Debugging method of compact quasi-zero stiffness vibration isolator with single inclined spring structure

Abstract

The invention relates to a debugging method of a compact quasi-zero stiffness vibration isolator constructed by a single inclined spring, the debugging method is based on the compact quasi-zero stiffness vibration isolator constructed by the single inclined spring, one end of the single inclined compression spring is hinged to a fixed support, and the other end of the single inclined compression spring is hinged to the top end of a vertical spring; the bottom end of the vertical spring is fixed; the inclined springs and the vertical springs are compression springs, and guide rods are arranged in the springs for supporting so as to prevent buckling instability. The single inclined spring generates negative stiffness in the vertical direction and is connected with the positive stiffness of the vertical spring in parallel, and the quasi-zero stiffness vibration isolator is constructed. The debugging method comprises the steps that the dimensionless pre-compression amount, the dimensionless projection length and the spring stiffness ratio of the oblique compression spring are determined, parameters are made to meet the quasi-zero stiffness parameter relation, and the nonlinear quasi-zero stiffness characteristic can be obtained; the quasi-zero stiffness vibration isolator is simple and compact in structure, few mechanical parts are used, and miniaturization can be achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of mechanical vibration isolation, in particular to a debugging method of a compact quasi-zero stiffness vibration isolator with single inclined spring structure. BACKGROUND

[0002] Vibration isolation technology has a wide range of applications in the fields of machinery, aerospace, precision instruments, etc. Quasi-zero stiffness vibration isolation structures are of great concern due to their excellent low-frequency vibration isolation performance. Quasi-zero stiffness vibration isolation structures are usually composed of positive stiffness elements and negative stiffness elements. By canceling the positive and negative stiffness, a dynamic stiffness close to zero is achieved near a specific working point, thereby achieving ideal vibration isolation effect.

[0003] Currently, common quasi-zero stiffness vibration isolation structures mainly use inclined compression springs or inclined rod mechanisms to generate negative stiffness effect. For example, CN115289178B discloses a debugging method of a constant value quasi-zero stiffness vibration isolation structure with double inclined rod negative stiffness, which includes double inclined rod negative stiffness mechanisms symmetrically arranged on both sides of the positive stiffness mechanism. By adjusting the pre-compression amount and stiffness parameters of the horizontal springs, constant quasi-zero stiffness characteristics near the static balance point are achieved. CN115325096B proposes a constant value quasi-zero stiffness vibration isolation structure based on horizontal tension springs and a debugging method. The structure uses the combination of inclined rods and horizontal tension springs to obtain constant quasi-zero stiffness characteristics, effectively solving the problem of low-frequency vibration isolation failure of traditional quasi-zero stiffness vibration isolators under large amplitude excitation.

[0004] In terms of quasi-zero stiffness vibration isolation devices composed of multiple pairs of inclined compression springs, CN111853127B discloses a quasi-zero stiffness vibration isolation device with high linear resonance frequency based on two pairs of inclined compression springs. The device achieves a wide quasi-zero stiffness range while reducing the distance from the initial position to the static balance position by arranging two pairs of inclined compression springs with the same stiffness and length such that their intersection point is within the vertical range between the upper inclined compression spring fixed point and the static balance position. Similarly, CN111853126B proposes a quasi-zero stiffness vibration isolation device with high linear resonance frequency based on three pairs of inclined compression springs. By arranging three pairs of inclined compression springs in a special way, the vibration isolation frequency band performance of the system is further improved. CN110529554B introduces a debugging method of a vibration isolation platform composed of two groups of inclined compression springs. The platform includes two pairs of inclined compression springs symmetrically arranged above and below. By adjusting the positions of the sliding members and support columns, the inclined compression springs are adjusted so that the negative stiffness generated by the two groups of inclined compression springs cancels out the positive stiffness of the vertical springs, thereby obtaining a wider zero stiffness characteristic interval.

[0005] However, the existing quasi-zero stiffness vibration isolation structure generally has the following problems: first, most structures use multiple pairs of inclined compression springs or inclined rod combination design, the structure is complex, the volume is large, and it is difficult to apply to space limited occasions; second, the complex structure design increases the manufacturing and assembly difficulty, and increases the cost; third, the interaction between the components in the multi-component structure makes the system debugging complex, and it is difficult to accurately realize the ideal quasi-zero stiffness characteristics; fourth, the guide mechanism in the existing structure often has friction problems, which affects the vibration isolation effect; finally, the present application not only has a simple structure, but also has a completely different debugging method from the above application, which is a brand new debugging method according to the structure characteristics of the present application. Therefore, the present application develops a vibration isolation structure with simple structure, compact size, few mechanical parts, easy debugging and good quasi-zero stiffness characteristics, which has important practical value. SUMMARY

[0006] In order to solve the technical problems of the existing vibration isolation structure, such as large volume, complex structure, difficult to realize compact design and quasi-zero stiffness characteristics, and affecting the vibration isolation effect, and to realize the technical effects of compact structure, quasi-zero stiffness characteristics, simple debugging, excellent vibration isolation performance and strong adaptability, a debugging method of a compact quasi-zero stiffness vibration isolator with a single inclined spring structure is provided.

[0007] The technical scheme adopted by the present application to solve its technical problems is:

[0008] A debugging method of a compact quasi-zero stiffness vibration isolation structure with a single inclined spring structure, the debugging method is based on a quasi-zero stiffness vibration isolation structure, the quasi-zero stiffness vibration isolation structure comprises a negative stiffness mechanism and a positive stiffness mechanism; the negative stiffness mechanism is composed of a single inclined compression spring; one end of the inclined compression spring is hinged to a fixed support, and the other end is hinged to the top end of the vertical compression spring; the single inclined compression spring has a first guide rod inside to prevent spring buckling instability; the positive stiffness mechanism comprises a vertical compression spring, the bottom of the vertical compression spring is fixed, and the top of the vertical compression spring is hinged to one end of the inclined compression spring; the vertical compression spring is provided with a second guide rod inside to prevent spring buckling instability; the debugging method comprises the following steps:

[0009] Step one, determine the dimensionless pre-compression amount of the inclined compression spring in the initial state , the dimensionless projection length of the distance between the two hinged points of the inclined compression spring in the horizontal direction The initial state refers to one hinged end of the inclined compression spring being hinged to the vertical compression spring, and the vertical compression spring being in a free length state;

[0010] Step two, construct the stiffness ratio a of the inclined compression spring and the vertical compression spring in the positive stiffness mechanism according to the following formula;

[0011] ;

[0012] Step three, draw the force-displacement curve of the quasi-zero stiffness vibration isolation structure, calculate the dimensionless form of the applied to the quasi-zero stiffness vibration isolation structure After; make the quasi-zero stiffness vibration isolation structure in static equilibrium position; At the same time, judge Whether the division of the gravitational acceleration g meets the design of the supported isolation mass And the vibration isolation frequency band requirements, if not meet the design requirements, repeat step one to step three.

[0013] Further, the process of constructing the stiffness ratio α of the inclined compression spring and the vertical compression spring in the positive stiffness mechanism includes:

[0014] The applied force f is normalized to obtain the normalized applied force expression:

[0015]

[0016] Wherein: ;

[0017] The expression The first derivative of , the normalized stiffness is obtained:

[0018]

[0019] The normalized stiffness parameter expression is:

[0020]

[0021] Wherein: The linear stiffness of the inclined compression spring is represented by The linear stiffness of the vertical compression spring is represented by The projection length of the inclined compression spring in the horizontal direction under the initial condition is represented by The pre-compression amount of the inclined compression spring in the initial state is represented by The displacement from the initial position is represented by The displacement from the static equilibrium position is represented by The vertical distance from the initial position to the static equilibrium position is represented by The dimensionless form of The dimensionless displacement and complies with

[0022] At the static equilibrium position, let the dimensionless stiffness equal to zero, and obtain the parameter condition of the quasi-zero stiffness characteristic:

[0023]

[0024] According to the above parameter conditions, the vertical nonlinear quasi-zero stiffness characteristic can be obtained.

[0025] Advantages

[0026] The present application has the advantages of:

[0027] 1. The structure is compact: a single inclined compression spring is used, which simplifies the structure design, reduces the use of mechanical parts, and reduces the overall volume. Compared with the vibration isolation structure in the prior art which requires multiple springs or complex mechanisms, the structure of the present application is more simple and compact.

[0028] 2. Based on the compact quasi-zero stiffness structure, the debugging method of the present application is simple and effective: through the explicit parameter relationship formula α = â / (1+δ̂-â), the quasi-zero stiffness characteristic of the vibration isolator can be accurately debugged, overcoming the shortcomings of difficult debugging in the prior art.

[0029] 3. The present application has strong adaptability: the parameters can be adjusted according to the design requirements of the bearing mass and the vibration isolation frequency band to meet the needs of different application scenarios.

[0030] In summary, the present application relates to the field of quasi-zero stiffness low-frequency vibration isolation, and is designed to achieve the purpose of miniaturization of quasi-zero stiffness vibration isolation structure. The existing quasi-zero stiffness vibration isolation structure is complex and requires a large number of parts, which cannot be used in some space-limited application scenarios. Therefore, a miniaturized and compact quasi-zero stiffness vibration isolator is designed to effectively expand the application scenarios of quasi-zero stiffness vibration isolators. The present application proposes a vertical quasi-zero stiffness vibration isolator with a single inclined compression spring. Compared with existing vibration isolators, only one inclined compression spring is needed, which greatly reduces the number of parts required to construct a quasi-zero stiffness vibration isolator. The existing literature Carrella et al. (Journal of Sound and Vibration 322 (2009) 707-717) relates to a quasi-zero stiffness structure with two inclined compression springs, which has a large number of parts and cannot achieve the purpose of miniaturization.

[0031] Compared with the existing literature, the present application has the following obvious differences. The purpose is different, the present application only needs one inclined compression spring to achieve quasi-zero stiffness, which can achieve the purpose of miniaturization and compactness. The structure is different, the present application only uses one inclined compression spring, and the existing literature uses two inclined compression springs, which is the fundamental reason for the difference in force, stiffness, quasi-zero stiffness parameter relationship and use purpose compared with the existing literature. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 is the initial position of the quasi-zero stiffness vibration isolator of the present application.

[0033] Figure 2 This is a schematic diagram of the static equilibrium position of the quasi-zero stiffness vibration isolator of the present invention;

[0034] Figure 3 The stiffness-displacement curve is the nonlinear quasi-zero stiffness characteristic of this invention.

[0035] Figure 4 This is the force-displacement curve of the nonlinear quasi-zero stiffness characteristic of the present invention. Detailed Implementation

[0036] The following will be combined with the appendix Figures 1-4 The technical solutions of the present invention are clearly and completely described with the aid of embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0037] Example 1

[0038] A method for commissioning a compact quasi-zero stiffness vibration isolator constructed with a single oblique spring is disclosed. The method is based on a quasi-zero stiffness isolation structure, which includes a negative stiffness mechanism and a positive stiffness mechanism. The negative stiffness mechanism consists of a single oblique compression spring. One end of the oblique compression spring is hinged to a fixed support, and the other end is hinged to the top of a vertical compression spring. The oblique compression spring contains a first guide rod to prevent spring buckling instability. The positive stiffness mechanism includes a vertical compression spring, the bottom of which is fixed, and the top of which is hinged to one end of the oblique compression spring. The vertical compression spring contains a second guide rod to prevent spring buckling instability.

[0039] like Figure 1 As shown, in this quasi-zero stiffness vibration isolation structure, the linear stiffness of the oblique compression spring is k1, and the linear stiffness of the vertical compression spring is k2. Under initial conditions, the projected length of the oblique compression spring in the horizontal direction is a, and the pre-compression of the oblique compression spring in the initial state is δ. The displacement from the initial position is denoted by x, the displacement from the static equilibrium position is denoted by y, and the distance from the initial position to the static equilibrium position is denoted by h.

[0040] The working principle of this quasi-zero stiffness vibration isolation structure is as follows: a single oblique compression spring k1 generates negative stiffness in the vertical direction, which is connected in parallel with a compression spring k2 that has positive stiffness in the vertical direction, thereby achieving quasi-zero stiffness characteristics in the vertical direction. This structural design enables the vibration isolation system to have extremely low stiffness near the static equilibrium position, thus achieving excellent vibration isolation performance.

[0041] In the quasi-zero stiffness vibration isolation structure, the dimensionless form of the applied force to the quasi-zero stiffness vibration isolation structure is calculated as wherein the dimensionless displacement is related to

[0042] The tuning method of the quasi-zero stiffness vibration isolation structure includes the following steps, i.e. as shown in Figure 2

[0043] Firstly, the dimensionless pre-compression amount of the oblique compression spring , the dimensionless projection length of the distance between the two hinged points of the oblique compression spring in the horizontal direction , and the stiffness ratio α of the oblique compression spring and the vertical compression spring are determined in the initial state. That is:

[0044]

[0045] Secondly, according to the parameter conditions of the quasi-zero stiffness characteristics, the values of these parameters satisfy the quasi-zero stiffness parameter relationship . The initial state here refers to the state that one hinged end of the oblique compression spring is hinged with the vertical compression spring, and the vertical compression spring is in the free length state.

[0046] Then, after the above parameters are determined, the force-displacement curve f-x is drawn, wherein f is the applied force, i.e. the force applied to the load disc. After the force is applied , the vibration isolator is in a static equilibrium position, and it is judged whether divided by the gravitational acceleration g meets the design requirements of the supported isolation mass and the isolation frequency band.

[0047] Finally, it is determined whether the design requirements of the supported isolation mass and the isolation frequency band are met. If the design requirements are not met, the above steps are repeated.

[0048] In order to analyze the structural parameter characteristics, the applied force f and its expression are dimensionless, and the dimensionless applied force expression is obtained:

[0049] (1)

[0050] wherein: ; ;

[0051] The first derivative of the expression is taken with respect to , and the dimensionless stiffness is obtained. As shown in Figure 3

[0052] (2) ​​​

[0053] The dimensionless parameter expression is:

[0054]

[0055] As shown in Figure 4 the static equilibrium position, let the dimensionless stiffness K̂ be equal to zero, and obtain the parameter condition for quasi-zero stiffness characteristics:

[0056]

[0057] According to the above parameter condition, the vertical nonlinear quasi-zero stiffness characteristic can be obtained.

[0058] In practical applications, appropriate parameter values can be selected according to specific vibration isolation requirements. For example, â=0.5, δ̂=0.2 can be selected, and α=0.714 can be calculated according to the quasi-zero stiffness parameter condition. This means that the stiffness of the inclined compression spring should be 0.714 times the stiffness of the vertical compression spring. In this parameter configuration, the vibration isolation structure exhibits quasi-zero stiffness characteristics near the static equilibrium position, and can effectively isolate low-frequency vibrations.

[0059] When external vibrations enter the system, the system has very low stiffness near the static equilibrium position, so the natural frequency of the system is low, and most of the vibrations of the frequency can be effectively isolated. At the same time, since the stiffness of the system increases at a larger displacement, the system has good stability and will not produce excessive displacement due to external disturbance.

[0060] The quasi-zero stiffness vibration isolation structure has the advantages of compact structure, only one inclined compression spring and one vertical spring are used, and has higher space utilization and lower manufacturing cost compared with traditional multi-spring quasi-zero stiffness vibration isolation structure. At the same time, by setting a guide rod inside the spring, buckling instability of the spring under force is effectively prevented, improving the reliability and stability of the system.

[0061] Embodiment two

[0062] A compact quasi-zero stiffness vibration isolation structure constructed by a single inclined compression spring and a debugging method, which has the same structure as embodiment one, including a vertical compression spring, an inclined compression spring, a guide rod, a bracket and a load plate. The bottom of the vertical compression spring is fixed on the base, and the guide rod is arranged inside the vertical compression spring to support the vertical compression spring and prevent the vertical compression spring from radial buckling instability under axial force. The top end of the vertical compression spring is connected to one end of the inclined compression spring through a hinge, and the other end of the inclined compression spring is hinged to the bracket. The guide rod is also arranged inside the inclined compression spring to support the inclined compression spring and prevent the inclined compression spring from radial buckling instability under axial force.

[0063] In this embodiment, the focus is on the debugging method of the quasi-zero stiffness vibration isolation structure, which includes the following steps:

[0064] Determine the dimensionless pre-compression of the inclined compression spring in the initial state , the dimensionless projection length of the distance between the two hinged points of the inclined compression spring in the horizontal direction, and the stiffness ratio of the inclined compression spring to the vertical compression spring. In this embodiment, = 0.3, â = 0.6, the selection of these parameters is based on the design requirements and space limitations of the system.

[0065] According to the parameter conditions of the quasi-zero stiffness characteristic, the values of these parameters satisfy the quasi-zero stiffness parameter relationship . According to the selected parameter values, it is calculated that α = 0.857. This means that the stiffness of the inclined compression spring should be 0.857 times the stiffness of the vertical compression spring. The initial state refers to the state that one hinged end of the inclined compression spring is hinged with the vertical compression spring, and the vertical compression spring is in the free length state.

[0066] After determining the above parameters, the force-displacement curve f-x is drawn. In this embodiment, f is the applied force, i.e. the force applied to the load disc. After applying a force = 0.8, the vibration isolator is in a static equilibrium position, , divided by the gravitational acceleration, is equal to the supported isolation mass m. Assuming the gravitational acceleration is 9.8 m / s², and the stiffness of the vertical compression spring k2 = 1000 N / m, the mass m that the system can support can be determined.

[0067] The advantage of this debugging method is that by adjusting the dimensionless parameters , â and α, the carrying capacity and vibration isolation performance of the system can be flexibly adjusted to adapt to different application scenarios. At the same time, this method is simple and intuitive, easy to implement, and does not require complex calculations and professional equipment.

[0068] In practical applications, different parameter combinations can be selected according to specific needs. For example, for scenarios that require isolation of lower frequency vibrations, appropriate parameters can be selected to make the quasi-zero stiffness range near the static equilibrium position wider; for scenarios that require to carry larger mass, a smaller â value can be selected. By flexibly adjusting these parameters, the quasi-zero stiffness vibration isolation structure can adapt to various vibration isolation needs.

[0069] It should be noted that both Embodiment One and Embodiment Two are a kind of compact quasi-zero stiffness vibration isolator and debugging method of single inclined spring structure.

[0070] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit the same; and although the present application has been described in detail with reference to the foregoing embodiments, it should be appreciated by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features thereof can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method of commissioning a compact quasi-zero stiffness vibration isolator of single-inclined-spring configuration, characterized by, The debugging method is based on a quasi-zero stiffness vibration isolation structure, the quasi-zero stiffness vibration isolation structure comprising a negative stiffness mechanism and a positive stiffness mechanism; the negative stiffness mechanism is composed of a single inclined compression spring, one end of the inclined compression spring is hinged to a fixed support, the other end of the inclined compression spring is hinged to the top end of a vertical compression spring, and the inclined compression spring has a first guide rod inside for preventing spring buckling instability; the positive stiffness mechanism comprises a vertical compression spring, the bottom of the vertical compression spring is fixed, the top of the vertical compression spring is hinged to one end of the inclined compression spring, and the vertical compression spring has a second guide rod inside for preventing spring buckling instability; the debugging method comprises the following steps: Step one, determining the dimensionless pre-compression of the oblique compression spring in the initial state the dimensionless projection length in the horizontal direction of the distance between the two hinge points of the oblique compression spring The initial state refers to the state that one end of the oblique compression spring is hinged with the vertical compression spring, and the vertical compression spring is in the free length state; Step two, construct the stiffness ratio α of the inclined compression spring and the vertical compression spring in the positive stiffness mechanism according to the following formula: ； Step three, draw the force displacement curve of the quasi-zero stiffness vibration isolation structure, calculate the dimensionless form of the quasi-zero stiffness vibration isolation structure After; make the quasi-zero stiffness vibration isolation structure in static equilibrium position; at the same time, judge Whether the design of the bearing mass And vibration isolation band requirements, if not meet the design requirements, repeat step one to step three.

2. The method of claim 1, wherein the compact quasi-zero stiffness vibration isolator is configured as a single-inclined-spring. The process of constructing the stiffness ratio α of the inclined compression spring and the vertical compression spring in the positive stiffness mechanism comprises: The applied force f is made dimensionless, resulting in a dimensionless applied force : ； wherein: ; ; The expression The first derivative of The dimensionless stiffness is obtained: ； The dimensionless stiffness parameter expression is: ； wherein: represents the linear stiffness of the oblique compression spring, represents the linear stiffness of the vertical compression spring, represents the projected length of the oblique compression spring in the horizontal direction at the initial condition, is the pre-compression amount of the oblique compression spring at the initial state, represents the displacement from the initial position, represents the displacement from the static equilibrium position, represents the vertical distance between the initial position and the static equilibrium position, the dimensionless form of the dimensionless displacement and the relationship between ; In the static equilibrium position, let the non-dimensional stiffness equal to zero, the parametric conditions for quasi-zero stiffness behavior are obtained: ； According to the above parameter conditions, the vertical nonlinear quasi-zero stiffness characteristic can be obtained.

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