CN114110066B - Zero-rigidity vibration isolation structure and method formed by single pair of diagonal rods through negative rigidity mechanism - Google Patents

Zero-rigidity vibration isolation structure and method formed by single pair of diagonal rods through negative rigidity mechanism Download PDF

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CN114110066B
CN114110066B CN202111347500.9A CN202111347500A CN114110066B CN 114110066 B CN114110066 B CN 114110066B CN 202111347500 A CN202111347500 A CN 202111347500A CN 114110066 B CN114110066 B CN 114110066B
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stiffness
guide rod
zero
rods
diagonal
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CN114110066A (en
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赵峰
曹树谦
侯远航
李博
宋茜
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Tianjin University
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Tianjin University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F7/00—Vibration-dampers; Shock-absorbers
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2228/00—Functional characteristics, e.g. variability, frequency-dependence
    • F16F2228/06—Stiffness
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2228/00—Functional characteristics, e.g. variability, frequency-dependence
    • F16F2228/06—Stiffness
    • F16F2228/063—Negative stiffness
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD

Abstract

The invention discloses a zero-stiffness vibration isolation structure and a zero-stiffness vibration isolation method formed by a single pair of diagonal rods through a negative stiffness mechanism, wherein the vibration isolation structure comprises a fixed plate, a bracket, a transverse guide rod, diagonal rods, a hinge support, a hollow pipe, a load carrying disc and a vertical spring guide rod; the two ends of the fixing plate are symmetrically provided with brackets, the brackets are provided with transverse guide rod linear bearings, the transverse guide rods are connected through the transverse guide rod linear bearings, the opposite ends of the two transverse guide rods are connected with the diagonal rods, the transverse guide rods are provided with clamping rings, and transverse springs are arranged between the clamping rings and the transverse guide rod linear bearings; the opposite ends of the two inclined rods are respectively provided with a hinge support, the two hinge supports are connected with a vertical guide rod linear bearing together, a hollow pipe is connected above the vertical guide rod linear bearing, and the top of the hollow pipe is connected with a load disc; a vertical spring guide rod is connected between the vertical guide rod linear bearing and the bracket, and a vertical spring is arranged on the vertical spring guide rod.

Description

Zero-rigidity vibration isolation structure and method formed by single pair of diagonal rods through negative rigidity mechanism
Technical Field
The invention relates to the field of zero-stiffness vibration isolation structures, in particular to a zero-stiffness vibration isolation structure formed by a single pair of diagonal rods through a negative stiffness mechanism and a method.
Background
Linear stiffness vibration isolators are widely used in engineering, but have a problem when the excitation frequency is less thanWhen the natural frequency of the vibration isolator is multiplied, the linear vibration isolator does not have vibration isolation effect; on the premise of ensuring the bearing quality, only the linear rigidity coefficient is reduced, but the processing result can lead to the static deformation of the linear vibration isolator to be large or the bearing capacity to be reduced. Therefore, high static low dynamic stiffness or quasi-zero stiffness vibration isolators are proposed that can have less dynamic stiffness to widen the vibration isolation band while having higher static stiffness to carry the mass.
Document [1] proposes a vibration isolation model and method of high static low dynamic stiffness, but the vibration isolator described in this document has three nonlinear stiffness, and under a large excitation, the vibration isolation frequency band will be reduced due to the characteristics of hard nonlinear stiffness; and the parameter design method given in this document is complex (contains several inequalities) and inconvenient to design and apply.
[1]Thanh Danh Le,Kyoung Kwan Ahn,A vibration isolation systemin low frequency excitation region using negative stiffness structure for vehicle seat,Journal of Sound and Vibration,2011,330,6311-6335.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a zero-rigidity vibration isolation structure and a zero-rigidity vibration isolation method formed by a single-pair diagonal rod negative rigidity mechanism.
The invention aims at realizing the following technical scheme:
a zero-rigidity vibration isolation structure formed by a single pair of diagonal rod negative rigidity mechanisms comprises a fixed plate, a bracket, a transverse guide rod, diagonal rods, a hinge support, a hollow pipe, a load disc and a vertical spring guide rod; the two ends of the fixing plate are symmetrically provided with brackets, the brackets are provided with transverse guide rod linear bearings, the transverse guide rods are connected through the transverse guide rod linear bearings, the opposite ends of the two transverse guide rods are connected with the diagonal rods, the transverse guide rods are provided with clamping rings, and transverse springs are arranged between the clamping rings and the transverse guide rod linear bearings; the opposite ends of the two inclined rods are respectively provided with a hinge support, the two hinge supports are connected with a vertical guide rod linear bearing together, a hollow pipe is connected above the vertical guide rod linear bearing, and the top of the hollow pipe is connected with a load disc; a vertical spring guide rod is connected between the vertical guide rod linear bearing and the bracket, and a vertical spring is arranged on the vertical spring guide rod.
Further, a rectangular through hole for the transverse guide rod to pass through is formed in the support, and side holes for fixing the linear bearing of the transverse guide rod are formed in two sides of the rectangular through hole.
Furthermore, connecting holes are formed in two ends of the inclined rod.
Further, the hinge support is of a U-shaped structure, a through hole is formed in the lower left corner of the hinge support, and a connecting hole for connecting the hollow pipe is formed in the top of the hinge support.
Further, a groove is formed in the connecting end of the transverse guide rod and the inclined rod, and a through hole is formed in the groove.
Further, the transverse guide rod is movably connected with the inclined rod through a radial bearing.
Furthermore, the debugging method for the zero-rigidity vibration isolation structure formed by the single pair of diagonal rod negative rigidity mechanisms comprises the following steps:
(1) Drawing a mechanical schematic diagram of the diagonal rod in the zero-stiffness vibration isolation structure in an initial state; by k 2 Representing vertical spring rate, f h The horizontal spring force is inward elastic force generated by the transverse spring, h is the vertical distance from the initial state to the static balance position, a is the horizontal length of a single inclined rod in the initial state, x is the displacement of the load disc from the initial position, and y is the displacement from the static balance position, namely the position of two inclined rods from the horizontal state; the initial state is a state that the vertical spring is in an original length, and the lower end of the vertical guide rod linear bearing fixedly connected with the load disc is in contact with the top end of the vertical spring;
(2) The application force f acting on the load disc and the expression thereof are subjected to quantitative stiffening see formula (3) to obtain dimensionless application forceExpression, expression->For->To obtain dimensionless stiffness +.>In the static equilibrium position, i.e. with the two diagonal rods in the horizontal state, a dimensionless stiffness +.>Respectively obtaining a first derivative and a second derivative to obtain a parameter condition of zero stiffness characteristic, wherein the parameter condition is shown in a formula (4);
wherein a represents the horizontal length of a single diagonal rod in an initial state; h represents the vertical distance from the position of the inclined rod to the position of the static balance point in the initial state; the ratio α of the transverse spring rate to the vertical spring rate; delta refers to the pre-compressed length of the transverse spring; p is p 1 And q 1 Is an intermediate parameter variable;
(3) The ratio alpha of the stiffness of the transverse spring to the stiffness of the vertical spring is equal to 0.5, and the precompressed length of the transverse spring is equal to the horizontal length a of the single inclined rod in the initial state, so that the zero-stiffness vibration isolation characteristic can be obtained.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
1. aiming at a single pair of diagonal rod quasi-zero stiffness vibration isolation model, a new parameter assumption is provided, and a force and stiffness expression is obtained; the displacement is carried out at a balance point, so that the rigidity is equal to zero and the second derivative of the rigidity is equal to zero, and the zero rigidity regulating and controlling method is provided for the first time by applying the two zero rigidity parameter conditions; compared with the prior art, the provided regulating and controlling method is simple, visual and easy to realize, and is convenient for the structural design of zero rigidity of the diagonal rod.
2. By the zero stiffness debugging method, zero stiffness characteristics of straight lines near the static balance point can be obtained, the resonance frequency of the linear vibrator can be reduced, and no nonlinear factors are attached; compared with the traditional quasi-zero stiffness vibration isolator with weak tertiary nonlinear characteristics, the vibration isolation frequency band cannot be reduced due to nonlinear rightward bending under the condition of large excitation.
3. In the research of quasi-zero stiffness of a single pair of diagonal rods, the single pair diagonal rod negative stiffness mechanism forms a zero stiffness vibration isolation structure, and the linear bearing and the optical axis replace the complex structure corresponding to the existing literature, so that the structure is simple and easy to process and assemble.
4. The invention provides a new model and a design method, so that the vibration isolator has the characteristics of high static and low dynamic stiffness, has no nonlinear stiffness, and keeps the vibration isolation frequency unchanged under the condition of large-scale excitation; and the design method is simple and is convenient for engineering application.
Drawings
Fig. 1 is a schematic structural view of the present invention.
Fig. 2 is a schematic left-hand structural view of the bracket.
Fig. 3 is a schematic diagram of the front view structure of the diagonal rod.
Fig. 4 is a schematic front view of the hinge bracket.
Fig. 5 is a left-hand structural schematic view of the hinge bracket.
Fig. 6 is a schematic view of the front view of the transverse guide bar.
Fig. 7 is a schematic top view of the lateral guide bar.
FIG. 8 is a mechanical diagram of zero stiffness for a single pair of diagonal rods.
Fig. 9a is a zero stiffness vibration isolation structure stiffness displacement curve and fig. 9b is a zero stiffness vibration isolation structure force displacement curve.
Reference numerals: the device comprises a 1-fixing plate, a 2-bracket, a 3-transverse guide rod, a 4-transverse guide rod linear bearing, a 5-radial bearing, a 6-diagonal rod, a 7-hinge support, an 8-hollow pipe, a 9-load disc, a 10-vertical guide rod linear bearing, an 11-clamping ring and a 12-transverse spring; 13-vertical spring guide bar; 14-vertical spring
Detailed Description
The invention is described in further detail below with reference to the drawings and the specific examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1 to 8, the invention provides a zero-rigidity vibration isolation structure formed by a single pair of diagonal rods through a negative rigidity mechanism, wherein two ends of the single pair of diagonal rods 6 are respectively connected with a hinge support 7 and a transverse guide rod 3 through a radial bearing 5 and a pin shaft hinge. The hinge support 7, the vertical guide rod linear bearing 10, the hollow pipe 8 and the load disc 9 are firmly connected through standard long bolts, and vibration isolation quality force received by the load disc 9 can be transmitted to the single pair of diagonal rods 6. The transverse guide rod 3 can move in the horizontal direction with low friction after being restrained by the transverse guide rod linear bearing 4. The transverse guide rod linear bearing 4 is fixedly connected with the bracket 2 through a standard component bolt. The bracket 2 is fixedly connected with the fixed plate 1 through standard rod bolts. The transverse spring 12 is restrained in axial length by the collar 11 and the transverse-rod linear bearing 4, and the elastic force can be transmitted to the load-carrying disc 9 through the diagonal rod 6 to obtain a vertical force, in particular a negative stiffness characteristic in the vertical direction. The vertical springs 14 are restrained by vertical spring guide bars 13 and the load carrying capacity is obtained by the load carrying discs 9 by limiting the displacement of the movement by vertical guide bar linear bearings 10 and the fixed plate 1.
Specifically, a rectangular through hole for the transverse guide rod to pass through is formed in the support, and side holes for fixing the linear bearing of the transverse guide rod are formed in two sides of the rectangular through hole. The connecting end of the transverse guide rod and the inclined rod is provided with a groove, and the groove is provided with a through hole.
And connecting holes are formed at two ends of the inclined rod. The hinge support is U-shaped structure, and the lower left corner of hinge support is equipped with the through-hole, and hinge support's top is equipped with the connecting hole that is used for connecting the hollow tube.
In the zero-stiffness vibration isolation structure, the diagonal rods 6 and the transverse springs 12 generate vertical negative stiffness, which is called a single pair of diagonal rod negative stiffness mechanism, and the vertical stiffness mechanism is connected in parallel with the positive stiffness of the vertical springs 14, and near a static balance point (the horizontal state of the diagonal rods 6), the zero-stiffness characteristic can be obtained vertically.
Specifically, the debugging method of the zero-stiffness vibration isolation structure comprises the following steps:
according to the mechanical diagram of FIG. 8 in the initial state of the single pair of diagonal rods, k 2 Is the vertical spring rate, f h Is an inward elastic force generated by a transverse spring (or a horizontal tension spring), h is a vertical distance from an initial state to a static balance position, a is a horizontal length of the diagonal rod in the initial state, x is displacement from the initial position, and y is displacement from the static balance position. In fig. 8, the character y indicates the displacement in the static balance state, i.e., y=0 in the static balance state, i.e., the two diagonal rod horizontal state.
Firstly, obtaining an expression of an application force f, carrying out quantitative rigidization on the application force f and the expression thereof in order to analyze wider structural parameter characteristics, and obtaining dimensionless application force according to a formula (3)Expression, expression->For->Is able to obtain dimensionless stiffness +.>In the static equilibrium position (two-bar horizontal state), for dimensionless stiffness +.>And respectively obtaining a first derivative and a second derivative to obtain a parameter condition of zero stiffness characteristic, wherein the parameter condition is shown in a formula (4). The static balance position is taken as zero displacement, and the rigidity displacement and force displacement relationship of the zero rigidity characteristic is shown in fig. 9a and 9 b.
a, the horizontal length between hinge points at two ends of the inclined rod; h, vertical distance from the initial position of the single pair of diagonal vibration isolators to the position of the static balance point; the ratio α of the transverse spring rate to the vertical spring rate; delta refers to the pre-compressed length of the transverse spring. P is p 1 And q 1 Is an intermediate parameter variable.
According to the obtained adjustment basis, the ratio alpha of the selected transverse spring stiffness to the vertical spring stiffness is equal to 0.5, the precompressed length delta of the transverse spring is equal to the horizontal length a between two hinge points of the diagonal rod in an initial state, and zero-stiffness vibration isolation characteristic can be obtained.
The invention is not limited to the embodiments described above. The above description of specific embodiments is intended to describe and illustrate the technical aspects of the present invention, and is intended to be illustrative only and not limiting. Numerous specific modifications can be made by those skilled in the art without departing from the spirit of the invention and scope of the claims, which are within the scope of the invention.

Claims (7)

1. A zero-rigidity vibration isolation structure formed by a single pair of diagonal rods and a negative rigidity mechanism is characterized by comprising a fixed plate, a bracket, a transverse guide rod, diagonal rods, a hinge support, a hollow pipe, a load carrying disc and a vertical spring guide rod; the two ends of the fixing plate are symmetrically provided with brackets, the brackets are provided with transverse guide rod linear bearings, the transverse guide rods are connected through the transverse guide rod linear bearings, the opposite ends of the two transverse guide rods are connected with the diagonal rods, the transverse guide rods are provided with clamping rings, and transverse springs are arranged between the clamping rings and the transverse guide rod linear bearings; the opposite ends of the two inclined rods are respectively provided with a hinge support, the two hinge supports are connected with a vertical guide rod linear bearing together, a hollow pipe is connected above the vertical guide rod linear bearing, and the top of the hollow pipe is connected with a load disc; a vertical spring guide rod is connected between the vertical guide rod linear bearing and the bracket, and a vertical spring is arranged on the vertical spring guide rod.
2. The zero-stiffness vibration isolation structure formed by a single pair of diagonal rods through a negative stiffness mechanism according to claim 1 is characterized in that rectangular through holes for the transverse guide rods to pass through are formed in the support, and side holes for fixing linear bearings of the transverse guide rods are formed in two sides of the rectangular through holes.
3. The zero-stiffness vibration isolation structure formed by a single pair of diagonal rods through a negative stiffness mechanism according to claim 1, wherein connecting holes are formed at two ends of each diagonal rod.
4. The zero-stiffness vibration isolation structure formed by the single-pair diagonal rod negative stiffness mechanism according to claim 1 is characterized in that the hinge support is of a U-shaped structure, a through hole is formed in the lower left corner of the hinge support, and a connecting hole for connecting the hollow tube is formed in the top of the hinge support.
5. The zero-stiffness vibration isolation structure formed by the single-pair diagonal rod negative stiffness mechanism according to claim 1 is characterized in that a groove is formed at the connecting end of the transverse guide rod and the diagonal rod, and a through hole is formed in the groove.
6. The zero-stiffness vibration isolation structure formed by a single pair of diagonal rods through a negative stiffness mechanism according to claim 1 is characterized in that the transverse guide rods are movably connected with the diagonal rods through radial bearings.
7. A method for debugging a zero-stiffness vibration isolation structure formed by a single pair of diagonal rod negative stiffness mechanisms, which is based on the single pair of diagonal rod negative stiffness mechanisms of any one of claims 1-6, and is characterized by comprising the following steps:
(1) Drawing a mechanical schematic diagram of the diagonal rod in the zero-stiffness vibration isolation structure in an initial state; by k 2 Representing vertical spring rate, f h The horizontal spring force is inward elastic force generated by the transverse spring, h is the vertical distance from the initial state to the static balance position, a is the horizontal length of a single inclined rod in the initial state, x is the displacement of the load disc from the initial position, and y is the displacement from the static balance position, namely the position of two inclined rods from the horizontal state; the initial state is a state that the vertical spring is in an original length, and the lower end of the vertical guide rod linear bearing fixedly connected with the load disc is in contact with the top end of the vertical spring;
(2) The application force f acting on the load disc and the expression thereof are subjected to quantitative stiffening see formula (3) to obtain dimensionless application forceExpression, expression->For->To obtain dimensionless stiffness +.>In the static equilibrium position, i.e. with the two diagonal rods in the horizontal state, a dimensionless stiffness +.>Respectively obtaining a first derivative and a second derivative to obtain a parameter condition of zero stiffness characteristic, wherein the parameter condition is shown in a formula (4);
by the expression for stiffness, at the static equilibrium position, the stiffness is made equal to 0And the second derivative of the stiffness is equal to 0 Obtaining a zero stiffness parameter condition, namely a formula (4);
wherein a represents the horizontal length of a single diagonal rod in an initial state; h represents the vertical distance from the position of the inclined rod to the position of the static balance point in the initial state; the ratio α of the transverse spring rate to the vertical spring rate; delta refers to the pre-compressed length of the transverse spring; p is p 1 And q 1 Is an intermediate parameter variable;
(3) The ratio alpha of the stiffness of the transverse spring to the stiffness of the vertical spring is equal to 0.5, and the precompressed length of the transverse spring is equal to the horizontal length a of the single inclined rod in the initial state, so that the zero-stiffness vibration isolation characteristic can be obtained.
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2001280418A (en) * 2000-03-29 2001-10-10 Fujikura Rubber Ltd Vibration isolator
CN106402267A (en) * 2016-05-23 2017-02-15 福州大学 Extension type quasi-zero stiffness vibration isolator and implementation method thereof
CN208804165U (en) * 2018-09-20 2019-04-30 南京航空航天大学 A kind of quasi- zero stiffness vibrating isolation system of centering type
CN110529554A (en) * 2019-09-12 2019-12-03 郑州轻工业学院 A kind of vibration-isolating platform being made of double groups of oblique springs
CN112178121A (en) * 2020-10-09 2021-01-05 北京理工大学 Quasi-zero stiffness vibration isolator with inclined compression rod

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2001280418A (en) * 2000-03-29 2001-10-10 Fujikura Rubber Ltd Vibration isolator
CN106402267A (en) * 2016-05-23 2017-02-15 福州大学 Extension type quasi-zero stiffness vibration isolator and implementation method thereof
CN208804165U (en) * 2018-09-20 2019-04-30 南京航空航天大学 A kind of quasi- zero stiffness vibrating isolation system of centering type
CN110529554A (en) * 2019-09-12 2019-12-03 郑州轻工业学院 A kind of vibration-isolating platform being made of double groups of oblique springs
CN112178121A (en) * 2020-10-09 2021-01-05 北京理工大学 Quasi-zero stiffness vibration isolator with inclined compression rod

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