Nonlinear energy sink with oblique coil springs and granular damping

Abstract

The application discloses a non-linear energy sink applying an inclined coil spring and particle damping, comprising a ring-shaped vibration-absorbing mass block, a V-shaped groove is formed in the inner side wall of the vibration-absorbing mass block, the V-shaped groove is formed along the inner side wall of the vibration-absorbing mass block in a circle, a ring-shaped radial inclined coil spring is arranged at the V-shaped groove, and a bearing is arranged at the inner side of the inclined coil spring; four particle containers are fixedly connected to the inner side wall of the vibration-absorbing mass block, and damping particles are placed in the particle containers; the particle containers are sealed by cover plates, and the cover plates are fixedly connected to the vibration-absorbing mass block; and a grounding support is connected to the outer side of the vibration-absorbing mass block through a connecting spring. The non-linear energy sink solves the problems of the vibration absorber applied to a rotor system in the prior art, i.e., the damping characteristic is difficult to adjust and the vibration suppression capacity is insufficient, and has excellent vibration reduction effect.

Description

Technical Field

[0001] This invention belongs to the technical field of rotor system vibration suppression devices, and relates to a nonlinear energy trap that uses a slanted coil spring and particle damping. Background Technology

[0002] Rotor systems are a crucial component of modern industrial equipment. During operation, they are inevitably affected by excitation sources and inherent structural characteristics, leading to vibration problems. This vibration can cause performance degradation, reduced accuracy, and even threaten system safety. Therefore, effectively suppressing rotor system vibration has become a focus of attention for both academia and industry.

[0003] Currently, the main technical means widely used in rotor system vibration suppression include adding active or passive vibration absorbers. Among them, the nonlinear energy sink (NES), as a passive vibration absorber with nonlinear elements, has the advantages of simple structure, reliable operation, wide vibration suppression bandwidth, and no need for an external energy source. It overcomes the limitations of traditional active or passive vibration absorbers in practical applications of rotor systems, and is therefore proposed as a high-efficiency vibration suppression device.

[0004] The vibration suppression mechanism of nonlinear energy traps is targeted energy transfer (TET), where vibration energy is transferred unidirectionally from the main system to the mass block of the NES. However, triggering the TET mechanism usually requires specific damping and stiffness conditions, and existing research focuses on how to design and implement different forms of nonlinear stiffness in NES. For example, a Chinese patent filed by our research group on September 12, 2023, with publication number CN116733902A, discloses a nonlinear vibration absorber that uses a slanted coil spring to suppress rotor system vibration. This nonlinear vibration absorber is essentially a combination of nonlinear stiffness and linear damping, which neglects the design of damping parameters and limits the vibration suppression effect of NES to some extent.

[0005] Based on the above technical background, developing a nonlinear energy trap that simultaneously possesses nonlinear stiffness and nonlinear damping has become a new direction for solving the vibration problem of rotor systems. Summary of the Invention

[0006] The purpose of this invention is to provide a nonlinear energy trap that uses a slanted coil spring and particle damping, which solves the problems of difficult-to-adjust damping characteristics and insufficient vibration suppression capability of vibration absorbers used in rotor systems in the prior art.

[0007] The technical solution adopted in this invention is a nonlinear energy trap using inclined coil springs and particle damping, comprising an annular vibration-absorbing mass block, a V-shaped groove formed on the inner wall of the vibration-absorbing mass block, the V-shaped groove being formed around the inner wall of the vibration-absorbing mass block, an annular radial inclined coil spring being provided at the V-shaped groove, and a bearing being provided inside the inclined coil spring; four particle containers are also fixedly connected to the inner wall of the vibration-absorbing mass block, and damping particles are placed in the particle containers; the particle containers are sealed with a cover plate, and the cover plate is fixedly connected to the vibration-absorbing mass block; a grounding bracket is connected to the outer side of the vibration-absorbing mass block through a connecting spring.

[0008] The invention is further characterized by:

[0009] The included angle of the V-groove is 120°.

[0010] The granular container has a cylindrical cavity structure.

[0011] Four particle containers are positioned on the same side of the inclined coil spring, and the four particle containers are evenly distributed along the inner wall of the vibration-absorbing mass block.

[0012] Four blind holes are provided on the outer circumferential surface of the vibration-absorbing mass block, and the four blind holes are evenly distributed along the circumferential surface.

[0013] One end of the connecting spring is inserted into the blind hole and fixed, while the other end is fixed to the grounding bracket.

[0014] The grounding bracket is a circular or regular polygonal frame structure.

[0015] The bottom of the grounding bracket is connected to a T-shaped connecting rod, and the two ends of the T-shaped connecting rod are connected to the rotor system.

[0016] The beneficial effects of this invention are:

[0017] (1) The geometric structure of the inclined coil spring in the nonlinear energy trap of the present invention is ring-shaped, which can be highly matched with the dynamic characteristics of the rotor system. At the same time, thanks to its unique nonlinear stiffness characteristics, it can provide a constant restoring force pointing to the center of the rotor. It can dynamically adjust its own load distribution under different vibration responses, effectively eliminating the phenomenon of inertial force concentration in the rotor system during operation.

[0018] (2) The nonlinear energy trap of this invention incorporates particle damping. On the one hand, the introduction of particle damping allows the system to quickly optimize vibration suppression by adjusting only the material properties (such as density and elastic modulus) and geometric parameters (such as particle size and filling rate) of the particles, given fixed parameters. This significantly reduces design and debugging time and improves engineering application efficiency. On the other hand, particle damping can provide dynamically adaptable nonlinear damping characteristics for different vibration frequencies and amplitude ranges, thereby achieving a wider frequency band and higher energy dissipation efficiency. Furthermore, maintenance and operation are simple and cost-effective.

[0019] (3) The nonlinear energy trap of the present invention overcomes the limitations of using only linear damping in broadband vibration suppression by combining the nonlinear stiffness characteristics of the inclined coil spring with the nonlinear damping characteristics of the particle damping, and significantly improves the vibration resistance and stability of the system. This dual nonlinear element design enables the nonlinear energy trap of the present invention to maintain excellent vibration reduction effect under complex vibration conditions, and further expands the application range of nonlinear energy traps in rotor systems;

[0020] (4) The nonlinear energy trap of the present invention is directly connected to the rotor system through the bearing. The nonlinear elements (helical coil spring and particle damping) are closer to the vibration source (rotor system shaft). Therefore, from the perspective of energy transfer path, when vibration occurs, the nonlinear energy trap of the present invention can transfer and dissipate energy more quickly.

[0021] (5) Compared with traditional designs, the nonlinear energy trap of the present invention can not only accurately adapt to the dynamic characteristics of the rotor system, but also has the advantages of simple operation and low maintenance cost, meeting the actual needs of efficient and low-cost vibration control in industrial scenarios. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the nonlinear energy trap of the present invention;

[0023] Figure 2 This is a partial structural schematic diagram of the nonlinear energy trap of the present invention;

[0024] Figure 3 This is a schematic diagram of the connection between the nonlinear energy trap and the rotor system of the present invention;

[0025] Figure 4 This is a schematic diagram of the rotor system.

[0026] Figure 5 This is a graph showing the theoretical stiffness and fitted stiffness curves of the nonlinear stiffness of the inclined coil spring in the nonlinear energy trap of this invention.

[0027] Figure 6 This is a physical model diagram of the entire system consisting of the nonlinear energy trap and the rotor system of the present invention;

[0028] Figure 7 This is the frequency domain response diagram of the rotor system before and after adding the nonlinear energy trap in Embodiment 3 of the present invention;

[0029] Figure 8 This is the time-domain response diagram of the rotor system in Embodiment 4 of the present invention;

[0030] Figure 9 This is the time-domain response diagram of the nonlinear energy trap in Embodiment 4 of the present invention;

[0031] Figure 10This is the wavelet time-frequency diagram of the rotor system in Embodiment 5 of the present invention;

[0032] Figure 11 This is the wavelet time-frequency diagram of the nonlinear energy trap in Embodiment 5 of the present invention;

[0033] Figure 12 This is the frequency domain response diagram of the rotor system in Embodiment 6 of the present invention.

[0034] In the diagram, 1. Motor, 2. Motor mount, 3. First bearing seat, 4. Shaft, 5. Cover plate, 6. Inclined spring, 7. Vibration-absorbing mass block, 8. Connecting spring, 9. Turntable, 10. Second bearing seat, 11. Bracket, 12. Eddy current sensor, 13. Grounding bracket, 14. Base, 15. Coupling, 16. Bearing, 17. Damping particle, 18. V-groove, 19. Particle container, 20. Blind hole, 21. T-shaped connecting rod. Detailed Implementation

[0035] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0036] Example 1

[0037] This invention utilizes a nonlinear energy trap with slanted coil springs and particle damping, the structure of which is as follows: Figure 1 and Figure 2 As shown, the device includes an annular vibration-absorbing mass block 7. A V-shaped groove 18 with an included angle of 120° is formed on the inner wall of the vibration-absorbing mass block 7, and the V-shaped groove 18 runs along the inner wall of the vibration-absorbing mass block 7. An annular radial inclined coil spring 6 is installed at the V-shaped groove 18, and the V-shaped groove 18 limits the movement of the inclined coil spring 6. A bearing 16 is installed inside the inclined coil spring 6. Four particle containers 19 are also fixedly connected to the inner wall of the vibration-absorbing mass block 7. The particle containers 19 have a cylindrical cavity structure and are located on the same side of the inclined coil spring 6, and are evenly distributed along the inner wall of the vibration-absorbing mass block 7. Damping particles 17 are filled in the four particle containers 19, and the particle parameters can be adjusted according to actual conditions. The particle containers 19 are sealed with a cover plate 5 to prevent the spillage of the damping particles 17. The cover plate 5 is fixedly connected to the vibration-absorbing mass block 7.

[0038] Four blind holes 20 are evenly distributed along the outer circumference of the vibration-absorbing mass block 7. The blind holes 20 are used to install connecting springs 8. One end of the connecting spring 8 is inserted into the blind hole 20 and fixed, while the other end is fixed to the grounding bracket 13. The grounding bracket 13 is a circular or regular polygonal frame structure, located on the outer ring of the vibration-absorbing mass block 7, and connected to the vibration-absorbing mass block 7 via the spring 8. A T-shaped connecting rod 21 is connected to the bottom of the grounding bracket 13, and both ends of the T-shaped connecting rod 21 are connected to the rotor system.

[0039] The nonlinear energy trap of this invention is used to suppress vibration of a rotor system, and its cooperation with the rotor system is as follows: Figure 3 As shown, the nonlinear energy sink is connected to the rotor system via bearing 16 and T-shaped connecting rod 21.

[0040] like Figure 4 The diagram shows the structure of the rotor system, which includes a base 14. Two parallel longitudinal T-slots are formed on the surface of the base 14. A motor mount 2 and an eddy current sensor 12 are fixed to the base 14 via these T-slots. A motor 1 is mounted on the motor mount 2, and the output shaft of the motor 1 is connected to a rotating shaft 4 via a coupling 15. A pair of brackets 11 are also fixed to the base 14, with a first bearing seat 3 and a second bearing seat 10 fixed to each bracket 11, supporting the rotating shaft 4. A turntable 9 is mounted on the rotating shaft 4; the turntable 9 is the main rotating component of the rotor system. When the motor 1 operates, its power output is transmitted to the rotating shaft 4 via the coupling 15, driving the turntable 9 to rotate. The vibration displacement signal generated by the turntable 9 during operation can be collected by the eddy current sensor 12.

[0041] When the nonlinear energy trap of the present invention is used, such as Figure 3 As shown, the two ends of its T-shaped connecting rod 21 are fixed to the base 14 through the longitudinal T-shaped groove, and the inner ring of the bearing 16 is connected to the rotating shaft 4, so that the nonlinear energy trap will not rotate with the rotating shaft 4.

[0042] The vibration suppression mechanism of the nonlinear energy trap of the present invention is as follows: when the rotor system resonates, the vibration energy transmitted by the system can be initially absorbed by the inclined coil spring 6, while the residual energy can be further dissipated by the collision and friction of the damping particles 17. At the same time, the elastic forces of the four connecting springs 8 can cancel each other out.

[0043] Example 2

[0044] Based on Example 1, referring to Figure 5 This refers to the nonlinear stiffness curve and its fitted curve of the inclined coil spring 6 in the nonlinear energy trap of this invention. The fitted nonlinear stiffness is in polynomial stiffness form, as shown in... ,in k 1 、k 2 、k 3 represents the nonlinear stiffness coefficient of the inclined coil spring 6. It can be seen that the inclined coil spring 6 has unique nonlinear mechanical characteristics due to the special nature of its structure.

[0045] Example 3

[0046] Based on Example 2, the nonlinear damping model of the damping particle 17 used in the nonlinear energy trap of the present invention is based on the equivalent viscous damping and equivalent Coulomb damping coefficient model generated by the drag force established by the gas-solid flow method.

[0047] The equivalent viscous damping coefficient can be expressed as:

[0048]

[0049] The equivalent Coulomb damping coefficient can be expressed as:

[0050]

[0051] In the above formula, d c The diameter of the particle container, h c For the height of the particle container, For gas density and particle density The equivalent bulk density of the mixed flow is composed of the two components. α p The filling rate of the particles. f The vibration frequency, E p It is the coefficient of restitution of the particles. d p It is the diameter of the particle. It is related to the filling ratio α p The relevant radial distribution function, It is the internal friction angle. It is a second-order invariant of the deviatoric stress tensor. This refers to solid-phase pressure.

[0052] Therefore, the nonlinear damping model used in the nonlinear energy trap of this invention can be further simplified to:

[0053]

[0054] Reference Figure 6 This is the physical model of the entire system consisting of the nonlinear energy trap and the rotor system of this invention. The system is isotropic, and the gyroscopic effect is ignored. The dynamic equation of the system can be expressed as:

[0055]

[0056] in, m For the quality of the turntable, k n To ensure the stiffness of the connecting spring, k x 、k y This refers to the stiffness at the bearing supports at both ends. c x 、c yThis refers to the damping at the bearing support. e d The eccentricity of the turntable. m n This represents the equivalent total mass of the vibration-absorbing mass block and the damping particles. k 1 、 k 2 、k 3 represents the nonlinear stiffness coefficient of the inclined coil spring. c eqx 、c eqy Let be the nonlinear damping coefficient of particle damping, and w be the rotor speed. x、 y For the displacement of the rotor system, x n 、y n For the displacement of the nonlinear energy trap, x, y, x n 、y n The point at the top represents the first derivative, i.e., velocity; x, y, x n 、y n The two dots at the top represent the second derivative, i.e., acceleration.

[0057] The system parameters given in this embodiment are: m= 1kg, k n = 1800 N / m k x = k y =7.6×10 4 N / m, c x = c y =5 N·s / m, e d =3×10 -5 m, m n =0.08kg, k 1 = 4.81 × 10 3 N / m, k 2 = -2.53 × 10 6 N / m 2 , k 3 = 0.533 × 10 9 N / m 3 , d c =2×10 -2 m, hc =2×10 -2 m, d p =1×10 -2 m, , , α p =10%, , , E p =0.6;

[0058] Reference Figure 7 Without the addition of the nonlinear energy trap, the maximum amplitude of the steady-state response of the rotor system is 1.65 mm, while with the addition of the nonlinear energy trap of the present invention, the maximum amplitude of the steady-state response of the rotor system is 0.56 mm. Compared with the addition of the nonlinear energy trap, the maximum amplitude has decreased by 1.09 mm, the effective vibration suppression rate has reached 66%, and the resonance frequency range is about 43~45.7 Hz. This shows that the nonlinear energy trap of the present invention has excellent steady-state resonance suppression performance and wideband vibration suppression effect.

[0059] Example 4

[0060] Based on Example 3, the time-domain response curves of the rotor system and the nonlinear energy trap at the resonant frequency of 44Hz are plotted as follows: Figure 8 and 9 As shown in the figure, the time-domain response of the resonant region is in the form of beat waves, indicating that the rotor system with the addition of the nonlinear energy trap of the present invention exhibits strongly modulated response (SMR) behavior in the resonant region. This proves that energy transfer occurs between the rotor system and the nonlinear energy trap, and the energy of the rotor system is transferred to the nonlinear energy trap and dissipated therein, thereby achieving the purpose of vibration suppression.

[0061] Example 5

[0062] Based on Example 3, an initial excitation speed of 0.5 m / s was applied to the rotor system described above, and wavelet time-frequency diagrams of the rotor system and the nonlinear energy trap were plotted as follows: Figure 10 and 11As shown, within the initial 0-0.4s, a 1:1 resonant trapping is maintained between the rotor system and the nonlinear energy trap. During this period, the energy of the rotor system is rapidly transferred to the nonlinear energy trap, resulting in targeted energy transfer (TET). In the subsequent 0.4-1s, as the vibration energy decays, the 1:1 resonant trapping between the coupled systems gradually disappears. This resonant trapping mechanism efficiently transfers the vibration energy of the rotor system to the nonlinear energy trap of this invention, where it is consumed by the internal particle damping. Furthermore, the vibration energy of the rotor system essentially disappears to zero in the first 0.4s, indicating that the nonlinear energy trap of this invention has a rapid energy dissipation response and excellent transient impact suppression performance.

[0063] Example 6

[0064] Based on Example 3, keeping other parameters unchanged and only changing the damping particle filling rate, the corresponding rotor system frequency domain response curve is as follows. Figure 12 As shown, when the damping particle filling rate is between 10% and 40%, the coupled system can produce SMR (Single-Melt-Morpho) phenomenon, and as the filling rate increases, the vibration suppression frequency band of the rotor system's resonance region gradually narrows. When the filling rate reaches 50%, the coupled system can no longer exhibit SMR behavior, at which point the damping particles lose sufficient space for movement, leading to the failure of the vibration suppression mechanism. Clearly, given a fixed system parameter, the nonlinear energy trap of this invention can adjust its damping characteristics by selecting a suitable particle filling rate, thereby improving the system's vibration suppression effect. Similarly, the damping characteristics can also be adjusted by selecting different particle materials, particle diameters, and particle container sizes.

Claims

1. A non-linear energy sink employing a coned disc spring and granular damping, characterized in that, The invention discloses a vibration absorbing device, which comprises a ring-shaped vibration absorbing mass (7), an inner side wall of the vibration absorbing mass (7) is provided with a V-shaped groove (18), the V-shaped groove (18) is provided along the inner side wall of the vibration absorbing mass (7), a ring-shaped radial inclined coil spring (6) is arranged at the V-shaped groove (18), an inner side of the inclined coil spring (6) is provided with a bearing (16), four particle containers (19) are fixed to the inner side wall of the vibration absorbing mass (7), damping particles (17) are placed in the particle containers (19), the particle containers (19) are sealed by cover plates (5), the cover plates (5) are fixed to the vibration absorbing mass (7), and an earthed support (13) is connected to the outer side of the vibration absorbing mass (7) through a connecting spring (8).

2. The non-linear energy sink using an inclined coil spring and granular damping according to claim 1, characterized in that, The included angle of the V-shaped groove (18) is 120°.

3. The non-linear energy sink using an inclined coil spring and granular damping according to claim 1, wherein, The particle container (19) is a cylindrical cavity structure.

4. The non-linear energy sink using an inclined coil spring and granular damping according to claim 1 or 3, characterized in that, The four particle containers (19) are arranged on the same side of the inclined coil spring (6), and the four particle containers (19) are uniformly distributed along the inner side wall of the vibration absorbing mass (7).

5. The non-linear energy sink using an inclined coil spring and granular damping according to claim 1, wherein, Four blind holes (20) are arranged on the outer circumferential surface of the vibration absorbing mass (7), and the four blind holes (20) are uniformly distributed along the circumferential surface.

6. The non-linear energy sink using an inclined coil spring and granular damping according to claim 5, characterized in that, One end of the connecting spring (8) is inserted into the blind hole (20) and fixed, and the other end is fixed to the earthed support (13).

7. The non-linear energy sink using an inclined coil spring and granular damping according to claim 1, wherein, The earthed support (13) is a circular or regular polygon frame structure.

8. The non-linear energy sink using an inclined coil spring and granular damping according to claim 1, wherein, A T-shaped connecting rod (21) is connected to the bottom of the earthed support (13), and two ends of the T-shaped connecting rod (21) are connected to a rotor system.

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