CN114110066A - Zero-rigidity vibration isolation structure formed by single-pair inclined rod negative rigidity mechanism and method - Google Patents

Zero-rigidity vibration isolation structure formed by single-pair inclined rod negative rigidity mechanism and method Download PDF

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CN114110066A
CN114110066A CN202111347500.9A CN202111347500A CN114110066A CN 114110066 A CN114110066 A CN 114110066A CN 202111347500 A CN202111347500 A CN 202111347500A CN 114110066 A CN114110066 A CN 114110066A
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stiffness
guide rod
transverse
zero
vertical
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CN114110066B (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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    • 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 formed by a single-pair inclined rod negative stiffness mechanism and a method, wherein the vibration isolation structure comprises a fixing plate, a bracket, a transverse guide rod, an inclined rod, a hinge support, a hollow pipe, a load bearing 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 inclined rods, the transverse guide rods are provided with clamping shaft rings, and transverse springs are arranged between the clamping shaft rings and the transverse guide rod linear bearings; hinge supports are arranged at the opposite ends of the two inclined rods, 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 carrying disc; and a vertical spring guide rod is connected between the vertical guide rod linear bearing and the support, and a vertical spring is arranged on the vertical spring guide rod.

Description

Zero-rigidity vibration isolation structure formed by single-pair inclined rod negative rigidity mechanism and method
Technical Field
The invention relates to the field of zero-rigidity vibration isolation structures, in particular to a zero-rigidity vibration isolation structure formed by a single-pair inclined rod negative rigidity mechanism and a method.
Background
Linear stiffness vibration isolator, which is widely used in engineering, has a problem that when excitation frequency is less than
Figure BDA0003354538430000011
When the natural frequency of the vibration isolator is multiplied, the linear vibration isolator has no vibration isolation effect; on the premise of ensuring the bearing quality, only the linear stiffness coefficient is reduced, but the static deformation of the linear vibration isolator is increased or the bearing capacity is reduced as a result of the treatment. Therefore, a high static low dynamic stiffness or quasi-zero stiffness vibration isolator is provided, which can have smaller dynamic stiffness to widen the vibration isolation frequency band and simultaneously has higher static stiffness to bear mass.
The document [1] proposes a high static state low dynamic stiffness vibration isolation model and a method, but the vibration isolator disclosed in the document has three times of nonlinear stiffness, and under large-amplitude excitation, due to the characteristic of hard nonlinear stiffness, the vibration isolation frequency band is reduced; and the parameter design method given by the document is complex (comprising a plurality of inequalities), and is inconvenient to design and apply.
[1]Thanh Danh Le,Kyoung Kwan Ahn,A vibration isolation system in 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 formed by a single-pair inclined rod negative rigidity mechanism and a method.
The purpose of the invention is realized by the following technical scheme:
a zero-stiffness vibration isolation structure formed by a single-pair inclined rod negative stiffness mechanism comprises a fixed plate, a bracket, a transverse guide rod, an inclined rod, a hinge support, a hollow tube, 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 inclined rods, the transverse guide rods are provided with clamping shaft rings, and transverse springs are arranged between the clamping shaft rings and the transverse guide rod linear bearings; hinge supports are arranged at the opposite ends of the two inclined rods, 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 carrying disc; and a vertical spring guide rod is connected between the vertical guide rod linear bearing and the support, and a vertical spring is arranged on the vertical spring guide rod.
Furthermore, the support is provided with a rectangular through hole for the transverse guide rod to pass through, and two sides of the rectangular through hole are provided with side holes for fixing the linear bearing of the transverse guide rod.
Furthermore, connecting holes are formed in two ends of the inclined rod.
Furthermore, 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 used for connecting a hollow pipe is formed in the top of the hinge support.
Furthermore, 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.
Furthermore, the transverse guide rod is movably connected with the inclined rod through a radial bearing.
Further, a debugging method for forming a zero-rigidity vibration isolation structure by a single-pair inclined rod negative rigidity mechanism comprises the following steps:
(1) drawing a mechanical schematic diagram of an inclined rod in a zero-rigidity vibration isolation structure in an initial state; by k2Representing vertical spring rate, fhIs the inward elastic force generated by the transverse spring, h is the vertical distance from the initial state to the static equilibrium position, a is the horizontal length of the single inclined rod in the initial state, x is the displacement of the load-carrying disc from the initial position, and y is the displacement from the static equilibrium position, namely the displacement of the two inclined rods from the horizontal state; the initial state is the original length of the vertical spring plate, and the lower end of the linear bearing of the vertical guide rod fixedly connected with the load-bearing disc is connected with the vertical springThe state of tip contact;
(2) the application force f acting on the load-bearing disc and the expression thereof are subjected to non-dimensionalization, see formula (3), so that the non-dimensionalized application force is obtained
Figure BDA0003354538430000021
Expression, evaluating the expression
Figure BDA0003354538430000022
To pair
Figure BDA0003354538430000023
First order derivative of (A) to obtain dimensionless stiffness
Figure BDA0003354538430000024
In static equilibrium position, i.e. with the two diagonal rods horizontal, for dimensionless stiffness
Figure BDA0003354538430000025
Respectively solving a first derivative and a second derivative to obtain a parameter condition of zero stiffness characteristic, which is shown in a formula (4);
Figure BDA0003354538430000026
Figure BDA0003354538430000027
Figure BDA0003354538430000028
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 alpha of the transverse spring stiffness to the vertical spring stiffness; δ denotes the pre-compression length of the transverse spring; p is a radical of1And q is1Is an intermediate parameter variable;
(3) the zero-stiffness vibration isolation characteristic can be obtained by making the ratio alpha of the stiffness of the transverse spring to the stiffness of the vertical spring equal to 0.5 and the pre-compression length of the transverse spring equal to the horizontal length a of a single diagonal rod in the initial state.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
1. aiming at a single-pair diagonal quasi-zero stiffness vibration isolation model, a new parameter hypothesis is provided, and a force and stiffness expression is obtained; the method is characterized in that the static balance point is displaced, the rigidity is equal to zero and the rigidity second derivative is equal to zero, and the zero rigidity regulation and control method is firstly provided by applying the two zero rigidity parameter conditions; compared with the prior documents, the provided adjusting and controlling method is simple, visual and easy to realize, and facilitates the structural design of the inclined rod with zero rigidity.
2. By the zero-stiffness debugging method, the zero-stiffness characteristic that a straight line is near a static balance point can be obtained, the resonance frequency of the linear vibrator can be reduced, and no nonlinear factor is attached; compared with the traditional quasi-zero stiffness vibration isolator with weak cubic nonlinear characteristics, under the condition of large-amplitude excitation, the vibration isolation frequency band cannot be reduced due to nonlinear rightward bending.
3. In the research of quasi-zero stiffness of a single-pair inclined rod, the negative stiffness mechanism of the single-pair inclined rod forms a zero-stiffness vibration isolation structure, and a linear bearing and an optical axis replace a complex structure corresponding to the existing document, so that the structure is simple, and the processing and the assembly are easy.
4. The invention provides a new model and a design method, so that the vibration isolator has the characteristics of high static state and low dynamic stiffness, no nonlinear stiffness exists, and the vibration isolation frequency is kept unchanged under large-amplitude excitation; and the design method is simple and convenient for engineering application.
Drawings
Fig. 1 is a schematic structural view of the present invention.
Fig. 2 is a left side view of the stent.
Fig. 3 is a front view structure diagram of the diagonal rod.
Fig. 4 is a front view of the hinge bracket.
Fig. 5 is a left side view of the hinge bracket.
Fig. 6 is a front view schematically showing the structure of the lateral guide.
Fig. 7 is a schematic top view of the cross guide.
FIG. 8 is a mechanical schematic diagram of zero stiffness for a single pair of diagonals.
Fig. 9a is a stiffness-displacement curve of a zero stiffness vibration isolation structure, and fig. 9b is a force-displacement curve of a zero stiffness vibration isolation structure.
Reference numerals: 1-a fixed plate, 2-a bracket, 3-a transverse guide rod, 4-a transverse guide rod linear bearing, 5-a radial bearing, 6-an inclined rod, 7-a hinge support, 8-a hollow tube, 9-a load disk, 10-a vertical guide rod linear bearing, 11-a clamping collar and 12-a transverse spring; 13-vertical spring guide bar; 14-vertical spring
Detailed Description
The invention is described in further detail below with reference to the figures and specific examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 1 to 8, the present invention provides a zero-stiffness vibration isolation structure formed by a single-pair diagonal rod negative-stiffness mechanism, wherein two ends of a single-pair diagonal rod 6 are respectively connected with a hinge support 7 and a transverse guide rod 3 through a radial bearing 5 and a pin hinge. The hinge support 7, the vertical guide rod linear bearing 10, the hollow pipe 8 and the load-carrying disc 9 are firmly fixed together through a standard part long bolt, and the vibration isolation mass force borne by the load-carrying disc 9 can be transmitted to the single pair of inclined rods 6. The transverse guide rod 3 can move in a low friction mode in the horizontal direction after being constrained 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 part bolt. The bracket 2 is fixedly connected with the fixed plate 1 through a standard rod bolt. The transverse spring 12 is axially length-constrained by the snap ring collar 11 and the transverse guide rod linear bearing 4, and the elastic force can be transmitted to the load plate 9 through the inclined rod 6 to obtain vertical force, particularly the negative stiffness characteristic in the vertical direction. The vertical spring 14 is restrained by the vertical spring guide rod 13 and limits the moving displacement through the vertical guide rod linear bearing 10 and the fixed plate 1, so that the load-carrying plate 9 can obtain the load-carrying capacity.
Specifically, the bracket is provided with a rectangular through hole for the transverse guide rod to pass through, and two sides of the rectangular through hole are provided with side holes for fixing the linear bearing of the transverse guide rod. The connecting end of the transverse guide rod and the inclined rod is provided with a groove, and a through hole is arranged on the groove.
The two ends of the diagonal rod are provided with connecting holes. 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 used for connecting the hollow pipe is formed in the top of the hinge support.
In the zero-stiffness vibration isolation structure, the inclined rod 6 and the transverse spring 12 generate vertical negative stiffness, which is called a single-pair inclined rod negative stiffness mechanism, the vertical negative stiffness mechanism is connected with the positive stiffness of the vertical spring 14 in parallel, and the zero-stiffness characteristic can be obtained vertically near a static balance point (the horizontal state of the inclined rod 6).
Specifically, the debugging method of the zero-stiffness vibration isolation structure is as follows:
according to the mechanical diagram of the single pair of diagonal rods in the initial state of FIG. 8, k2Is the vertical spring rate, fhIs the inward spring force generated by the lateral spring (or horizontal tension spring), h is the vertical distance from the initial state to the static equilibrium position, a is the horizontal length of the diagonal bar in the initial state, x is the displacement from the initial position, and y is the displacement from the static equilibrium position. In fig. 8, the character "y" indicates a displacement in a static equilibrium state, i.e., a state in which both diagonal rods are horizontal, i.e., y is 0.
Firstly, obtaining an expression of the application force f, carrying out non-dimensionalization on the application force f and the expression thereof in order to analyze wider structural parameter characteristics, and obtaining the non-dimensionalized application force according to the formula (3)
Figure BDA0003354538430000041
Expression, evaluating the expression
Figure BDA0003354538430000042
To pair
Figure BDA0003354538430000043
First derivative of (3), obtaining dimensionless stiffness
Figure BDA0003354538430000044
In static equilibrium position (two-bar horizontal state), for dimensionless rigidity
Figure BDA0003354538430000045
The first derivative and the second derivative are respectively solved to obtain the parameter condition of the zero stiffness characteristic, which is shown in formula (4). The relationship between the stiffness displacement and the force displacement with the static equilibrium position as the zero point displacement and the zero stiffness characteristic is shown in fig. 9a and 9 b.
Figure BDA0003354538430000046
Figure BDA0003354538430000051
Figure BDA0003354538430000052
a, the horizontal length between hinge points at two ends of the diagonal rod; h is the vertical distance from the position of the single-pair inclined rod vibration isolator to the position of the static balance point in the initial state; the ratio alpha of the transverse spring stiffness to the vertical spring stiffness; delta refers to the pre-compression length of the lateral spring. p is a radical of1And q is1Is an intermediate parameter variable.
According to the obtained debugging basis, the ratio alpha of the selected transverse spring stiffness to the selected vertical spring stiffness is equal to 0.5, and the pre-compression length delta of the transverse spring is equal to the horizontal length a between two hinge points of the inclined rod in the initial state, so that the zero-stiffness vibration isolation characteristic can be obtained.
The present invention is not limited to the above-described embodiments. The foregoing description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention, and the above specific embodiments are merely illustrative and not restrictive. Those skilled in the art can make many changes and modifications to the invention without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (7)

1. A zero-stiffness vibration isolation structure formed by a single-pair inclined rod negative stiffness mechanism is characterized by comprising a fixing plate, a bracket, a transverse guide rod, an inclined rod, a hinge support, a hollow tube, a load bearing 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 inclined rods, the transverse guide rods are provided with clamping shaft rings, and transverse springs are arranged between the clamping shaft rings and the transverse guide rod linear bearings; hinge supports are arranged at the opposite ends of the two inclined rods, 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 carrying disc; and a vertical spring guide rod is connected between the vertical guide rod linear bearing and the support, and a vertical spring is arranged on the vertical spring guide rod.
2. The single-pair diagonal bar negative stiffness mechanism as claimed in claim 1, wherein the bracket is provided with a rectangular through hole for the transverse guide bar to pass through, and side holes for fixing the linear bearing of the transverse guide bar are provided at two sides of the rectangular through hole.
3. The negative stiffness mechanism of the single pair of sway bars of claim 1 configured as a zero stiffness vibration isolation structure, wherein the sway bars are provided with attachment holes at both ends.
4. The vibration isolation structure with zero stiffness formed by the negative stiffness mechanism of the single pair of the diagonal rods as claimed in claim 1, wherein 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 negative stiffness mechanism of the single pair of inclined rods to form the zero stiffness vibration isolation structure according to claim 1, wherein the connecting ends of the transverse guide rods and the inclined rods are provided with grooves, and the grooves are provided with through holes.
6. The negative stiffness mechanism of the single pair of inclined rods to form a zero stiffness vibration isolation structure according to claim 1, wherein the transverse guide rod is movably connected with the inclined rod through a radial bearing.
7. A debugging method for forming a zero-rigidity vibration isolation structure by a single-pair inclined rod negative rigidity mechanism is characterized by comprising the following steps:
(1) drawing a mechanical schematic diagram of an inclined rod in a zero-rigidity vibration isolation structure in an initial state; by k2Representing vertical spring rate, fhIs the inward elastic force generated by the transverse spring, h is the vertical distance from the initial state to the static equilibrium position, a is the horizontal length of the single inclined rod in the initial state, x is the displacement of the load-carrying disc from the initial position, and y is the displacement from the static equilibrium position, namely the displacement of the two inclined rods from the horizontal state; the initial state is the original long state of the vertical spring plate, and the lower end of the linear bearing of the vertical guide rod fixedly connected with the loading disc is in contact with the top end of the vertical spring;
(2) the application force f acting on the load-bearing disc and the expression thereof are subjected to non-dimensionalization, see formula (3), so that the non-dimensionalized application force is obtained
Figure FDA0003354538420000011
Expression, evaluating the expression
Figure FDA0003354538420000012
To pair
Figure FDA0003354538420000013
First order derivative of (A) to obtain dimensionless stiffness
Figure FDA0003354538420000014
In static equilibrium position, i.e. with the two diagonal rods horizontal, for dimensionless stiffness
Figure FDA0003354538420000015
Respectively find oneThe first derivative and the second derivative, and obtaining the parameter condition of the zero stiffness characteristic, see formula (4);
Figure FDA0003354538420000021
Figure FDA0003354538420000022
by expression of the stiffness, at the position of static equilibrium, the stiffness is made equal to
Figure FDA0003354538420000023
And the second derivative of stiffness is equal to
Figure FDA0003354538420000024
Figure FDA0003354538420000025
The condition of zero rigidity parameter, namely formula (4), can be obtained;
Figure FDA0003354538420000026
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 alpha of the transverse spring stiffness to the vertical spring stiffness; δ denotes the pre-compression length of the transverse spring; p is a radical of1And q is1Is an intermediate parameter variable;
(3) the zero-stiffness vibration isolation characteristic can be obtained by making the ratio alpha of the stiffness of the transverse spring to the stiffness of the vertical spring equal to 0.5 and the pre-compression length of the transverse spring equal to the horizontal length a of a single diagonal rod in the initial state.
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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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