Negative stiffness vibration isolator and design method thereof

Abstract

The invention relates to a negative stiffness vibration isolator and a design method thereof.The vibration isolator comprises a base composed of a bottom plate and a cylinder, four first springs are evenly distributed on the bottom plate in the base in the circumferential direction, the tops of the first springs are connected with a vibration reduction platform, and four connecting plates are evenly distributed on the bottom of the vibration reduction platform in the circumferential direction with the center of the bottom face of the vibration reduction platform as the circle center; each connecting plate is connected with the side wall of the cylinder through a set of negative stiffness adjusting mechanism, each negative stiffness adjusting mechanism comprises an Euler buckling beam and two Euler beam clamps located at the two ends of the Euler buckling beam, and the two Euler beam clamps are fixed to the connecting plates and the side wall of the cylinder through bolts and nuts. The distance between the two Euler beam clamps can be adjusted through nuts and bolts. A supporting rod is arranged in the center of the bottom plate and sleeved with a second spring, a mass block is arranged at the top of the second spring, and the top of the supporting rod is located in a groove in the bottom of the mass block and is spaced from the groove bottom. The top of the mass block is connected with the vibration reduction platform through a spring damping system.

Description

Technical Field

[0001] The invention relates to the technical field of vibration reduction, and specifically designs a negative stiffness vibration isolator and a design method thereof. Background Art

[0002] With the development of science and technology, the fields of national defense, energy, shipbuilding, biomedicine, automobiles, robots, etc. have put forward higher requirements for vibration and noise reduction; when facing low-frequency and ultra-low-frequency vibrations, the requirements for vibration reduction are particularly urgent; in some working environments with relatively small spaces, the static deformation magnitude of traditional vibration isolators makes them quite constrained in their application. Therefore, the use of new vibration reduction methods to achieve better vibration reduction effects and reduce the static deformation magnitude is the main research direction of scholars at present.

[0003] The principle of vibration isolators and vibration absorbers is to use a spring damping system, by connecting a mass block to an object with springs and damping. When faced with excitation, the mass block will absorb part of the energy to reduce the vibration of the object. Vibration isolators and vibration absorbers each have their own advantages and disadvantages: vibration isolators have good effects at all frequencies, but resonance effects will occur near the resonant frequency, and no vibration reduction effect will be achieved; vibration absorbers have good vibration reduction effects near the resonant frequency, and the effects at other frequencies are not obvious. Existing vibration reduction methods generally use vibration isolators and vibration absorbers in combination, using vibration isolators to isolate vibrations at the first level and using vibration absorbers to absorb part of the energy to reduce the input secondary energy. However, there are two major regrets in the application of the above method: first, the dynamic vibration absorber requires a large static deformation, which is difficult to apply in a small space; second, the relevant parameters of the vibration isolator and vibration absorber cannot be accurately determined. When using relevant vibration reduction measures, the relevant parameters can only be selected through experience and most of the parameters are fixed values. When the load changes, the vibration reduction effect also changes. Summary of the invention

[0004] In order to address the deficiencies in the prior art, the present invention provides a negative stiffness vibration isolator and a design method thereof, so that a negative stiffness vibration isolator suitable for a small space with no harmonic peak and adjustable stiffness is designed by combining a negative stiffness vibration isolation component, a traditional vibration absorption component and a negative stiffness adjustment mechanism, so that it can achieve better vibration reduction effect and reduce the magnitude of static deformation.

[0005] The purpose of the present invention and the technical problem to be solved are achieved by adopting the following technical solutions. According to a negative stiffness vibration isolator proposed in the present invention, it includes a base composed of a bottom plate and a cylinder, in which four first springs are evenly distributed along the circumferential direction with the center of the bottom plate as the center of the circle, and the top of the first spring is connected to a vibration reduction platform for carrying the vibration-damped equipment, and the bottom of the vibration reduction platform is centered at the center of its bottom surface, and four connecting plates are evenly distributed along the circumferential direction; each connecting plate is connected to the position on the side wall of the cylinder opposite to the connecting plate through a group of negative stiffness adjustment mechanisms, and the negative stiffness adjustment mechanism includes an Euler buckling beam and two Euler beam clamps located at both ends of the Euler buckling beam, and the two Euler beam clamps are fixed on the connecting plate and the side wall of the cylinder by bolts and nuts, and the spacing between the two Euler beam clamps can be adjusted by nuts and bolts; a support rod is provided at the center of the bottom plate, and a second spring is sleeved on the support rod, and a mass block is provided on the top of the second spring, and the top of the support rod is located in the groove at the bottom of the mass block and has a spacing from the bottom of the groove; the top of the mass block is connected to the vibration reduction platform through a spring damping system.

[0006] The purpose of the present invention and the solution to its technical problems can be further achieved by adopting the following technical measures.

[0007] The negative stiffness isolator mentioned above is provided with a reinforcing plate at the position where the cylinder is adapted to be connected with the Euler fixture beam. The reinforcing plate is fixed on the outer wall of the cylinder and has threaded holes corresponding to the through holes on the cylinder for the bolts to pass through.

[0008] The negative stiffness vibration isolator mentioned above has a first groove matched with the first spring and a second groove matched with the second spring on the bottom plate.

[0009] The purpose of the present invention and the technical problem to be solved are achieved by adopting the following technical solutions. According to the design method of the negative stiffness vibration isolator proposed by the present invention, it includes the following steps:

[0010] Step 1: Design of negative stiffness vibration isolation assembly. The negative stiffness vibration isolation assembly includes a base, a first spring, and a vibration isolation platform and the vibration isolation equipment carried thereon. The mass is M. c The load,

[0011] 1) Determine the size and weight of the base according to the space size b , and set the natural frequency ω of the negative stiffness isolator n , the stiffness K of the negative stiffness isolator is calculated based on the base mass and the natural frequency of the negative stiffness isolator s ;

[0012] 2) According to the vibration principle diagram of the negative stiffness isolator, the Euler equation is established and Laplace transformation is performed, and get

[0013] Force transmissibility function:

[0014]

[0015] 3) Set the value of a, and according to the conditions for the force transmissibility function to be established, draw the value ranges of b and c, and then set the value of c, and combine it with the actual value range of b (b min ,b max ), and the value of ξ is between 0 and 1, and finally the value of b and ξ that minimizes the force transmission rate is selected through a cycle, which includes the following steps:

[0016] First, choose b=b max , and then enter the big loop, in which we set ξ=1 and determine whether b is satisfied. min , if not, then enter the small cycle; in the small cycle, first determine whether ξ>0 is true, if true, then solve the minimum value of the force transmission rate T under this set of parameters min , and the minimum value T min The smallest of the minimum values ​​of the force transmissibility corresponding to the parameters previously involved in the cycle T min_old Compare, does not meet T min <T min_old , then let ξ decrease the set value and enter the small cycle again. When the force transmission rate corresponding to a certain set of parameters is the minimum value T min Less than T min_old When the group T min Cover T min_old , and the values ​​of b and ξ of this group replace the previous T min_old The corresponding optimal parameters are a new set of optimal parameters bopt and ξopt. Then, ξ in the set of optimal parameters is reduced by the set value and the small cycle is entered again until ξ does not satisfy ξ>0 after the set value is reduced. Then the small cycle is ended and the large cycle is entered. After b is reduced by the set value, ξ=1 is set again, and it is judged whether b is satisfied. min If not, then enter the small loop, if satisfied, then end the loop and output the last set of optimal parameters;

[0017] 4) Select the appropriate base and vibration isolation platform based on the calculated and selected parameters;

[0018] The second step is to design the traditional vibration absorption component. The traditional vibration absorption component includes a support rod, a second spring, a mass block and a spring damping system. The mass M of the mass block is calculated according to the values ​​of parameters a, c, b and ξ. d , the stiffness k of the second spring b and the stiffness k of the spring-damper system d and damping coefficient Cd, and select a suitable second spring, mass block and spring damping system;

[0019] ​​The third step is to design a negative stiffness adjustment mechanism, which includes a stiffness of K h Euler buckled beam with stiffness K v The first spring of the Euler buckling beam is subjected to a separate force analysis and the derivative is derived to obtain the formula:

[0020] where F h is the vertical load F of the Euler buckled beam h , l is the length of the Euler buckled beam after deformation, Z s is the relative displacement between the load and the base;

[0021] Finally, select the appropriate Euler buckled beam and the first spring.

[0022] The purpose of the present invention and the solution to its technical problems can be further achieved by adopting the following technical measures.

[0023] The design method of the negative stiffness isolator mentioned above, the formula of the third step and the selection of the Euler buckling beam and the first spring are obtained by the following method:

[0024] Assume that in the initial state, the initial deflection of the single Euler buckled beam is ω0, and the axial load F h The relationship between the terminal vertical displacement y and the terminal inclination angle α is:

[0025] F h =4EIK 2 (p 2 ) / l0 2 (1-2)

[0026] y=2l0[1-E(p 2 ) / K(p 2 )] (1-3)

[0027]

[0028] Where: l0 is the length of the Euler buckled beam when it is not deformed, E is the elastic modulus of the material, I is the moment of inertia of the Euler buckled beam section, K and E are the elliptic integral parameters p respectively. 2 The first and second elliptic integrals of the same kind, It is a parameter that is not affected by other parameters and plays the role of a dependent variable;

[0029] Elliptic integral parameter p 2 , and the end displacement y are defined as:

[0030]

[0031] Where: α is the angle between the tangent line at the end of the beam and the line connecting the two end points;

[0032] Combining the above six equations, we can find the vertical force F:

[0033]

[0034] The formula for the third step can be obtained by differentiating the force F. Matlab software is used to solve the elliptic integral expansion to select the appropriate Euler buckling beam and the first spring.

[0035] The design method of the negative stiffness vibration isolator mentioned above, when the load changes, determines the value of a according to the changed load, and then repeats the first step 3) when designing the negative stiffness vibration isolation component to obtain the optimal b and, then obtains the changed negative stiffness Ks' according to the definition of b, and then reversely derives the length l' that the Euler buckling beam should have after deformation through Ks', and then adjusts the bolts to a spacing of l' between the two clamps through the bolt pitch. '

[0036] In the design method of the negative stiffness isolator, the calculation of the length l' after deformation is achieved by the following method: first, define the error δ = |(K s '-K s ) / K s '|, and let l'=l0, then enter the loop to determine whether l' is greater than zero. If so, substitute it into the equations 1-1 to 1-8, and combine the eight equations to solve the corresponding negative stiffness coefficient K s , then calculate δ, if δ is less than the minimum value δ_old in the previously calculated δ, let δ cover the previous δ_old, and let l' corresponding to this δ cover the previous optimal value lopt, then let l' decrease the set value and enter the loop again until l' is less than or equal to zero, then exit the loop and output the last set of lopt, which is the target l' of the present invention.

[0037] Compared with the prior art, the present invention has obvious advantages and beneficial effects. By means of the above technical solution, the present invention can achieve considerable technical advancement and practicality, and has wide industrial utilization value, and has at least the following advantages:

[0038] The parameter selection of the present invention can also eliminate the peaks on both sides to achieve "top clipping" by sacrificing the vibration reduction effect near the resonance frequency, thereby improving the overall vibration reduction effect in the full frequency range of low frequency and ultra-low frequency.

[0039] The present invention adopts a negative stiffness adjustment mechanism to replace the spring in the prior art, which can achieve the purpose of a more stable negative stiffness coefficient. Through Matlab numerical analysis, it can be seen that the maximum displacement of the vibration isolator of the present invention when facing a 0.5Hz impact is only 14% of the maximum impact displacement; the negative stiffness adjustment mechanism composed of the Euler buckling beam has a stiffness change of no more than 1.6% when facing an impact, while the stiffness change of the traditional system with the relative displacement change is up to 7.89%, which greatly improves the stiffness stability and also has a good ultra-low frequency vibration reduction effect.

[0040] In the negative stiffness adjustment mechanism, the steady-state deformation displacement of the Euler buckling beam can be adjusted by adjusting the tightness of the two bolts, thereby changing the stiffness of the system to optimize the vibration reduction effect when facing different mass loads. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a cross-sectional view of the negative stiffness vibration isolator of the present invention;

[0042] Figure 2 is a perspective view of a negative stiffness vibration isolator in the present invention;

[0043] Figure 3 is a schematic diagram of a negative stiffness adjustment mechanism;

[0044] Figure 4 is a schematic diagram of the mass block, the second spring and the support rod;

[0045] Figure 5 is a schematic front view of the negative stiffness vibration isolator of the present invention;

[0046] Figure 6 is a schematic top view of the negative stiffness vibration isolator of the present invention;

[0047] Figure 7 It is a dynamic model diagram of the vibration isolator in the prior art;

[0048] Figure 8 It is a dynamic model diagram of the negative stiffness vibration isolator of the present invention;

[0049] Fig. 9 The value range of parameters b and c drawn by Matlab when a=0.2;

[0050] Fig.10 A flow chart for selecting parameters of the present invention;

[0051] Fig.11 Schematic diagram of force transmission rate under different mechanisms;

[0052] Fig.12a and Figure 12b They are the front view and top view of the simplified model for solving the system parameters of the negative stiffness adjustment mechanism;

[0053] Fig.13 A comparison diagram of the stiffness curve of the vibration isolator provided with the Euler buckling beam of the present invention and the stiffness curves of other vibration isolators;

[0054] Fig.14 A flow chart of calculation of target parameters when the negative stiffness adjustment component of the present invention performs negative stiffness adjustment;

[0055] Figure 15a-15c The impact response of the impact response model of the negative stiffness isolator of the present invention under different parameters at a frequency of 0.5 Hz;

[0056] Fig.15d It is the impact response of the impact response model of the negative stiffness isolator without using the Euler buckling beam at a frequency of 0.5 Hz;

[0057] Fig.16a and Fig.16b They are the two-dimensional contour map and three-dimensional variation cloud map of the vibration reduction effect with the change of parameters b and ξ respectively;

[0058] Fig.17 The influence of different parameter groups on the force transmissibility function.

[0059]

Main component symbol description

[0060] 1: Support rod

[0061] 2: Base

[0062] 3: Quality block

[0063] 4: Euler Buckled Beam

[0064] 5: Euler beam fixture

[0065] 6: Vibration reduction platform

[0066] 7: Spring damping system

[0067] 8: First Spring

[0068] 9-Second spring

[0069] 11-First groove

[0070] 12-Second groove

[0071] 51-Bolt

[0072] 52-Nut

[0073] 53-Reinforcement plate

[0074] 61-Connection plate DETAILED DESCRIPTION

[0075] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the specific implementation method, structure, characteristics and effects of the negative stiffness isolator proposed according to the present invention are described in detail below in combination with the accompanying drawings and preferred embodiments.

[0076] The negative stiffness vibration isolator of the present invention comprises a vibration reduction mechanism and a negative stiffness adjustment mechanism. The vibration reduction mechanism comprises a negative stiffness vibration isolation component and a traditional vibration absorption component. The specific structure of each component is described in detail below.

[0077] See also Figure 1-4 The negative stiffness vibration isolation component includes a base 2 which is surrounded by a bottom plate and a cylinder and opens upward. A plurality of first springs 8 which are elastically retractable along the axial direction of the cylinder are evenly distributed on the base along the circumferential direction with the center of the bottom plate as the circle point. The end of the first spring 8 away from the bottom plate is connected to a vibration reduction platform 6 for carrying the equipment to be damped. The vibration reduction platform 6 is installed in the cylinder of the base 2 and is consistent with the axis of the cylinder and has clearance fit, that is, the vibration reduction platform 6 can elastically float along the axial direction of the cylinder of the base 2, and can also elastically float along the radial direction of the cylinder of the base 2. The vibration reduction platform 6 and the equipment to be damped carried thereon together constitute a load, and the load is damped by the negative stiffness vibration isolator of the present invention. On the bottom surface of the vibration reduction platform 6, a plurality of vertically extending connecting plates 61 are evenly distributed along the circumferential direction with the center of the bottom surface as the circle point.

[0078] The negative stiffness adjustment mechanism is provided in plurality, and the negative stiffness adjustment mechanism can connect each connecting plate 61 with the inner wall of the cylinder. Each negative stiffness adjustment mechanism includes a group of Euler beam clamps 5 and an Euler buckling beam 4 connected between the group of Euler beam clamps 5. The group of Euler beam clamps 5 are respectively installed on the connecting plate 61 and the side wall of the cylinder at positions corresponding to the connecting plate 61, so that each connecting plate 61 is connected to the inner wall of the cylinder through an Euler buckling beam 4 and a group of Euler beam clamps 5.

[0079] In the embodiment of the present invention, the end of the Euler buckling beam 4 is connected to the corresponding group of Euler beam clamps 5 by bolts. The Euler beam clamps 5 forming a group are connected and fixed to the inner wall of the cylinder and the connecting plate 61 by bolts 51 and nuts 52 respectively. As a result, the present invention can adjust the distance between the two Euler beam clamps 5 forming a group by adjusting the locking position of the bolts 51 and the nuts 52, thereby adjusting the performance of the Euler buckling beam 4 connected between the two, so that the negative stiffness of the negative stiffness vibration isolation assembly is adjustable.

[0080] In the embodiment of the present invention, a reinforcing plate 53 is further provided at the position where the cylinder is adapted to be connected with the Euler clamp beam 5. The reinforcing plate 53 is fixed to the outer wall of the cylinder and has a threaded hole corresponding to the through hole on the cylinder through which the bolt 51 passes. The provision of the reinforcing plate 53 increases the wall thickness of the cylinder, so that the bolt 51 can be threadedly locked with the cylinder at that position.

[0081] The conventional vibration absorbing assembly includes a second spring 9 arranged at the center of the bottom plate, a mass block 3 is arranged on the top of the second spring 9, and a support rod 1 is also arranged at the center of the bottom plate for providing a guide for the mass block 3 and the second spring 9 to move along the axial direction of the cylinder. The second spring 9 is sleeved on the support rod 1 and elastically contacts the bottom end face of the mass block 3. A groove with an opening facing downward for matching with the support rod is arranged at the center of the lower middle part of the mass block 3, so that the second spring 9 can be compressed through its bottom end face when the mass block 3 moves downward relative to the support rod 1. The center of the top surface of the mass block 3 is connected to the vibration reduction platform through the spring damping system 7. Preferably, the mass block 3 is pinned to the spring damping system 7 through the pin hole at the top center. In this embodiment, the mass block is a stepped cylindrical structure with a small diameter at both ends and a large diameter in the middle, but it is not limited to this.

[0082] In the embodiment of the present invention, the bottom plate of the base 2 is provided with a first groove 11 adapted to the first spring 8 and a second groove 12 adapted to the second spring 9. The provision of the first groove 11 and the second groove 12 of the present invention can realize the positioning of the support rod 1 and the first spring 8 on the bottom plate, and can also radially constrain the first spring 8 to prevent it from sliding in the horizontal direction (radial direction of the cylinder) relative to the bottom plate.

[0083] Figure 5 and Figure 6 The schematic diagrams are respectively the front view and the top view of the negative stiffness vibration isolator of the present invention. Since the application scenario of the present invention is a small space, the changes in the horizontal acceleration and angular acceleration are small and can be effectively suppressed in the structural design. Figure 7 The following is a simplified diagram of a conventional vibration isolator. Figure 8 The schematic diagram of the vibration reduction mechanism in the present invention is shown as follows. Figure 7 and Figure 8 It can be seen that the vibration reduction mechanism of the present invention is based on the traditional vibration isolator, and a mass M is added. d The mass block 3 and the Euler buckling beam, and the mass block 3 is connected by a stiffness K d , the damping coefficient is C d The spring-damper system 7 with mass M c The load is connected through the stiffness K b The second spring 9 with a mass of M bIn order to achieve the effect of ultra-low frequency vibration reduction, the present invention adopts a vibration reduction mechanism composed of a superposition of a "negative stiffness vibration isolation component + a traditional vibration absorption component", that is, the stiffness K of the spring damping system 7 d and the second spring stiffness K b is positive, and the stiffness K of the negative stiffness system composed of all first springs 8 and Euler buckling beams s is negative.

[0084] The negative stiffness vibration isolator of the present invention is designed through the following steps.

[0085] (1) Design of negative stiffness vibration isolation components

[0086] In this embodiment, the negative stiffness vibration isolation assembly includes a base 2, four first springs 8, and a mass M composed of the vibration isolation device and the vibration isolation platform 6. c The load is the natural frequency ω of the negative stiffness isolator to be designed. n It is tentatively set at 2.5Hz. First, the base 2 is designed to determine the stiffness of the negative stiffness vibration isolation component. In the embodiment of the present invention, the base 2 adopts a barrel-shaped base with a diameter of 500mm and a height of 400mm. The bottom plate of the barrel-shaped base 2 is 50mm thick and the wall thickness is 10mm. Since the base 2 needs to be processed with positioning grooves and install springs and other parts, its volume deviates from the pre-designed volume, so the stiffness of the negative stiffness vibration isolation component is designed based on the ideal volume:

[0087] M b =ρV (1-1)

[0088] K s =-ω n 2 M b (1-2)

[0089] Wherein, ρ is the density of the base 2, which is related to its material selection; V is the volume of the base 2.

[0090] In this embodiment, the material of the base 2 is selected to be structural steel, and it is known that its density is 7.85×10 3 Kg / m 3 , its volume is calculated to be 0.015m 3 , by substituting into equations (1-1) and (1-2), we can know that the stiffness K of the negative stiffness vibration isolation component is s It needs to be designed to -735.93N / m.

[0091] Considering that the first spring 8 is a nonlinear system, its stiffness cannot be always stable at a certain value. s It is only the negative stiffness value under ideal conditions. Therefore, when designing the first spring, the negative stiffness value under the equilibrium state of the system is set to K s That's it.

[0092] According to Grange's equation and D'Alembert's principle Figure 8 The differential equation of the structure shown is:

[0093]

[0094] Where: Z c , Z d , Z b are the displacements of the load, mass block 3 and base 2 relative to the vibration receiving platform on which the negative stiffness isolator is placed; F and F T are the imaginary forces applied to the load and the vibration platform respectively.

[0095] By performing Laplace transformation on differential equations (2-1), (2-2) and (2-3), we can obtain:

[0096] M c Z c S 2 +K s (Z c -Z b )+K d (Z c -Z b )+C d S(Z c -Z d )=F (3-1)

[0097] M d Z d S 2 =K d (Z c -Z d )+C d (Z c -Z d )S+K b (Z b -Z d ) (3-2)

[0098] M b Z b S 2 =K s (Z c -Z b )+F T +K b (Z d -Z b ) (3-3)

[0099] Fixed load, that is, Z c And its first-order and second-order differentials are always zero, we can get

[0100] -Ks Z b -K d Z d -C d Z d S=F (4-1)

[0101] M d Z d S 2 =-K d Z d -C d Z d S+K b (Z b -Z d ) (4-2)

[0102] M b Z b S 2 =-K s Z b +F T +K b (Z d -Z b ) (4-3)

[0103] Force transmission rate Combining equations (4-1), (4-2) and (4-3) we get

[0104]

[0105] Let the frequency response function F.F T All are zero, forcing the base 2 to move. The differential equations (2-1), (2-2) and (2-3) can be simplified and Laplace transformed to:

[0106] M c Z c S 2 +K s (Z c -Z b )+K d (Z c -Z d )+C d S(Z c -Z d )=0 (5-1)

[0107] M d Z d S 2 =K d (Z c -Z d )+C d (Zc -Z d )S+K b (Z b -Z d ) (5-2)

[0108] In order to facilitate data processing and simplify the calculation process, let S = ωi, ω is the excitation frequency, i is the imaginary number introduced by Laplace change; transform equation (4-4) into frequency domain, and then for the convenience of analysis, assume that the mass of base 2 is M b With the load M c Similarly, the following 6 parameters are introduced through dimensionless transformation: Substituting in the simplification, we can deduce;

[0109] Force transmissibility function:

[0110]

[0111] The vibration reduction effect of the vibration reduction structure is evaluated by the magnitude of the force transmission rate, and then the ideal parameter group of the vibration isolator is found when there is a negative stiffness vibration isolation component. Using the control variable method, referring to the contents of "Negative stiffness nonlinear vibration absorber vibration reduction method for urban rail vehicles" and "Impact response analysis of hybrid vibration isolation system containing negative stiffness dynamic vibration absorption", combined with economic considerations, set a = 0.2 and use Matlab to draw the value range of the two parameters b and c, such as Fig. 9 As shown. Set c = -3 again, and combine the Routh-Hurwitz criterion and Laplace transformation to know that equation (6-1) must satisfy the following three equations at the same time to achieve stability:

[0112] b+c+a+ac<0 (7-1)

[0113] 1+c<0 (7-2)

[0114] b+c+bc>0 (7-3)

[0115] It can be concluded that the value range of b is (-∞, -1.5), and in actual use, the difference between the stiffness of the negative stiffness isolation system and the stiffness of the spring damping system is not too large, so the value range of b is within (-5, -1.5). Considering that the damping ratio usually cannot reach above 0.5 in actual situations, the value range of ξ is set to (0, 0.5).

[0116] According to the values ​​of the two parameters a and c and the value range of b and ξ, the values ​​of b and ξ that make the force transfer function reach the maximum value within the value range are obtained. The values ​​of b and ξ are obtained by the following steps, such as Fig.10 As shown:

[0117] First, select b = -1.5, then enter the large loop. In the large loop, set ξ = 1, and determine whether b < -5 is satisfied. If not, enter the small loop. In the small loop, first determine whether ξ > 0 is true. If so, substitute the values ​​of b and ξ into the force transfer function, and solve for the minimum force transfer function under this set of parameters T. min , and the minimum value T min The smallest value of the force transmissibility function corresponding to the parameters of the previous cycle T min_old Compare, does not meet T min <T min_old , then let ξ decrease the set value and enter the small cycle again. When the minimum value T of the force transfer function corresponding to a certain set of parameters is min Less than T min_old When the group T min Cover T min_old , that is, let T min_old =T min , and the b and ξ values ​​of this group replace the previous T min_old The corresponding optimal parameters are a new set of optimal parameters bopt and ξopt. Then, ξ in the set of optimal parameters is reduced by a set value and enters the small cycle again until ξ does not satisfy ξ>0 after the set value is reduced. Then, the small cycle is terminated and the large cycle is entered. After b is reduced by a set value, ξ=1 is set again, and it is determined whether b<-5 is satisfied. If not, the small cycle is entered; if satisfied, the cycle is terminated and the last set of optimal parameters is output. In this embodiment, ξ is reduced by a set value of 0.02 in the small cycle, and b is reduced by a set value of 0.06. In an embodiment of the present invention, the last set of optimal parameters is b=-1.6, ξ=0.01.

[0118] In the embodiment of the present invention, the optimal parameters collected in the above cycle are also used to draw the function minimum value image of the force transmission rate of the two parameters b and ξ near β=1, such as Fig.16a and Fig.16b As shown, in the region where the force transfer rate is the smallest in the above graph, select the values ​​of b and ξ, and draw the force transfer graph under different b and ξ, as shown in Fig.17 As shown. Fig.17 It can be seen that when ξ remains unchanged, the smaller the absolute value of b, the earlier the first harmonic peak appears, and the better the vibration reduction effect at the resonance frequency β equals 1; when b remains unchanged, the increase in the damping ratio will reduce the force transfer rate value at the harmonic peak, which is the "top clipping" effect, but increasing the damping ratio will also lead to a weakening of the vibration reduction effect near the resonance frequency β equals 1. Therefore, combined with Fig.17 The law shown is adjusted according to the required vibration reduction effect. The present invention intends to design a vibration isolator with good full-range vibration reduction effect in low frequency and ultra-low frequency and small resonance peak. Fig.16a and Fig.16b In the range of low force transmission rate, a point with b=-1.6 and a large ξ is selected. In this embodiment, b=-1.6 and ξ=0.16. When the present invention requires a vibration isolator with good vibration reduction effect near the resonance frequency, a smaller damping ratio can be selected.

[0119] Fig.11 The diagram is a schematic diagram of the force transmission rate change of the vibration isolator composed of the negative stiffness vibration isolation component and the transmission vibration absorption component, the traditional vibration isolation component, the vibration isolator composed of the transmission vibration isolation component and the traditional vibration absorption component, and the negative stiffness vibration isolation component when the parameters are a=0.2, c=-3, b=-1.6, ξ=0.16. It can be clearly seen from the diagram that the vibration isolator composed of the negative stiffness vibration isolation component and the transmission vibration absorption component effectively shifts the first resonance peak to the left. Under the configuration of the negative stiffness vibration isolation component + the traditional dynamic vibration absorption component, the first resonance frequency can be reduced to about 0.2 times of the original natural frequency if the parameters are properly adjusted; and the frequency near β equals 1 enters the trough between the two harmonic peaks, which greatly improves the vibration reduction effect when β equals 1. The combination of the traditional vibration isolation component + the traditional dynamic vibration absorption component can only reduce the harmonic peak and shift the harmonic peak to the right. The effect of reducing ultra-low frequency vibration is not as ideal as the configuration of the negative stiffness vibration isolation component + the traditional dynamic vibration absorption component. Although the simple use of negative stiffness vibration isolation components can achieve good vibration reduction effects in a wide frequency range, it is not stable according to the Routh stability criterion and cannot be used alone. When β = 1, the force transmission rate of the traditional vibration isolation component is 45.6, the force transmission rate of the traditional vibration isolator + traditional dynamic vibration absorber is 2.05, and the force transmission rate of the negative stiffness vibration isolation component + traditional dynamic vibration absorption component can reach an astonishing 0.0891. Based on the above analysis, compared with the traditional vibration reduction method, the negative stiffness vibration isolator composed of the negative stiffness vibration isolation component + the traditional dynamic vibration absorption component of the present invention can have a good vibration reduction effect when β = 1, and when β = 0.3, it also has a good vibration reduction effect. The negative stiffness vibration isolator of the present invention only needs to be configured with a lower natural frequency ω n The ultra-low frequency vibration reduction target can be achieved and the ultra-low frequency vibration reduction demand can be met.

[0120] (2) Traditional vibration absorption component design

[0121] The conventional vibration absorbing assembly includes a support rod 1 , a second spring 9 , a mass block 3 , and a spring damping system 7 .

[0122] like Figure 1 As shown, the support rod 1 of the present invention is provided with a second spring 9, and the second spring 9 is kept vertical; a mass block 3 is provided at the top of the support rod 9, and the upper end of the mass block 3 is connected to the load through a spring damping system 7. The stiffness k of the second spring can be obtained by the following formula: b , the stiffness k of the spring-damper system d, damping coefficient Cd and mass M of the mass block d :

[0123] k b =ck s (8-1)

[0124]

[0125] M d =aM c (8-3)

[0126]

[0127]

[0128]

[0129] Where: ΔZ is the static deformation under stable state, M c is the load weight, set to 11.775Kg; G is the shear elastic modulus of the selected spring material; d2 is the diameter of the first spring; D2 is the middle diameter of the first spring; n2 is the number of available turns of the first spring, a, c, b, ξ are the variables in the force transfer function, a is 0.2, c is -3, b = -1.6, ξ = 0.16. It can be concluded that k b =2207.79N / m, M d =2.355Kg; K d =117.75N / m, C d =11.07N / (m / s). ΔZ is 64mm. According to the above parameters, the spring parameters are selected using the national standard: cylindrical helical compression spring, carbon spring steel wire, grade C, shear elastic modulus G2=80Mpa, material diameter d2=6mm, spring center diameter D2=48mm, available number of coils n2=8, spring length l2=760mm.

[0130] In the embodiment of the present invention, the support rod 1 is connected to the base by using four studs with code name GB-T M6×20, and is connected to the mass block 3 at the top. Since the mass block 3 also has the risk of overturning, the length of the support rod is greater than the length of the second spring, so that it can also guide the mass block 3. The volume V of the mass block d for

[0131]

[0132] Find M d and V d They are 23.55Kg and 0.003m 3Through design, a mass block structure is obtained that meets the quality standards, fits correctly with the support rod, and can carry the vibration-damped equipment and spring damping system above it. Figure 4 As shown, the middle of the mass block fits with the support rod below through a groove to prevent the risk of overturning; and the groove still has a certain reserved space after matching with the support rod, and can fully recover when facing an impact. A pin hole is reserved on the top to install the required spring damping system.

[0133] (3) Analysis of negative stiffness adjustment mechanism

[0134] In order to facilitate the establishment of the model and the solution of the stiffness function of the negative stiffness system, the negative stiffness system is first simplified. The structural schematic diagram of the new negative stiffness system established by the present invention is shown in FIG. Fig.12a As shown in 12b (the model has been dimensionless in the previous article, and the traditional dynamic vibration absorber inside has been simplified and "eliminated", but its parameters are still involved in the subsequent calculations and will not cause distortion of the Euler beam parameters). Four identical Euler buckling beams are used in the horizontal direction to provide elastic force, and their stiffness is K h , the first spring is installed vertically, and its stiffness is K v To find out the deformation force on the vibration-isolated equipment, we need to first find out the force of the Euler buckled beam on the vibration-isolated equipment. Now we conduct a separate force analysis on the Euler buckled beam:

[0135] Assume that in the initial state, the initial deflection of a single Euler buckled beam is ω0, and the axial load F h Under the action of , the end displacement is y. Axial load F h The relationship between the terminal vertical displacement y and the terminal inclination angle α is:

[0136] F h =4EIK 2 (p 2 ) / l0 2 (10-1)

[0137] y=2l0[1-E(p 2 ) / K(p 2 )] (10-2)

[0138]

[0139] Where: l0 is the length of the Euler buckled beam when it is not deformed, E is the elastic modulus of the material, I is the moment of inertia of the Euler buckled beam section, K and E are the elliptic integral parameters p respectively. 2 The first and second elliptic integrals of the same kind, It is a parameter that is not affected by other parameters and plays the role of a dependent variable.

[0140] Elliptic integral parameter p2 , and the end displacement y are defined as:

[0141]

[0142] Where: α is the angle between the tangent line at the end of the beam and the line connecting the two end points; Z s is the relative displacement between the two objects in the system, Z s =Z c -Z b , l is the length of the Euler buckled beam after deformation, and l0 is selected to be 1.2 times of l.

[0143] Combining equations 10-1 to 10-6, we can find the vertical force F:

[0144]

[0145] The stiffness of the negative stiffness system can be obtained by differentiating the force F:

[0146]

[0147] The elliptic integral was expanded and solved using Matlab software, and appropriate values ​​of the parameters were selected, namely, the material of the Euler buckling beam was beryllium bronze, elastic modulus E = 89 Gpa, original length l0 = 0.12 m, stable length l = 0.1 m, moment of inertia I = 3.6 × 10 -11 , section width w = 0.02m, section thickness h = 0.0006m, vertical spring stiffness K v =1200N / m, then the stiffness of the four first springs distributed around the circumference is K v '=K v / 4=300N / m. The first spring specification is selected from the national standard: the material is stainless steel, the shear elastic modulus G1 is 69Gpa, the material diameter d1 is 5mm, the spring middle diameter D1 is 64mm, the number of available coils n1=70, and the spring length l1=360mm. The above eight equations are discretized and solved using Matlab software to obtain the nonlinear stiffness, which is compared with the traditional negative stiffness system (the difference from the negative stiffness system in the present invention is that 4 springs are used in the horizontal direction). Fig.13 As shown in the figure, it can be seen that the negative stiffness system made of Euler buckling beam has good stability. In the working range, that is, when Zs belongs to (-5mm, 5mm), its stiffness change does not exceed 1.508%; while the traditional negative stiffness system, in order to keep the stiffness close to the ideal stiffness as much as possible during operation, not only does the stiffness exceed the ideal stiffness in the stable state, but also the stiffness changes greatly within the relative displacement range, with the maximum being 7.89%.

[0148] Since the load of the equipment to be damped is not constant, if the stiffness cannot be adjusted, it can only achieve the best damping effect under a fixed load, which is contrary to the design concept. This problem can be effectively solved by designing a negative stiffness adjustment mechanism. The negative stiffness adjustment mechanism adjusts the steady-state deformation displacement of the Euler buckling beam by adjusting the tightness of bolt 51, and the buckling beam itself has a preload, so the clamp will not loosen. The higher the initial bending degree, the greater its negative stiffness coefficient. In this way, the stiffness of the system can be changed to optimize the damping effect when facing different mass loads.

[0149] When the load of the vibration isolator of the present invention changes, the value of the changed parameter a is calculated according to the method of designing the negative stiffness vibration isolation component according to the changed load, and the value ranges of the two parameters b and c are plotted using Matlab, and then the value of c is set, and then the value range of b is determined (b min , b max ), and finally through Fig.10 The loop shown obtains the final b and ξ.

[0150] Then, use Origin to draw the function minimum image of the force transmission rate of the two parameters b and ξ near β=1 with the optimal parameters collected in the above cycle, and select the appropriate ξ according to the image and usage requirements, and adjust the damping of the damping system.

[0151] According to the b value obtained by the cycle and the definition of b, the negative stiffness K after the load change is obtained s ', and then substitute it into the 10-1 to 10-8 formulas to calculate the deformed length l' that the Euler buckled beam should have after the load changes, and then adjust the bolts to a spacing of l' between the two clamps through the bolt pitch.

[0152] In the embodiment of the present invention, the determination of the deformation l' that the Euler buckled beam should have is achieved by the following steps: first, define the error δ = |(K s '-K s ) / K s '∣, then through Fig.14 The loop shown finds the length of the Euler buckled beam when the error value δ is minimized, and thus determines the bolt pitch that needs to be adjusted.

[0153] The above loop includes the following steps: first, let l'=l0, then enter the loop to determine whether l' is greater than zero. If so, substitute it into the formulas from 10-1 to 10-8, and solve the corresponding negative stiffness coefficient K by combining the eight formulas. s, then calculate δ, if δ is less than the minimum value δ_old in the previously calculated δ, then let δ cover the previous δ_old, and let l' corresponding to this δ cover the previous optimal value l'opt, then let l' decrease by a set value and enter the loop again, until l' is less than or equal to zero, then exit the loop, and output the last set of l'opt, which is the target l' of the present invention. In this embodiment, the set value of l' decrease is 0.01, but it is not limited to this.

[0154] The cycles performed in the present invention are all performed in Matlab.

[0155] Figures 15a-15c The shock response model of the graph uses an Euler buckled beam. Fig.15d Euler beam buckling is not used. Fig.15a The parameters are the optimal parameters of the parameter selection results of the present invention, Fig.15b and Fig.15c It is a general parameter. It can be seen that the parameters taken by the present invention have the shortest stabilization time, while also taking into account the smaller vibration reduction displacement and speed. n =0.5Hz), the vibration reduction equipment with negative stiffness isolators also has a good vibration reduction effect. When the dimensionless time τ is 10, it has reached a stable state and has a small vibration reduction displacement and speed.

[0156] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with the profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A negative stiffness vibration isolator, characterized in that: It comprises a base consisting of a bottom plate and a cylinder, wherein four first springs are evenly distributed on the bottom plate in a circumferential direction, a vibration reduction platform for carrying the vibration-reduced equipment is connected to the top of the first spring, and four connecting plates are evenly distributed on the bottom of the vibration reduction platform in a circumferential direction; each connecting plate is connected to the side wall of the cylinder through a group of negative stiffness adjustment mechanisms, and the negative stiffness adjustment mechanisms comprise an Euler buckling beam and two Euler beam clamps located at both ends of the Euler buckling beam, the two Euler beam clamps are fixed on the connecting plate and the side wall of the cylinder by bolts and nuts, and the spacing between the two Euler beam clamps can be adjusted by nuts and bolts; a support rod is provided at the center of the bottom plate, a second spring is sleeved on the support rod, and a mass block is provided on the top of the second spring, the top of the support rod is located in a groove at the bottom of the mass block and is spaced from the bottom of the groove; the top of the mass block is connected to the vibration reduction platform through a spring damping system.

2. The negative stiffness isolator according to claim 1, characterized in that: A reinforcing plate is also provided at the position where the cylinder is adapted to be connected with the Euler clamp beam. The reinforcing plate is fixed on the outer wall of the cylinder and has threaded holes corresponding to the through holes on the cylinder for the bolts to pass through.

3. The negative stiffness isolator according to claim 1, characterized in that: The bottom plate is provided with a first groove matched with the first spring and a second groove matched with the second spring.

4. A method for designing a negative stiffness vibration isolator according to any one of claims 1 to 3, comprising the following steps: Step 1: Design of negative stiffness vibration isolation assembly. The negative stiffness vibration isolation assembly includes a base, a first spring, and a vibration isolation platform and the vibration isolation equipment carried thereon. The mass is M. c The load, 1) Determine the size and weight of the base according to the space size b , and set the natural frequency ω of the negative stiffness isolator n , the stiffness K of the negative stiffness isolator is calculated based on the base mass and the natural frequency of the negative stiffness isolator s ; 2) According to the vibration principle diagram of the negative stiffness isolator, establish the differential equation and perform Laplace transformation, and let The force transmissibility function is obtained: 3) Set the value of a, and according to the stability condition of the force transfer function, draw the value range of b and c, and then set the value of c, and combine it with the actual value range of b (b min ,b max ), and the value of ξ is between 0 and 1, and finally the value of b and ξ that minimizes the force transmission rate is selected through a cycle, which includes the following steps: First, choose b=b max , and then enter the big loop, in which we set ξ=1 and determine whether b is satisfied. min , if not, then enter the small cycle; in the small cycle, first determine whether ξ>0 is true, if true, then solve the minimum value of the force transmission rate T under this set of parameters min , and the minimum value T min The smallest of the minimum values ​​of the force transmissibility corresponding to the parameters previously involved in the cycle T min _ old Compare, does not meet T min <T min _ old , then let ξ decrease the set value and enter the small cycle again. When the force transmission rate corresponding to a certain set of parameters is the minimum value T min Less than T min _ old When the group T min Cover T min_old , and the values ​​of b and ξ of this group replace the previous T min_old The corresponding optimal parameters are a new set of optimal parameters bopt and ξopt. Then, ξ in the set of optimal parameters is reduced by the set value and the small cycle is entered again until ξ does not satisfy ξ>0 after the set value is reduced. Then the small cycle is ended and the large cycle is entered. After b is reduced by the set value, ξ=1 is set again, and it is judged whether b is satisfied. min If not, then enter the small loop, if satisfied, then end the loop and output the last set of optimal parameters;​​ 4) Select the appropriate base and vibration isolation platform based on the calculated and selected parameters; The second step is to design the traditional vibration absorption component. The traditional vibration absorption component includes a support rod, a second spring, a mass block and a spring damping system. The mass M of the mass block is calculated according to the values ​​of parameters a, c, b and ξ. d , the stiffness k of the second spring b and the stiffness k of the spring-damper system d and damping coefficient Cd, and select a suitable second spring, mass block and spring damping system; The third step is to design a negative stiffness adjustment mechanism, which includes a stiffness of K h Euler buckled beam with stiffness K v The first spring of the Euler buckling beam is subjected to a separate force analysis and the derivative is derived to obtain the formula: where F h is the axial load of the Euler buckled beam, l is the length of the Euler buckled beam after deformation, Z s is the relative displacement between the load and the base; Finally, select the appropriate Euler buckled beam and the first spring.

5. The design method of the negative stiffness isolator according to claim 4, characterized in that: The formula for the third step and the selection of the Euler buckled beam and the first spring are obtained by the following method: Assume that in the initial state, the initial deflection of the single Euler buckled beam is ω0, and the axial load F h The relationship between the terminal vertical displacement y and the terminal inclination angle α is: F h =4EIK 2 (p 2 ) / l0 2 (1-2) Where: l0 is the length of the Euler buckled beam when it is not deformed, E is the elastic modulus of the material, I is the moment of inertia of the Euler buckled beam section, K and E are the elliptic integral parameters p respectively. 2 The first and second elliptic integrals of the same kind, It is a parameter that is not affected by other parameters and plays the role of a dependent variable; Elliptic integral parameter p 2 , and the end displacement y are defined as: Where: α is the angle between the tangent line at the end of the beam and the line connecting the two end points; Combining the above six equations, we can find the vertical force F: The formula for the third step can be obtained by differentiating the force F. Matlab software is used to solve the elliptic integral expansion to select the appropriate Euler buckling beam and the first spring.

6. The design method of the negative stiffness isolator according to claim 5, characterized in that: When the load changes, determine the value of a according to the changed load, and then repeat the first step of step 3) when designing the negative stiffness vibration isolation component to obtain the optimal b and ξ, and then calculate the changed negative stiffness K according to the definition of b. s ', then through the K s 'Reversely deduce and calculate the deformed length l' that the Euler buckling beam should have, and then adjust the bolts to a distance of l' between the two clamps through the bolt pitch.

7. The design method of the negative stiffness isolator according to claim 6, characterized in that: After the load changes and the optimal set of b and ξ is obtained through the loop, the array collected in the loop is also used to use Origin to draw the minimum value image of the force transfer rate function of the two parameters b and ξ near β=1. Then, according to the requirements of the vibration isolation frequency, the damping ratio value is adjusted through this image, and the damping of the spring damping system is adjusted after the final damping ratio is determined.

8. The design method of the negative stiffness vibration isolator according to claim 6 or 7, characterized in that: The calculation of the deformed length l' is achieved by the following method: First, define the error δ = |(K s '-K s ) / K s '|, and let l'=l0, then enter the loop to determine whether l' is greater than zero. If so, substitute it into the equations 1-1 to 1-8, and combine the eight equations to solve the corresponding negative stiffness coefficient K s , then calculate δ, if δ is less than the minimum value δ-old among the previously calculated δ, let δ cover the previous δ - old, and let l' corresponding to this δ cover the previous optimal value lopt, then let l' decrease by the set value and enter the loop again until l' is less than or equal to zero, then exit the loop and output the last set of lopt, which is the target l' of the present invention.

9. The design method of the negative stiffness isolator according to claim 4, characterized in that: In the first step of designing the negative stiffness vibration isolation component, after outputting the last set of optimal parameters in step 3), the array collected in the loop is used to use Origin to draw the minimum value image of the force transfer rate function of the two parameters b and ξ near β=1, and then the damping ratio value is selected based on the image in combination with the usage requirements.

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