A roller-type eddy current inertial mass tuned mass damper and its design method

Abstract

This invention relates to a roller-type eddy current inertial mass tuned mass damper and its design method. When the controlled main structure vibrates, the roller moves relative to the track under inertia. The gear rotates along the track through the meshing action of the gear and the track teeth, which can amplify the mass of the tuned mass damper. This allows the tuned mass damper to be made smaller, making it easier to install on space-constrained structures. By setting conductors and permanent magnets, the roller's rolling process can utilize the conductor to cut the magnetic field lines generated by the permanent magnet to form eddy currents. The eddy current magnetic field interacts with the original magnetic field of the permanent magnet to generate eddy current damping force. This allows the roller's kinetic energy to be converted into electrical energy first, and then into heat energy and consumed in the atmosphere. It can achieve non-contact, wear-free damping, and can meet the needs of a larger mass with a smaller mass. The structure is simple, and the use of a quadratic parabolic track gives it a wide vibration reduction frequency band and high robustness.

Description

Technical Field

[0001] This invention relates to the field of tuned mass damper technology, and in particular to a rolling track type eddy current inertial mass tuned mass damper and its design method. Background Technology

[0002] As modern engineering structures develop towards taller, longer-span, and lighter designs, the stiffness of high-rise buildings, wind turbine towers, and long-span bridges continues to decrease, and their inherent damping becomes smaller. Under lateral dynamic excitations such as wind loads and seismic forces, they are prone to large-scale vibrations, severely impacting the comfort, safety, and durability of the structures. Therefore, vibration control of tall structures such as high-rise buildings and wind turbines is particularly important.

[0003] Tuned mass dampers (TMDs) are a common method for passive vibration control of structures. Their core consists of mass elements, stiffness elements, and damping elements. By tuning the natural frequency of the TMD system to near the controlled frequency of the main structure, the resonance effect is used to absorb and dissipate the vibration energy of the main structure, thereby achieving vibration reduction.

[0004] Traditional pendulum-type TMDs provide restoring stiffness using a simple pendulum, and their natural period is directly determined by the pendulum length. To achieve long-period vibration control, an extremely long pendulum is required, resulting in a large vertical installation space requirement, poor layout flexibility, and difficulty in meeting the installation needs of confined spaces. To overcome these shortcomings, rolling mass tuned dampers have emerged.

[0005] For example, Chinese invention patent CN102995787B discloses a rolling mass tuned damper, which uses gears to fix a large-mass disk, and a rack-and-pinion arc support fixed to the building structure. The gears and rack mesh, causing the large-mass disk to roll on the support. This scheme utilizes the rotational inertia of the large-mass disk to obtain a larger equivalent mass with the same physical mass, thereby improving the vibration reduction effect without significantly increasing the vertical load, while avoiding the large vertical space occupation of traditional pendulum-type TMDs. Its damping energy dissipation method is: a damping fluid tank or friction plate is installed at the lower part of the rack-and-pinion arc support, and the vibration energy is dissipated by partially immersing the large-mass disk in damping fluid or contacting the friction plate. However, this scheme has the following shortcomings:

[0006] Both the damping fluid tank and the friction plate are contact-type energy dissipators. The friction plate will wear out during long-term operation and needs to be replaced regularly. The damping fluid may change in viscosity due to temperature changes, affecting damping stability, and there is also a risk of leakage.

[0007] The ability to adjust damping force characteristics is limited: frictional damping is approximately a constant resistance and is independent of speed; although viscous damping is related to speed, it is difficult to achieve an ideal damping force curve over a wide speed range.

[0008] The damping fluid tank or friction plate needs to be placed under the support, which takes up extra installation space and is not conducive to the compact design of the damper.

[0009] Another type of improvement, such as Chinese invention patent CN112900672B, proposes a rolling mass tuned damper based on the inertial amplification mechanism. It adds an independent inertial body above the rolling mass block, transmitting motion through gear meshing. Simultaneously, a permanent magnet is placed inside the arc-shaped slide rail, utilizing the rolling mass block cutting magnetic field lines to generate eddy current damping, achieving non-contact, wear-free energy dissipation. However, this scheme has a relatively complex structure: it requires an additional inertial body, additional mass, and even a gearbox, leading to an increase in total physical mass, a significant impact on the vertical load of the main structure, and higher manufacturing costs.

[0010] Furthermore, all the aforementioned existing technologies employ a circular arc track as the rolling path. The circular arc track determines that the restoring force of the damper has an approximately linear relationship with the rolling displacement, and its equivalent stiffness is essentially constant. Therefore, the natural frequency of the damper is locked within a relatively narrow bandwidth. When the actual controlled frequency of the main structure shifts due to damage accumulation, changes in non-structural components, or environmental factors (such as temperature and wind-induced additional stiffness), the damper's tuning state is disrupted, and the vibration reduction effect significantly decreases. Existing circular arc track rolling mass tuned dampers generally suffer from small vibration reduction bandwidth and low robustness, making them unsuitable for the actual operating conditions of the main structure's frequency vibration.

[0011] In summary, the existing technology lacks a rolling mass tuned damper that can maintain structural simplicity, minimize the increase in vertical load on the main structure, achieve non-contact, wear-free damping, and simultaneously possess a wide vibration reduction frequency band and high robustness. Summary of the Invention

[0012] The purpose of this invention is to overcome the shortcomings of existing technologies that lack a rolling mass tuned damper that can maintain a simple structure, minimize the increase in vertical load on the main structure, achieve non-contact and wear-free damping, and simultaneously possess a wide vibration reduction frequency band and high robustness. This invention provides a rolling track type eddy current inertial mass tuned mass damper and its design method.

[0013] In a first aspect, the present invention provides a roller-type eddy current inertial mass tuned mass damper, comprising: a base, two tracks, rollers, two gears, and a plurality of permanent magnets. The base is used to fix the main structure under control. The two tracks are arranged side by side and spaced apart on the base. The top of the two tracks is provided with meshing teeth continuously along the length direction. The rollers are fixed with coaxially arranged gears on both sides of the axial direction. The gears mesh with the meshing teeth on the tracks, and the rollers can roll on the meshing teeth on the tracks by rotating through the gears. The top surface of the track with meshing teeth is arranged in a quadratic parabola. Only one of the roller and the track is a conductor. When the roller is a conductor, all the permanent magnets are fixedly disposed on the inner side between the two tracks. When the track is a conductor, all the permanent magnets are fixedly disposed on both sides of the roller along its axial direction.

[0014] Preferably, when the roller is a conductor, the roller is provided with heat dissipation holes, and the axial direction of the heat dissipation holes is the same as that of the roller.

[0015] Preferably, the roller has a ring of heat dissipation holes evenly spaced along its circumference.

[0016] Preferably, when the roller is a conductor, each track is provided with a row of spaced permanent magnets along the quadratic parabola of the track.

[0017] Preferably, the magnetic poles of two adjacent permanent magnets in each column are opposite, and the magnetic poles of the permanent magnets in the two tracks that are arranged opposite to each other are opposite.

[0018] Preferably, when the track is a conductor, all the permanent magnets are arranged in a circle around the axial direction on both sides of the roller, with uniform spacing.

[0019] Preferably, the top of both ends of the track is provided with limiting members.

[0020] Preferably, the roller and the gear are fixedly connected by a coaxial connecting shaft, and the limiting member is in the shape of a barb, with the inner arc of the barb-shaped limiting member adapting to the arc of the connecting shaft.

[0021] Preferably, the roller and the gear are detachably connected.

[0022] In a second aspect, the present invention provides a design method for a rolling track type eddy current inertial mass tuned mass damper, comprising the following steps: S1. Determine the dynamic characteristic parameters m of the controlled main structure. s k s and ω s m s k s and ω s These are the mass, stiffness, and frequency of the controlled main structure, respectively. S2. Based on engineering requirements or installation constraints, and combined with the dynamic characteristic parameters m of the controlled main structure. s k s and ω s The mass m of the rolling element of the roller-type eddy current inertial mass tuned mass damper and the mass m of the controlled main structure are pre-selected. sThe mass ratio μ is 1%-5%; the mass m of the rolling element is determined according to the mass ratio μ; wherein, when all the permanent magnets are fixedly disposed on the inner side between the two tracks, the rolling element includes the roller and all gears and the connecting structure between them as a whole; when all the permanent magnets are fixedly disposed on both axial sides of the roller, the rolling element includes the roller, all gears and all permanent magnets and the connecting structure between them as a whole; S3. Based on the rolling element mass m and the requirements of installation space, allowable stroke, and processing conditions, first determine the coefficient a of the quadratic parabolic track and the roller radius R, where the quadratic parabolic function of the quadratic parabolic track is: x is the horizontal coordinate of the contact point between the gear and the track. Let be the vertical coordinate of the contact point between the gear and the track; S4. Substitute the coefficient a and the roller radius R into the optimal frequency ratio f of the roller-type eddy current inertial mass tuned mass damper. opt The formula and the linearized frequency relationship of small displacement are used to solve the radius r of the gear through programming iteration, so that the roller-type eddy current inertial mass tuned mass damper meets the target frequency. Optimal frequency ratio f opt The formula is:

[0023] The linearized frequency relationship for small displacements is:

[0024] The formula for iteratively solving for the radius r of the gear using simultaneous programming is:

[0025] Based on the optimal damping ratio ζ bopt The formula determines the damping parameters of the roller-type eddy current inertial mass tuned mass damper, and the optimal damping ratio ζ. bopt The formula is:

[0026] In the formula, , This is the acceleration due to gravity.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention provides a roller-type eddy current inertial mass tuned mass damper. The vibration of the controlled main structure can cause the gear to rotate, and the roller can roll on the meshing teeth on the track through the rotation of the gear. This can amplify the mass of the tuned mass damper, thereby making the tuned mass damper smaller and easier to install on space-constrained structures. By setting a conductor and a permanent magnet, the rolling process of the roller can cause the conductor to cut the magnetic field lines generated by the permanent magnet to form eddy currents. The magnetic field of the eddy currents interacts with the original magnetic field of the permanent magnet to generate eddy current damping force. This causes the kinetic energy of the roller to be converted into electrical energy first, and then into heat energy and consumed in the atmosphere, playing a role in energy dissipation and vibration reduction. It can achieve non-contact, wear-free damping, and can meet the mass requirements with a smaller mass. The structure is simple, and the use of a quadratic parabolic track is a non-linear structure, which gives it a wide vibration reduction frequency band and high robustness.

[0028] 2. This invention provides a design method for a roller-type eddy current inertial mass tuned mass damper. Through the above design method, the vibration reduction requirements of the roller-type eddy current inertial mass tuned mass damper for a quadratic parabolic trajectory can be met, and the frequency of the roller-type eddy current inertial mass tuned mass damper can be adjusted by changing the roller radius and gear radius. Attached Figure Description

[0029] Figure 1 A three-dimensional structural schematic diagram of a roller-track type eddy current inertial mass tuned mass damper. Figure 2 A front view of a roller-type eddy current inertial mass tuned mass damper; Figure 3 for Figure 2 Sectional view at point AA; Figure 4 A top view of a roller-type eddy current inertial mass tuned mass damper; Figure 5 for Figure 4 Sectional view at point BB; Figure 6 This is a schematic diagram of the gear and meshing teeth meshing engagement of a roller-type eddy current inertial mass tuned mass damper. Figure 7 This is a schematic diagram of the magnetic field of a rolling track type eddy current inertial mass tuned mass damper.

[0030] Figure 8 A three-dimensional structural schematic diagram of another type of roller-track type eddy current inertial mass tuned mass damper; Figure 9 A front view of another type of roller-track eddy current inertial mass tuned mass damper; Figure 10 A top view of another type of roller-track eddy current inertial mass tuned mass damper; Figure 11 A side view of another type of roller-type eddy current inertial mass tuned mass damper; Figure 12 This is a schematic diagram of the gear and meshing teeth meshing engagement of another type of roller-type eddy current inertial mass tuned mass damper. Figure 13 This is a schematic diagram of the mechanical model of the roller-type eddy current inertial mass tuned mass damper described in this invention. Figure 14 This is a schematic diagram of the quadratic parabolic model of the track of the rolling track type eddy current inertial mass tuned mass damper described in this invention.

[0031] The markings in the diagram are: 1. Base; 2. Track; 21. Meshing teeth; 22. Limiting component; 23. Reinforcing connecting plate; 3. Roller; 31. Heat dissipation hole; 4. Gear; 41. Connecting shaft; 5. Permanent magnet. Detailed Implementation

[0032] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0033] Unless otherwise specified, the terms "upper," "lower," "left," "right," "center," "inner," and "outer," etc., used in the description of specific embodiments of the present invention to indicate orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is usually placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, and for enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.

[0034] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," "parallel," and "coaxial" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, parallel, or coaxial. Slight tilt or deviation is permissible, as long as it does not affect the normal function of the relevant component. For example, "horizontal" simply means that its direction is more horizontal relative to "vertical," not that the structure must be perfectly horizontal; a slight tilt is acceptable. "Coaxial" means that two components are arranged as coaxially as possible, allowing them to move coaxially or approximately coaxially when their relative positions change. Alternatively, it can be simplified to mean that the corresponding device / component / element, when arranged in "horizontal," "vertical," "suspended," "parallel," or "coaxial" directions, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. For example, the deviation in the "coaxial" direction is controlled within 0.2-1mm, preferably within 0.2-0.5mm. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the solution of the present invention.

[0035] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing descriptions of identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0036] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as two, three, four, five, six, seven, eight, or nine, and can even exceed nine.

[0037] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to connection methods commonly used in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0038] Example 1 like Figures 1-14As shown, a roller-type eddy current inertial mass tuned mass damper includes: a base 1, two tracks 2, rollers 3, two gears 4, and several permanent magnets 5. The base 1 is used to fix the main structure under control. The two tracks 2 are arranged side by side and spaced apart on the base 1. The top of the two tracks 2 is continuously provided with meshing teeth 21 along the length direction. The rollers 3 are fixed with coaxially arranged gears 4 on both sides of the axial direction. The gears 4 mesh with the meshing teeth 21 on the tracks 2. The rollers 3 can roll on the meshing teeth 21 on the tracks 2 by rotating through the gears 4. like Figure 1 and Figure 6 As shown, the roller 3 and the gear 4 are fixedly connected by a coaxial connecting shaft 41.

[0039] In an optional embodiment, the roller 3 and the gear 4 are detachably connected, facilitating the replacement of worn gear 4. For example... Figure 6 As shown, gear 4 is sleeved on one end of connecting shaft 41, and the other end of connecting shaft 41 is detachably connected to one side of roller 3 via flange and bolts.

[0040] The top surface of the meshing teeth 21 of the track 2 is arranged in a quadratic parabola. The quadratic parabola track has a restoring force that is displacement-dependent and nonlinear. The equivalent stiffness changes with the displacement. Compared with the circular arc track, it has the advantages of wide vibration reduction bandwidth and good robustness.

[0041] Only one of the roller 3 and the track 2 is a conductor.

[0042] like Figures 1-7 As shown, when the roller 3 is a conductor, all the permanent magnets 5 are fixedly arranged on the inner side between the two tracks 2, and the roller 3 can pass through a stronger and more stable magnetic field, thereby improving the energy consumption capacity.

[0043] Traditional eddy current damping devices are prone to thermal degradation of their internal magnet components when operating at excessively high temperatures. This can lead to problems such as thermal demagnetization of the permanent magnet, damping force attenuation, and unstable performance. In extreme cases, damping failure may occur, significantly reducing the device's lifespan and vibration reduction reliability. In an optional embodiment, the roller 3 is provided with heat dissipation holes 31, the axial direction of which is the same as that of the roller 3. The shape of the heat dissipation holes can be square, circular, or other perforations capable of heat dissipation. The perforated design on the roller improves the heat dissipation of the eddy current damper, stabilizes damping characteristics, prevents permanent magnet demagnetization, increases energy dissipation capacity, and extends service life.

[0044] Furthermore, the roller 3 is provided with a ring of heat dissipation holes 31 evenly spaced along its circumference, which further improves the heat dissipation of the eddy current damper, stabilizes the damping characteristics, prevents permanent magnet demagnetization, improves energy dissipation capacity, and extends service life.

[0045] In an optional embodiment, each track 2 is provided with a row of spaced permanent magnets 5 along a quadratic parabolic trajectory. Each row of permanent magnets 5 also follows a quadratic parabolic trajectory, mirroring the movement path of the rollers. This allows the rollers 3 to pass through a stronger and more stable magnetic field, thereby improving energy dissipation. The reciprocating motion of the rollers along the tracks enables frequency tuning. Furthermore, the arrangement of the permanent magnets 5 results in a shorter travel distance and smaller space requirement, significantly enhancing applicability in space-constrained structures.

[0046] Furthermore, the magnetic poles of two adjacent permanent magnets 5 in each column are opposite, and the magnetic poles of the oppositely arranged permanent magnets 5 in the two tracks 2 are also opposite, such as... Figure 6 As shown, the alternating magnetic pole arrangement can form an alternating magnetic field. When the roller moves, it will continuously pass through magnetic field regions of different polarities, increasing the rate of change of the magnetic field when the roller cuts the magnetic field, thereby enhancing the eddy current damping. Compared with the single pole arrangement, its damping effect is better.

[0047] When the track 2 is a conductor, all the permanent magnets 5 are fixedly mounted on both sides of the roller 3 along its axial direction. In this configuration, the permanent magnets 5, roller 3, and gear 4 are all part of the mass block of the tuned mass damper. The permanent magnets 5 not only provide a magnetic field but also serve as the mass of the mass block. Furthermore, during the rotation of the roller, by utilizing the rotational inertia amplification mechanism, a larger equivalent inertial mass can be obtained with a smaller physical mass of the permanent magnets 5, resulting in higher vibration reduction efficiency.

[0048] In an optional embodiment, when the track 2 is a conductor, all the permanent magnets 5 are arranged in a uniform and spaced ring around the circumference on both sides of the roller 3. This provides a stable magnetic field, ensuring that the track 2 can continuously cut the magnetic field lines generated by the permanent magnets 5 on the roller 3. Furthermore, the magnetic poles of adjacent permanent magnets 5 in each ring are also arranged in opposite directions. As the roller moves, the track continuously cuts magnetic field regions of different polarities, increasing the rate of change of the magnetic field when the track cuts the magnetic field, thereby enhancing eddy current damping. Compared to a single-pole arrangement, its damping effect is better.

[0049] In an optional embodiment, limiting members 22 are provided at the top of both ends of the track 2 to prevent the rollers 3 from leaving the track and to ensure safety during use.

[0050] Furthermore, the roller 3 and the gear 4 are fixedly connected by a coaxial connecting shaft 41. The limiting member 22 is in the shape of a barb, and the inner arc of the barb-shaped limiting member 22 is adapted to the arc of the connecting shaft 41, which can better prevent the roller 3 from leaving the track.

[0051] In addition, such as Figure 4 , Figure 5 , Figure 10 and Figure 11As shown, by arranging reinforcing connecting plates 23 at intervals along the length of the base, the two tracks are reinforced. Furthermore, the reinforcing connecting plates 23 connect the inner sides of the two tracks and the upper side of the base to form a whole, improving the stability of the tracks when the rollers roll, ensuring the shape of the quadratic parabola of the rollers' rolling trajectory, and thus ensuring stable vibration damping capability. The reinforcing connecting plates 23 are located below the two tracks and connected to the top surface of the base, but do not interfere with the rolling of the rollers on the tracks.

[0052] This embodiment provides a roller-type eddy current inertial mass tuned mass damper. When the controlled main structure vibrates, the roller moves relative to the track under inertia. Through the meshing of the gear and the track teeth, the gear rotates along the track. The roller can roll on the meshing teeth on the track through the rotation of the gear, which can amplify the mass of the tuned mass damper. This allows the tuned mass damper to be made smaller, making it easier to install on space-constrained structures. By setting a conductor and a permanent magnet, the roller's rolling process causes the conductor to cut the magnetic field lines generated by the permanent magnet, forming eddy currents. The eddy current magnetic field interacts with the original magnetic field of the permanent magnet, generating eddy current damping force. This causes the roller's kinetic energy to be first converted into electrical energy and then into heat energy, which is then consumed in the atmosphere, thus playing a role in energy dissipation and vibration reduction. It can achieve non-contact, wear-free damping, with stable damping and fast response. It can meet the needs of a larger mass with a smaller mass. The structure is simple, and the use of a quadratic parabolic track, which is a nonlinear structure, gives it a wide vibration reduction frequency band and high robustness.

[0053] Among them, such as Figure 13 and Figure 14 The control theory of the roller-type eddy current inertial mass tuned mass damper is as follows: For the quadratic parabolic orbit The equations of motion are derived using the Lagrange equations: centroid coordinates Center of mass velocity

[0054] In the formula, 'a' represents the coefficient of the quadratic parabola of the track, 'R' is the radius of the conductor roller, 'r' is the radius of the gear, and 'x' is the horizontal coordinate of the contact point between the gear and the track. Let x represent the first and second derivatives of the variable x with respect to time, respectively.

[0055] kinetic energy Therefore, the equivalent mass of the rotational inertia amplification mechanism is In the formula, T trans and T rot These represent the translational and rotational kinetic energies of the rolling element, respectively, where m is the mass of the rolling element, and v is the rotational kinetic energy. cThe velocity of the center of mass of the rolling element is given. Specifically, when all the permanent magnets 5 are fixedly disposed on the inner side between the two tracks 2, the rolling element comprises the roller 3, all the gears 4, and the connecting structure between them; when all the permanent magnets 5 are fixedly disposed on both axial sides of the roller 3, the rolling element comprises the roller 3, all the gears 4, all the permanent magnets 5, and the connecting structure between them.

[0056] Potential energy

[0057] In the formula, m is the mass of the rolling element, and g is the acceleration due to gravity.

[0058] Substituting into the Lagrange equation In the formula, T represents the system's kinetic energy, and V represents the system's potential energy. Non-conservative generalized force; The equation of motion is: .

[0059] In the formula, c is the damping coefficient.

[0060] consider If we perform linear simplification, then Therefore, the equation of motion for the rolling tuned mass damper simplifies to:

[0061] Therefore, natural frequency

[0062] A tuned mass damper is placed on a single-degree-of-freedom controlled master structure, while the damping of the controlled master structure is neglected. When the controlled master structure is subjected to horizontal harmonic excitation... When the system is linearly simplified, the equations of motion are:

[0063] In the formula, m s k s x s These represent the mass, stiffness, and displacement of the controlled main structure, respectively; m, c, and ζ. d ω d x and Ω represent the rolling element mass, damping coefficient, damping ratio, natural frequency, and displacement of the tuned mass damper, respectively. F0 is the external harmonic excitation amplitude, Ω is the external harmonic excitation frequency, e is the base of the natural logarithm, and i is the imaginary unit.

[0064] Let the solution be... Substituting into the equation of motion, the displacement dynamic amplification factor of the controlled main structure is derived. : In the formula, x s The complex amplitude of x;

[0065] Define a dimensionless parameter:

[0066] The dimensionless displacement dynamic amplification factor is obtained as follows:

[0067] In the formula, f is the frequency ratio of the tuned mass damper to the controlled main structure, ν is the frequency ratio of the external harmonic excitation to the controlled main structure, μ is the mass ratio of the tuned mass damper to the controlled main structure, and ζ is the frequency ratio of the external harmonic excitation to the controlled main structure. d The damping ratio of the tuned mass damper is given by i, where i is the imaginary unit.

[0068] Based on Den Hartog's fixed-point theory, the optimal frequency ratio f is derived. opt and the optimal damping ratio ζ bopt :

[0069] Based on the foregoing derivation, the equation of motion for the quadratic parabolic trajectory TMD can be written as:

[0070] Furthermore, resilience is

[0071] Its equivalent restoring stiffness can then be expressed as:

[0072] Therefore, the system's equivalent natural frequency can be approximately expressed as:

[0073] As can be seen, due to the variation of B with displacement x, the restoring force and equivalent stiffness of the tuned mass damper are no longer constant, but exhibit significant displacement-dependent characteristics. Consequently, the equivalent natural frequency of the tuned mass damper is not fixed, but dynamically adjusts with changes in the motion state. Therefore, the tuned mass damper can achieve instantaneous resonance capture with different modes of the main structure within a certain range, thereby expanding its damping bandwidth. This tuned mass damper does not only function for a single fixed condition, but maintains its energy absorption and dissipation capabilities over a wide range of conditions. Therefore, its performance degradation is typically slower when facing changes in external excitation, structural parameter perturbations, or environmental disturbances, exhibiting better robustness.

[0074] The roller-type eddy current inertial mass tuned mass damper described in this embodiment has its base mounted on the controlled main structure. When the controlled main structure vibrates under loads such as wind or earthquakes, it drives the rollers to roll on the guide rail. Through reasonable parameter design, its frequency can be made close to the natural frequency of the controlled main structure. It has the advantage of short stroke, thus facilitating installation on space-constrained structures. Using eddy current damping, damping is generated based on the principle of electromagnetic induction. There is no friction or working fluid, resulting in advantages such as simple structure, high reliability, good durability, and easily adjustable damping coefficient. The roller-type tuned mass damper utilizes the inertial amplification mechanism of rotating mass to achieve a larger equivalent mass. The quadratic parabolic track exhibits a displacement-dependent nonlinear restoring force, and the equivalent stiffness varies with displacement. Compared to circular arc tracks, it has the advantages of wide vibration reduction bandwidth and good robustness. The frequency of the tuned mass damper can be adjusted by changing the roller radius and gear radius. Alternating magnetic pole arrangement can form an alternating magnetic field. When the conductor plate moves, it will continuously pass through magnetic field regions of different polarities, increasing the rate of change of the magnetic field when the conductor cuts the magnetic field, thereby enhancing the damping of eddy currents. Compared with a single pole arrangement, its damping effect is usually better.

[0075] Example 2 A design method for a roller-track type eddy current inertial mass tuned mass damper, comprising the following steps: S1. Determine the dynamic characteristic parameters m of the controlled main structure. s k s and ω s m s k s and ω s These are the mass, stiffness, and frequency of the controlled main structure, respectively. S2. Based on engineering requirements or installation constraints, and combined with the dynamic characteristic parameters m of the controlled main structure. s k s and ω s The mass m of the rolling element of the roller-type eddy current inertial mass tuned mass damper and the mass m of the controlled main structure are pre-selected. s The mass ratio μ is 1%-5%; the mass m of the rolling element is determined according to the mass ratio μ; wherein, when all the permanent magnets 5 are fixedly disposed on the inner side between the two tracks 2, the rolling element includes the roller 3 and all the gears 4 and the connecting structure between them as a whole; when all the permanent magnets 5 are fixedly disposed on both axial sides of the roller 3, the rolling element includes the roller 3, all the gears 4 and all the permanent magnets 5 and the connecting structure between them as a whole; S3. Based on the rolling element mass m and the requirements of installation space, allowable stroke, and processing conditions, first determine the coefficient a of the quadratic parabolic track 2 and the radius R of the roller 3. The quadratic parabolic function of the quadratic parabolic track 2 is: x is the horizontal coordinate of the contact point between gear 4 and track 2. Let be the vertical coordinate of the contact point between gear 4 and track 2; S4. Substitute the coefficient a and the roller radius R into the optimal frequency ratio f of the roller-type eddy current inertial mass tuned mass damper. opt The formula and the linearized frequency relationship of small displacement are used to solve the radius r of gear 4 by programming iteratively, so that the roller-type eddy current inertial mass tuned mass damper meets the target frequency. Optimal frequency ratio f opt The formula is:

[0076] The linearized frequency relationship for small displacements is:

[0077] The formula for iteratively solving for the radius r of gear 4 using simultaneous programming is:

[0078] Specifically, the target frequency of the tuned mass damper can be obtained based on the optimal frequency ratio. for

[0079] Further

[0080] Based on the aforementioned derivation, the small displacement linearization frequency of the tuned mass damper is...

[0081] The two equations combined are:

[0082] Based on the optimal damping ratio ζ bopt The formula determines the damping parameters of the roller-type eddy current inertial mass tuned mass damper, and the optimal damping ratio ζ. bopt The formula is:

[0083] In the above formula, , Let ω be the acceleration due to gravity. s ω is the natural frequency of the controlled master structure. dThe natural frequency of the tuned mass damper is given by μ, the mass ratio of the tuned mass damper to the controlled main structure is given by a, the coefficient of the quadratic parabola of the track is given by R, the radius of the roller is given by r, and the radius of the gear is given by r.

[0084] In the above embodiments, the unit of gravitational acceleration g is m / s², and the unit of the quadratic parabola coefficient a is m. -¹ The roller radius R is in meters, the gear radius r is in meters, the rolling element mass m is in kilograms, and the mass of the controlled main structure m is... s The unit is kg, and the stiffness k of the controlled main structure is... s The unit is N / m; the rolling element displacement x is in meters, and the displacement x of the controlled main structure is in meters. s The unit is m; the damping coefficient c of the tuned mass damper is N·s / m; the external harmonic excitation amplitude F0 is in N; and the natural frequency ω of the rolling element is... d The unit is rad / s, and the frequency ω of the controlled main structure is... s The unit is rad / s, and the velocity of the center of mass of the rolling body is v. c The units are m / s, the system kinetic energy T is in J, and the system potential energy V is in J.

[0085] This embodiment provides a design method for a roller-type eddy current inertial mass tuned mass damper. Through the above design method, the vibration reduction requirements of the roller-type eddy current inertial mass tuned mass damper for a quadratic parabolic trajectory can be met, and the frequency of the roller-type eddy current inertial mass tuned mass damper can be adjusted by changing the roller radius and gear radius.

[0086] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A rolling-element eddy current inertial tuned mass damper comprising: The system comprises a base (1), two tracks (2), rollers (3), two gears (4), and several permanent magnets (5). The base (1) is used to fix the main structure under control. The two tracks (2) are arranged side by side and spaced apart on the base (1). The tops of the two tracks (2) are continuously provided with meshing teeth (21) along the length direction. The rollers (3) are fixed with coaxially arranged gears (4) on both sides of the axial direction. The gears (4) mesh with the meshing teeth (21) on the tracks (2). The rollers (3) can rotate on the meshing teeth (21) on the tracks (2) through the rotation of the gears (4). The system is characterized in that... The top surface of the meshing teeth (21) of the track (2) is arranged in a quadratic parabola. Only one of the roller (3) and the track (2) is a conductor. When the roller (3) is a conductor, all the permanent magnets (5) are fixedly arranged on the inner side between the two tracks (2). When the track (2) is a conductor, all the permanent magnets (5) are fixedly arranged on both sides of the roller (3) along the axial direction.

2. The roller-track type eddy current inertial mass tuned mass damper according to claim 1, characterized in that, When the roller (3) is a conductor, the roller (3) is provided with heat dissipation holes (31), and the axial direction of the heat dissipation holes (31) is the same as that of the roller (3).

3. A rolling element eddy current inertial tuned mass damper according to claim 2, wherein, The roller (3) has a ring of heat dissipation holes (31) evenly spaced along its circumference.

4. A rolling element eddy current inertial tuned mass damper according to claim 1 wherein, When the roller (3) is a conductor, each track (2) is provided with a row of permanent magnets (5) arranged at intervals along the quadratic parabola of the track (2).

5. A rolling element eddy current inertial tuned mass damper according to claim 4 wherein, The magnetic poles of two adjacent permanent magnets (5) in each column are opposite, and the magnetic poles of the permanent magnets (5) arranged opposite to each other in the two tracks (2) are opposite.

6. A rolling element eddy current inertial tuned mass damper according to claim 1 wherein, When the track (2) is a conductor, all the permanent magnets (5) are arranged in a circle on each side of the roller (3) in a uniform and spaced manner along the circumference.

7. A rolling element eddy current inertial tuned mass damper according to any one of claims 1 to 6, wherein, The top of both ends of the track (2) is provided with limiting members (22).

8. A rolling element eddy current inertial tuned mass damper according to claim 7, wherein, The roller (3) and the gear (4) are fixedly connected by a coaxial connecting shaft (41). The limiting member (22) is hook-shaped, and the inner arc of the hook-shaped limiting member (22) is adapted to the arc of the connecting shaft (41).

9. A rolling element eddy current inertial tuned mass damper according to any one of claims 1 to 6, wherein, The roller (3) and the gear (4) are detachably connected.

10. A design method for a roller-track type eddy current inertial mass tuned mass damper, characterized in that, Designing a roller-type eddy current inertial mass tuned mass damper as described in any one of claims 1-9 includes the following steps: S1, determine the dynamic characteristic parameters m of the controlled main structure s , k s , and ω s ; m s , k s , and ω s are the mass, stiffness, and frequency of the controlled main structure, respectively S2. Based on engineering requirements or installation constraints, and combined with the dynamic characteristic parameters m of the controlled main structure. s k s and ω s The mass m of the rolling element of the roller-type eddy current inertial mass tuned mass damper and the mass m of the controlled main structure are pre-selected. s The mass ratio μ is 1%-5%; the mass m of the rolling element is determined according to the mass ratio μ; wherein, when all the permanent magnets (5) are fixedly disposed on the inner side between the two tracks (2), the rolling element includes the roller (3) and all the gears (4) and the connecting structure between them to form an integral whole; when all the permanent magnets (5) are fixedly disposed on both sides of the axial direction of the roller (3), the rolling element includes the roller (3), all the gears (4) and all the permanent magnets (5) and the connecting structure between them to form an integral whole; S3. Based on the rolling element mass m and the requirements of installation space, allowable stroke, and processing conditions, first determine the coefficient a of the quadratic parabolic track (2) and the radius R of the roller (3), where the quadratic parabolic function of the quadratic parabolic track (2) is: x is the horizontal coordinate of the contact point between gear (4) and track (2). Let be the vertical coordinate of the contact point between gear (4) and track (2); S4. Substitute the coefficient a and the radius R of the roller (3) into the optimal frequency ratio f of the roller-type eddy current inertial mass tuned mass damper. opt The formula and the linearized frequency relationship of small displacement are used to solve the radius r of the gear (4) in a programming iteration, so that the roller-type eddy current inertial mass tuned mass damper meets the target frequency. Optimum frequency ratio f opt The formula is: The linearized frequency relationship for small displacements is: The formula for solving the radius r of gear (4) using simultaneous programming iteration is as follows: According to the optimal damping ratio ζ bopt The damping parameter of the rolling rail type eddy current inertial mass tuned mass damper is determined by the formula bopt The formula is: In the formula, , This is the acceleration due to gravity.

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