CN202132428U - Nonlinear magnetic vibration isolator with para-zero rigidity - Google Patents

Abstract

The utility model discloses a nonlinear magnetic vibration isolator with para-zero rigidity, which comprises a vertically arranged linear spring (4) and is characterized in that: two linear guide rails (5) are respectively arranged on two opposite sides of the axis of the linear spring (4) and are on the same straight line; the straight line is orthogonal to the axis of the linear spring (4); the distance (h) from the top end of the linear spring to the intersection point (B) of the straight line and the axis of the linear spring (4) is smaller than the length of the linear spring; two fixed magnets (1) are fixed to each linear guide rail (5) and the two fixed magnets (1) have a distance; a sliding magnet (2) capable of sliding on the linear guide rails (5) is arranged between the two fixed magnets (1); the two poles of the sliding magnet (2) have the same polarity with the adjacent poles of the adjacent fixed magnets (1); and two ends of a connecting rod (3) are respectively articulated with the top ends of the sliding magnet (2) and the linear spring (4). The vibration isolator has large static rigidity but has small movable rigidity, thereby having good low-frequency vibration isolation effect; besides, the vibration isolator is compact in structure, light in weight and convenient to process; the magnetic force has no contact, so the mutual collision between mechanical structures is prevented; and no extra energy is added because the vibration isolator is a passive vibration isolation equipment.

Description

Non-linear magnetic force vibration isolator with accurate zero stiffness

Technical field

The present invention relates to be applicable to the magnetic force vibration isolator of low frequency or superlow frequency vibration isolating; This vibration isolator can be widely used in the middle of the vibrating isolation system of automobile, precision machine tool, surveying instrument, naval vessel, submarine, aerospace craft etc.

Background technique

Along with being growing more intense of expanding economy and social competition, people require increasingly high to the vibration isolation technique of some equipment.Yet those bad vibrations affect a lot of mechanical structures, make their normal operations run into problem, or the work of affect people's, make the people produce discomfort, or produce the problem of others.Latent sound property during such as the high-comfort requirement of, automobile, navigation of submarine, the proper functioning of high-precision surveying instrument etc., all more and more stricter to the requirement of vibration isolation.So, how to limit unnecessary vibration? Wherein most important also is that the modal method that is used for controlling bad vibration is to use passive vibration isolation equipment.Traditional linear system vibration isolator only exists (ω, ω _nBe respectively the natural frequency of energizing frequency and system) vibration isolating effect just arranged.In order to improve the low frequency vibration isolation effect, with regard to the natural frequency of necessary reduction system, this will cause the reduction of system stiffness.Yet the stiffness coefficient of spring is more little, and the off-position of being put it by the vibration isolation mass block moves can be very big, and we should move by little off-position like this, reach low frequency vibration isolation again simultaneously, just are difficult to realize.If can develop little static displacement and have the nonlinear spring of little dynamic rate,, just can reach the purpose of carrying out vibration isolation and can bear the bigger mass block of quality simultaneously again at low frequency with the natural frequency of effective reduction system.

Summary of the invention

The technical problem that the present invention will solve is; In the deficiency that exists aspect low frequency or the superlow frequency vibration isolating, propose a kind of non-linear magnetic force vibration isolator with accurate zero stiffness (QZS) to existing technology, this vibration isolator has bigger quiet rigidity and less dynamic rate; Thereby have good low frequency or a superlow frequency vibration isolating effect; And compact structure is simple, in light weight, and non-contact etc. are applicable to the vibration isolation of in comparing narrow space, carrying out vibration source.

Technological scheme of the present invention is; Said non-linear magnetic force vibration isolator with accurate zero stiffness comprises a vertically disposed Hookean spring; Its structural feature is; Respectively there are linear guide rail and this two linear rail in the relative both sides of the axis of said Hookean spring on same straight line, and said linear rail is with this Hookean spring orthogonal axe, and straight line arrives the length of the distance h on Hookean spring top less than this Hookean spring with the intersection points B of this Hookean spring axis; Be fixed with on each linear rail between two fixed magnets and this two fixed magnets spacing is arranged; Be provided with a sliding magnet that can on this linear rail, slide between two fixed magnets, the polarity of 2 liang of magnetic poles of sliding magnet is identical with the polarity of the adjacent pole of adjacent fixed magnet 1; The two ends of connecting rod are hinged with sliding magnet and Hookean spring top respectively; The linear rail of said Hookean spring one side and two fixed magnets and sliding magnet, connecting rod are symmetry axis and in a symmetrical arrangement with the linear rail of said Hookean spring opposite side and two fixed magnets and sliding magnet, connecting rod with said Hookean spring axis.

Below further specify what the present invention made.

Shown in Figure 1 is the original state of vibration isolator when not receiving any external force effect.The centre is a single line property spring 4, and its stiffness coefficient is k, and the length of connecting rod 3 is L.One end of two connecting rods 3 is connected at an A place with vertical Hookean spring 4.The other end of two connecting rods 3 is connected with two sliding magnets that are free to slide 2 respectively.When a suitable quality placed the A point by the vibration isolation mass block time, vertical linearity spring 4 is compressed, two connecting rods 3 promote corresponding sliding magnet 2 respectively and slide to linear rail 5 both sides of correspondence.Just made the A point arrive the B point by vibration isolation mass block pressure spring, at this moment, two connecting rods 3 just are positions in the horizontal direction.And this position is also just by the equilibrium position of vibration isolation mass block.Being supported by vertical linearity spring 4 fully at this moment by the weight of vibration isolation mass block, as shown in Figure 2.Under original state, a is the distance that sliding magnet 2 and B are ordered, and h is A point and B point distance.T be free to slide in the middle of being magnet left, part on the right side not Yi Dong the time leave the distance of original initial rest position.Connecting rod 3 is θ with the initial angle of linear rail 5 ₀In addition, α hereinafter, β are the magnetic force coefficients.The magnetic force coefficient records through experiment, does not elaborate herein.

Working principle of the present invention is (referring to Fig. 1 and Fig. 2), after being placed the A point by the vibration isolation mass block, arrives equilibrium position B point, as long as we select suitable systematic parameter; Make when the equilibrium position; The rigidity of whole system is zero, and when being done the small magnitude vibration in the equilibrium position by the vibration isolation mass block so, its dynamic stiffness is very little; The natural frequency of whole system is very low naturally, so can reach the purpose of low frequency vibration isolation.

As shown in Figure 1, the power f that whole system receives can be expressed as:

$f=2[\mathrm{\α}(\sqrt{L^2-{(h-x)}^2}-a)+\mathrm{\β}(\sqrt{L^2-{(h-x)}^2}-a{)}^3]\frac{h-x}{\sqrt{L^2-{(h-x)}^2}}+\mathrm{kx}---\left(1\right)$

If v=x-h, formula (1) can be expressed as so:

$f=2[\mathrm{\α}(\sqrt{L^2-v^2}-a)+\mathrm{\β}{(\sqrt{L^2-v^2}-a)}^3]\frac{-v}{\sqrt{L^2-v^2}}+k(v+h)---\left(2\right)$

The rigidity of whole system can draw through the differentiate to formula (2):

$K=6\mathrm{\&beta;}{v}^2+6\mathrm{a\&beta;}\sqrt{L^2-v^2}+k-2\mathrm{\&alpha;}-2\mathrm{\&beta;}{L}^2-6\mathrm{\&beta;}{a}^2-\frac{6\mathrm{a\&beta;}{v}^2}{\sqrt{L^2-v^2}}+\frac{2\mathrm{\&alpha;a}{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000072095060000011.png,HDA0000072095060000012.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+2\mathrm{\&beta;}{a}^3{L}^2}{{[L^2-v^2]}^{\frac{3}{2}}}---\left(3\right)$

When making v=0, K=0 can draw the rigidity and the magnetic force alpha of vertical linearity spring, β and the geometric parameter a of system, and the relation of L:

$k_{\mathrm{azs}}=2\mathrm{\&alpha;}+2\mathrm{\&beta;}{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000072095060000011.png,HDA0000072095060000012.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+6a^2\mathrm{\&beta;}-6\mathrm{a\&beta;L}-\frac{2\mathrm{a\&alpha;}}{L}-\frac{2a^3\mathrm{\&beta;}}{L}---\left(4\right)$

The rigidity of whole system can be expressed as:

$K_{\mathrm{azs}}=6\mathrm{\&beta;}{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA0000072095060000011.png,HDA0000072095060000012.png"\; state="\{\{state\}\}">v</figure-callout>}}^2+6\mathrm{a\&beta;}\sqrt{L^2-{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA0000072095060000011.png,HDA0000072095060000012.png"\; state="\{\{state\}\}">v</figure-callout>}}^2}+k_{\mathrm{azs}}-2\mathrm{\&alpha;}-2\mathrm{\&beta;}{L}^2-6\mathrm{\&beta;}{a}^2-\frac{6\mathrm{a\&beta;}{v}^2}{\sqrt{L^2-{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA0000072095060000011.png,HDA0000072095060000012.png"\; state="\{\{state\}\}">v</figure-callout>}}^2}}+\frac{2\mathrm{\&alpha;a}{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000072095060000011.png,HDA0000072095060000012.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+2\mathrm{\&beta;}{a}^3{L}^2}{{[L^2-v^2]}^{\frac{3}{2}}}---\left(5\right)$

According to the different values of vertical linearity spring, integral rigidity K is the function about displacement v, and is as shown in Figure 3.Here, system's geometric parameter and magnetic force coefficient value are following:

A=0.065 (m), h=0.03 (m), α=3404.4 (N/m) and β=8.1 * 10 ⁶(N/m ³)

As k＞k _AzsThe time, the negative stiffness that two connecting rods 3 are provided plays main effect in integral rigidity, and integral rigidity shows the negative stiffness characteristic near v=0; As k＜k _AzsThe time, integral rigidity all is positive rigidity, and only shows non-linearly weak; Has only the k=k of working as _AzsThe time, the rigidity value during v=0 is zero to total system in the equilibrium position.At this moment, the negative stiffness of two total systems that connecting rod offers is just offset with the positive rigidity of vertical linearity total system that spring offers.

When one suitable when being placed system by the vibration isolation mass block, two connecting rods 3 are just at horizontal position, and the system stiffness when the equilibrium position is zero, can be expressed as by the quality of vibration isolation mass block so:

$m=(2\mathrm{\&alpha;}+2\mathrm{\&beta;}{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000072095060000011.png,HDA0000072095060000012.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+6a^2\mathrm{\&beta;}-6\mathrm{a\&beta;L}-\frac{2\mathrm{a\&alpha;}}{L}-\frac{2a^3\mathrm{\&beta;}}{L})h/g---\left(6\right)$

Can know that from Fig. 4 a certain definite mass block will be by vibration isolation, we can select suitable geometric parameter, make system have the characteristic of accurate zero stiffness, thereby design the non-linear magnetic force vibration isolator with accurate zero stiffness.

Next the vibration isolating effect that will show the non-linear magnetic force vibration isolator of accurate zero stiffness.Because harmonic balance method has tangible simplicity and applicability when finding the solution strongly non-linear system, therefore, utilizes harmonic balance method (HB), the dynamic behavior of research strongly non-linear system calculates its transmissibility.

As harmonic excitation power f ₀When acting on by the vibration isolation mass block, the damping constant of system is c, and mass block can move up and down in the equilibrium position, and its nondimensional kinetic equations is:

$\stackrel{\&CenterDot;\&CenterDot;}{\hat{v}}+2\mathrm{\&zeta;}\stackrel{\&CenterDot;}{\hat{v}}+\mathrm{\&gamma;}{\hat{v}}^3=\hat{f}\cos \left({\mathrm{\&Omega;}}_{\mathrm{\&tau;}}\right)---\left(7\right)$

Wherein: $\hat{k}=\frac{1}{2}{K}_{\mathrm{Azs}}^{\&prime;\&prime;}\left(0\right),\hat{v}=\frac{v}{L},$ ${\mathrm{\&omega;}}_0^2=\frac{k_{\mathrm{Azs}}}{m},\mathrm{\&tau;}={\mathrm{\&omega;}}_{0}t,\mathrm{\&zeta;}=\frac{c{\mathrm{\&omega;}}_0}{2k_{\mathrm{Azs}}},\mathrm{\&Omega;}=\frac{\mathrm{\&omega;}}{{\mathrm{\&omega;}}_0},\mathrm{\&gamma;}=\frac{\hat{k}{L}^2}{k_{\mathrm{Azs}}},\hat{f}=\frac{f_0}{k_{\mathrm{Azs}}L},$

$\mathrm{\&gamma;}=\frac{6\mathrm{\&beta;}{L}^3-9\mathrm{a\&beta;}{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000072095060000011.png,HDA0000072095060000012.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+3(\mathrm{\&alpha;a}+\mathrm{\&beta;}{a}^3)}{2\mathrm{\&alpha;L}+2\mathrm{\&beta;}{\mathrm{<figure-callout\; id="3"\; label="L"\; filenames="HDA0000072095060000011.png,HDA0000072095060000012.png"\; state="\{\{state\}\}">L</figure-callout>}}^3+6{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="HDA0000072095060000011.png,HDA0000072095060000012.png"\; state="\{\{state\}\}">a</figure-callout>}}^2\mathrm{\&beta;L}-6\mathrm{a\&beta;}{L}^2-2\mathrm{a\&alpha;}-2a^3\mathrm{\&beta;}}.$

If separating of equation (7) is

So whole system through the power that the OZS vibration isolator passes to ground is:

$f_t=\mathrm{\&gamma;}{\hat{v}}^3+2\mathrm{\&zeta;}\stackrel{\&CenterDot;}{\hat{v}}=\mathrm{\&gamma;}{\mathrm{<figure-callout\; id="3"\; label="A"\; filenames="HDA0000072095060000011.png,HDA0000072095060000012.png"\; state="\{\{state\}\}">A</figure-callout>}}^3{\cos }^3({\mathrm{\&Omega;}}_{\mathrm{\&tau;}}+\mathrm{\&theta;})-2\mathrm{\&zeta;\&Omega;}A\sin ({\mathrm{\&Omega;}}_{\mathrm{\&tau;}}+\mathrm{\&theta;})---\left(8\right)$

The amplitude of power is:

$F_t=\sqrt{{\left(\frac{3}{4}\mathrm{\&gamma;}{A}^3\right)}^2+{\left(2\mathrm{\&zeta;\&Omega;A}\right)}^2}---\left(9\right)$

Being defined as of transmissibility: whole system passes to the ratio of amplitude of amplitude and excitation force of the power on ground.That is:

$\mathrm{\&eta;}=\frac{F_t}{\hat{f}}=\frac{\sqrt{{\left(\frac{3}{4}\mathrm{\&gamma;}{A}^3\right)}^2+{\left(2\mathrm{\&zeta;\&Omega;A}\right)}^2}}{\hat{f}}---\left(10\right)$

And the transmissibility of linear system is:

$T=\sqrt{\frac{1+4{\mathrm{\&zeta;}}^2{\mathrm{\&Omega;}}^2}{{(1-{\mathrm{\&Omega;}}^2)}^2+4{\mathrm{\&zeta;}}^2{\mathrm{\&Omega;}}^2}}---\left(11\right)$

Wherein:

is damping ratio.

Centrifugal force is coefficient

Can be clear that very that from Fig. 5 if we get suitable excitation force, it is much lower that the present invention begins the frequency ratio Hookean spring of vibration isolation, and the amplitude of transmissibility is also much lower than linear system, for low frequency or ultra-low frequency vibration isolation provide a kind of design method.

The utility model has the vibration isolator of accurate zero stiffness with permanent magnet and Hookean spring design, and the magnetic force that permanent magnet provided is non-linear.The geometrical construction of this vibration isolator is the greatest feature of our the accurate zero stiffness vibration isolator that designs, because it has embodied geometrical non-linearity.

Known that by above the present invention is a kind of non-linear magnetic force vibration isolator with accurate zero stiffness, it has bigger quiet rigidity and less dynamic rate; Thereby good low frequency or superlow frequency vibration isolating effect arranged; Big by the isolation frequency scope, be very easy to realize, and simple in structure, volume is little, in light weight, non-contact etc.; Also be convenient to fabrication and processing, be applicable to the vibration isolation of in comparing narrow space, carrying out vibration source.That is the present invention is for having the non-linear magnetic force vibration isolator of accurate zero stiffness (QZS), and it has solved the difficult problem of conventional linear vibrating isolation system when isolating low frequency or superlow frequency vibrating.

Description of drawings

Fig. 1 is the theory structure schematic representation of apparatus of the present invention;

Fig. 2 is that device shown in Figure 1 is put by the theory structure schematic representation of vibration isolation mass block;

Fig. 3 is as k＞k _Azs, k＜k _AzsAnd k=k _AzsThe time, the stiffness curve of total system;

Fig. 4 is by the quality of vibration isolation mass block and the geometric parameter a of system, the relation of h;

Fig. 5 is the comparison of transmissibility with non-linear magnetic force vibration isolator and linear system of accurate zero stiffness, and dotted line is represented the transmissibility of magnetic force vibration isolator power, and solid line is represented the transmissibility of linear system power.

In the drawings: the 1-fixed magnet, the 2-sliding magnet, the 3-connecting rod,

The 4-Hookean spring, the 5-linear rail.

Embodiment

Referring to Fig. 1; Said non-linear magnetic force vibration isolator with accurate zero stiffness comprises a vertically disposed Hookean spring 4; Respectively there are linear guide rail 5 and this two linear rail 5 in the relative both sides of the axis of said Hookean spring 4 on same straight line; Said straight line is with these Hookean spring 4 orthogonal axes, straight line with the intersection points B of these Hookean spring 4 axis to the distance h on Hookean spring top length (length of Hookean spring is meant the distance between the Hookean spring two ends) less than this Hookean spring; Be fixed with on each linear rail 5 between two fixed magnets 1 and this two fixed magnets 1 spacing is arranged; Be provided with a sliding magnet 2 that can on this linear rail 5, slide between two fixed magnets 1, the polarity of 2 liang of magnetic poles of sliding magnet is identical with the polarity of the adjacent pole of adjacent fixed magnet 1; The two ends of connecting rod 3 are hinged with sliding magnet 2 and Hookean spring 4 tops respectively; The linear rail 5 of said Hookean spring 4 one sides and two fixed magnets 1 and sliding magnet 2, connecting rod 3 are symmetry axis and in a symmetrical arrangement with the linear rail 5 of said Hookean spring 4 opposite sides and two fixed magnets 1 and sliding magnet 2, connecting rod 3 with said Hookean spring 4 axis.

Device is used for low frequency or ultra-low frequency vibration isolation; The geometrical construction that is designed has geometrical non-linearity.

Employed magnet (each fixed magnet 1 with sliding magnet 2) preferably adopts ndfeb magnet, and (be commonly called as: strong magnetic), it is in the middle of all magnet in the market, and performance is the highest, and in the price, intensity is good.

For a certain definite vibration source (such as: the motor on the submarine) will be by vibration isolation; We will know earlier how many its quality is, confirm magnetic force alpha, β through experiment then; Geometric parameter a through adjust system; L makes formula (4) set up, and has so just obtained having the non-linear magnetic force vibration isolator of accurate zero stiffness.Be positioned over vibration source on the vibrating isolation system at last, vibration source is when work, and the bad vibration that it produces has been realized the purpose of vibration isolation by the vibration isolator vibration damping.

Claims (1)

1. non-linear magnetic force vibration isolator with accurate zero stiffness; Comprise a vertically disposed Hookean spring (4); It is characterized in that; Respectively there are linear guide rail (5) and this two linear rail (5) in the relative both sides of axis of said Hookean spring (4) on same straight line, and said straight line is with this Hookean spring (4) orthogonal axe, and straight line arrives the length of the distance (h) on Hookean spring top less than this Hookean spring with the intersection point (B) of this Hookean spring (4) axis; Be fixed with on each linear rail (5) between two fixed magnets (1) and this two fixed magnets (1) spacing is arranged; Be provided with a sliding magnet (2) that can on this linear rail (5), slide between two fixed magnets (1), the polarity of sliding magnet (2) two magnetic poles is identical with the polarity of the adjacent pole of adjacent fixed magnet (1); Same respectively sliding magnets in the two ends of connecting rod (3) (2) and Hookean spring (4) top are hinged; The linear rail (5) of said Hookean spring (4) one sides and two fixed magnets (1) and sliding magnet (2), connecting rod (3) are symmetry axis and in a symmetrical arrangement with the linear rail (5) of said Hookean spring (4) opposite side and two fixed magnets (1) and sliding magnet (2), connecting rod (3) with said Hookean spring (4) axis.

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