Debugging method of inclined quasi-zero stiffness vibration isolator with single pair of inclined springs

Abstract

The invention discloses a debugging method of an inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs. A reference compression spring is arranged in an inclined mode in the direction perpendicular to the longitudinal direction at a certain angle, and the bottom end of the reference compression spring is fixed; the two inclined compression springs are symmetrically arranged on the two sides of the reference compression spring, the top ends are hinged to the top end of the reference compression spring, and the bottom ends are hinged to the support; the two oblique compression springs generate negative stiffness in the oblique movement direction and are connected with the positive stiffness of the reference compression spring in parallel, and the quasi-zero stiffness characteristic in the oblique movement direction is generated. The method comprises the following steps: determining the parameters in an initial state, constructing dimensionless parameters, drawing a force displacement curve, enabling the parameters to meet the parameters, enabling the parameters to be in a static balance position after an upper force is applied, dividing the force by the gravitational acceleration to be equal to the borne vibration isolation mass, and judging whether the design requirements of the bearing mass and the vibration isolation frequency band are met or not. The whole device is obliquely arranged, and the problem of low-frequency vibration caused by excitation in the oblique direction can be solved.

Description

Technical Field

[0001] The present invention relates to the field of quasi-zero stiffness low-frequency vibration isolation, and more particularly to a debugging method for an inclined quasi-zero stiffness vibration isolator with a single pair of oblique springs. Background Art

[0002] In modern industry and engineering, low-frequency vibration control technology is crucial for ensuring stable equipment operation, extending structural service life, and improving system reliability. Traditional quasi-zero-stiffness vibration isolators, with their unique zero-stiffness characteristics in the vertical direction, can effectively reduce vibrations caused by vertical excitation. They are widely used in precision machining equipment, high-rise building shock absorption, and aerospace instrument protection. For example, in semiconductor manufacturing, photolithography machines are extremely sensitive to vertical vibrations during operation. Traditional vertical quasi-zero-stiffness vibration isolators can significantly reduce equipment errors caused by ground vibrations, ensuring chip manufacturing accuracy.

[0003] However, the vibration excitation directions in actual working conditions are complex and changeable, and low-frequency vibration problems in non-vertical tilt directions are common. In bridge engineering, under the action of strong winds, the bridge will not only produce vertical swaying, but also bear dynamic loads from different tilt angles due to the turbulent characteristics of the wind; when a ship is sailing, the impact of waves from all directions causes the hull to be subjected to low-frequency vibrations in the tilt direction, which will have a serious impact on the ship's precision navigation equipment, engines, etc. Traditional vertical quasi-zero stiffness isolators are based on the vertical direction for structural design and mechanical performance optimization. When faced with such tilt excitation, they are unable to effectively absorb and dissipate vibration energy, and the vibration isolation effect is greatly reduced, or even completely fails, leading to equipment failure, structural fatigue damage and other problems.

[0004] To address the challenge of vibration isolation in non-vertical directions, researchers have proposed quasi-zero stiffness vibration isolation structures using oblique springs. Among them, the single-pair oblique spring quasi-zero stiffness structure, published by Carrella et al. in the Journal of Sound and Vibration 322 (2009) 707–717, achieves quasi-zero stiffness in the vertical direction through a clever spring layout, offering new insights into the development of vibration isolation technology. However, the core design focus of this structure is the vertical direction, with parameters such as the spring's tilt angle and stiffness coefficient optimized for vertical excitation. When subjected to oblique excitation, the spring's force pattern changes, disrupting its original mechanical equilibrium and making it impossible to produce a quasi-zero stiffness response adapted to the oblique direction. This makes it difficult to meet the control requirements for low-frequency vibration in the oblique direction in practical engineering applications.

[0005] In addition, although existing quasi-zero stiffness vibration isolation structures such as double-oblique springs have enhanced the adaptability of the vibration isolation direction to a certain extent, they still have many disadvantages. These structures are usually more complex and require multiple springs, connectors and auxiliary components to work together, resulting in high manufacturing costs; at the same time, due to the coupling of multiple parameters, it is difficult to accurately match the mechanical requirements under different working conditions when debugging for the oblique direction, and it is impossible to achieve efficient vibration isolation of low-frequency vibrations in the oblique direction. Therefore, the development of a new quasi-zero stiffness vibration isolation structure and debugging method that can be effectively applied to oblique direction excitation has become the key to solving the problem of low-frequency vibration control in complex engineering environments, and is of great significance to promoting the development of related technologies. Summary of the Invention

[0006] The purpose of the present invention is to overcome the deficiencies in the prior art and propose a debugging method for an inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs. By tilting the entire vibration isolation structure in one direction, the low-frequency vibration problem caused by excitation in the inclined direction can be overcome.

[0007] The purpose of the present invention can be achieved through the following technical solutions.

[0008] A debugging method for an inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs, the vibration isolator comprising a reference compression spring and two inclined compression springs, the reference compression spring being inclined at a certain angle to a longitudinal direction, the two inclined compression springs being symmetrically arranged on both sides of the reference compression spring, the top ends of the two inclined compression springs being hinged to the top end of the reference compression spring, the bottom ends of the two inclined compression springs being hinged to a bracket, and the bottom ends of the reference compression springs being fixed to a base; the two inclined compression springs generating negative stiffness in the direction of inclined motion, which is connected in parallel with the positive stiffness of the reference compression spring to generate a quasi-zero stiffness characteristic in the direction of inclined motion;

[0009] The specific debugging process includes:

[0010] S1, determines the pre-compression amount of the oblique compression spring that produces negative stiffness in the initial state , the projected length of the distance between the upper and lower hinge points of the negative stiffness oblique compression spring perpendicular to the direction of tilting motion , the distance from the initial position to the static equilibrium position along the tilt motion direction , the inclination angle between the reference compression spring and the vertical direction , the linear stiffness of the negative stiffness oblique compression spring , the linear stiffness of the positive stiffness reference compression spring ; Construct dimensionless pre-compression , dimensionless projected length , the stiffness ratio of the negative stiffness oblique compression spring to the positive stiffness reference compression spring ;

[0011] S2, according to the parameter conditions of the quasi-zero stiffness characteristics, make the values ​​of these parameters satisfy the quasi-zero stiffness parameter relationship , nonlinear quasi-zero stiffness characteristics can be obtained;

[0012] S3. After determining the above parameters, draw the force-displacement curve , represents the vertical displacement from the initial position, To apply force, i.e. the force applied to the load plate, apply force The rear isolator is in a static equilibrium position, and this force divided by the acceleration of gravity is equal to the vibration isolation mass carried. , determine whether the vibration isolation mass and the corresponding vibration isolation frequency band at this time meet the design requirements of the vibration isolator's bearing mass and vibration isolation frequency band. If they do not meet the design requirements, repeat steps S1 to S3.

[0013] Furthermore, guide rods are provided inside the two oblique compression springs and the reference compression spring, and the two oblique compression springs and the reference compression spring are located on the same longitudinal plane.

[0014] Furthermore, the initial state refers to a state in which one hinged end of the oblique compression spring with negative stiffness is hinged to the reference compression spring with positive stiffness, and the reference compression spring with positive stiffness is in a free length state.

[0015] Furthermore, the static equilibrium position refers to the position of the oblique compression spring perpendicular to the direction of the tilting movement; , dimensionless displacement and The relationship conforms to ,in, , , It represents the vertical displacement from the static equilibrium position.

[0016] Furthermore, the applied force And its expression is non-dimensionalized to obtain the dimensionless applied force , find the expression right The first derivative of , we get the dimensionless stiffness ,in, ; In the static equilibrium position, let the dimensionless stiffness is equal to zero, obtaining the parameter condition of quasi-zero stiffness characteristics.

[0017] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0018] (1) In the present invention, after one end of the three compression springs is hinged together, two oblique springs with negative stiffness are symmetrically arranged on both sides of the reference compression spring with positive stiffness, and then the entire vibration isolation structure is tilted in one direction. This can solve the problem of low-frequency vibration caused by excitation in the tilted direction, and the vibration isolation effect is significantly improved.

[0019] (2) The vibration isolator structure of the present invention is in an inclined state, and the inclination angle is taken into consideration. Compared with the existing vertical vibration isolators, it is obviously different in structural form, physical meaning of parameters, force expression, stiffness expression, static equilibrium position, bearing capacity, vibration isolation direction, etc.

[0020] (3) By the debugging method of the inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs of the present invention, the dimensionless stiffness is set at the static equilibrium position. is equal to zero, and the parameter condition for obtaining the quasi-zero stiffness characteristic is: By adjusting the parameters according to the formula, nonlinear quasi-zero stiffness characteristics can be obtained.

[0021] Figures in the specification

[0022] Figure 1 This is a schematic diagram of the initial position of the inclined quasi-zero stiffness vibration isolator constructed with a single pair of inclined springs of the present invention.

[0023] Figure 2 is the stiffness-displacement curve of the nonlinear quasi-zero stiffness characteristic.

[0024] Figure 3 It is the force-displacement curve of nonlinear quasi-zero stiffness characteristics. DETAILED DESCRIPTION

[0025] The present invention will be further described below in conjunction with the accompanying drawings.

[0026] The traditional quasi-zero stiffness vibration isolator has an effective working direction of vertical direction. However, in the actual environment, the excitation direction is not always vertical. Low-frequency vibration caused by excitation in non-vertical inclined direction often exists in the actual environment. If a quasi-zero stiffness vibration isolator in the vertical direction is used to solve the low-frequency vibration problem caused by excitation in the inclined direction, the vibration isolation effect will be reduced or even fail. Therefore, in order to solve the low-frequency vibration problem caused by excitation in the inclined direction, the present invention proposes an inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs, such as Figure 1 As shown, it mainly includes a reference compression spring and two oblique compression springs. The reference compression spring is perpendicular to the longitudinal direction at a certain angle. The two oblique compression springs are symmetrically arranged on both sides of the reference compression spring, and the top ends of the two oblique compression springs are connected to the top ends of the reference compression springs by hinges (such as Figure 1The bottom ends of the two oblique compression springs are respectively hinged to the bracket (such as Figure 1 A and B in the figure). The bottom end of the reference compression spring is fixedly connected to the base (such as Figure 1 E), produces positive stiffness The two oblique compression springs generate negative stiffness in the direction of tilting motion. , with the positive stiffness of the reference compression spring When connected in parallel, a quasi-zero stiffness characteristic is produced in the direction of tilt motion.

[0027] In the above-mentioned vibration isolator, preferably, guide rods are provided inside the two oblique compression springs and the reference compression spring for support, so as to prevent radial buckling instability caused by axial force.

[0028] In the above-mentioned vibration isolator, preferably, the two oblique compression springs and the reference compression spring are located on the same longitudinal plane. The two oblique compression springs have the same structure and generate the same linear negative stiffness. .

[0029] Figure 1 The meaning of the parameters in is, represents the linear stiffness of the oblique compression spring that produces negative stiffness, represents the linear stiffness of the positive stiffness reference compression spring, It represents the projected length of the distance between the upper and lower hinge points of the negative stiffness oblique compression spring in the direction perpendicular to the oblique motion under initial conditions. is the pre-compression amount of the negative stiffness oblique compression spring in the initial state, represents the vertical displacement from the initial position, represents the vertical displacement from the static equilibrium position, represents the distance from the initial position to the static equilibrium position along the tilt motion direction, Indicates the inclination angle between the reference compression spring and the vertical direction. , dimensionless displacement and The relationship conforms to The initial state refers to the state where one hinged end of the oblique compression spring with negative stiffness is hinged to the reference compression spring with positive stiffness, and the reference compression spring with positive stiffness is in a state of free length. The corresponding position at this time is the initial position. The static equilibrium position refers to the position of the oblique compression spring perpendicular to the direction of the oblique movement, see Figure 1 Middle dotted line.

[0030] First, we obtain the expression of the applied force f. In order to analyze the structural parameter characteristics, we need to The dimensionless applied force is obtained by performing the dimensionless stiffening formula (1) and its expression. expression, find expression right The first derivative of , we get the dimensionless stiffness , see formula (2); formula (3) is the dimensionless parameter expression; in the static equilibrium position, let the dimensionless stiffness Equal to zero, the parameter conditions for obtaining the quasi-zero stiffness characteristic are shown in formula (4). According to the debugging method of formula (4), the nonlinear quasi-zero stiffness characteristic in the motion direction can be obtained, including the stiffness displacement curve and the force displacement curve, such as Figure 2 、 Figure 3 shown.

[0031] (1),

[0032] (2),

[0033] (3),

[0034] (4),

[0035] in, 、 is the intermediate variable, is the dimensionless displacement corresponding to x, is the dimensionless displacement corresponding to y, is the stiffness ratio of the negative stiffness oblique compression spring to the positive stiffness reference compression spring, is the dimensionless pre-compression of the oblique compression spring that produces negative stiffness in the initial state, is the dimensionless projection length of the oblique compression spring in the initial state perpendicular to the direction of the oblique motion, is the dimensionless stiffness, is the dimensionless applied force.

[0036] The debugging method of the inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs of the present invention is as follows:

[0037] S1, determines the pre-compression amount of the oblique compression spring that produces negative stiffness in the initial state , the projected length of the distance between the upper and lower hinge points of the negative stiffness oblique compression spring perpendicular to the direction of tilting motion , the distance from the initial position to the static equilibrium position along the tilt motion direction , the inclination angle between the reference compression spring and the vertical direction , the linear stiffness of the negative stiffness oblique compression spring , the linear stiffness of the positive stiffness reference compression spring ; According to formula (3), construct dimensionless parameters and determine dimensionless pre-compression , dimensionless projected length , stiffness ratio ;

[0038] S2, adjust the parameters according to the parameter conditions of the quasi-zero stiffness characteristics so that the values ​​of these parameters meet the quasi-zero stiffness parameter relationship , nonlinear quasi-zero stiffness characteristics can be obtained;

[0039] S3. After determining the above parameters, draw the force-displacement curve ,See Figure 3 , Figure 2 is the corresponding stiffness displacement curve, both curves have nonlinear characteristics, where represents the vertical displacement from the initial position, To apply force, that is, to apply force to the load plate (the load plate is generally installed on the top of the vibration isolation structure, as shown in the figure at point O), apply force The rear isolator is in a static equilibrium position, and this force divided by the acceleration of gravity is equal to the vibration isolation mass carried. , further determine whether the vibration isolation mass and the corresponding vibration isolation frequency band at this time meet the design requirements of the vibration isolator's bearing mass and vibration isolation frequency band. If they do not meet the design requirements, repeat steps S1 to S3.

[0040] The existing literature, Carrella et al. (Journal of Sound and Vibration 322 (2009) 707–717), involves a quasi-zero stiffness structure with a single pair of oblique springs, but the vibration isolation direction is vertical and cannot be applied to oblique directions. The present invention is significantly different from the existing literature in the following aspects. The purpose is different. The present invention solves the low-frequency vibration problem caused by excitation in the oblique direction. The inclination angle is taken into account in the structural model. This parameter, while the existing literature does not consider the tilt angle. The structure is different, the structure involved in the present invention is in a tilted state, so the tilt angle is taken into account This is the fundamental reason for the differences from existing literature in terms of parameter physical meaning, force expression, stiffness expression, static equilibrium position, load-bearing capacity, and usage purpose. Although two inclined spring quasi-zero stiffness vibration isolation structures have been proposed in existing literature for decades, the inclined quasi-zero stiffness vibration isolation structure and debugging method constructed with a single pair of inclined springs in this application have not yet been proposed.

[0041] Although the functions and working processes of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific functions and working processes. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which are all protected by the present invention.

Claims

1. A method for debugging an inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs, wherein the vibration isolator comprises a reference compression spring and two inclined compression springs, characterized in that: The reference compression spring is arranged at an angle perpendicular to the longitudinal direction, and the two oblique compression springs are symmetrically arranged on both sides of the reference compression spring. The top ends of the two oblique compression springs are connected to the top end of the reference compression spring by hinges, and the bottom ends of the two oblique compression springs are respectively hinged to the brackets, and the bottom ends of the reference compression springs are fixed to the base; the two oblique compression springs generate negative stiffness in the direction of tilting movement, which is connected in parallel with the positive stiffness of the reference compression spring to generate a quasi-zero stiffness characteristic in the direction of tilting movement; The specific debugging process includes: S1, determines the pre-compression amount of the negative stiffness oblique compression spring in the initial state , the projected length of the distance between the upper and lower hinge points of the negative stiffness oblique compression spring perpendicular to the direction of tilting motion , the distance from the initial position to the static equilibrium position along the tilt motion direction , the inclination angle between the reference compression spring and the vertical direction , the linear stiffness of the negative stiffness oblique compression spring , the linear stiffness of the positive stiffness reference compression spring ; Construct dimensionless pre-compression , dimensionless projected length , the stiffness ratio of the negative stiffness oblique compression spring to the positive stiffness reference compression spring ; S2, according to the parameter conditions of the quasi-zero stiffness characteristics, make the values ​​of these parameters satisfy the quasi-zero stiffness parameter relationship , nonlinear quasi-zero stiffness characteristics can be obtained; S3. After determining the above parameters, draw the force-displacement curve , represents the vertical displacement from the initial position, To apply force, i.e. the force applied to the load plate, apply force The rear isolator is in a static equilibrium position, and this force divided by the acceleration of gravity is equal to the vibration isolation mass carried. , determine whether the vibration isolation mass and the corresponding vibration isolation frequency band at this time meet the design requirements of the vibration isolator's bearing mass and vibration isolation frequency band. If they do not meet the design requirements, repeat steps S1 to S3.

2. The debugging method of the inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs according to claim 1 is characterized in that: Guide rods are provided inside the two oblique compression springs and the reference compression spring, and the two oblique compression springs and the reference compression spring are located on the same longitudinal plane.

3. The debugging method of the inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs according to claim 1 is characterized in that: The two oblique compression springs are identical and produce the same linear negative stiffness.

4. The debugging method of the inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs according to claim 1 is characterized in that: The initial state refers to a state in which one hinged end of the oblique compression spring with negative stiffness is hinged to the reference compression spring with positive stiffness, and the reference compression spring with positive stiffness is in a free length state.

5. The debugging method of the inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs according to claim 1 is characterized in that: The static equilibrium position refers to the position of the oblique compression spring perpendicular to the direction of the tilting movement; , dimensionless displacement and The relationship conforms to ,in, , , It represents the vertical displacement from the static equilibrium position.

6. The debugging method of the inclined quasi-zero stiffness vibration isolator with a single pair of inclined springs according to claim 1 is characterized in that: Applied force And its expression is non-dimensionalized to obtain the dimensionless applied force , find the expression right The first derivative of , we get the dimensionless stiffness ,in, ; In the static equilibrium position, let the dimensionless stiffness is equal to zero, obtaining the parameter condition of quasi-zero stiffness characteristics.

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