CN203641365U - Quasi zero stiffness vibration isolator - Google Patents

Abstract

The utility model discloses a quasi zero stiffness vibration isolator. The quasi zero stiffness vibration isolator is characterized in that resilience is supplied by four horizontal springs and one vertical spring, and a horizontal moving device and a vertical moving device are connected through a roller-cam device to form a nonlinear geometric mechanism; the stiffness of a system at the static equilibrium position is enabled to be zero by reasonably designing the stiffness coefficient of the vertical spring and the horizontal springs and regulating the amount of compression of the horizontal springs, so that low or ultra-low frequency vibration isolation can be realized. The vibration isolator features in large static stiffness and small dynamic stiffness, the ratio of the static stiffness to the dynamic stiffness is low, the low frequency vibration isolation can be realized, and heavier equipment can be borne; the quasi zero stiffness vibration isolator is simple in structure, convenient to process and manufacture and easy to implement engineering.

Description

A kind of accurate zero stiffness vibration isolator

Technical field

The utility model relates to a kind of low frequency or ultralow frequency nonlinear isolation device, this vibration isolator, all there being good effect aspect power vibration isolation, motional vibration isolation, can be widely used in the vibrating isolation system of automobile, precision machine tool, surveying instrument, naval vessel, submarine, aerospace craft etc.

Background technique

Along with the high speed development of engineering science technology and the lifting at full speed of people's living standard, people require more and more higher to the vibration isolation technique of some equipment.Under many circumstances, vibration is considered to negative factor.For example, vibration can affect the function of precision instrument and equipment, reduces machining accuracy, aggravates the tired and wearing and tearing of member, thereby shortens the working life of its structure.Vibration also may cause that the large deformation of structure destroys, and some bridges are once because of vibration disrepair; The flutter of aircraft wing, the buffeting of wheel often cause the accident; The deteriorated carrying condition of vibration meeting in car, ship and cabin.So, how to suppress the vibration of these passivenesses? modal method is to use passive vibration isolation equipment.Traditional linear vibrating isolation system only has and is greater than when the ratio of energizing frequency and system frequency

time just have a vibration isolating effect.Therefore, linear vibrating isolation system need reduce self natural frequency can isolate low-frequency excitation, and usual way is to reduce system stiffness.But rigidity is crossed young pathbreaker and is caused that off-position moves past greatly, system is unstable.

Model utility content

Technical problem to be solved in the utility model is, for prior art deficiency, provides a kind of and has enough large quiet rigidity and support by device for vibration insutation, accurate zero stiffness vibration isolator that vibration isolating effect is good.

For solving the problems of the technologies described above, the technological scheme that the utility model adopts is: a kind of accurate zero stiffness vibration isolator, comprise supporting base, described supporting base middle part is provided with the vertically linear bearing through described supporting base, described linear bearing is enclosed within on a central shaft bottom mobile under can in the vertical direction, and described central shaft top is fixed with for placing by the upper backup pad of device for vibration insutation by support block; On the central shaft of described support block below, the regulating block that can move up and down along described central shaft is installed, described regulating block lower surface is connected with the uprighting spring top being enclosed within on described central shaft, and described uprighting spring bottom is connected with described linear bearing upper end; On the supporting base in described central shaft left side, be fixed with cushion block; On described cushion block, linear rail is installed; Described linear rail is fixed with fixed base away from one end of described central shaft, and described linear rail is provided with the sliding seat that can move horizontally along described linear rail near one end of described central shaft; Between described fixed base and described sliding seat, be connected by horizontal spring; Described sliding seat is provided with roller near a side of described central shaft; The upper backup pad lower surface in described central shaft left side is fixedly connected with baffle plate one end, and the cam of outer surface and described roller contact is installed on described baffle plate; The symmetrical configuration of the described central shaft left and right sides.

On the fixed base on described central shaft left side or right side and sliding seat, be respectively fixed with a spring fastenings, and the spring fastenings on described fixed base is relative with the spring fastenings position on described sliding seat, described horizontal spring two ends are connected with two spring fastenings respectively.

Cushion block is fixed with vertical support block away from one end of described central shaft, is fixed with the Level tune axle vertical with described vertical support block on described vertical support block, described Level tune axle one end and fixed base one side contacts near this Level tune axle.

On the cushion block of the described central shaft left and right sides, be respectively provided with two fixed bases and two sliding seats.

Horizontal spring parameter between each fixed base and the sliding seat of the described central shaft left and right sides is identical.

Compared with prior art, the beneficial effect that the utility model has is: accurate zero stiffness vibration isolator of the present utility model has enough large quiet rigidity to be supported by device for vibration insutation, simultaneously, when system is vibrated near equipoise, dynamic stiffness is very low, equipoise place dynamic stiffness is even zero, therefore, the utility model is very suitable for low frequency, superlow frequency vibration isolating even.The utility model vibration isolator has large quiet rigidity petty action rigidity characteristic, and springrate ratio is very low, not only can realize low frequency vibration isolation, also can bear larger weight of equipment, and simple in structure, convenient processing and manufacture, is easy to realize through engineering approaches.

Accompanying drawing explanation

Fig. 1 is the utility model one example structure sketch;

Fig. 2 is the utility model one example structure schematic diagram;

Fig. 3 puts by the theory structure schematic diagram after device for vibration insutation for Fig. 2 shown device;

Fig. 4 is the relation curve of the utility model one embodiment's horizontal spring pre compressed magnitude and accurate zero stiffness system dimensionless rigidity;

Fig. 5 is for the utility model vibration isolator of power excitation and the transmissibility comparison diagram of equivalent linear system;

Fig. 6 is the displacement transmissibility comparison diagram for the utility model vibration isolator of foundation displacement excitation and equivalent linear system.

Embodiment

As depicted in figs. 1 and 2, the utility model one embodiment comprises supporting base 11, described supporting base 11 middle parts are provided with the vertically linear bearing 15 through described supporting base 11, described linear bearing 15 is enclosed within on central shaft 16 bottoms mobile under can in the vertical direction, and described central shaft 16 tops are fixed with for placing by the upper backup pad 7 of device for vibration insutation by support block 8; The regulating block 18 that can move up and down along described central shaft 16 is installed on the central shaft 16 of described support block 8 belows, described regulating block 18 lower surfaces are connected with uprighting spring 14 tops that are enclosed within on described central shaft 16, and described uprighting spring 14 bottoms are connected with described linear bearing 15 upper ends; On the supporting base 11 in described central shaft 16 left sides, be fixed with cushion block 12; On described cushion block 12, linear rail 13 is installed; Described linear rail 13 is fixed with fixed base 1 away from one end of described central shaft 16, and described linear rail 13 is provided with the sliding seat 4 that can move horizontally along described linear rail 13 near one end of described central shaft 16; Between described fixed base 1 and described sliding seat 4, be connected by horizontal spring 3; Described sliding seat 4 is provided with roller 5 near a side of described central shaft 16; Upper backup pad 7 lower surfaces in described central shaft 16 left sides are fixedly connected with baffle plate 17 one end, and the cam 6 that outer surface contacts with described roller 5 is installed on described baffle plate 17; The symmetrical configuration of described central shaft 16 left and right sides.

On the fixed base 1 on described central shaft 16 left sides or right side and sliding seat 4, be respectively fixed with a spring fastenings 2, and the spring fastenings 2 on described fixed base 1 is relative with spring fastenings 2 positions on described sliding seat 4, described horizontal spring 3 two ends are connected with two spring fastenings 2 respectively.

Cushion block 12 is fixed with vertical support block 9 away from one end of described central shaft 16, on described vertical support block 9, be fixed with the Level tune axle 10 vertical with described vertical support block 9, described Level tune axle 10 one end and fixed base 1 one side contacts near this Level tune axle 10.

On the cushion block 12 of described central shaft 16 left and right sides, be respectively provided with two fixed bases 1 and two sliding seats 4.

In the present embodiment, the parameter that has 3, four horizontal springs 3 of four horizontal springs is identical.

In the present embodiment, central shaft 16 is Bearing Steel optical axis; On linear bearing 15, with flange, conveniently install.

The present embodiment working principle is as follows: the rigidity of uprighting spring 14 is k _v, roller 5 radiuses are r ₁, cam 6 radiuses are r ₂, roller 5 is fixed on sliding seat 4, and cam 6 is fixed on baffle plate 17, and roller 5 is α with the line at cam 6 centers and the initial angle of horizontal plane, and between support block 8 and regulating block 18, reserved certain distance is for regulating the decrement of uprighting spring 14.When be placed on upper backup pad 7 by device for vibration insutation, uprighting spring 14 is compressed, the sliding seat 4 of cam 6 pushing rolling wheels 5 slides to corresponding linear rail 13 both sides, by support block 8 and regulating block 18, the position in central shaft 16 can adjustment cam 6 move up and down, keep roller 5 and cam 6 centers in same level, this position is just by the equipoise of device for vibration insutation, now, supported by uprighting spring 14 completely by the weight of device for vibration insutation, as shown in Figure 3.

In the time that load capacity changes, can make upper backup pad 7, baffle plate 17, cam 6 move on the whole or move down by adjusting the position of regulating block 18 in central shaft 16, thus make by device for vibration insutation be placed on upper backup pad 7 rear roller 5 with the center of cam 6 in same level.

When by device for vibration insutation low-frequency vibration, shaking platform moves up and down, thereby cam 6 moves up and down, because horizontal precompression exists all the time, roller 5 remains and contacts with cam 6, roller 5 is fixed on sliding seat 4, can only on linear rail 13, horizontally slip by along continuous straight runs, so roller 5 can only be close to cam 6 curved surface circular arc side-to-side vibrations.

Working principle of the present utility model is (referring to Fig. 2 and Fig. 3), when by device for vibration insutation as for upper backup pad 7 on after, while reaching equilibrium position, as long as select suitable systematic parameter, the rigidity that makes whole system is zero, and while vibration in equilibrium position by device for vibration insutation so, dynamic stiffness is very little, the natural frequency of whole system is naturally very low, so can reach the object of low frequency vibration isolation.

Aiming at zero stiffness vibration isolator sets up mathematical model and carries out static analysis (referring to Fig. 1):

The rigidity of uprighting spring is k _v, the rigidity of horizontal spring is k _h.The radius of roller is r ₁, cam radius is r ₂.Equipoise place, the decrement of uprighting spring is △ x=Mg/k _v, horizontal spring decrement is δ.Under the effect of power f (x) in the vertical direction, when by device for vibration insutation M, displacement x is satisfied in vertical direction

time, roller and cam keep in touch, and f (x) with the relation of x is

f(x)=Mg-f _v-4f _htanα (1)

Wherein f _v=k _v(△ x-x), f _h=k _h[δ-(r ₁+ r ₂) (1-cos α)],

$\tan \mathrm{\&alpha;}=x/\sqrt{{({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2)}^2-x^2}.$

The relation of power and displacement can further be written as

$f\left(x\right)=k_{v}x-4k_{h}x[1+\frac{\mathrm{\&delta;}-(r_1+r_2)}{\sqrt{{(r_1+r_2)}^2-x^2}}]---\left(2\right)$

For designing accurate zero stiffness vibration isolator, suppose near quality little displacement vibration equilibrium position,

| x|<x _d, order

with

restoring force can be expressed as Dimensionless Form

$\stackrel{\&OverBar;}{f}\left(\stackrel{\&OverBar;}{x}\right)=\stackrel{\&OverBar;}{x}-4\mathrm{\&beta;}\stackrel{\&OverBar;}{x}[1+\frac{\stackrel{\&OverBar;}{\mathrm{\&delta;}}-1}{\sqrt{1-{\stackrel{\&OverBar;}{x}}^2}}]---\left(3\right)$

Wherein

and β=k _h/ k _v.To above-mentioned equation about

differentiate can obtain the dimensionless rigidity of system

$\stackrel{\&OverBar;}{K}=1-4\mathrm{\&beta;}[1+\frac{\stackrel{\&OverBar;}{\mathrm{\&delta;}}-1}{{(1-{\stackrel{\&OverBar;}{x}}^2)}^{3/2}}]---\left(4\right)$

As can be seen from the above equation, when parameter beta and while meeting certain relation, vibration isolator will produce zero stiffness in equilibrium position.Order

can obtain accurate zero stiffness condition

${\stackrel{\&OverBar;}{\mathrm{\&delta;}}}_{\mathrm{QZS}}=\frac{1}{4\mathrm{\&beta;}}---\left(5\right)$

Meet the force-displacement relationship of accurate zero stiffness vibrating isolation system

${\stackrel{\&OverBar;}{f}}_{\mathrm{QZS}}\left(\stackrel{\&OverBar;}{x}\right)=\stackrel{\&OverBar;}{x}[1-\frac{1}{{\stackrel{\&OverBar;}{\mathrm{\&delta;}}}_{\mathrm{QZS}}}(1+\frac{{\stackrel{\&OverBar;}{\mathrm{\&delta;}}}_{\mathrm{QZS}}-1}{\sqrt{1-{\stackrel{\&OverBar;}{x}}^2}})]---\left(6\right)$

The system stiffness that meets accurate zero stiffness condition is

${\stackrel{\&OverBar;}{K}}_{\mathrm{QZS}}=1-\frac{1}{{\stackrel{\&OverBar;}{\mathrm{\&delta;}}}_{\mathrm{QZS}}}[1+\frac{{\stackrel{\&OverBar;}{\mathrm{\&delta;}}}_{\mathrm{QZS}}-1}{{(1-{\stackrel{\&OverBar;}{x}}^2)}^{3/2}}]---\left(7\right)$

For convenience of follow-up driving force Epidemiological Analysis, force-displacement relationship formula (6) is carried out to Taylor expansion at equilibrium position place, formula (6) can approximate representation be

${\stackrel{\&OverBar;}{f}}_{\mathrm{QZS}}^a\left(\stackrel{\&OverBar;}{x}\right)=\mathrm{\&gamma;}{\stackrel{\&OverBar;}{x}}^3---\left(8\right)$

Wherein $\mathrm{\&gamma;}=(1-{\stackrel{\&OverBar;}{\mathrm{\&delta;}}}_{\mathrm{QZS}})/\left(2{\stackrel{\&OverBar;}{\mathrm{\&delta;}}}_{\mathrm{QZS}}\right).$

Dimensionless rigidity

curve as shown in Figure 4.When

time

it is larger,

curve is more smooth, larger between little stiffness region.

Dimensionless rigidity

only depend on

the i.e. decrement of horizontal spring and the ratio of two-wheeled radius sum in the time that roller and cam center are in same level

irrelevant with the absolute size in wheel footpath.The amplitude that quality moves up and down is relevant with wheel footpath, and wheel footpath is less, stronger to the receptance of little displacement, largest motion amplitude $x_d=\sqrt{r_2(2{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2).}$

In the time being placed on vibration isolator by device for vibration insutation, to produce quiet distortion, make after quiet distortion by vibration isolation quality in equilibrium position, can complete by regulating block, therefore,, for the equipment of any quality, all can pass through design system parameter, make system there is the characteristic of accurate zero stiffness, thereby realize low frequency vibration isolation.

Show the effect of this accurate zero stiffness vibration isolator aspect power vibration isolation and motional vibration isolation below.

Power vibration isolation is defined as: reduce vibrating machine to basic effect.As harmonic excitation power F ₀sin ω ₀when t acts on by vibration isolation mass block, the damping constant of system is c, and mass block can move up and down in equilibrium position, when

time, its nondimensional kinetic equations is:

$M\stackrel{\&CenterDot;\&CenterDot;}{x}+c\stackrel{\&CenterDot;}{x}+k_{v}x-2k_{h}x[1+\frac{\mathrm{\&delta;}-({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2)}{\sqrt{{({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2)}^2-x^2}}]=F_o\mathrm{sim\&omega;t}---\left(9\right)$

Wherein $\stackrel{\&OverBar;}{x}=\frac{x}{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_2},{\stackrel{\&OverBar;}{x}}_d=\frac{\sqrt{r_2(2{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2)}}{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_2},{\stackrel{\&OverBar;}{F}}_0=\frac{F_0}{k_v({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2)},\stackrel{\&OverBar;}{t}=\sqrt{\frac{k_v}{M}}t,\mathrm{\&Omega;}=\frac{\mathrm{\&omega;}}{\sqrt{k_v/M}},$

by accurate zero stiffness condition

in kinetic equations described in substitution (9),

${\stackrel{\&OverBar;}{x}}^{\&prime;\&prime;}+2\mathrm{\&zeta;}{\stackrel{\&OverBar;}{x}}^{\&prime;}+[1-\frac{1}{{\stackrel{\&OverBar;}{\mathrm{\&delta;}}}_{\mathrm{QZS}}}(1+\frac{{\stackrel{\&OverBar;}{\mathrm{\&delta;}}}_{\mathrm{QZS}}-1}{\sqrt{1-{\stackrel{\&OverBar;}{x}}^2}})]\stackrel{\&OverBar;}{x}={\stackrel{\&OverBar;}{F}}_0\sin \mathrm{\&Omega;}\stackrel{\&OverBar;}{t}---\left(10\right)$

As previously mentioned, the representation of restoring force can be approximated to a cube function (8), so kinetic equations can be approximated by

${\stackrel{\&OverBar;}{x}}^{\&prime;\&prime;}+2\mathrm{\&zeta;}{\stackrel{\&OverBar;}{x}}^{\&prime;}+\mathrm{\&gamma;}{\stackrel{\&OverBar;}{x}}^3={\stackrel{\&OverBar;}{F}}_0\sin \mathrm{\&Omega;}\stackrel{\&OverBar;}{t}---\left(11\right)$

If the solution of equation (11) is:

$\stackrel{\&OverBar;}{x}=A\sin (\mathrm{\&Omega;}\stackrel{\&OverBar;}{t}+\mathrm{\&phi;})---\left(12\right)$

Wherein, A refers to the dimensionless amplitude of system cycle response.By formula (12) substitution motion equation (11), application harmonic balance method obtains amplitude-frequency and phase frequency relation

${[-{\mathrm{\&Omega;}}^{2}A+\frac{3}{4}\mathrm{\&gamma;}{A}^3]}^2+{\left(2\mathrm{\&zeta;\&Omega;A}\right)}^2={\stackrel{\&OverBar;}{F}}_0^2---\left(13\right)$

Suppose that basic harmonic response occupies an leading position, being delivered to basic power can be expressed as

$\begin{array}{c}{f}_T\left(\stackrel{\&OverBar;}{t}\right)=2\mathrm{\&zeta;\&Omega;}A\cos (\mathrm{\&Omega;}\stackrel{\&OverBar;}{t}+\mathrm{\&phi;})+\mathrm{\&gamma;}{A}^3{\sin }^3(\mathrm{\&Omega;}\stackrel{\&OverBar;}{t}+\mathrm{\&phi;})\\ \&ap;2\mathrm{\&zeta;\&Omega;}A\cos (\mathrm{\&Omega;}\stackrel{\&OverBar;}{t}+\mathrm{\&phi;})+\frac{3}{4}\mathrm{\&gamma;}{A}^3\sin (\mathrm{\&Omega;}\stackrel{\&OverBar;}{t}+\mathrm{\&phi;})\end{array}---\left(14\right)$

Wherein φ is phase angle.Transmissibility is defined as: whole system passes to the ratio of the amplitude of power and the amplitude of excitation force on ground.Can be expressed as

$T=20\mathrm{lo}{g}_{10}\left(\sqrt{\frac{\frac{9}{16}{\mathrm{\&gamma;}}^2{A}^6+{\left(2\mathrm{\&zeta;\&Omega;}\right)}^2{A}^2}{{\stackrel{\&OverBar;}{F}}_0^2}}\right)---\left(15\right)$

And the transmissibility of linear system is:

$T=\sqrt{\frac{1+4{\mathrm{\&zeta;}}^2{\mathrm{\&Omega;}}^2}{{(1-{\mathrm{\&Omega;}}^2)}^2+4{\mathrm{\&zeta;}}^2{\mathrm{\&Omega;}}^2}}---\left(16\right)$

Wherein: ζ is damping ratio.ζ=0.1, excitation force is

coefficient gamma=0.0556.

Can clearly be seen that from Fig. 5, δ=0.9 o'clock vibration isolating effect is best, if we get suitable horizontal spring pre compressed magnitude and excitation force, it is much lower that the utility model starts the frequency ratio Hookean spring of vibration isolation, and the amplitude of transmissibility is also much lower than equivalent linear system.

The definition of motional vibration isolation is: precision optical machinery, instrument, instrument will prevent the vibration of transmitting from basis.For displacement excitation, first need to determine its weight, then determine the stiffness coefficient of spring, finally adjust front and back position and the upper-lower position of regulating block in central shaft of Level tune axle, making horizontal spring pre compressed magnitude meet formula (5) sets up, just can obtain having the low frequency vibration isolation device of accurate zero stiffness, will weaken the vibration of foundation affects equipment, has realized the object of motional vibration isolation.Refer to the amplitude of basic excitation at simple harmonic quantity basic excitation y=Ysin ω t(Y) effect under, moved up and down in equipoise by device for vibration insutation, its displacement is x, makes z=x-y, motion equation can be write:

$M\stackrel{\&CenterDot;\&CenterDot;}{z}+x\stackrel{\&CenterDot;}{z}+f\left(z\right)=-M\stackrel{\&CenterDot;\&CenterDot;}{y}---\left(17\right)$

Wherein c is damping constant, and f (z) is shown in formula (2).Order $\stackrel{\&OverBar;}{z}=z/({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+r_2),\stackrel{\&OverBar;}{Y}=Y/{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA0000453972590000022.png,HDA0000453972590000031.png"\; state="\{\{state\}\}">r</figure-callout>}}_2,\stackrel{\&OverBar;}{t}=t\sqrt{k_v/M},$

by formula (5) substitution formula (17), the motion equation of accurate zero stiffness vibration isolator is

${\stackrel{\&OverBar;}{z}}^{\&prime;\&prime;}+2\mathrm{\&zeta;}{\stackrel{\&OverBar;}{z}}^{\&prime;}+{\stackrel{\&OverBar;}{f}}_{\mathrm{QZS}}\left(\stackrel{\&OverBar;}{z}\right)={\mathrm{\&Omega;}}^2\stackrel{\&OverBar;}{Y}\sin \mathrm{\&Omega;}\stackrel{\&OverBar;}{t}---\left(18\right)$

Wherein symbol () ' expression is about independent variable

derivative,

see formula (6).Because formula (6) can have simple formula (8) approximate, therefore motion equation can be write as approx:

${\stackrel{\&OverBar;}{z}}^{\&prime;\&prime;}+2\mathrm{\&zeta;}{\stackrel{\&OverBar;}{z}}^{\&prime;}+{\stackrel{\&OverBar;}{f}}_{\mathrm{QZS}}^a\left(\stackrel{\&OverBar;}{z}\right)={\mathrm{\&Omega;}}^2\stackrel{\&OverBar;}{Y}\sin \mathrm{\&Omega;}\stackrel{\&OverBar;}{t}---\left(19\right)$

Supposing the system vibration frequency is dominated by harmonic excitation frequency, and so, the periodic solution of system can be made as:

$\stackrel{\&OverBar;}{z}=A\cos (\mathrm{\&Omega;}\stackrel{\&OverBar;}{t}-\mathrm{\&theta;})---\left(20\right)$

Wherein A refers to the dimensionless amplitude of system cycle response.By formula (20) substitution motion equation (19), application harmonic balance method is tried to achieve amplitude-frequency and phase frequency relation:

${[{\mathrm{\&Omega;}}^{2}A-\frac{3}{4}\mathrm{\&gamma;}{A}^3]}^2+{\left(2\mathrm{\&zeta;A\&Omega;}\right)}^2={\mathrm{\&Omega;}}^4{\stackrel{\&OverBar;}{Y}}^2---\left(21\right)$

$\sin \mathrm{\&theta;}=\frac{\frac{3}{4}\mathrm{\&gamma;}{A}^3-{\mathrm{A\&Omega;}}^2}{\stackrel{\&OverBar;}{Y}{\mathrm{\&Omega;}}^2}---\left(22\right)$

Displacement transmissibility so can be expressed as

$\begin{array}{c}T=\frac{\left|x\right|}{\left|y\right|}=\frac{\sqrt{{(A+\stackrel{\&OverBar;}{Y}\sin \mathrm{\&theta;})}^2+{\left(\stackrel{\&OverBar;}{Y}\cos \mathrm{\&theta;}\right)}^2}}{\stackrel{\&OverBar;}{Y}}\\ =\sqrt{1+{\left(\frac{A}{\stackrel{\&OverBar;}{Y}}\right)}^2+2{\left(\frac{A}{\stackrel{\&OverBar;}{Y}}\right)}^2\&times;\frac{\frac{3}{4}\mathrm{\&gamma;}{A}^2-{\mathrm{\&Omega;}}^2}{{\mathrm{\&Omega;}}^2}}\end{array}---\left(23\right)$

Wherein: ζ is damping ratio.ζ=0.1, δ=0.9, coefficient gamma=0.0556.

As can be seen from Figure 6, for not too large basic excitation, the utility model can be realized low frequency vibration isolation, and transmissibility is more much lower than corresponding linear system.Reach the object of motional vibration isolation.

Claims (5)

1. an accurate zero stiffness vibration isolator, comprise supporting base (11), it is characterized in that, described supporting base (11) middle part is provided with the vertically linear bearing (15) through described supporting base (11), described linear bearing (15) is enclosed within on central shaft (16) bottom mobile under can in the vertical direction, and described central shaft (16) top is fixed with for placing by the upper backup pad of device for vibration insutation (7) by support block (8); On the central shaft (16) of described support block (8) below, the regulating block (18) that can move up and down along described central shaft (16) is installed, described regulating block (18) lower surface is connected with uprighting spring (14) top being enclosed within on described central shaft (16), and described uprighting spring (14) bottom is connected with described linear bearing (15) upper end; On the supporting base (11) in described central shaft (16) left side, be fixed with cushion block (12); Linear rail (13) is installed on described cushion block (12); Described linear rail (13) is fixed with fixed base (1) away from one end of described central shaft (16), and described linear rail (13) is provided with the sliding seat (4) that can move horizontally along described linear rail (13) near one end of described central shaft (16); Between described fixed base (1) and described sliding seat (4), be connected by horizontal spring (3); Described sliding seat (4) is provided with roller (5) near a side of described central shaft (16); Upper backup pad (7) lower surface in described central shaft (16) left side is fixedly connected with baffle plate (17) one end, and the cam (6) that outer surface contacts with described roller (5) is installed on described baffle plate (17); The symmetrical configuration of described central shaft (16) left and right sides.

2. accurate zero stiffness vibration isolator according to claim 1, it is characterized in that, on the fixed base (1) on described central shaft (16) left side or right side and sliding seat (4), be respectively fixed with a spring fastenings (2), and the spring fastenings (2) on described fixed base (1) is relative with spring fastenings (2) position on described sliding seat (4), and described horizontal spring (3) two ends are connected with two spring fastenings (2) respectively.

3. accurate zero stiffness vibration isolator according to claim 1, it is characterized in that, described cushion block (12) is fixed with vertical support block (9) away from one end of described central shaft (16), on described vertical support block (9), be fixed with the Level tune axle (10) vertical with described vertical support block (9), described Level tune axle (10) one end and fixed base (1) one side contacts near this Level tune axle (10).

4. according to the accurate zero stiffness vibration isolator one of claim 1～3 Suo Shu, it is characterized in that, on the cushion block (12) of described central shaft (16) left and right sides, be respectively provided with two fixed bases (1) and two sliding seats (4).

5. accurate zero stiffness vibration isolator according to claim 4, is characterized in that, horizontal spring (3) parameter between each fixed base (1) and the sliding seat (4) of described central shaft (16) left and right sides is identical.

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