CN116329061A - Method for constructing extremely low frequency micro mechanical resonator harmonic by utilizing combined potential field - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 28
- 230000005484 gravity Effects 0.000 claims abstract description 22
- 238000005339 levitation Methods 0.000 claims description 20
- 239000000725 suspension Substances 0.000 claims description 20
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 claims description 17
- 229910002804 graphite Inorganic materials 0.000 claims description 17
- 239000010439 graphite Substances 0.000 claims description 17
- 230000005415 magnetization Effects 0.000 claims description 13
- 229910052771 Terbium Inorganic materials 0.000 claims description 11
- GZCRRIHWUXGPOV-UHFFFAOYSA-N terbium atom Chemical compound [Tb] GZCRRIHWUXGPOV-UHFFFAOYSA-N 0.000 claims description 11
- 229920003229 poly(methyl methacrylate) Polymers 0.000 claims description 10
- 239000004926 polymethyl methacrylate Substances 0.000 claims description 10
- 229910001172 neodymium magnet Inorganic materials 0.000 claims description 9
- 230000005298 paramagnetic effect Effects 0.000 claims description 8
- 230000005294 ferromagnetic effect Effects 0.000 claims description 7
- 239000003365 glass fiber Substances 0.000 claims description 7
- QJVKUMXDEUEQLH-UHFFFAOYSA-N [B].[Fe].[Nd] Chemical compound [B].[Fe].[Nd] QJVKUMXDEUEQLH-UHFFFAOYSA-N 0.000 claims description 5
- 230000005292 diamagnetic effect Effects 0.000 claims description 4
- 239000000463 material Substances 0.000 claims description 4
- 229910000828 alnico Inorganic materials 0.000 claims description 3
- KPLQYGBQNPPQGA-UHFFFAOYSA-N cobalt samarium Chemical compound [Co].[Sm] KPLQYGBQNPPQGA-UHFFFAOYSA-N 0.000 claims description 3
- 238000010276 construction Methods 0.000 claims description 3
- 229910000938 samarium–cobalt magnet Inorganic materials 0.000 claims description 3
- 238000001514 detection method Methods 0.000 abstract description 3
- 230000005291 magnetic effect Effects 0.000 description 57
- BGPVFRJUHWVFKM-UHFFFAOYSA-N N1=C2C=CC=CC2=[N+]([O-])C1(CC1)CCC21N=C1C=CC=CC1=[N+]2[O-] Chemical compound N1=C2C=CC=CC2=[N+]([O-])C1(CC1)CCC21N=C1C=CC=CC1=[N+]2[O-] BGPVFRJUHWVFKM-UHFFFAOYSA-N 0.000 description 10
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- 230000001133 acceleration Effects 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 238000013461 design Methods 0.000 description 2
- 238000005040 ion trap Methods 0.000 description 2
- 229910052751 metal Inorganic materials 0.000 description 2
- 239000002184 metal Substances 0.000 description 2
- 238000012576 optical tweezer Methods 0.000 description 2
- 230000035699 permeability Effects 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 239000000126 substance Substances 0.000 description 2
- 230000009471 action Effects 0.000 description 1
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Abstract
The invention provides a method for constructing ultra-low frequency micro mechanical resonator harmonic by utilizing combined potential fields, which solves the problems that the vertical frequency of a conventional micro mechanical vibrator system is above 10Hz and the ultra-low frequency detection of a mechanical harmonic oscillator system is limited, and comprises the following main steps: s1, constructing a mechanical vibrator; s2, constructing a corresponding xyz three-axis system by taking the gravity direction of the vibrator as a z axis, and introducing a first potential field U 1 And solving the eigenvalue of the vibrator in the z-axis direction, wherein U 1 The force on the z-axis of the vibrator is equal to the gravity of the vibrator, U 1 The second derivatives on the three axes are all larger than 0; s3, at U 1 On the basis of (1) introducing an independent second potential field U 2 The intrinsic frequency of the vibrator z axis is reduced, a total potential field U is formed, the intrinsic frequency of the vibrator z axis at the moment is solved, the force of U on the vibrator z axis is equal to the gravity of the vibrator, the second derivative of U on the triaxial is larger than 0, and meanwhile, the requirement of U is met 2 The force on the vibrator in the z-axis direction is far smaller than U 1 Force on vibrator z-axis.
Description
Technical Field
The invention relates to the field of mechanical harmonic oscillator systems, in particular to a method for constructing extremely low-frequency miniature mechanical resonator harmonic by utilizing a combined potential field.
Background
The mechanical vibrator is a common high-sensitivity force measurement or acceleration measurement device, the common mechanical vibrator comprises a cantilever beam, an optical tweezers, a superconductive suspension, an ion trap, a micro-electro-mechanical system (MEMS), an anti-magnetic suspension and the like, and in addition, a torsional pendulum for measuring moment or rotational acceleration is also provided, and the principle that the mechanical vibrator can perform precise measurement is that the mechanical vibrator is utilized at the eigenfrequency f 0 (the eigenfrequency can be represented by a circle frequency f or an angular frequency omega, the relation is omega=2pi f, and the symbol frequency refers to a high quality factor Q near the circle frequency f unless the symbol is used for description, so that the action intensity of an external force signal or an acceleration signal on the mechanical vibrator is amplified, and the external weak signal can be detected.
In the process of detecting external signals by the mechanical vibrator, once the frequency of the external signals to be detected deviates from the resonance frequency of the mechanical vibrator, the detection capacity of a vibrator system is greatly reduced, so that the mechanical vibrator is utilized to measure external weak signals, namely the intrinsic frequency of the mechanical vibrator is adjusted. In the various mechanical vibrator systems, the eigenfrequency of the cantilever beam is about 10kHz, the eigenfrequency of the ion trap and the optical tweezers system is about 1MHz, the frequency of the superconducting suspension is about 20 Hz-10 kHz, the common eigenfrequency of the MEMS system is also more than 3Hz, and the anti-magnetic suspension is about 10Hz-20Hz.
The vertical eigenfrequency of the micro mechanical system reported at present is almost more than 10Hz, which limits the application range of the mechanical vibrator system to the detection of extremely low frequency, namely weak signals lower than 1 Hz. The signals have application values in a plurality of important fields such as earth mapping, earthquake monitoring, gravity measurement and the like.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and aims to provide a means for constructing a low-frequency miniature mechanical vibrator by combining two or more potential fields, wherein the frequency in the vertical direction can be as low as below 1Hz, the mass of the mechanical vibrator is less than 1g, and the volume is also 1cm 3 The method is used for solving the problem that the existing mechanical vibrator system is difficult to detect the low-frequency signals in the vertical direction.
In order to solve the technical problems, the invention adopts the following technical scheme: a method of constructing an extremely low frequency micromechanical resonator harmonic using a combined potential field, comprising the steps of:
s1, constructing a mechanical vibrator;
S2constructing a corresponding xyz three-axis system by taking the gravity direction of the vibrator as a z-axis, and introducing a first potential field U 1 And solving the eigenvalue omega of the vibrator z-axis at the moment 0 Wherein U is 1 The force on the z-axis of the vibrator is equal to the gravity of the vibrator, U 1 The second derivatives in the xyz triaxial directions are all greater than 0;
s3, at U 1 On the basis of (1) introducing an independent second potential field U 2 To reduce the eigenfrequency of the vibrator in the z-axis, to form a total potential field U and to solve the eigenfrequency omega of the vibrator in the z-axis 1 Wherein u=u 1 +U 2 The force of U on the z axis of the vibrator is equal to the gravity of the vibrator, the second derivative of U on the xyz three axis is larger than 0, and simultaneously, the force of U on the z axis of the vibrator is equal to the gravity of the vibrator 2 The force on the vibrator in the z-axis direction is far smaller than U 1 Force on vibrator z-axis.
Further, the construction method in the step S1 comprises anti-magnetic levitation or ferromagnetic levitation combined with anti-magnetic levitation.
Further, the step of reducing the eigenfrequency of the vibrator on the z-axis is as follows,
8 magnets with magnetization directions pointing to the center are used as an upper layer, and 8 magnets with magnetization directions pointing outwards are used as a lower layer, so that a first potential field is constructed;
a diamagnetic PMMA small ball is suspended in a central hole reserved at the upper layer of the first potential field, and a strong paramagnetic terbium ball is connected below the PMMA small ball through glass fibers;
a plurality of plate magnets having magnetization directions upward in the z-direction are added to the lower layer of the first potential field to construct a second potential field.
Further, the types of magnets at the upper layer and the lower layer of the first potential field are different, and the magnet materials comprise neodymium iron boron, samarium cobalt and alnico.
Further, the step of reducing the eigenfrequency of the vibrator on the z-axis is as follows in a way of constructing a mechanical vibrator by combining ferromagnetic suspension with antimagnetic suspension,
attracting the small magnet positively magnetized in the z direction by the attracting magnet positively magnetized in the z direction to counteract the gravity of the small magnet and construct a first potential field;
a piece of pyrolytic graphite is added on each of the upper and lower sides of the small magnet to build up a second potential field.
Further, the second potential field may be constructed by adding a compensation magnet magnetized in the reverse direction along the z-axis between the attracting magnet and the small magnet.
Further, the eigenfrequency ω of the vibrator z-axis in the step S2 0 The calculation steps of (a) are as follows,
wherein F is the force of the current potential field to the z axis direction of the vibrator, m is the vibrator mass, z 0 Is used as a balance position of the vibrator,
then there is
The eigenfrequency omega of the vibrator z-axis in the step S3 1 The calculation steps are as follows,
further, wherein z 1 Is a new balance position of the vibrator, due to U 2 The force on the vibrator in the z-axis direction is far smaller than U 1 Force on vibrator z-axis, so z 1 ≈z 0 ，
Then there is
Compared with the prior art, the invention has the beneficial effects that:
1. the intrinsic frequency of the miniature mechanical vibrator in the vertical direction is reduced by combining various binding potential fields, and the frequency is lower than 1Hz which is difficult to reach by a front vibrator system;
2. by simply changing the position of the potential well, the frequency can be adjusted
3. The whole volume of the system is reduced, the influence of the deformation of the device caused by the fluctuation of the external temperature on the stability of the vibrator is reduced, the requirement on the magnetic shielding of the external environment is reduced, and the stability of the system is improved.
Drawings
The disclosure of the present invention is described with reference to the accompanying drawings. It is to be understood that the drawings are designed solely for the purposes of illustration and not as a definition of the limits of the invention. In the drawings, like reference numerals are used to refer to like parts. Wherein:
fig. 1 schematically shows a schematic diagram of an apparatus for constructing a low frequency vibrator by combining paramagnetic potential fields according to a first embodiment of the present invention;
FIG. 2 is a schematic diagram showing the relative distance between the vibrator and the magnet, the magnetic field gradient and the eigenfrequency according to the first embodiment of the present invention;
FIG. 3 is a schematic diagram showing a device for constructing a low-frequency oscillator by combining paramagnetic potential fields according to the first embodiment of the invention;
fig. 4 schematically shows a schematic diagram of a device for constructing a low-frequency vibrator by combining ferromagnetic paramagnetic potential fields according to a second embodiment of the present invention;
FIG. 5 is a schematic diagram showing a device for constructing a low-frequency vibrator by combining ferromagnetic paramagnetic potential fields according to a second embodiment of the present invention;
fig. 6 schematically shows a schematic diagram of an apparatus for constructing a low frequency vibrator by combining a compensation magnet according to a first embodiment of the present invention;
fig. 7 is a schematic diagram showing a low-frequency oscillator device constructed by combining a compensation magnet according to the first embodiment of the invention.
In the figure: 1. a permanent magnet; 2. PMMA pellets; 3. glass fibers; 4. terbium balls; 5. a large magnet; 6. a small magnet; 7. pyrolytic graphite; 8. and (3) compensating the magnet.
Detailed Description
It is to be understood that, according to the technical solution of the present invention, those skilled in the art may propose various alternative structural modes and implementation modes without changing the true spirit of the present invention. Accordingly, the following detailed description and drawings are merely illustrative of the invention and are not intended to be exhaustive or to limit the invention to the precise form disclosed.
An embodiment according to the present invention is shown in connection with fig. 1-6.
The invention aims to provide a method for constructing a low-frequency miniature mechanical vibrator by combining two or more potential fields, so that the frequency in the vertical direction can be reduced to below 1Hz, the mass is less than 1g, and the volume is also 1cm 3 The method is used for solving the problem that the existing mechanical vibrator system is difficult to detect the low-frequency signals in the vertical direction.
In principle, a mechanical vibrator with mass m is stably bound to a potential field U 1 In the process, firstly, the force of a potential field on the vibrator in the vertical direction needs to be satisfied to sufficiently offset the gravity of the vibrator:
(wherein z 0 Namely the balance position of the mechanical vibrator); in addition, the second derivative of the potential field is required to be greater than 0 to form stable confinement, and the second derivative is also required to be valid in the xyz direction. At this time, the eigenfrequency omega of the vibrator in the z direction 0 The method comprises the following steps:
to reduce the eigenfrequency v of the vibrator 0 Introducing another independent potential field U 2 . As described above, the total potential field u=u at this time 1 +U 2 Similar conditions need to be met, namely, the vertical direction counteracts the gravity:
(z 1 new equilibrium position) and the second derivatives of the total potential field U need to be both greater than 0 for the xyz direction.
If through reasonable design U 2 Potential field, such that U 2 Satisfy the following requirements
I.e. in the mechanical vibratorOriginal binding position z 0 U at the position 2 The potential field has little effect on the constraint equation caused by gravity balance, so a new equilibrium position z can be considered 1 ≈z 0 Then the eigenfrequency of the vibrator is:
it can be seen that if the potential field U 2 At the same time satisfy
Then there is omega 1 <ω 0 I.e. by introducing an independent potential field U meeting the conditions at this time 2 The purpose of reducing the frequency of the mechanical vibrator is achieved.
Further, the potential field U 1 Can only be used for counteracting the gravity of the vibrator, but cannot form stable constraint, namely
In the case of (a), a potential field U is introduced 2 . So that the total potential field U t ＝U 1 +U 2 The method meets the following conditions: />
The corresponding oscillator frequency at this time is:
i.e. by introducing potential field U 2 Finishing the stable constraint of the mechanical vibrator, if the vibrator frequency omega is the same 1 The purpose of constructing a low frequency mechanical resonator using the combined potential field is also achieved if it is small.
Three examples will be given below to illustrate how to construct an extremely low frequency micromechanical vibrator by introducing additional independent potential fields, all three devices have been practically validated in the laboratory.
Example 1
As an embodiment of the present invention, the present invention provides the following technical solutions: the method for constructing the low-frequency mechanical vibrator by combining the antimagnetic paramagnetic means comprises the following steps:
1. as shown in figure 1, the mechanical vibrator is constructed by combining an antimagnetic suspension means
As shown in fig. 1, a diamagnetic PMMA (polymethyl methacrylate) pellet 2 is suspended in a magnetomotive force well, the design of a neodymium-iron-boron magnet is similar to that of a CN113917552a patent, the upper layer is 8 pieces of N52 neodymium-iron-boron magnets 1 with magnetization directions pointing to the center, the waist length is 10mm, the height is 1mm, and the diameter of a central binding area is 2mm; the lower layer is 8 neodymium iron boron magnets 1 with magnetization directions of which the centers are outwards, the waist is 10mm long and 3mm high, and the center is provided with a small hole with the diameter of about 20um, so that glass fibers 3 used for connection can pass through. Radius r 1 PMMA pellets 2 of 0.5mm are suspended in an antimagnetic potential well, and a strong paramagnetic property with radius r is connected below the pellets through glass fibers 3 with diameter of 5 mu m 2 Terbium sphere 4 =11 μm. Wherein the magnet material can be selected according to the situation but is not limited to neodymium-iron-boron or samarium-cobalt, alnico and the like, and the related geometric dimensions can be finely adjusted according to the situation. The PMMA sphere 2, the glass fiber 3 and the terbium sphere 4 are integrally used as mechanical vibrators.
According to the above formula, the initial confining potential field at this time satisfies:
wherein the method comprises the steps of
Is the total mass of the mechanical vibrator (neglecting glass fiber and TB 2 O 3 Ball mass), χ v1 ＝-9.1×10 -6 Magnetic susceptibility, mu, of PMMA sphere 0 ＝4π×10 -7 H/m is vacuum permeability, B 1 Magnetic field generated for combined NdFeB magnetsA field. Simulating the magnetic field in the COMSOL to obtain the initial eigenfrequency omega of the mechanical vibrator in the vertical direction 0 = 125.70Hz, corresponding to a circular frequency f 0 ＝ω 0 /2pi=20.01 Hz, which corresponds to the usual eigenfrequency of the diamagnetic levitation system described above.
2. The extra independent magnetic fields are combined to reduce the intrinsic frequency of the mechanical vibrator
Combining magnets as shown creates a new magnetic potential field U 2 Wherein 8N 35 NdFeB isosceles triangle magnets with 45-degree vertex angles are arranged above the magnet, the waist length is 5mm, the height is 1mm, and the magnetization direction points to the center. Similarly, 8N 52 NdFeB magnets with waist length of 5mm, height of 6mm and magnetization direction center pointing outwards are arranged below, and magnets with different brands are selected to ensure that the magnetic field intensity B at the center of the upper surface of the magnets is finally achieved 2 As small as possible while allowing for magnetic field gradients thereat
As large as possible. In practical use, it is considered to add several pieces of sheet magnets with magnetization directions upward in the z direction at the bottom, further reducing the magnetic field strength. According to the above, the eigenfrequency of the mechanical vibrator at this time is:
wherein the method comprises the steps of
Magnetic susceptibility of terbium metal, V 2 Is terbium sphere volume.
As shown in FIG. 2, the magnetic field B generated by the lower magnet is simulated in COMSOL 2 And brings in omega as described above 1 The formula is used for obtaining the distance d between the terbium ball and the magnet below and the magnetic field gradient
Intrinsic frequency omega of corresponding mechanical vibrator 1 Is a relationship of (3).
At this time, the magnetic field strength B at the terbium metal ball 2 <500Gs, corresponding potential fieldU 2 The magnetic force generated on terbium balls is less than 4.7X10 -8 N, and potential field U 1 The force to the vibrator is 5.9×10 of the gravity of the vibrator -6 N, meeting the requirements of the foregoing
Requirements. See independent potential field U generated by the underlying magnet 2 Is introduced without changing the original balance position z of the mechanical vibrator 0 . And the eigenvalue omega of the mechanical vibrator is reduced along with the decrease of the relative distance d between the terbium ball and the magnet below 1 Will also gradually decrease below 10Hz, satisfying the requirement of the previous description for the independent potential field U 2 Is not limited. In laboratory actual measurement, the frequency of the vibrator in the system reaches omega at the minimum 1 =5.7 Hz, corresponding to a circle frequency f 1 =0.91 Hz, well below the original eigenfrequency of 20Hz.
Embodiment two:
as a second embodiment of the present invention, the present invention provides the following technical solutions: the method for constructing the small-size low-frequency mechanical vibrator by combining ferromagnetic suspension with a antimagnetic means comprises the following steps:
1. the use of a large magnet 5 magnetized positively in the z-direction attracts a small magnet 6 also magnetized positively in the z-direction, counteracting the weight of the small magnet 6.
The potential field generated by the attracting magnet is:
wherein B is 1 For the intensity of the magnetic field generated by the large magnet 5, M 2 For suspending the internal magnetization of the small magnet 6, V, dependent only on the type of magnet 2 Is the volume of the small magnet 6 (here considered V 2 Small volume, simplified calculation), m is the mass of the small magnet 6. If the levitation position of the small magnet 6 is taken as the origin of coordinates in the z direction, the position is z=z 0 When the attractive force between the magnets is equal to the gravity of the small levitation magnet, namely +.>
Then z 0 I.e. the distance d between the large magnet 5 and the small magnet 6 for this time.
At this time potential field U 1 Although the gravity of the small levitation magnet 6 can be counteracted, the binding position is changed to an unstable equilibrium point. For example, when the levitation magnet is deflected upward, the magnetic field of the large magnet 5 is further increased, causing the levitation magnet to continue to deflect upward, and thus not be balanced stably, i.e
2. A piece of pyrolytic graphite 7 is respectively added on the upper side and the lower side of the small magnet 6, and a magnetic field B is generated by the small magnet 6 2 (z) construction of repulsive potential field U to pyrolytic graphite 7 2 Satisfies the following conditions
Wherein χ is v Is pyrolytic graphite with 7 equal magnetic susceptibility (χ here) v <0 indicates pyrolytic graphite 7 as antimagnetic substance), μ 0 Is vacuum permeability, V 3 Is pyrolytic graphite 7 volume. The potential field felt by the small levitation magnet at this time is U t ＝U 1 +U 2 . When->
When in use, the small magnet 6 can stably suspend, namely, the following conditions are satisfied:
since pyrolytic graphite 7 is antimagnetic substance χ v <0, i.e. the first term of the above equation is positive and the second term is negative, while the corresponding eigenfrequency of the small magnet 6 in the z direction is:
from the above analysis, it is known that only the potential field U generated by the large magnet 5 1 The small magnet 6 cannot be stably suspended, and a potential field U is formed by introducing pyrolytic graphite 7 2 When meeting the following requirements
In this case, a stable restraint can be formed. Wherein U is 1 The potential field is mainly used for counteracting the gravity of the vibrator, i.e. F is required to be satisfied B1 The =mg condition, equivalent to the attractive magnet magnetic field gradient satisfying: />
However, the second derivative of the magnetic field of the attracting magnet may cause the floating magnet to be unable to be stably restrained, so that the distance between two pieces of graphite needs to be reduced, the acting force of the small floating magnet 6 on the graphite is enhanced, but the local oscillation frequency omega of the vibrator is increased 0 。
In practical use, therefore, in order to reduce the frequency rise of the levitated small magnet 6 caused by this effect, it is necessary to reduce the second order gradient of the magnetic field generated by the large magnet 5. The usual solution is to choose a larger attracting magnet while increasing the distance d so that the magnetic field gradient felt by the small magnet 6 is maintained
While the magnetic field second order gradient is reduced>
Thereby reducing the eigenfrequency omega of the small magnet 6 0 . However, increasing the distance d will increase the volume of the experimental device, putting higher demands on the temperature control of the system, and in addition, increasing the volume of the attracting magnet will also generate a higher magnetic field B 1 The magnetic shielding effect of the magnetic levitation system is weakened.
In practical use, the diameter of the upper large magnet 5 is selected to be 40mm, the thickness is 4mm, the small magnet 6 is arranged at the position about 60mm below the attracting magnet, a piece of pyrolytic graphite 7 is respectively arranged at the positions 1mm away from the small magnet 6 on the upper side and the lower side, the diameter is about 30mm, the thickness is 3mm, the small magnet 6 can stably suspend at the moment, and the intrinsic frequency of the small magnet 6 in the vertical direction is measured to be f z ＝0.95Hz。
Example III
As a third embodiment of the present invention, the following modifications are made on the basis of the above second embodiment:
1. in the same way as in the second embodiment, the magnetic field B is generated by the large magnet 5 1 (z) generating a magnetic field B with the levitation magnet 6 2 (z) the repulsive potential field generated by pyrolytic graphite 7, together constructing a confining field U 1 And the potential field U above t Identical U 1 The method meets the following conditions:
2. a compensation magnet 8 which is magnetized reversely along the z axis is additionally arranged between the attracting magnet and the small suspension magnet to generate a potential field U 2 At the same time, the position of the upper attracting magnet is lowered to z 1 A new equilibrium is reached. The magnetic field force applied to the small levitation magnet at this time satisfies the following formula:
at z=z 1 When true, B is 3 (z) represents the magnetic field generated by the bucking magnet, (due to the position z of the uppermost attracting magnet) 1 The overall dimensions of the system in the z-direction will be characterized and therefore mainly take into account the influence of the change in the position of the upper magnet on the attractive force of the magnetic field to which the levitation magnet is subjected, considering that the bucking magnet 8 is already in the optimal position). Since the direction of magnetization of the bucking magnet 8 is opposite to that of the upper attracting magnet, it is necessary to lower the attracting magnet position, thereby creating a larger magnetic field gradient for maintaining the effect of counteracting the weight of the levitating small magnet. I.e. having z as compared with example 2 1 <z 0 By introducing the compensation magnet, the overall dimension d of the resonator device in the vertical direction is reduced.
On the other hand, similar to the formula (2) above, the frequencies of the magnetic levitation vibrator under the new structure satisfy:
compared with omega 0 Although the upper attracting magnet position is lowered to z 1 Will cause the attracting magnet to produce a second order gradient of magnetic field
The magnetic field strength B-1/r is increased because the magnetostatic body magnetic field is similar to a magnetic dipole 2 (r is distance), i.e. the second derivative of the magnetic field is inversely proportional to r to the power of 4. Thus, under the structure, the compensating magnet and the suspension magnet are positioned closer, the effect of generating the second-order gradient of the magnetic field is stronger, i.e. the new structure satisfies omega 1 <ω 0 . By introducing compensation magnets, the magnetic potential field U generated by the compensation magnetic field is utilized 2 The eigenfrequency omega of the small levitation magnet can be further reduced 1 。
Furthermore, as can be seen from the above calculation formula, the main constraints that make the suspension structure in this system hold are: the attractive force of the magnet to which the levitation magnet 6 is subjected needs to counteract its own weight. It can also be explained by the above formula (3) that the introduction of the compensation magnet 8 can lower the position of the large magnet 5 to z 1 In the same way, the volume of the attracting magnet 6 can be reduced to correspond to the new magnetic field B 1 ′ (z), and further lowering the position to z 2 So long as it satisfies its total magnetic field gradient
The method is unchanged.
Therefore, the overall size of the magnetic suspension device can be further reduced, and the stability of the system is improved; meanwhile, as the mechanical vibrator of the system is a magnet and is easily influenced by external magnetic field noise, a magnetic shielding layer is usually required to be added to the outer side of the suspension device, a strong polarized magnetic field is generated in the magnetic shielding layer by the attraction magnet with larger volume, the polarized magnetic field not only can influence the suspension magnetic vibrator, but also can reduce fluctuation of the polarized magnetic field due to the fact that the magnetic polarization coefficient of the magnetic shielding material is greatly influenced by temperature, and a temperature control system is further required to be added. The temperature stability of the system will further increase if the volume of the attracting magnet can be reduced.
In actual measurement, the upper attracting magnet is selected to be a cylinder with the diameter of 12mm and the height of 2mm and magnetized vertically upwards; a cylindrical compensation magnet with the diameter of 5mm and the thickness of 0.5mm is arranged at the position 25mm below and magnetized vertically downwards; then the square magnetic sheet with the suspension side length of 5mm x 1mm is magnetized upwards along the vertical direction at the position of about 23mm below; two pyrolytic graphite sheets are placed at the 3 mm-apart position of the upper side and the lower side of the suspension magnetic sheet, and meanwhile, pyrolytic graphite 7 is placed in the xy direction for providing binding force in the xy direction, improving the xy direction frequency of the pyrolytic graphite sheets and being used for directional measurement in the z direction. In actual measurement, the eigenfrequency f of the vibrator in the vertical direction z =0.85 Hz, xy direction frequencies are 5Hz and 7Hz, respectively. Compared with the second example, the size of the large magnet 5 is reduced from a cylinder with the previous diameter of 40mm and the thickness of 4mm to a diameter of 12mm and the thickness of 2mm; the overall dimension of the device in the vertical direction is reduced from 60mm to about 48mm; the vertical eigenfrequency of the small magnet 6 is again reduced from 0.95Hz to 0.85Hz (frequency adjustment accordingly). It can be seen that by adding a compensation magnet 8 magnetized in the vertical direction again, the potential field generated by the compensation magnet is utilized to improve the magnetic shielding, temperature control, eigenfrequency and the like of the magnetic suspension vibrator system.
The technical scope of the present invention is not limited to the above description, and those skilled in the art may make various changes and modifications to the above-described embodiments without departing from the technical spirit of the present invention, and these changes and modifications should be included in the scope of the present invention.
Claims (8)
1. A method of constructing an extremely low frequency micromechanical resonator harmonic using a combined potential field, comprising the steps of:
s1, constructing a mechanical vibrator;
s2, constructing a corresponding xyz three-axis system by taking the gravity direction of the vibrator as a z axis, and introducing a first potential field U 1 And solving the eigenvalue omega of the vibrator z-axis at the moment 0 Wherein U is 1 The force on the z-axis of the vibrator is equal to the gravity of the vibrator, U 1 The second derivatives in the xyz triaxial directions are all greater than 0;
s3, at U 1 On the basis of (1) introducing an independent second potential field U 2 To reduce the eigenfrequency of the vibrator in the z-axis, to form a total potential field U and to solve the eigenfrequency omega of the vibrator in the z-axis 1 Wherein u=u 1 +U 2 The force of U on the z axis of the vibrator is equal to the gravity of the vibrator, the second derivative of U on the xyz three axis is larger than 0, and simultaneously, the force of U on the z axis of the vibrator is equal to the gravity of the vibrator 2 The force on the vibrator in the z-axis direction is far smaller than U 1 Force on vibrator z-axis.
2. A method of constructing an extremely low frequency micromechanical resonator resonance using a combined potential field according to claim 1, characterized in that: the construction mode in the step S1 comprises anti-magnetic levitation or ferromagnetic levitation combined with anti-magnetic levitation.
3. A method of constructing an extremely low frequency micromechanical resonator resonance using a combined potential field according to claim 2, characterized in that: the method for constructing the mechanical vibrator by anti-magnetic suspension reduces the eigenfrequency of the vibrator on the z axis as follows,
8 magnets with magnetization directions pointing to the center are used as an upper layer, and 8 magnets with magnetization directions pointing outwards are used as a lower layer, so that a first potential field is constructed;
a diamagnetic PMMA small ball is suspended in a central hole reserved at the upper layer of the first potential field, and a strong paramagnetic terbium ball is connected below the PMMA small ball through glass fibers;
a plurality of plate magnets having magnetization directions upward in the z-direction are added to the lower layer of the first potential field to construct a second potential field.
4. A method of constructing an extremely low frequency micromechanical resonator harmonic using a combined potential field according to claim 3, characterized by: the upper layer magnet model and the lower layer magnet model of the first potential field are different, and the magnet materials comprise neodymium iron boron, samarium cobalt and alnico.
5. A method of constructing an extremely low frequency micromechanical resonator resonance using a combined potential field according to claim 2, characterized in that: the method for constructing the mechanical vibrator by combining ferromagnetic suspension and antimagnetic suspension comprises the following steps of,
attracting the small magnet positively magnetized in the z direction by the attracting magnet positively magnetized in the z direction to counteract the gravity of the small magnet and construct a first potential field;
a piece of pyrolytic graphite is added on each of the upper and lower sides of the small magnet to build up a second potential field.
6. A method of constructing an extremely low frequency micromechanical resonator resonance using a combined potential field according to claim 5, characterized by: the second potential field may also be constructed by adding a bucking magnet between the attracting magnet and the small magnet that is magnetized in the opposite direction along the z-axis.
7. A method of constructing an extremely low frequency micromechanical resonator resonance using a combined potential field according to claim 1, characterized in that: the eigenfrequency omega of the vibrator z-axis in the step S2 0 The calculation steps of (a) are as follows,
wherein F is the force of the current potential field to the z axis direction of the vibrator, m is the vibrator mass, z 0 Is used as a balance position of the vibrator,
then there is
8. A method of constructing an extremely low frequency micromechanical resonator resonance using a combined potential field according to claim 1, characterized in that: the eigenfrequency omega of the vibrator z-axis in the step S3 1 The calculation steps are as follows,
wherein z is 1 Is a new balance position of the vibrator, due to U 2 The force on the vibrator in the z-axis direction is far smaller than U 1 Force on vibrator z-axis, so z 1 ≈z 0 ，
Then there is
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