated because there is no velocity component in the direction perpendicular to the z-direction magnetic flux, so that the damping force generated in the z-direction is generated by cutting the y-direction magnetic flux by the conductor plate 31, and the damping force and the damping coefficient can be expressed as
Wherein, ctTo be a damping coefficient, δ and v are the thickness of the conductor plate 31 and the vertical relative velocity between the permanent magnets, respectively. As can be seen from (G7) and (G9), since the magnetic flux density is symmetrical about the z-axis, the damping force components generated by the eddy current in the x and y directions are 0. Since the equation (G11) has elliptic integral, the value of the damping coefficient is obtained by calculating (G11) by numerical integration.
⑥, calculating to obtain each parameter of the eddy current tuned mass damper according to ① - ⑤, and assembling each component in sequence to obtain the eddy current tuned mass damper for the ropeway bridge.
The above description is only a preferred embodiment of the present invention, and all equivalent changes or modifications of the structure, characteristics and principles described in the present invention are included in the scope of the present invention.
Claims (4)
1. An eddy current tuned mass damper for a cableway bridge, comprising a frame (1) and a damping element, characterized in that: the frame (1) is vertically provided with a plurality of guide rails (2), the lower ends of the guide rails (2) are fixedly connected with a bottom plate (12) of the frame (1), and the upper ends of the guide rails (2) are arranged on a top plate (11) of the frame (1) in a penetrating manner and are connected with the top plate in a matching manner; the damping elements can be assembled on the guide rails (2) in a vertically movable manner, and a plurality of pressure springs (21) are arranged between the two ends of each damping element and the top plate (11) and the bottom plate (12); conductor plates (31) are arranged on the upper end face and the lower end face of the damping element, and permanent magnet (13) arrays are arranged on the top plate (11) and the bottom plate (12);
the method for designing the eddy current tuned mass damper for the ropeway bridge comprises the following steps:
① establishing finite element model according to the design parameters of the cableway bridge, and determining the modal mass M of the cableway bridgebNatural frequency fbDamping ratio ξbAnd the first three vertical vibration modes;
② determining the mass m of the tuned mass damper of eddy currents according to the modal mass of the ropeway bridgetThe ratio of the mass of the eddy current tuned mass damper to the modal mass of the cableway bridge is 5-10%, so that m is equal tot＝μMb；
③ according to natural frequency f of cableway bridgebDetermining the natural frequency f of an eddy current tuned mass dampertHere, use is made of ft＝n×fbWherein n is 0.85-1.0;
④ tuning the mass m of a mass damper according to eddy currentstAnd natural frequency ftDetermining the stiffness coefficient k of the compression spring (21)t＝mt×(2πft)2；
⑤ calculating the damping coefficient of the eddy current tuned mass damper, when the conductor plate (31) and the permanent magnet generate relative motion, the permanent magnet (13) has a moving speed in the z direction, the damping force generated in the z direction is generated by cutting the magnetic flux in the y direction by the conductor plate (31), the damping force and the damping coefficient can be expressed as
Wherein, ctFor the damping coefficient, δ and v are the thickness of the conductor plate (31) and the vertical relative velocity between the permanent magnets, respectively, ByMagnetic induction, r, generated for cylindrical magnetseIs the equivalent radius of the conductor plate (31) |dIs a gap between the conductor plate (31) and the permanent magnet0、M0Respectively, the space permeability, the magnetization per unit length of the permanent magnet, r is the radius of the cylindrical permanent magnet, H1Is an expression containing elliptic integral;
⑥, calculating to obtain each parameter of the eddy current tuned mass damper according to ① - ⑤, and assembling each component in sequence to obtain the eddy current tuned mass damper for the ropeway bridge.
2. The tuned mass damper for a cableway bridge according to claim 1, characterized in that: damping element includes foundatin block (3), is equipped with on foundatin block (3) with a plurality of guide rail (2) complex linear bearing (33), a plurality of pressure spring (21) suit respectively on guide rail (2) and with the setting of contradicting of foundatin block (3), conductor board (31) transversely set up on the upper and lower terminal surface of foundatin block (3).
3. The tuned mass damper for a cableway bridge according to claim 2, characterized in that: be equipped with a plurality of adjustable quality pieces (32) between conductor plate (31) and basic block (3), be equipped with stock bolt (34) on basic block (3), thereby the both ends of stock bolt (34) are connected with conductor plate (31) of upper and lower floor respectively and are connected foundation block (3) and a plurality of adjustable quality pieces (32) into an organic whole.
4. The tuned mass damper for a cableway bridge according to claim 3, characterized in that: frame (1) is upper end open-ended closed structure, and frame (1) port activity from top to bottom can be followed in roof (11), through right angle sign indicating number (14) fixed connection between roof (11) and frame (1), guide rail (2) lower extreme and bottom plate (12) fixed connection are equipped with a plurality of through-holes that correspond with guide rail (2) on roof (11).
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| CN112160438A (en) * | 2020-09-24 | 2021-01-01 | 湖南大学 | Magnetic screw type eddy current damper with negative-stiffness nonlinear energy trap |
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| CN110485788A (en) * | 2019-08-21 | 2019-11-22 | 震安科技股份有限公司 | A kind of tuned mass damper |
| CN110822000B (en) * | 2019-11-18 | 2023-12-22 | 珠海格力电器股份有限公司 | Vibration absorber with adjustable vibration reduction frequency band and air conditioning unit |
| CN113136973A (en) * | 2021-04-18 | 2021-07-20 | 东北电力大学 | Horizontal eddy current tuned mass damper |
| CN114704586B (en) * | 2022-03-18 | 2023-09-15 | 徐州徐工基础工程机械有限公司 | Universal coordination mass damper |
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| KR101499886B1 (en) * | 2013-10-24 | 2015-03-12 | 주식회사 브이테크 | Permanent magnet damper and tuned mass damper having the same |
| CN203834722U (en) * | 2014-04-11 | 2014-09-17 | 湖南科技大学 | Self-powered type semi-active tuned mass damper |
| CN204098268U (en) * | 2014-08-28 | 2015-01-14 | 华北水利水电大学 | Permanent magnetism type magnetic suspension horizontal tuned mass damper |
| CN205152774U (en) * | 2015-10-21 | 2016-04-13 | 华北水利水电大学 | Harmonious mass damper of assembled current vortex |
| CN106368488A (en) * | 2016-11-10 | 2017-02-01 | 兰州理工大学 | Bidirectional TMD control device and parameter determination method |
| CN107355509B (en) * | 2017-08-10 | 2019-07-30 | 东南大学 | A kind of current vortex vibration absorber using lever principle |
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