Non-linear energy trap using canted coil spring and particle damping

Abstract

The nonlinear energy trap comprises an annular vibration absorption mass block, a V-shaped groove is formed in the inner side wall of the vibration absorption mass block, the V-shaped groove is formed along the inner side wall of the vibration absorption mass block by a circle, the annular radial inclined ring spring is arranged at the V-shaped groove, and a bearing is arranged on the inner side of the inclined ring spring; the inner side wall of the vibration absorption mass block is further fixedly connected with four particle containers, and damping particles are placed in the particle containers. The particle container is sealed by a cover plate, and the cover plate is fixedly connected with the vibration absorption mass block; the outer side of the vibration absorption mass block is connected with a grounding support through a connecting spring. The nonlinear energy trap solves the problems that in the prior art, the damping characteristic of a vibration absorber applied to a rotor system is difficult to adjust, and the vibration suppression capacity is insufficient, and the nonlinear energy trap has the excellent vibration reduction effect.

Description

Technical Field

[0001] The invention belongs to the technical field of rotor system vibration suppression devices and relates to a nonlinear energy well using canted coil springs and particle damping. Background Art

[0002] The rotor system is an important part of modern industrial equipment. During its operation, it is inevitably affected by the excitation source and the inherent characteristics of the structure, which can cause vibration problems. This vibration may lead to a decline in equipment performance, loss of accuracy, and even a threat to system safety. Therefore, how to effectively suppress the vibration of the rotor system has become the focus of academic and industrial circles.

[0003] At present, the technical means widely used in vibration suppression of rotor systems mainly include adding active or passive vibration absorbers. Among them, nonlinear energy sink (NES), as a passive vibration absorber with nonlinear elements, has the characteristics of simple structure, reliable operation, wide vibration suppression frequency band and no need for external energy source. It overcomes the limitations of traditional active or passive vibration absorbers in practical applications of rotor systems, so it is proposed as an efficient vibration suppression device.

[0004] The vibration suppression mechanism of the nonlinear energy well is targeted energy transfer (TET), that is, the vibration energy will be 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 of NES. For example: the Chinese patent previously applied by our research group with a publication date of September 12, 2023 and a publication number of CN116733902A discloses a nonlinear vibration absorber that uses a canted coil spring to suppress the vibration of the rotor system. The nonlinear vibration absorber is essentially a combination of nonlinear stiffness and linear damping. It ignores the parameter design of damping, which limits the vibration suppression effect of NES to a certain extent.

[0005] Based on the above technical background, the development of a nonlinear energy well with both nonlinear stiffness and nonlinear damping has become a new direction for solving the vibration problem of the rotor system. Summary of the invention

[0006] The purpose of the present invention is to provide a nonlinear energy well using canted coil springs and particle damping, which solves the problems in the prior art that the damping characteristics of the vibration absorber used in the rotor system are difficult to adjust and the vibration suppression ability is insufficient.

[0007] The technical solution adopted by the present invention is to use a nonlinear energy well with canted coil springs and particle damping, including an annular vibration-absorbing mass block, the inner wall of the vibration-absorbing mass block is provided with a V-shaped groove, the V-shaped groove is provided along the inner wall of the vibration-absorbing mass block, an annular radial canted coil spring is arranged at the V-shaped groove, and a bearing is arranged on the inner side of the canted 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; the outer side of the vibration-absorbing mass block is connected to a grounding bracket through a connecting spring.

[0008] The present invention is also characterized in that: The included angle of the V-groove is 120°.

[0009] The particle container is a cylindrical cavity structure.

[0010] The four particle containers are arranged on the same side of the canted coil spring, and the four particle containers are evenly distributed along the inner side wall of the vibration absorbing mass block.

[0011] The outer circumferential surface of the vibration absorbing mass block is provided with four blind holes, and the four blind holes are evenly distributed along the circumferential surface.

[0012] One end of the connecting spring is inserted into the blind hole and fixed, and the other end is fixedly connected to the grounding bracket.

[0013] The grounding bracket is a circular or regular polygonal frame structure.

[0014] A T-shaped connecting rod is connected to the bottom of the grounding bracket, and both ends of the T-shaped connecting rod are connected to the rotor system.

[0015] The beneficial effects of the present invention are: (1) The geometric structure of the canted coil spring in the nonlinear energy well of the present invention is annular, which can be highly compatible with the dynamic characteristics of the rotor system. At the same time, due to its unique nonlinear stiffness characteristics, it can provide a constant restoring force pointing to the center of the rotor, and can dynamically adjust its own load distribution under different vibration responses, effectively eliminating the inertial force concentration phenomenon of the rotor system during operation; (2) Particle damping is set in the nonlinear energy well of the present invention. On the one hand, the introduction of particle damping enables the system to quickly optimize the vibration suppression effect by only adjusting the material properties of the particles (such as density, elastic modulus, etc.) and geometric parameters (such as particle size, filling rate) when the parameters are determined, significantly reducing the design and debugging time and improving the efficiency of engineering applications. On the other hand, particle damping can provide dynamically adaptive nonlinear damping characteristics for different vibration frequencies and amplitude ranges, thereby achieving a wider bandwidth and more efficient energy dissipation effect. At the same time, the maintenance operation is simple and the cost is low; (3) The nonlinear energy well of the present invention overcomes the limitation of using only linear damping in broadband vibration suppression through the synergistic effect of the nonlinear stiffness characteristics of the canted coil spring and 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 well of the present invention to maintain excellent vibration reduction effect under complex vibration conditions, and further expands the application scope of the nonlinear energy well in the rotor system; (4) The nonlinear energy sink of the present invention is directly connected to the rotor system through the bearing, and the nonlinear elements (canted coil spring and particle damping) are closer to the vibration source (rotating shaft of the rotor system). Therefore, from the perspective of the energy transfer path, when vibration occurs, the nonlinear energy sink of the present invention can transfer and dissipate energy faster; (5) Compared with the traditional design, the nonlinear energy sink of the present invention can not only accurately adapt to the requirements of 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic diagram of the structure of the nonlinear energy well of the present invention; Figure 2 It is a schematic diagram of the local structure of the nonlinear energy well of the present invention; Figure 3 It is a schematic diagram of the connection between the nonlinear energy sink and the rotor system of the present invention; Figure 4 It is a schematic diagram of the structure of the rotor system; Figure 5 It is a graph of theoretical stiffness and fitted stiffness of the nonlinear stiffness of the canted coil spring in the nonlinear energy well of the present invention; Figure 6 It is a physical model diagram of the whole system consisting of the nonlinear energy sink and the rotor system of the present invention; Figure 7 is a frequency domain response diagram of the rotor system before and after the nonlinear energy well is added in Example 3 of the present invention; Figure 8 is a time domain response diagram of the rotor system in Example 4 of the present invention; Fig. 9 is a time domain response diagram of the nonlinear energy well in Example 4 of the present invention; Fig.10 is a wavelet time-frequency diagram of the rotor system in Example 5 of the present invention; Fig.11 is a wavelet time-frequency diagram of the nonlinear energy sink in Example 5 of the present invention; Fig.12 It is a frequency domain response diagram of the rotor system in Example 6 of the present invention.

[0017] In the figure, 1. motor, 2. motor seat, 3. first bearing seat, 4. rotating shaft, 5. cover plate, 6. bevel coil 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 particles, 18. V-groove, 19. particle container, 20. blind hole, 21. T-type connecting rod. DETAILED DESCRIPTION

[0018] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Example 1 The present invention uses a nonlinear energy sink with canted coil springs and particle damping, and the structure is as follows: Figure 1 and Figure 2 As shown, it includes an annular vibration-absorbing mass block 7, and the inner wall of the vibration-absorbing mass block 7 is provided with a V-shaped groove 18 with an angle of 120°, and the V-shaped groove 18 is provided along the inner wall of the vibration-absorbing mass block 7. An annular radial bevel spring 6 is arranged at the V-shaped groove 18, and the V-shaped groove 18 plays a limiting role on the bevel spring 6. A bearing 16 is arranged on the inner side of the bevel spring 6. The inner wall of the vibration-absorbing mass block 7 is also fixed with four particle containers 19, and the particle container 19 is a cylindrical cavity structure. The four particle containers 19 are arranged on the same side of the bevel spring 6, and the four particle containers 19 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 container 19 is sealed with a cover plate 5 to prevent the damping particles 17 from spilling, and the cover plate 5 is fixed to the vibration-absorbing mass block 7.

[0020] Four blind holes 20 are provided on the outer circumferential surface of the vibration absorbing mass block 7, and the four blind holes 20 are evenly distributed along the circumferential surface. The blind holes 20 are used to install the connecting spring 8, one end of the connecting spring 8 is inserted into the blind hole 20 and fixed, and the other end is fixed to the grounding bracket 13. The grounding bracket 13 is a circular or regular polygonal frame structure, which is arranged on the outer ring of the vibration absorbing mass block 7 and connected to the vibration absorbing mass block 7 through 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.

[0021] The nonlinear energy sink of the present invention is used to suppress the vibration of the 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 a bearing 16 and a T-shaped connecting rod 21 .

[0022] like Figure 4As shown, the structure of the rotor system includes a base 14, the surface of the base 14 is provided with two longitudinal T-shaped slots parallel to each other, the motor base 2 and the eddy current sensor 12 are fixed to the base 14 through the longitudinal T-shaped slots, the motor base 2 is mounted with a motor 1, and the output shaft of the motor 1 is connected to the rotating shaft 4 through a coupling 15. A pair of brackets 11 are also fixed to the base 14, and the first bearing seat 3 and the second bearing seat 10 are respectively fixed to the two brackets 11, and the two bearing seats are used to support the rotating shaft 4. A turntable 9 is also mounted on the rotating shaft 4, and the turntable 9 is the main rotating component of the rotor system. When the motor 1 is running, the power source outputted by the motor 1 can be transmitted to the rotating shaft 4 through the coupling 15 and drive the turntable 9 to rotate, and the vibration displacement signal generated by the turntable 9 during operation can be collected by the eddy current sensor 12.

[0023] When the nonlinear energy sink of the present invention is used, Figure 3 As shown, the two ends of the T-shaped connecting rod 21 are fixed to the base 14 through longitudinal T-shaped grooves, and the inner ring of the bearing 16 is connected to the rotating shaft 4, so that the nonlinear energy sink will not rotate with the rotating shaft 4.

[0024] The vibration suppression mechanism of the nonlinear energy sink of the present invention is as follows: when the rotor system resonates, the canted coil spring 6 can initially absorb the vibration energy transmitted by the system, and the residual energy can be further dissipated through the mutual collision and friction of the damping particles 17. At the same time, the elastic forces of the four connecting springs 8 can offset each other.

[0025] Example 2 Based on Example 1, Figure 5 , is the nonlinear stiffness curve of the canted coil spring 6 in the nonlinear energy well of the present invention and its fitting curve. The fitted nonlinear stiffness is in the form of a polynomial stiffness, as shown in ,in k 1 、k 2 、k 3 is the nonlinear stiffness coefficient of the canted coil spring 6. It can be seen that the canted coil spring 6 has unique nonlinear mechanical characteristics due to the particularity of its structure.

[0026] Example 3 On the basis of Example 2, the nonlinear damping model of the damping particles 17 used in the nonlinear energy well of the present invention is an equivalent viscous damping and equivalent Coulomb damping coefficient model generated by the drag force established based on the gas-solid flow method.

[0027] The equivalent viscous damping coefficient can be expressed as:

[0028]

[0029] The equivalent Coulomb damping coefficient can be expressed as:

[0030]

[0031] In the above formula, d c is the particle container diameter, h c is the particle container height, is the gas density and particle density The equivalent volume density of the mixed flow composed of them is, α p is the filling rate of particles, f is the vibration frequency, E p is the coefficient of restitution of the particle, d p is the diameter of the particle, Is the filling ratio α p The associated radial distribution function, is the internal friction angle, is the quadratic invariant of the deviatoric stress tensor, is the solid phase pressure.

[0032] Therefore, the nonlinear damping model used by the nonlinear energy sink of the present invention can be further simplified as follows:

[0033] Reference Figure 6 , is the physical model of the whole system composed of the nonlinear energy sink and the rotor system of the present invention. The system is isotropic and the gyroscopic effect is ignored. The dynamic equation of the system can be expressed as:

[0034] in, m is the mass of the turntable, k n is the stiffness of the connecting spring, k x 、k y is the stiffness of the bearing supports at both ends, c x 、c y is the damping at the bearing support, e d is the eccentricity of the turntable, m n is the equivalent total mass of the vibration-absorbing mass block and the damping particles, k 1 、k 2 、k 3 is the nonlinear stiffness coefficient of the canted coil spring, c eqx 、c eqy is the nonlinear damping coefficient of particle damping, w is the rotor speed, x、 y is the displacement of the rotor system, x n 、y n is the displacement of the nonlinear energy well, x, y, x n 、y n A dot on top represents the first derivative, which is velocity; x, y, x n 、y n The two points above represent the second derivative, which is the acceleration.

[0035] The system parameters given in this embodiment are: m= 1kg, k n = 1800N / m, k x = k y =7.6×10 4 N / m, c x = c y =5N.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, h c =2×10 -2 m, d p =1×10-2 m, , , α p =10%, , , E p =0.6; Reference Figure 7 When the nonlinear energy well is not added, the maximum amplitude of the steady-state response of the rotor system is 1.65 mm, while after the nonlinear energy well of the present invention is added, the maximum amplitude of the steady-state response of the rotor system is 0.56 mm. Compared with not adding the nonlinear energy well, the maximum amplitude is reduced by 1.09 mm, the effective vibration suppression rate reaches 66%, and the resonance frequency range is about 43~45.7 Hz, indicating that the nonlinear energy well of the present invention has excellent steady-state resonance suppression performance and wide-band vibration suppression effect.

[0036] Example 4 Based on Example 3, the time domain response curves of the rotor system and the nonlinear energy sink at the resonant frequency of 44 Hz are plotted as follows: Figure 8 and 9 As shown in the figure, it can be seen that the time domain response of the resonance zone is in the form of beat waves, indicating that the rotor system with the nonlinear energy well of the present invention has a strongly modulated response (SMR) behavior in the resonance zone, that is, it proves that energy transfer occurs between the rotor system and the nonlinear energy well, and the energy of the rotor system is transferred to the nonlinear energy well and dissipated by it, thereby achieving the purpose of vibration suppression.

[0037] Example 5 On the basis of Example 3, the initial excitation speed is 0.5 m / s for the rotor system, and the wavelet time-frequency diagrams of the rotor system and the nonlinear energy sink are drawn as follows: Fig.10 and 11 As shown, it can be seen that in the initial 0-0.4s, a 1:1 resonant capture is maintained between the rotor system and the nonlinear energy well, during which the energy of the rotor system is rapidly transferred to the nonlinear energy well, and targeted energy transfer (TET) occurs; in the subsequent 0.4-1s, as the vibration energy decays, the 1:1 resonant capture between the coupled systems gradually disappears. The above-mentioned resonance capture form can efficiently transfer the vibration energy of the rotor system to the nonlinear energy well of the present invention, and it is consumed by the particle damping inside it. In addition, in the first 0.4s alone, the vibration energy of the rotor system basically disappears to 0, indicating that the nonlinear energy well of the present invention has a rapid energy dissipation response and has excellent transient impact suppression performance.

[0038] Example 6 On the basis of Example 3, other parameters are kept unchanged, and only the filling rate of damping particles is changed. The frequency domain response curve of the corresponding rotor system is as follows: Fig.12 As shown, it can be seen that when the filling rate of the damping particles is between 10% and 40%, the coupling system can produce the SMR phenomenon, and as the filling rate increases, the vibration suppression frequency band in the resonance zone of the rotor system gradually narrows. When the filling rate reaches 50%, the coupling system can no longer undergo SMR behavior. At this time, the damping particles lose sufficient space for movement, resulting in the failure of the vibration suppression mechanism. Obviously, when the system parameters of the nonlinear energy well of the present invention are determined, the damping characteristics can be adjusted by selecting a suitable particle filling rate, thereby improving the system 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 nonlinear energy sink using canted coil springs and particle damping, characterized in that: The invention comprises an annular vibration-absorbing mass block (7), the inner side wall of the vibration-absorbing mass block (7) being provided with a V-shaped groove (18), the V-shaped groove (18) being provided along the inner side wall of the vibration-absorbing mass block (7), an annular radial canted coil spring (6) being provided at the V-shaped groove (18), and a bearing (16) being provided on the inner side of the canted coil spring (6); four particle containers (19) being fixedly connected to the inner side wall of the vibration-absorbing mass block (7), damping particles (17) being placed in the particle containers (19); the particle containers (19) being sealed by a cover plate (5), and the cover plate (5) being fixedly connected to the vibration-absorbing mass block (7); and the outer side of the vibration-absorbing mass block (7) being connected to a grounding bracket (13) via a connecting spring (8).

2. The nonlinear energy sink using canted coil springs and particle damping according to claim 1, characterized in that: The included angle of the V-shaped groove (18) is 120°.

3. The nonlinear energy sink using canted coil springs and particle damping according to claim 1, characterized in that: The particle container (19) is a cylindrical cavity structure.

4. The nonlinear energy sink using canted coil springs and particle damping according to claim 1 or 3, characterized in that: The four particle containers (19) are arranged on the same side of the canted coil spring (6), and the four particle containers (19) are evenly distributed along the inner side wall of the vibration absorbing mass block (7).

5. The nonlinear energy sink using canted coil springs and particle damping according to claim 1, characterized in that: Four blind holes (20) are provided on the outer circumferential surface of the vibration absorbing mass block (7), and the four blind holes (20) are evenly distributed along the circumferential surface.

6. The nonlinear energy sink using canted coil springs and particle damping according to claim 5, characterized in that: One end of the connection spring (8) is inserted into the blind hole (20) and fixed, and the other end is fixedly connected to the grounding bracket (13).

7. The nonlinear energy sink using canted coil springs and particle damping according to claim 1, characterized in that: The grounding bracket (13) is a circular or regular polygonal frame structure.

8. The nonlinear energy sink using canted coil springs and particle damping according to claim 1, characterized in that: 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.

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