Apparatus and method for alignment of resonator rigid and damped shafts

Abstract

The application provides a device and a method for aligning a rigid axis and a damping axis of a resonator, the device comprising: a chamber; a resonator in the chamber, the resonator comprising a support column, a hemispherical resonant shell connected to the support column; a resonator connector, one end of the resonator connector being connected to a bottom end of the support column; a turntable, the turntable being fixed at the other end of the bottom of the resonator connector; an ion source in the chamber and on the side of the hemispherical resonant shell, the ion source being used for emitting an ion beam; a diaphragm between the ion source and the hemispherical resonant shell, the ion beam passing through the diaphragm being used for etching the hemispherical resonant shell to change the position of the rigid axis of the hemispherical resonant shell; and first to eighth electrodes, the first to eighth electrodes being arranged in a uniform interval on the outer side of the hemispherical resonant shell in a circumferential direction of the central axis of the support column.

Description

Technical Field

[0001] This invention relates to the field of vibrating gyroscope technology, and more particularly to a device and alignment method for aligning the rigid axis and damping axis of a resonator. Background Technology

[0002] A resonant gyroscope is a solid-state wave gyroscope based on the Coriolis effect, possessing advantages such as high precision, low cost, small size, long lifespan, maintenance-free operation, shock resistance, and radiation resistance. It has broad application prospects in various fields, including missile guidance, ship navigation, vehicle navigation, rocket attitude control, and individual soldier north-finding in the defense sector, as well as indoor navigation, vehicle navigation, unmanned aerial vehicle navigation, underground exploration, and underwater navigation in the national economy.

[0003] The resonant oscillator is the core component of a resonant gyroscope, and its performance parameters directly determine the gyroscope's accuracy. Actual manufactured resonant oscillators often exhibit defects such as uneven wall thickness and structural damage. These defects severely disrupt the oscillator's consistency and symmetry, leading to uneven stiffness and damping along the circumferential direction. Stiffness inhomogeneity causes the original single operating mode to split into two degenerate modes at 45-degree angles. These two degenerate modes have different resonant frequencies, the difference being frequency splitting. The resonant oscillator has a direction axis with the maximum and minimum resonant frequencies in the circumferential direction; these axes are called rigid axes. The rigid axis with the lower resonant frequency is called the low-frequency axis, and the rigid axis with the higher resonant frequency is called the high-frequency axis. Damping inhomogeneity causes the decay time of the resonant oscillator to vary along the circumferential direction. The location of the maximum decay time is called the damping minimum axis, and the location of the minimum decay time is called the damping maximum axis. Typically, the damping and rigid axis orientations of a manufactured resonant oscillator are randomly distributed. Misalignment between the damping axis and the rigid axis will cause gyroscope output errors and reduce gyroscope accuracy.

[0004] Currently, how to further improve the working accuracy of resonant gyroscopes is a technical problem that needs to be solved. Summary of the Invention

[0005] This invention provides a device and alignment method for aligning the rigid axis and damping axis of a resonator, thereby further improving the working accuracy of the resonant gyroscope.

[0006] This invention provides a device for aligning the rigid axis and damping axis of a resonator, comprising: a chamber; a resonator located within the chamber, the resonator including a support column and a hemispherical resonant housing connected to the support column, the opening of the hemispherical resonant housing facing the bottom of the chamber; a resonator connector, one end of which is connected to the bottom end of the support column; a turntable, the other end of which is fixed at the bottom of the resonator connector; an ion source located in the chamber and on the side of the hemispherical resonant housing, the ion source being used to emit an ion beam; and an aperture located between the ion source and the hemispherical resonant housing, through which the ion beam passes for... The hemispherical resonant housing is etched to change the position of the rigid axis of the hemispherical resonant housing; a first electrode, a second electrode, a third electrode, a fourth electrode, a fifth electrode, a sixth electrode, a seventh electrode, and an eighth electrode are arranged circumferentially around the central axis of the support column, with the first to eighth electrodes being concentric circles whose centers coincide with the central axis of the resonator; excitation signals are applied to the first, fifth, second, and sixth electrodes; the third, seventh, fourth, and eighth electrodes are used to detect the vibration signal of the hemispherical resonant housing.

[0007] Optionally, the gaps between the first to eighth electrodes and the hemispherical resonant housing are equal, and the gaps between the first to eighth electrodes and the hemispherical resonant housing are 20μm-80μm.

[0008] Optionally, the diameter of the through hole of the aperture is 1 / 5 to 1 / 3 of the outer diameter of the hemispherical resonator shell.

[0009] Optionally, the first electrode and the fifth electrode are short-circuited and symmetrically arranged, the second electrode and the sixth electrode are short-circuited and symmetrically arranged, the third electrode and the seventh electrode are short-circuited and symmetrically arranged, and the fourth electrode and the eighth electrode are short-circuited and symmetrically arranged.

[0010] Optionally, the roughness of the outer surface of the hemispherical resonator housing is 0.1 μm to 1 μm.

[0011] Optionally, it also includes: a resonator control unit; a plurality of excitation cables and a plurality of detection cables, wherein the first electrode, the fifth electrode, the second electrode and the sixth electrode are electrically connected to the resonator control unit via the excitation cables, the excitation cables being used to transmit the sinusoidal excitation signal generated by the resonator control unit, and the third electrode, the seventh electrode, the fourth electrode and the eighth electrode are electrically connected to the resonator control unit via the detection cables, the detection cables being used to transmit the vibration signal of the hemispherical resonator shell.

[0012] This invention also provides a method for aligning the rigid axis and damping axis of a resonator, comprising: step S1: applying a first excitation signal to the hemispherical resonator shell only on the first and fifth electrodes; disconnecting the first excitation signal and obtaining the first free decay signal of the hemispherical resonator shell from the third, seventh, fourth, and eighth electrodes; step S2: sequentially applying a second excitation signal to the Nth excitation signal, wherein any kth excitation signal is applied to the first, fifth, second, and sixth electrodes, and N is an integer greater than or equal to 3; the excitation directions of the first to Nth excitation signals increase by a first angular step; the angle between the excitation direction of the Nth excitation signal and the excitation direction of the first excitation signal is greater than 45 degrees; and obtaining the second free decay signal of the hemispherical resonator shell. The steps for obtaining the k-th free attenuation signal from the Nth free attenuation signal are as follows: Disconnect any k-th excitation signal and obtain the k-th free attenuation signal from the third, seventh, fourth, and eighth electrodes; k is an integer greater than or equal to 2 and less than or equal to N; Step S3: Obtain the first characteristic excitation direction corresponding to the free attenuation signal with the smallest beat frequency from the first free attenuation signal to the Nth free attenuation signal; Step S4: Sequentially apply the (N+1)th to (N+M)th excitation signals, with any j-th excitation signal applied to the first, fifth, second, and sixth electrodes, where M is an integer greater than 1; j is an integer greater than or equal to N+1 and less than or equal to N+M; the excitation directions from the Nth to the (N+M)th excitation signals are... The second angle step size increases, and the second angle step size is much smaller than the first angle step size; the angle bisector direction from the (N+1)th excitation direction to the (N+M)th excitation direction is the first characteristic excitation direction; the steps to obtain the (N+1)th to (N+M)th free attenuation signals of the hemispherical resonant shell and obtain the jth free attenuation signal are as follows: disconnect any jth excitation signal, and obtain the jth free attenuation signal from the third, seventh, fourth, and eighth electrodes; Step S5: obtain the second characteristic excitation direction corresponding to the free attenuation signal with the smallest beat frequency from the (N+1)th to (N+M)th free attenuation signals as the orientation of the first rigid axis; Step S6: along the orientation of the first rigid axis and the orientation of the second rigid axis 45° away from the orientation of the first rigid axis. The resonant frequency of the hemispherical resonant housing 213 is measured. The direction of change from the excitation direction of the first excitation signal to the excitation direction of the Nth excitation signal is consistent with the direction of change from the orientation of the first rigid axis to the orientation of the second rigid axis. If the resonant frequency measured along the orientation of the second rigid axis is greater than the resonant frequency measured along the orientation of the first rigid axis, then the second rigid axis is a high-frequency axis and the first rigid axis is a low-frequency axis. If the resonant frequency measured along the orientation of the second rigid axis is less than the resonant frequency measured along the orientation of the first rigid axis, then the second rigid axis is a low-frequency axis and the first rigid axis is a high-frequency axis. Step S7: Obtain the free attenuation signal at the intermediate orientation between the orientation of the first rigid axis and the orientation of the second rigid axis, and obtain the frequency split based on the beat frequency period of the free attenuation signal at the intermediate orientation.Step S8: Set a first adjustment position on the outer surface of the hemispherical resonator shell with the low-frequency axis orientation; obtain a second, third, and fourth adjustment position based on the orientation of the first adjustment position; the orientations of the first, second, third, and fourth adjustment positions are spaced 90 degrees apart; rotate the hemispherical resonator shell, and the ion source emits an ion beam that etches the first to fourth adjustment positions respectively through the aperture; Step S9: After performing step S8, determine whether the frequency splitting is high. If the frequency split is higher than the first target value, repeat steps S1 to S8 until the frequency split is lower than the first target value. At this time, the low-frequency axis orientation is denoted as θω, and the frequency split is denoted as Δf. Step S10: Obtain the damping minimum axis and damping maximum axis of the hemispherical resonant shell. Step S11: Obtain the angle α between the orientation θτ of the damping maximum axis and the orientation θω of the low-frequency axis. When |θτ-θω| < 45°, α = |θτ-θω|; when |θτ-θω| ≥ 45°, α = |θτ-θω|. =90-|θτ-θω|; Step S12: Obtain the etching time t of the ion beam according to the formula t=k*α*Δf / U, where k is a constant coefficient and U is the ion beam pressure; Step S13: Set the first etching position on the outer surface of the hemispherical resonant shell 213 with the angle bisector of the included angle α; Obtain the second, third, and fourth etching positions according to the orientation of the first etching position; The orientations of the first, second, third, and fourth etching positions are spaced 9 degrees apart. 0 degrees; Step S14: Rotate the hemispherical resonator shell, and the ion source emits an ion beam to etch the first to fourth etching positions through the aperture. The etching time for each of the first to fourth etching positions is t; Step S15: After performing step S14, determine whether the angle between the damping maximum axis and the low-frequency axis is greater than the second target value; if the angle between the damping maximum axis and the low-frequency axis is greater than the second target value, repeat steps S1-S14 until the angle between the damping maximum axis and the low-frequency axis is less than the second target value.

[0013] Optionally, the second angle step size is 0.2° to 1°; the first angle step size is 5° to 10°.

[0014] Optionally, the angle between the excitation direction of the (N+1)th excitation signal and the excitation direction of the (N+M)th excitation signal is 6° to 18°.

[0015] Optionally, the first target value is 1 mHz to 5 mHz; the second target value is 0.1° to 1°.

[0016] The technical solution of the present invention has the following beneficial effects:

[0017] The device for aligning the rigid axis and damping axis of a resonator provided by the technical solution of the present invention can achieve the coincidence of the damping axis, the rigid axis, and the mode orientation, while reducing the influence of damping non-uniformity and stiffness non-uniformity on the output of the resonant gyroscope and improving the accuracy of the resonant gyroscope. Attached Figure Description

[0018] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the device used in this invention for aligning the rigid axis and damping axis of the resonator;

[0020] Figure 2 This is a schematic diagram of the etching position of the resonator in an embodiment of the present invention;

[0021] Figure 3 This is a schematic diagram of the resonator axis system in an embodiment of the present invention;

[0022] Figure 4 This is a flowchart of an embodiment of the method for aligning the rigid axis and damping axis of the resonator in this invention;

[0023] Reference numerals: 101-Resonator connector; 102-Aperture; 103-Ion beam; 104-Ion source; 105-Cavity; 201-First electrode; 202-Second electrode; 203-Third electrode; 204-Fourth electrode; 205-Fifth electrode; 206-Sixth electrode; 207-Seventh electrode; 208-Eighth electrode; 209-First etching position; 210-Second etching position; 211-Third etching position; 212-Fourth etching position; 213-Hemispherical resonator housing; 214-Turntable. Detailed Implementation

[0024] Studies have found that applying excitation to an ideal harmonic oscillator only induces stable standing wave vibrations. However, in practice, due to frequency fragmentation, when the excitation direction does not coincide with the rigid axis, it leads to a shift in the mode shape of the harmonic oscillator. The greater the frequency fragmentation, the greater the mode shape shift, and the mode shape shift gradually increases over time until it reaches stability. There are two ways to reduce the mode shape shift caused by frequency fragmentation: (1) reduce frequency fragmentation by adjusting the harmonic oscillator; (2) align the excitation direction with the rigid axis. The presence of damping inhomogeneity causes the mode shape to shift towards the axis of minimum damping during the decay process. There are two ways to reduce the mode shape shift caused by damping inhomogeneity: (1) reduce damping inhomogeneity; (2) align the excitation direction with the damping axis.

[0025] Ultra-high precision resonant gyroscopes primarily operate in force-balanced mode. In force-balanced mode, the gyroscope's output contains error terms related to the angles between the excitation direction and the rigid axis, and between the excitation direction and the damping axis. Currently, although numerous methods exist to reduce the frequency fragmentation and damping inhomogeneity of the resonator, further reduction of these issues becomes increasingly difficult as they decrease. Residual frequency fragmentation and damping inhomogeneity in the resonator continue to constrain improvements in gyroscope accuracy. By altering the magnitude of the forces applied to multiple excitation electrodes, alignment of the excitation direction with the rigid axis or with the damping axis can be achieved. However, since the rigid and damping axes of the resonator are often not coincident, it is impossible to achieve simultaneous alignment of the excitation direction with both the rigid and damping axes.

[0026] Further research: If the alignment of the rigid axis and damping axis of the resonator can be achieved, it will be of great significance for further improving the accuracy of the resonant gyroscope.

[0027] This invention proposes a device and method for aligning the rigid axis and damping axis of a resonator, which realizes the alignment of the rigid axis and damping axis of the resonator, and achieves the coincidence of the damping axis, rigid axis and mode orientation of the resonator. At the same time, it reduces the influence of damping non-uniformity and stiffness non-uniformity on the output of the resonant gyroscope, and improves the working accuracy of the resonant gyroscope.

[0028] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0030] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can also refer to the internal connection of two components; and they can refer to a wireless connection or a wired connection. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0031] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0032] One embodiment of the present invention provides a device for aligning the rigid axis and damping axis of a resonator, see reference. Figure 1 ,include:

[0033] Chamber 105;

[0034] The resonator located in the chamber 116 includes a support column and a hemispherical resonator housing 213 connected to the support column. The opening of the hemispherical resonator housing 213 faces the bottom of the chamber 105.

[0035] A resonator connector 101, one end of which is connected to the bottom end of the support column;

[0036] Turntable 214, which is fixed at the other end of the bottom of the resonator connector 101;

[0037] An ion source 104 is located in the chamber 105 and on the side of the hemispherical resonant housing 213. The ion source 115 is used to emit an ion beam 103.

[0038] An aperture 102 is located between the ion source 104 and the hemispherical resonant housing 213. The ion beam passing through the aperture 102 is used to etch the hemispherical resonant housing 213 to change the position of the rigid axis of the hemispherical resonant housing 213.

[0039] The first electrode 201, the second electrode 202, the third electrode 203, the fourth electrode 204, the fifth electrode 205, the sixth electrode 206, the seventh electrode 207, and the eighth electrode 208 are arranged sequentially and evenly around the central axis of the support column on the outer side of the hemispherical resonant housing 213. The center points of the first electrode 201 to the eighth electrode 208 are concentric circles, and the center of the circle coincides with the central axis of the resonator. The first electrode 201, the fifth electrode 205, the second electrode 202, and the sixth electrode 206 are used to apply excitation signals. The third electrode 203, the seventh electrode 207, the fourth electrode 204, and the eighth electrode 208 are used to detect the vibration signals of the hemispherical resonant housing 213.

[0040] The chamber 105 is used to provide a vacuum environment to meet the requirements of rigid axis measurement and damped axis measurement of the hemispherical resonant housing 213.

[0041] The ion source 104 is disposed on the side of the hemispherical resonant housing 213, and can emit an ion beam with energy of several hundred to several thousand electron volts. The ion source 104 is a DC ion source or a radio frequency ion source. The ion source 104 uses electrons to bombard the working gas to generate positively charged ion gas, which gains energy under the acceleration of the DC electric field inside the ion source 104 to form an ion beam.

[0042] The aperture 102 is disposed between the ion source 104 and the hemispherical resonant housing 213. The aperture 102 has a through hole, and the central axis of the through hole coincides with the central axis of the ion source 104. The aperture 102 is used to intercept an ion beam of a specific beam diameter.

[0043] The diameter of the through hole of the aperture 102 is determined according to the outer diameter of the hemispherical resonant housing 213. In one embodiment, the diameter of the through hole of the aperture 102 is 1 / 5 to 1 / 3 of the outer diameter of the hemispherical resonant housing 213, and the shape of the through hole can be circular or elliptical.

[0044] In one embodiment, the diameter of the through hole is 3.5 mm to 4.5 mm, for example, 4 mm.

[0045] The first electrode 201, the second electrode 202, the third electrode 203, the fourth electrode 204, the fifth electrode 205, the sixth electrode 206, the seventh electrode 207, and the eighth electrode 208 are arranged in a circumferentially evenly spaced manner around the central axis of the support column on the outer side of the hemispherical resonant housing 213. The first electrode 201 and the fifth electrode 205 are short-circuited and symmetrically arranged, the second electrode 202 and the sixth electrode 206 are short-circuited and symmetrically arranged, the third electrode 203 and the seventh electrode 207 are short-circuited and symmetrically arranged, and the fourth electrode 204 and the eighth electrode 208 are short-circuited and symmetrically arranged. Specifically, the angle between the line connecting the center point of the first electrode 201 to the central axis of the support column and the line connecting the center point of the second electrode 202 to the central axis of the support column is 45 degrees; the angle between the line connecting the center point of the second electrode 202 to the central axis of the support column and the line connecting the center point of the third electrode 203 to the central axis of the support column is 45 degrees; the angle between the line connecting the center point of the third electrode 203 to the central axis of the support column and the line connecting the center point of the fourth electrode 204 to the central axis of the support column is 45 degrees; the angle between the line connecting the center point of the fourth electrode 204 to the central axis of the support column and the line connecting the center point of the fifth electrode 205 to the central axis of the support column is 45 degrees. The angle between the line connecting the center point of the fifth electrode 205 to the central axis of the support column and the line connecting the center point of the sixth electrode 206 to the central axis of the support column is 45 degrees; the angle between the line connecting the center point of the sixth electrode 206 to the central axis of the support column and the line connecting the center point of the seventh electrode 207 to the central axis of the support column is 45 degrees; the angle between the line connecting the center point of the seventh electrode 207 to the central axis of the support column and the line connecting the center point of the eighth electrode 208 to the central axis of the support column is 45 degrees; the angle between the line connecting the center point of the eighth electrode 208 to the central axis of the support column and the line connecting the center point of the first electrode 201 to the central axis of the support column is 45 degrees.

[0046] When the resonator is working, an excitation signal with the same frequency as the resonant frequency of the hemispherical resonant shell 213 is applied to the first electrode 201, the fifth electrode 205, the second electrode 202, and the sixth electrode 206. This excitation signal can be a sinusoidal excitation signal. Based on the principle of vector synthesis, the excitation direction of the hemispherical resonant shell 213 can be adjusted by changing the amplitude of the electrical signals on the first electrode 201, the fifth electrode 205, the second electrode 202, and the sixth electrode 206. The third electrode 203, the seventh electrode 207, the fourth electrode 204, and the eighth electrode 208 are used to detect the vibration signal of the hemispherical resonant shell 213.

[0047] The gaps between the first electrode 201 to the eighth electrode 208 and the hemispherical resonant housing 213 are equal. In one embodiment, the gaps between the first electrode 201 to the eighth electrode 208 and the hemispherical resonant housing 213 are 20μm-80μm.

[0048] The turntable 214 is fixed to the resonator connector by bolts, and can control the resonator to rotate in a counterclockwise or clockwise direction. The bottom of the turntable is fixedly connected to the chamber.

[0049] The turntable 214 is fixed at the other end of the bottom of the resonator connector 101. In one embodiment, the turntable 214 is fixed to the other end of the bottom of the resonator connector 101 by bolts. By rotating the turntable 214, the rotation of the resonator can be controlled, causing the positions of the first electrode 201, the second electrode 202, the third electrode 203, the fourth electrode 204, the fifth electrode 205, the sixth electrode 206, the seventh electrode 207, and the eighth electrode 208 relative to the ion source 104 to change.

[0050] The outer surface of the hemispherical resonant housing 213 has a first etched position 209, a second etched position 210, a third etched position 211, and a fourth etched position 212. The first etched position 209, the second etched position 210, the third etched position 211, and the fourth etched position 212 are uniformly distributed around the central axis of the hemispherical resonant housing 213 in a circumferential direction. The first etched position 209 is located on the bisector of the angle between the damping maximum axis and the low-frequency axis (the rigid axis with a low resonant frequency is called the low-frequency axis) of the hemispherical resonant housing 213. The centers of the first etched position 209, the second etched position 210, the third etched position 211, and the fourth etched position 212 are located on the same plane. The first etched position 209, the second etched position 210, the third etched position 211, and the fourth etched position 212 are located on the outer surface of the hemispherical resonant housing 213 near the opening of the hemispherical resonant housing 213. The angle between the line connecting the center of the first etching position 209 to the central axis of the hemispherical resonant housing 213 and the line connecting the center of the second etching position 210 to the central axis of the hemispherical resonant housing 213 is 90 degrees. The angle between the line connecting the center of the second etching position 210 to the central axis of the hemispherical resonant housing 213 and the line connecting the center of the third etching position 211 to the central axis of the hemispherical resonant housing 213 is 90 degrees. The angle between the line connecting the center of the third etching position 211 to the central axis of the hemispherical resonant housing 213 and the line connecting the center of the fourth etching position 212 to the central axis of the hemispherical resonant housing 213 is 90 degrees. The angle between the line connecting the center of the fourth etching position 212 to the central axis of the hemispherical resonant housing 213 and the line connecting the center of the first etching position 209 to the central axis of the hemispherical resonant housing 213 is 90 degrees.

[0051] In one embodiment, the lower edges of the first etching position 209, the second etching position 210, the third etching position 211, and the fourth etching position 212 are tangent to the end face around the opening of the hemispherical resonant housing 213 to improve alignment efficiency.

[0052] In other embodiments, the lower edges of the first etching position 209, the second etching position 210, the third etching position 211, and the fourth etching position 212 are at a certain distance from the end face around the opening of the hemispherical resonant housing 213. For example, the distances between the lower edges of the first etching position 209, the second etching position 210, the third etching position 211, and the fourth etching position 212 and the end face around the opening of the hemispherical resonant housing 213 are 1mm to 4mm, such as 1mm, 2mm, 3mm, or 4mm.

[0053] In one embodiment, the outer surface of the hemispherical resonator housing 213 is subjected to ultra-precision magnetorheological polishing to remove the surface damage layer and reduce surface defects of the hemispherical resonator housing 213. In one embodiment, the roughness of the outer surface of the hemispherical resonator housing 213 is 0.1 μm to 1 μm, for example, 0.1 μm, 0.3 μm, 0.5 μm, 0.8 μm or 1 μm.

[0054] Preferably, the device is used in a high-precision constant temperature laboratory to reduce the influence of temperature on the measurement of the resonant frequencies of the low-frequency and high-frequency axes. In this embodiment, the control accuracy of the constant temperature laboratory is higher than 0.5℃.

[0055] Preferably, when measuring the damping axis of the resonator, the vacuum level inside chamber 105 is greater than or equal to 1*10. -5 Pa.

[0056] As a preferred method, the excitation and detection of the harmonic oscillator vibration can be achieved using time-division multiplexing.

[0057] The damping of the hemispherical resonator housing 213 mainly consists of its thermoelastic damping, support loss, surface loss, and air damping. The thermoelastic damping of the hemispherical resonator housing 213 is determined by its structural and material parameters. The outer diameter of the hemispherical resonator housing 213 is 5mm-10mm, and its wall thickness is 0.5mm-1.5mm. Ion beam etching typically removes material thicknesses of several hundred nanometers, such as 100nm-300nm. Therefore, the effect of ion beam etching on the structure of the hemispherical resonator housing 213 is negligible and will not significantly affect its thermoelastic damping. The support loss of the hemispherical resonator housing 213 is mainly determined by its support structure and fixing method. During the alignment of the rigid shaft and the damping shaft, the support structure and fixing method of the hemispherical resonator housing 213 are not changed, and therefore, the support loss of the hemispherical resonator housing 213 will not be affected. The surface loss of the hemispherical resonator housing 213 is mainly determined by its surface defects. In this embodiment, the outer surface of the hemispherical resonator housing 213 undergoes ultra-precision magnetorheological polishing, which greatly reduces surface defects. Furthermore, ion beam etching only etches at localized locations on the outer surface of the hemispherical resonator housing 213, minimizing its impact on surface defects. Air damping is primarily determined by the vacuum level of the resonator's operating environment. When the vacuum level is better than 1*10... -4 When Pa, the effect of air damping can be ignored. Therefore, ion beam etching has almost no effect on the damping distribution of the hemispherical resonator housing 213. The orientation of the rigid axis of the hemispherical resonator housing 213 is determined by the mass distribution of the hemispherical resonator housing 213. By etching the lower edges of the first etching position 209, the second etching position 210, the third etching position 211, and the fourth etching position 212, the rigid axis of the hemispherical resonator housing 213 can be deflected toward the damping axis, ultimately achieving alignment between the damping axis and the rigid axis.

[0058] The device for aligning the rigid axis and damping axis of the resonator further includes: a resonator control unit; several excitation cables and several detection cables. The first electrode 201, the fifth electrode 205, the second electrode 202 and the sixth electrode 206 are electrically connected to the resonator control unit through the excitation cables. The excitation cables are used to transmit the sinusoidal excitation signal generated by the resonator control unit. The third electrode 203, the seventh electrode 207, the fourth electrode 204 and the eighth electrode 208 are electrically connected to the resonator control unit through the detection cables. The detection cables are used to transmit the vibration signal of the hemispherical resonator housing 213.

[0059] In one embodiment, the voltage of the sinusoidal excitation signal is 50V to 200V.

[0060] The resonator control unit is used for digital-to-analog conversion, analog-to-digital conversion, amplification, and filtering of signals. The first electrode 201, fifth electrode 205, second electrode 202, and sixth electrode 206 are used to apply sinusoidal excitation signals to the hemispherical resonator housing 213. The third electrode 203, seventh electrode 207, fourth electrode 204, and eighth electrode 208 are used to detect minute vibrations of the hemispherical resonator housing 213. Minor changes in the gaps between the hemispherical resonator housing 213 and the third, seventh, fourth, and eighth electrodes cause changes in capacitance, resulting in weak electrical signals on these electrodes. These electrical signals are transmitted to the resonator control unit via detection cables for amplification and filtering.

[0061] Another embodiment of the present invention provides a method for aligning the rigid axis and damping axis of a resonator, using the apparatus for aligning the rigid axis and damping axis of a resonator provided in the above embodiments, comprising the following steps:

[0062] Step S1: Apply the first excitation signal to the hemispherical resonant housing 213 only on the first electrode 201 and the fifth electrode 205; disconnect the first excitation signal and obtain the first free decay signal of the hemispherical resonant housing 213 from the third electrode 203, the seventh electrode 207, the fourth electrode 204 and the eighth electrode 208;

[0063] Step S2: Apply the second excitation signal to the Nth excitation signal sequentially, and apply any kth excitation signal to the first electrode 201, the fifth electrode 205, the second electrode 202, and the sixth electrode 206, where N is an integer greater than or equal to 3; the excitation directions of the first excitation signal to the Nth excitation signal increase by a first angular step; the angle between the excitation direction of the Nth excitation signal and the excitation direction of the first excitation signal is greater than 45 degrees; obtain the second free decay signal to the Nth free decay signal of the hemispherical resonant shell 213. The step of obtaining the kth free decay signal is as follows: disconnect any kth excitation signal, and obtain the kth free decay signal from the third electrode 203, the seventh electrode 207, the fourth electrode 204, and the eighth electrode 208; k is an integer greater than or equal to 2 and less than or equal to N;

[0064] Step S3: Obtain the first characteristic excitation direction corresponding to the free decay signal with the smallest beat frequency from the first free decay signal to the Nth free decay signal;

[0065] Step S4: Apply the (N+1)th to (N+M)th excitation signals sequentially. Any j-th excitation signal is applied to the first electrode 201, the fifth electrode 205, the second electrode 202, and the sixth electrode 206. M is an integer greater than 1; j is an integer greater than or equal to N+1 and less than or equal to N+M. The excitation directions of the Nth to (N+M)th excitation signals increase with a second angular step size, which is much smaller than the first angular step size. The angle bisector of the (N+1)th to (N+M)th excitation directions is the first characteristic excitation direction. Obtain the (N+1)th to (N+M)th free decay signals of the hemispherical resonant shell 213. The step to obtain the j-th free decay signal is: disconnect any j-th excitation signal and obtain the j-th free decay signal from the third electrode 203, the seventh electrode 207, the fourth electrode 204, and the eighth electrode 208.

[0066] Step S5: Obtain the second characteristic excitation direction corresponding to the free decay signal with the smallest beat frequency from the (N+1)th free decay signal to the (N+M)th free decay signal as the orientation of the first rigid axis;

[0067] Step S6: Measure the resonant frequency of the hemispherical resonant housing 213 along the orientation of the first rigid axis and along the orientation of the second rigid axis, which is 45° away from the first rigid axis. The direction of change from the excitation direction of the first excitation signal to the excitation direction of the Nth excitation signal is consistent with the direction of change from the orientation of the first rigid axis to the orientation of the second rigid axis. If the resonant frequency measured along the orientation of the second rigid axis is greater than the resonant frequency measured along the orientation of the first rigid axis, then the second rigid axis is a high-frequency axis and the first rigid axis is a low-frequency axis. If the resonant frequency measured along the orientation of the second rigid axis is less than the resonant frequency measured along the orientation of the first rigid axis, then the second rigid axis is a low-frequency axis and the first rigid axis is a high-frequency axis. The frequency of the low-frequency axis is denoted as ω. L The frequency of the high-frequency axis is denoted as ω. H ;

[0068] Step S7: Obtain the free attenuation signal at the intermediate position between the orientation of the first rigid axis and the orientation of the second rigid axis, and obtain the frequency split based on the beat frequency period of the free attenuation signal at the intermediate position.

[0069] Step S8: Set a first adjustment position on the outer surface of the hemispherical resonator shell with the orientation of the low-frequency axis; obtain a second adjustment position, a third adjustment position, and a fourth adjustment position according to the orientation of the first adjustment position; the orientations of the first adjustment position, the second adjustment position, the third adjustment position, and the fourth adjustment position are spaced 90 degrees apart; rotate the hemispherical resonator shell, and the ion source emits an ion beam that etches the first adjustment position to the fourth adjustment position through the aperture respectively;

[0070] Step S9: After performing step S8, determine whether the frequency split is higher than the first target value; if the frequency split is higher than the first target value, repeat steps S1 to S8 until the frequency split is lower than or equal to the first target value. At this time, the low-frequency axis orientation is recorded as θω and the frequency split is recorded as Δf.

[0071] Step S10: Obtain the minimum and maximum damping axes of the hemispherical resonant shell 213, and denote the maximum damping value as τ. H The damping minimum is denoted as τ. L ;

[0072] Step S11: Obtain the orientation θ of the damping maximum axis. τ Orientation θ of the low-frequency axis ω The included angle α between them, when |θ τ -θ ω When |<45°, α=|θ τ -θ ω |;When|θ τ -θ ω When |≥45°, α=90-|θ τ -θ ω |;

[0073] Step S12: Obtain the etching time t of the ion beam according to the formula t=k*α*Δf / U, where k is a constant coefficient and U is the ion beam pressure;

[0074] Step S13: Set the first etching position on the outer surface of the hemispherical resonant housing 213 with the angle bisector of the included angle α; obtain the second, third, and fourth etching positions according to the orientation of the first etching position; the orientations of the first, second, third, and fourth etching positions are spaced 90 degrees apart.

[0075] Step S14: Rotate the hemispherical resonant housing 213, and the ion source emits an ion beam to etch the first to the fourth etching positions through the aperture 102. The etching time for the first to the fourth etching positions is t.

[0076] Step S15: After performing step S14, determine whether the angle between the damping maximum axis and the low-frequency axis is greater than the second target value; if the angle between the damping maximum axis and the low-frequency axis is greater than the second target value, repeat steps S1-S14 until the angle between the damping maximum axis and the low-frequency axis is less than the second target value.

[0077] In step S2, a second excitation signal is applied to the first electrode 201, the fifth electrode 205, the second electrode 202, and the sixth electrode 206. The angle between the excitation direction of the second excitation signal on the hemispherical resonant housing 213 and the excitation direction of the first excitation signal on the hemispherical resonant housing 213 is a first angular step. The second excitation signal is disconnected, and a second free decay signal is obtained from the third electrode 203, the seventh electrode 207, the fourth electrode 204, and the eighth electrode 208. Then, a third excitation signal is applied to the first electrode 201, the fifth electrode 205, the second electrode 202, and the sixth electrode 206. The angle between the excitation direction of the third excitation signal on the hemispherical resonant housing 213 and the excitation direction of the second excitation signal on the hemispherical resonant housing 213 is a first angular step. The third excitation signal is disconnected, and a third free decay signal is obtained from the third electrode 203, the seventh electrode 207, the fourth electrode 204, and the eighth electrode 208. The second free decay signal to the Nth free decay signal is obtained in this manner.

[0078] In one embodiment, the first angle step is 5 to 10 degrees, for example, 5 degrees or 6 degrees.

[0079] The angle between the excitation direction of the Nth excitation signal and the excitation direction of the first excitation signal is greater than 45 degrees. For example, the angle between the excitation direction of the Nth excitation signal and the excitation direction of the first excitation signal is 46 degrees to 60 degrees, such as 50 degrees.

[0080] In step S3, the free attenuation signal with the smallest beat frequency is obtained from the first free attenuation signal to the Nth free attenuation signal. Then, based on the obtained free attenuation signal, the corresponding excitation signal is obtained from the first excitation signal to the Nth excitation signal. The excitation direction of the obtained excitation signal is then used as the first characteristic excitation direction. For example, when the second free attenuation signal is the free attenuation signal with the smallest beat frequency from the first free attenuation signal to the Nth free attenuation signal, the excitation direction of the second excitation signal is used as the first characteristic excitation direction; when the fifth free attenuation signal is the free attenuation signal with the smallest beat frequency from the first free attenuation signal to the Nth free attenuation signal, the excitation direction of the fifth excitation signal is used as the first characteristic excitation direction.

[0081] In step S4, an N+1 excitation signal is applied to the first electrode 201, the fifth electrode 205, the second electrode 202, and the sixth electrode 206. The angle between the excitation direction of the N+1 excitation signal on the hemispherical resonant housing 213 and the excitation direction of the Nth excitation signal on the hemispherical resonant housing 213 is the second angular step size. The N+1 excitation signal is disconnected, and the N+1 free decay signal is obtained from the third electrode 203, the seventh electrode 207, the fourth electrode 204, and the eighth electrode 208. The N+1 excitation signal is applied to the first electrode 201, the fifth electrode 205, the second electrode 202, and the sixth electrode 206. An N+2 excitation signal is applied to electrode 205, the second electrode 202, and the sixth electrode 206. The angle between the excitation direction of the N+2 excitation signal on the hemispherical resonant shell 213 and the excitation direction of the N+1 excitation signal on the hemispherical resonant shell 213 is the second angular step size. The N+2 excitation signal is disconnected, and the N+2 free decay signal is obtained from the third electrode 203, the seventh electrode 207, the fourth electrode 204, and the eighth electrode 208. This process is repeated to obtain the N+1 to N+M free decay signals.

[0082] In one embodiment, the second angle step size is 0.2 degrees to 1 degree, for example, 0.5 degrees.

[0083] In one embodiment, the angle between the excitation direction of the N+1th excitation signal and the excitation direction of the N+Mth excitation signal is 6 to 18 degrees, for example, 6 degrees or 10 degrees.

[0084] In step S5, the free attenuation signal with the smallest beat frequency is obtained from the (N+1)th to the (N+M)th free attenuation signals. Then, based on the obtained free attenuation signal, the corresponding excitation signal is obtained from the (N+1)th to the (N+M)th excitation signals. The excitation direction of the obtained excitation signal is then used as the second characteristic excitation direction. For example, when the second free attenuation signal is the free attenuation signal with the smallest beat frequency among the first to the Nth free attenuation signals, the excitation direction of the second excitation signal is used as the first characteristic excitation direction; when the fifth free attenuation signal is the free attenuation signal with the smallest beat frequency among the first to the Nth free attenuation signals, the excitation direction of the fifth excitation signal is used as the first characteristic excitation direction.

[0085] In step S6, the direction of change from the excitation direction of the first excitation signal to the excitation direction of the Nth excitation signal is consistent with the direction of change from the orientation of the first rigid shaft to the orientation of the second rigid shaft. Specifically, when the direction of change from the excitation direction of the first excitation signal to the excitation direction of the Nth excitation signal is clockwise, the direction of change from the orientation of the first rigid shaft to the orientation of the second rigid shaft is clockwise; when the direction of change from the excitation direction of the first excitation signal to the excitation direction of the Nth excitation signal is counterclockwise, the direction of change from the orientation of the first rigid shaft to the orientation of the second rigid shaft is counterclockwise.

[0086] In step S7, the free attenuation signal at the intermediate azimuth between the azimuth of the first rigid axis and the azimuth of the second rigid axis is obtained, and the frequency split is obtained based on the beat frequency period of the free attenuation signal at the intermediate azimuth. In one embodiment, in step S7, the frequency split is 7.8 mHz.

[0087] In step S8, a first adjustment position is set on the outer surface of the hemispherical resonator shell with the orientation of the low-frequency axis; a second adjustment position, a third adjustment position, and a fourth adjustment position are obtained according to the orientation of the first adjustment position; the orientations of the first adjustment position, the second adjustment position, the third adjustment position, and the fourth adjustment position are spaced 90 degrees apart; the hemispherical resonator shell is rotated, and the ion source emits an ion beam that etches the first adjustment position to the fourth adjustment position through the aperture.

[0088] The first, second, third, and fourth adjustment positions are evenly distributed around the central axis of the hemispherical resonator housing 213. The centers of the first, second, third, and fourth adjustment positions are located on the same plane. The first, second, third, and fourth adjustment positions are located on the outer surface of the hemispherical resonator housing 213 near the opening of the hemispherical resonator housing 213. The angle between the line connecting the center of the first adjustment position to the central axis of the hemispherical resonator housing 213 and the line connecting the center of the second adjustment position to the central axis of the hemispherical resonator housing 213 is 90 degrees. The angle between the line connecting the center of the second adjustment position to the central axis of the hemispherical resonator housing 213 and the line connecting the center of the third adjustment position to the central axis of the hemispherical resonator housing 213 is 90 degrees. The angle between the line connecting the center of the third adjustment position to the central axis of the hemispherical resonator housing 213 and the line connecting the center of the fourth adjustment position to the central axis of the hemispherical resonator housing 213 and the line connecting the center of the fourth adjustment position to the central axis of the hemispherical resonator housing 213 and the line connecting the center of the first adjustment position to the central axis of the hemispherical resonator housing 213 is 90 degrees. In step S8, the hemispherical resonant housing 213 is rotated so that the first adjustment position faces the through-hole of the aperture 102, and the ion source emits an ion beam through the aperture 102 to etch the first adjustment position; the hemispherical resonant housing 213 is rotated so that the second adjustment position faces the through-hole of the aperture 102, and the ion source emits an ion beam through the aperture 102 to etch the second adjustment position; the hemispherical resonant housing 213 is rotated so that the third adjustment position faces the through-hole of the aperture 102, and the ion source emits an ion beam through the aperture 102 to etch the third adjustment position; the hemispherical resonant housing 213 is rotated so that the fourth adjustment position faces the through-hole of the aperture 102, and the ion source emits an ion beam through the aperture 102 to etch the fourth adjustment position. In step S8, the etching order of the first, second, third, and fourth adjustment positions can be arbitrarily adjusted.

[0089] In one embodiment, the first target value is 1mHz to 5mHz, for example, 1mHz.

[0090] In step S10, the method for obtaining the minimum and maximum damping axes of the hemispherical resonant housing 213 includes: applying test excitation signals to the first electrode 201, the fifth electrode 205, the second electrode 202, and the sixth electrode 206; measuring the free decay signal in the circumferential direction of the hemispherical resonant housing 213; the orientation of the minimum decay time is defined as the orientation θτ of the maximum damping axis; and the orientation of the maximum decay time is defined as the orientation of the minimum damping axis. In one embodiment, the orientation of the maximum damping axis is 47.4°.

[0091] The first, second, third, and fourth etching positions are evenly distributed around the central axis of the hemispherical resonant housing 213. The centers of the first etching position 209, the second etching position 210, the third etching position 211, and the fourth etching position 212 are located on the same plane. The first etching position 209, the second etching position 210, the third etching position 211, and the fourth etching position 212 are located on the outer surface of the hemispherical resonant housing 213 near the opening of the hemispherical resonant housing 213. The angle between the line connecting the center of the first etching position 209 to the central axis of the hemispherical resonant housing 213 and the line connecting the center of the second etching position 210 to the central axis of the hemispherical resonant housing 213 is 90 degrees. The angle between the line connecting the center of the second etching position 210 to the central axis of the hemispherical resonant housing 213 and the line connecting the center of the third etching position 211 to the central axis of the hemispherical resonant housing 213 is 90 degrees. The angle between the line connecting the center of the third etching position 211 to the central axis of the hemispherical resonant housing 213 and the line connecting the center of the fourth etching position 212 to the central axis of the hemispherical resonant housing 213 is 90 degrees. The angle between the line connecting the center of the fourth etching position 212 to the central axis of the hemispherical resonant housing 213 and the line connecting the center of the first etching position 209 to the central axis of the hemispherical resonant housing 213 is 90 degrees.

[0092] In one embodiment, the lower edges of the first etching position 209, the second etching position 210, the third etching position 211, and the fourth etching position 212 are tangent to the end face around the opening of the hemispherical resonant housing 213 to improve alignment efficiency.

[0093] In other embodiments, the lower edges of the first etching position 209, the second etching position 210, the third etching position 211, and the fourth etching position 212 are at a certain distance from the end face around the opening of the hemispherical resonant housing 213. For example, the distances between the lower edges of the first etching position 209, the second etching position 210, the third etching position 211, and the fourth etching position 212 and the end face around the opening of the hemispherical resonant housing 213 are 1 mm to 4 mm, respectively.

[0094] In step S14, the hemispherical resonant housing 213 is rotated so that the first etching position faces the through hole of the aperture 102. The ion source emits an ion beam through the aperture 102 to etch the first etching position for a time t, and the beam voltage of the ion source emitted an ion beam is U. The hemispherical resonant housing 213 is then rotated so that the second etching position faces the through hole of the aperture 102. The ion source emits an ion beam through the aperture 102 to etch the second etching position for a time t, and the beam voltage of the ion source emitted an ion beam is U. The beam pressure is U. The hemispherical resonant housing 213 is rotated so that the third etching position faces the through-hole of the aperture 102. The ion source emits an ion beam through the aperture 102 to etch the third etching position for a time t. The beam pressure of the ion source emitted by the ion beam is U. The hemispherical resonant housing 213 is rotated so that the fourth etching position faces the through-hole of the aperture 102. The ion source emits an ion beam through the aperture 102 to etch the fourth etching position for a time t. The beam pressure of the ion source emitted by the ion beam is U. In step S14, the etching order of the first, second, third, and fourth etching positions can be arbitrarily adjusted.

[0095] In one embodiment, the second target value is 0.1° to 1°, for example, 0.1°, 0.3°, 0.5°, or 1°.

[0096] In one embodiment, after the above method, the angle between the damping maximum axis and the low-frequency axis is 0.6°.

[0097] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A device for aligning the rigid axis and damping axis of a resonator, characterized in that, include: Chamber; A resonator located within the cavity, the resonator comprising a support column and a hemispherical resonant housing connected to the support column, the opening of the hemispherical resonant housing facing the bottom of the cavity; A resonator connector, one end of which is connected to the bottom end of the support column; A turntable, which is fixed at the other end of the bottom of the resonator connector; An ion source located in the chamber and on the side of the hemispherical resonant shell, the ion source being used to emit an ion beam; An aperture is located between the ion source and the hemispherical resonant housing. The ion beam passing through the aperture is used to etch the hemispherical resonant housing to change the position of the rigid axis of the hemispherical resonant housing. The diameter of the through hole of the aperture is 1 / 5 to 1 / 3 of the outer diameter of the hemispherical resonant housing. The first, second, third, fourth, fifth, sixth, seventh, and eighth electrodes are arranged sequentially and evenly around the central axis of the support column on the outer side of the hemispherical resonant shell. The center points of the first to eighth electrodes are concentric circles, and the center of the circle coincides with the central axis of the resonator. Excitation signals are applied to the first, fifth, second, and sixth electrodes. The third, seventh, fourth, and eighth electrodes are used to detect the vibration signal of the hemispherical resonant shell. The first and fifth electrodes are short-circuited and symmetrically arranged, the second and sixth electrodes are short-circuited and symmetrically arranged, the third and seventh electrodes are short-circuited and symmetrically arranged, and the fourth and eighth electrodes are short-circuited and symmetrically arranged.

2. The device for aligning the rigid shaft and damping shaft of a resonator according to claim 1, characterized in that, The gaps between the first to eighth electrodes and the hemispherical resonant shell are equal, and the gaps between the first to eighth electrodes and the hemispherical resonant shell are 20μm-80μm respectively.

3. The device for aligning the rigid shaft and damping shaft of a resonator according to claim 1, characterized in that, The roughness of the outer surface of the hemispherical resonator shell is 0.1 μm to 1 μm.

4. The device for aligning the rigid shaft and damping shaft of a resonator according to claim 1, characterized in that, It also includes: a resonator control unit; several excitation cables and several detection cables, wherein the first electrode, the fifth electrode, the second electrode and the sixth electrode are electrically connected to the resonator control unit via the excitation cables, the excitation cables being used to transmit the sinusoidal excitation signal generated by the resonator control unit, and the third electrode, the seventh electrode, the fourth electrode and the eighth electrode are electrically connected to the resonator control unit via the detection cables, the detection cables being used to transmit the vibration signal of the hemispherical resonator shell.

5. A method for aligning the rigid axis and damping axis of a resonator, wherein the resonator includes a hemispherical resonator housing, and a first electrode, a second electrode, a third electrode, a fourth electrode, a fifth electrode, a sixth electrode, a seventh electrode, and an eighth electrode are disposed on the outer side of the hemispherical resonator housing, the first to eighth electrodes being arranged at uniform intervals around the central axis of the hemispherical resonator housing, characterized in that, include: Step S1: Apply the first excitation signal to the hemispherical resonant shell only on the first electrode and the fifth electrode; Disconnect the first excitation signal and obtain the first free decay signal of the hemispherical resonant shell from the third, seventh, fourth and eighth electrodes; Step S2: Apply the second excitation signal to the Nth excitation signal in sequence. Any kth excitation signal is applied to the first electrode, the fifth electrode, the second electrode, and the sixth electrode. N is an integer greater than or equal to 3. The excitation directions of the first excitation signal to the Nth excitation signal increase by a first angle step. The angle between the excitation direction of the Nth excitation signal and the excitation direction of the first excitation signal is greater than 45 degrees. The steps for obtaining the second to Nth free decay signals of the hemispherical resonant shell and obtaining the kth free decay signal are as follows: disconnect any kth excitation signal and obtain the kth free decay signal from the third, seventh, fourth and eighth electrodes; k is an integer greater than or equal to 2 and less than or equal to N. Step S3: Obtain the first characteristic excitation direction corresponding to the free decay signal with the smallest beat frequency from the first free decay signal to the Nth free decay signal; Step S4: Apply the (N+1)th to (N+M)th excitation signals sequentially. Any j-th excitation signal is applied to the first electrode, the fifth electrode, the second electrode, and the sixth electrode. M is an integer greater than 1; j is an integer greater than or equal to N+1 and less than or equal to N+M. The excitation directions of the Nth to (N+M)th excitation signals increase with a second angle step size, which is much smaller than the first angle step size. The angle bisector direction from the (N+1)th to the (N+M)th excitation direction is the first characteristic excitation direction. The steps to obtain the N+1th to N+Mth free decay signals of the hemispherical resonant shell and to obtain the jth free decay signal are as follows: disconnect any jth excitation signal and obtain the jth free decay signal from the third, seventh, fourth and eighth electrodes. Step S5: Obtain the second characteristic excitation direction corresponding to the free decay signal with the smallest beat frequency from the (N+1)th free decay signal to the (N+M)th free decay signal as the orientation of the first rigid axis; Step S6: Measure the resonant frequency of the hemispherical resonant shell along the orientation of the first rigid axis and the orientation of the second rigid axis which is 45° away from the orientation of the first rigid axis. The direction of change from the excitation direction of the first excitation signal to the excitation direction of the Nth excitation signal is consistent with the direction of change from the orientation of the first rigid axis to the orientation of the second rigid axis. If the resonant frequency measured along the second rigid axis is greater than the resonant frequency measured along the first rigid axis, then the second rigid axis is a high-frequency axis and the first rigid axis is a low-frequency axis; if the resonant frequency measured along the second rigid axis is less than the resonant frequency measured along the first rigid axis, then the second rigid axis is a low-frequency axis and the first rigid axis is a high-frequency axis. Step S7: Obtain the free attenuation signal at the intermediate position between the orientation of the first rigid axis and the orientation of the second rigid axis, and obtain the frequency split based on the beat frequency period of the free attenuation signal at the intermediate position. Step S8: Set a first adjustment position on the outer surface of the hemispherical resonator shell with the orientation of the low-frequency axis; obtain a second adjustment position, a third adjustment position, and a fourth adjustment position according to the orientation of the first adjustment position; the orientations of the first adjustment position, the second adjustment position, the third adjustment position, and the fourth adjustment position are spaced 90 degrees apart; rotate the hemispherical resonator shell, and the ion source emits an ion beam that etches the first adjustment position to the fourth adjustment position through the aperture respectively; Step S9: After performing step S8, determine whether the frequency split is higher than the first target value; if the frequency split is higher than the first target value, repeat steps S1 to S8 until the frequency split is lower than the first target value. At this time, the low-frequency axis orientation is recorded as θω, and the frequency split is recorded as Δf. Step S10: Obtain the minimum and maximum damping axes of the hemispherical resonant shell; Step S11: Obtain the angle α between the orientation θτ of the damping maximum axis and the orientation θω of the low-frequency axis. When |θτ-θω| < 45°, α = |θτ-θω|; when |θτ-θω| ≥ 45°, α = 90 - |θτ-θω|. Step S12: According to the formula t=k α Δf / U is used to obtain the etching time t of the ion beam, where k is a constant coefficient and U is the ion beam pressure; Step S13: Set the first etching position on the outer surface of the hemispherical resonator shell with the angle bisector of the included angle α; obtain the second, third and fourth etching positions according to the orientation of the first etching position; the orientations of the first, second, third and fourth etching positions are spaced 90 degrees apart. Step S14: Rotate the hemispherical resonant shell, and the ion source emits an ion beam to etch the first to the fourth etching positions through the aperture. The etching time for each of the first to the fourth etching positions is t. Step S15: After performing step S14, determine whether the angle between the damping maximum axis and the low-frequency axis is greater than the second target value; if the angle between the damping maximum axis and the low-frequency axis is greater than the second target value, repeat steps S1-S14 until the angle between the damping maximum axis and the low-frequency axis is less than the second target value.

6. The method for aligning the rigid axis and damping axis of a resonator according to claim 5, characterized in that, The second angle step size is 0.2°~1°; the first angle step size is 5°~10°.

7. The method for aligning the rigid axis and damping axis of a resonator according to claim 5, characterized in that, The angle between the excitation direction of the (N+1)th excitation signal and the excitation direction of the (N+M)th excitation signal is 6°~18°.

8. The method for aligning the rigid axis and damping axis of a resonator according to claim 5, characterized in that, The first target value is 1mHz~5mHz; the second target value is 0.1°~1°.

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