High-precision equal-mass-density modification method for hemispherical harmonic oscillator

Abstract

The invention discloses a hemispherical harmonic oscillator high-precision equal-mass-density modification method, which comprises the following steps: determining the axis direction of a central anchor post of a hemispherical harmonic oscillator through multi-position detection analysis, and taking the axis direction as a measurement basis; measuring three-dimensional contour point cloud coordinates of the outer spherical surface and the inner spherical surface and eccentric coordinates relative to the axis reference, and establishing actual contour models of the outer spherical surface and the inner spherical surface; a modification area and a corresponding removal thickness are determined, and a three-dimensional modification removal model is established; carrying out three-dimensional continuous modification removal processing on the to-be-modified areas of the outer spherical surface and the inner spherical surface by adopting an etching method; and evaluating a modification result according to the middle surface diameter and thickness distribution of the section circles of the outer spherical surface and the inner spherical surface. According to the invention, the mass trimming of the three-dimensional spherical shell of the hemispherical resonator can be realized, and the hemispherical resonator with relatively symmetrical mass density distribution can be obtained through the combined mass trimming of the outer spherical surface and the inner spherical surface, so that the precision of the hemispherical resonator gyroscope can be improved.

Description

Technical Field

[0001] The invention belongs to the technical field of hemispherical resonator gyroscopes, and in particular relates to a high-precision equal-mass density shaping method for a hemispherical resonator. Background Art

[0002] The hemispherical resonant gyroscope is a solid wave gyroscope based on the Coriolis vibration principle. It has the advantages of small size, high precision, long life, resistance to electromagnetic radiation and high reliability. It has broad application prospects in aerospace and other fields.

[0003] The working principle of the hemispherical resonator is to detect the external rotation angle according to the standing wave precession of the hemispherical resonator. Therefore, the hemispherical resonator needs to have extremely high circumferential symmetry. However, there are errors in the actual processing of the hemispherical resonator, which leads to mass imbalance of the hemispherical resonator, which directly affects the accuracy of the hemispherical resonator. The circumferential distribution of the mass imbalance of the hemispherical resonator can be expanded into a harmonic distribution form according to the Fourier series. Among them, the first three harmonic defects have a greater impact on the damping unevenness of the hemispherical resonator, and the fourth harmonic defect has a greater impact on the frequency splitting of the hemispherical resonator. In order to reduce the mass defects of the hemispherical resonator, it is necessary to perform mass leveling on the hemispherical resonator. At present, various domestic mass leveling methods have a good effect on the fourth harmonic defect of the hemispherical resonator, but cannot achieve mass adjustment on the entire hemispherical shell, which seriously affects the vibration performance of the hemispherical resonator and is the core factor restricting the accuracy of the hemispherical resonator. Therefore, it is necessary to explore and develop mass adjustment methods for the three-dimensional spherical shell of the hemispherical resonator to improve the accuracy of the hemispherical resonator. Summary of the invention

[0004] In view of the above problems, the present invention provides a high-precision equal-mass-density shaping method for a hemispherical resonator, which can realize the mass adjustment of the three-dimensional spherical shell of the hemispherical resonator, and obtain a relatively symmetrical hemispherical resonator with equal-mass-density distribution centered on the axis of the anchor column, which is beneficial to improving the accuracy of the hemispherical resonator gyroscope.

[0005] The technical solution of the present invention:

[0006] A high-precision equal-mass density shaping method for a hemispherical resonator, the method comprising the following steps:

[0007] Step 1: Perform multi-position detection and analysis on the central anchor column of the hemispherical resonator to determine the axis orientation of the central anchor column of the hemispherical resonator and use it as the axis reference for the contour measurement of the hemispherical resonator;

[0008] Step 2: Measure the three-dimensional contours of the outer sphere and the inner sphere to obtain the three-dimensional point cloud coordinates (x w ,y w ,z w ) and the 3D point cloud coordinates of the inner sphere (xn ,y n ,z n );

[0009] Step 3: interpolate and fit the outer spherical surface and the inner spherical surface contours according to the point cloud coordinates, and divide the point cloud data into multiple cross-sectional circles according to different cross-sectional circle angles;

[0010] Determine the measured contour coordinates (x wΦ ',y wΦ ') and the measured contour coordinates (x) of the inner sphere at different cross-sectional circle angles nΦ ',y nΦ ');

[0011] Determine the eccentric coordinate (x wΦ ',y wΦ ') and the eccentric coordinate (x nΦ ',y nΦ ');

[0012] Step 4: According to the contour coordinates of the outer sphere and the inner sphere, and the eccentric coordinates of the outer sphere and the inner sphere relative to the central anchor column axis, the actual contour coordinates (x wΦ -x wΦ ',y wΦ -y wΦ ') and the actual contour coordinates of the inner sphere (x nΦ -x nΦ ',y nΦ -y nΦ ');

[0013] Step 5: Calculate the mid-surface diameter R of each cross-sectional circle Φ and thickness distribution h Φ ,

[0014] h Φ =R wΦ '-R nΦ '

[0015] in

[0016] Step 6: Determine the starting position of the modification and removal of the different cross-section circles of the inner and outer spheres according to the thickness distribution of the outer sphere and the inner sphere, and determine the removal thickness h corresponding to the different cross-section circles of the outer sphere according to the set threshold. wΦ The removal thickness h corresponding to the different cross-section circles of the inner sphere nΦ :

[0017] h wΦ=R wΦ '-min(R wΦ '),h nΦ =max(R nΦ ')-R nΦ '

[0018] Step 7: Perform splicing and fitting of the trimming starting position and trimming removal thickness in each cross-sectional circle to establish a three-dimensional trimming removal model for the outer spherical surface [h wΦ1 ;h wΦ2 ;h wΦ3 …] and the three-dimensional shape removal model of the inner sphere [h nΦ1 ;h nΦ2 ;h nΦ3 …];

[0019] Step 8, performing three-dimensional continuous shaping and removing processing on the areas to be modified on the outer spherical surface and the inner spherical surface by etching method, so as to obtain a hemispherical resonator after shaping and removal;

[0020] Step 9, repeat steps 2 to 7 until the mid-surface diameter and thickness distribution of the outer spherical surface and the inner spherical surface cross-section circle after modification meet the set threshold value, and evaluate the vibration performance of the hemispherical resonator.

[0021] Furthermore, in step 1, the axis orientation of the central anchor column is determined by measuring the cross-sectional profiles of the central anchor column at different heights, fitting the center of each cross-sectional profile, and determining the reference axis based on the line connecting all the center points.

[0022] Furthermore, in step 2, the three-dimensional contours of the outer spherical surface and the inner spherical surface are measured by points, lines or surfaces to generate point cloud coordinate data, and the point cloud coordinate data are the absolute coordinate positions or relative error contours of the outer spherical surface and the inner spherical surface.

[0023] Furthermore, in step 3, the outer spherical surface and the inner spherical surface contours are interpolated and fitted, and interpolated and fitted along the latitude direction and the longitude direction according to the point cloud coordinates.

[0024] Furthermore, in step 5, during the process of dividing the actual contours of the outer spherical surface and the inner spherical surface into multiple cross-sectional circles, the division interval range is 0.1 mm-4 mm.

[0025] Furthermore, in step 6, the starting position for the outer spherical surface modification and removal is the position of the minimum radius of the first cross-sectional circle, and the first cross-sectional circle is the circle with the largest radius among all cross-sectional circles; the starting position for the inner spherical surface modification and removal is the position of the maximum radius of the first cross-sectional circle.

[0026] Furthermore, in step 6 and step 7, the modified thicknesses of different cross-sectional circles of the outer spherical surface and the inner spherical surface are distributed at equal phase intervals on the cross-sectional circles, and the phase interval is 2π / m, where m is an integer and m≥10.

[0027] Furthermore, in step 8, the outer spherical surface and the inner spherical surface are modified by a processing tool in a controllable manner in a spiral path, or the modification areas of the outer spherical surface and the inner spherical surface are masked, and different processing times are set for different modification areas to achieve effective modification.

[0028] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0029] The present invention proposes a surface mass removal shaping method based on the requirements of gyroscope performance. Compared with the traditional point mass removal leveling (four-point leveling), the present method is easier to approximate the contour uniformity and balance of the resonator; the present invention proposes a method for joint mass shaping of inner and outer spherical surfaces, which can obtain a relatively symmetrical hemispherical resonator with equal mass density centered on the axis of the anchor column, thereby improving the vibration performance of the hemispherical resonator; the present invention proposes a three-dimensional contour error modeling method for a hemispherical resonator, which can establish a three-dimensional error model of the hemispherical resonator by measuring the outer spherical contour, the inner spherical contour and the eccentricity relative to the axis of the anchor column, thereby evaluating the machining accuracy of the hemispherical resonator; the present invention adopts the minimum radius principle for the outer spherical shaping and the maximum radius principle for the inner spherical shaping, which can establish an accurate three-dimensional shaping model while ensuring the minimum The present invention removes mass and improves the shaping efficiency; the present invention jointly evaluates the shaping effect with the median diameter value and thickness value of different cross-section circles of the hemispherical resonator, which can reasonably take into account the radius and relative profile error size of the hemispherical resonator and ensure the shaping accuracy; the present invention calibrates the central axis of the anchor column through multi-position detection, which can improve the axis reference accuracy and thus ensure the error model accuracy; the present invention performs interpolation fitting in both directions along the latitude and longitude according to the measured profiles of the outer spherical surface and the inner spherical surface, which can smooth the shaping error model and improve the dynamic performance of the three-dimensional shaping processing; the present invention sets different processing times according to the profile errors of the outer spherical surface and the inner spherical surface, which can perform deterministic shaping and improve the shaping accuracy of the hemispherical resonator; the present invention determines the processing parameters by optimizing the matching of the processing tool, the processing pitch and the processing path, which can reasonably distribute the processing errors and improve the three-dimensional shaping accuracy of the hemispherical resonator. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 A flow chart of the high-precision equal-mass density shaping method for a hemispherical resonator;

[0031] Figure 2 It is a schematic diagram of the contours of the outer spherical surface and the inner spherical surface of the hemispherical resonator before and after the modification;

[0032] Figure 3 A schematic diagram of a three-dimensional shape removal model of an outer sphere or inner sphere of a hemispherical resonator;

[0033] In the figure: 1-outer spherical contour before shaping, 2-outer spherical contour after shaping, 3-inner spherical contour after shaping, 4-inner spherical contour before shaping, 5-outer spherical contour removal area, 6-inner spherical contour removal area. DETAILED DESCRIPTION

[0034] The present invention will be described clearly and specifically below with reference to the accompanying drawings and specific implementation methods.

[0035] refer to Figure 1 The embodiment of the present invention provides a high-precision equal-mass density shaping method for a hemispherical resonator, comprising the following steps:

[0036] Step 1), performing multi-position detection and analysis on the central anchor column of the hemispherical resonator, determining the axis orientation of the central anchor column of the hemispherical resonator, and using it as the axis reference for the contour measurement of the hemispherical resonator;

[0037] Step 2) Measure the three-dimensional contours of the outer sphere and the inner sphere to obtain the three-dimensional point cloud coordinates (x w ,y w ,z w ) and the 3D point cloud coordinates of the inner sphere (x n ,y n ,z n );

[0038] Step 3), interpolate and fit the outer spherical surface and inner spherical surface contours according to the point cloud coordinates, and divide the point cloud data into multiple cross-sectional circles according to different cross-sectional circle angles; Indicates the angles of circles with different cross sections;

[0039] Determine the measured contour coordinates (x wΦ ',y wΦ ') and the measured contour coordinates (x) of the inner sphere at different angles of the cross-section circle nΦ ',y nΦ ');

[0040] Determine the eccentric coordinate (x wΦ ',y wΦ ') and the eccentric coordinate (x nΦ ',y nΦ ');

[0041] Step 4) According to the contour coordinates of the outer sphere and the inner sphere, and the eccentric coordinates of the outer sphere and the inner sphere relative to the central anchor column axis, the actual contour coordinates (x wΦ -x wΦ ',y wΦ -ywΦ ') and the actual contour coordinates of the inner sphere (x nΦ -x nΦ ',y nΦ -y nΦ ');

[0042] Step 5) Refer to Figure 2 , divide the actual contours of the outer sphere 1 and the inner sphere 4 into multiple cross-sectional circles, and calculate the mid-surface diameter R of each cross-sectional circle Φ and thickness distribution h Φ ,

[0043] h Φ =R wΦ '-R nΦ '

[0044] in

[0045] Step 6) Refer to Figure 2 According to the thickness distribution of the outer spherical surface and the inner spherical surface, the starting position of the inner and outer spherical surface with different cross-section circles is determined, and the removal thickness h corresponding to the outer spherical surface with different cross-section circles is determined according to the set threshold. wΦ The removal thickness h corresponding to the different cross-section circles of the inner sphere nΦ :

[0046] h wΦ =R wΦ '-min(R wΦ '),h nΦ =max(R nΦ ')-R nΦ '

[0047] Step 7), refer to Figure 3 , the trimming starting position and trimming removal thickness in each cross-sectional circle are spliced ​​and fitted to establish a three-dimensional trimming removal model for the outer spherical surface [h wΦ1 ;h wΦ2 ;h wΦ3 …] and the three-dimensional shape removal model of the inner sphere [h nΦ1 ;h nΦ2 ;h nΦ3 …];

[0048] Step 8), the outer spherical surface and the inner spherical surface are subjected to three-dimensional continuous shaping and removal processing by etching to obtain the hemispherical resonator after shaping and removal;

[0049] Step 9), repeat step 2)-step 7) until the mid-surface diameter and thickness distribution of the modified outer spherical and inner spherical cross-section circles meet the set thresholds, and evaluate the vibration performance of the hemispherical resonator.

[0050] In the step 1), the axis orientation of the central anchor column is determined by measuring the cross-sectional profiles of the central anchor column at different heights, fitting the center of each cross-sectional profile, and determining the reference axis according to the line connecting all the center points;

[0051] In the step 2), the three-dimensional contours of the outer spherical surface and the inner spherical surface are measured by points, lines or surfaces to generate point cloud coordinate data, and the point cloud coordinate data are the absolute coordinate positions or relative error contours of the outer spherical surface and the inner spherical surface;

[0052] In the step 3), the outer spherical surface and the inner spherical surface contours are interpolated and fitted, and interpolated and fitted along the latitude direction and the longitude direction according to the point cloud coordinates;

[0053] In the step 5), during the multi-section circle division process of the actual contour of the outer spherical surface and the inner spherical surface, the division interval range is 0.1mm-4mm;

[0054] In step 6), the starting position of the outer spherical surface modification is the position of the minimum radius of the first cross-sectional circle, and the first cross-sectional circle is the circle with the largest radius among all cross-sectional circles, that is, min(R wΦ '); The starting position of the inner spherical surface modification is the maximum radius of the first section circle, that is, max(R nΦ ');

[0055] In the step 6) and step 7), the modified thicknesses of the different cross-sectional circles of the outer spherical surface and the inner spherical surface are distributed at equal phase intervals on the cross-sectional circles, and the phase interval is 2π / m, where m is an integer and m≥10;

[0056] In the step 8), the shaping of the outer spherical surface and the inner spherical surface is controlled by the processing tool in a spiral path, or the shaping areas of the outer spherical surface and the inner spherical surface are masked, and different processing times are set for different shaping areas to achieve effective shaping. In the process of shaping the outer spherical surface with a spiral path, the processing tool follows the height according to the change of the steepness of the outer spherical surface to ensure the equal height processing of the outer spherical surface. At the same time, the processing time is compensated according to the change of the cross-sectional circle diameter under different steepness of the outer spherical surface to ensure the equal point density processing of the outer spherical surface. In the process of shaping the inner spherical surface with a spiral path, the angle between the normal direction of the inner spherical surface and the axis of the processing tool is adjusted in real time to ensure the vertical processing of the inner spherical surface. At the same time, according to the shielding of the inner spherical surface shaping area by the central anchor column, the spiral path is optimized by geometric model to ensure the unobstructed processing of the inner spherical surface.

[0057] In view of the problem that the existing hemispherical resonator mass leveling technology only removes mass at a local point position for the fourth harmonic defect, the present invention provides a high-precision equal mass density shaping method for a hemispherical resonator, which can achieve mass leveling of the three-dimensional spherical shell of the hemispherical resonator. By jointly shaping the outer spherical surface and the inner spherical surface, a completely symmetrical hemispherical resonator with equal mass density distribution can be obtained, which is beneficial to improving the precision of the hemispherical resonator gyroscope.

[0058] Example 1

[0059] This embodiment provides a high-precision equal-mass density shaping method for a hemispherical resonator, including the following process:

[0060] Step 1), using a roundness meter to perform four-section circle detection on the central anchor column of the hemispherical resonator, determine the axis orientation of the central anchor column of the hemispherical resonator, and use it as the axis reference for the relative error profile measurement of the hemispherical resonator;

[0061] Step 2) Use a roundness meter to measure the three-dimensional contour roundness error of the outer spherical surface 1 and the inner spherical surface 4, and obtain the three-dimensional error point cloud coordinates (x w ,y w ,z w ) and the three-dimensional error point cloud coordinates of the inner sphere (x n ,y n ,z n );

[0062] Step 3) According to the error point cloud coordinates, the error contours of the outer sphere 1 and the inner sphere 4 are interpolated and fitted along the latitude and longitude directions, and the error point cloud data is divided into multiple cross-sectional circles. The pitch between the cross-sectional circles is 0.1 mm, and the eccentric coordinates (x wΦ ',y wΦ ') and the eccentric coordinate (x nΦ ',y nΦ ');

[0063] Step 4) According to the relative error contour coordinates of the outer spherical surface 1 and the inner spherical surface 4, and the eccentric coordinates of the outer spherical surface and the inner spherical surface relative to the central anchor column axis reference, the actual error contour coordinates (x wΦ -x wΦ ',y wΦ -y wΦ ') and the actual error contour coordinates of the inner sphere (x nΦ -x nΦ ',y nΦ -y nΦ ');

[0064] Step 5) Divide the actual error contours of the outer spherical surface 1 and the inner spherical surface 4 into multiple cross-sectional circles, with a pitch of 0.1 mm between the cross-sectional circles and a phase interval of 2π / 100 on the cross-sectional circles, and calculate the mid-surface diameter R of each cross-sectional circle. Φ and thickness distribution h Φ ;

[0065] Step 6), the starting position of the outer spherical surface with different cross-section circles is the minimum radius position, and the starting position of the inner spherical surface with different cross-section circles is the maximum radius position. The trimming area 5 and the corresponding removal thickness h of the outer spherical surface with different cross-section circles are determined according to the set threshold. wΦ The modified area 6 with different cross-section circles from the inner sphere and the corresponding removal thickness h nΦ :

[0066] Step 7) perform splicing and fitting of the trimming starting position and trimming removal thickness in each cross-sectional circle to establish a three-dimensional trimming removal model for the outer spherical surface [h wΦ1 ;h wΦ2 ;h wΦ3 …] and the three-dimensional shape removal model of the inner sphere [h nΦ1 ;h nΦ2 ;h nΦ3 …];

[0067] Step 8), calculating the processing time according to the areas to be modified on the outer spherical surface and the inner spherical surface, and directly performing three-dimensional spiral continuous modification and removal processing on the areas to be modified by an ion beam etching method;

[0068] Step 9), repeat step 2)-step 7) until the mid-surface diameter and thickness distribution of the cross-section circles of the outer spherical surface 2 and the inner spherical surface 3 after modification meet the set threshold value, and evaluate the vibration performance of the hemispherical resonator.

[0069] Example 2

[0070] The high-precision equal-mass density shaping method of a hemispherical resonator in this embodiment is basically the same as step 5) to step 9) in embodiment 1, except that in this embodiment:

[0071] Step 1), using a three-coordinate measuring instrument to perform four-point detection on more than two cross sections of the central anchor column of the hemispherical resonator, determine the axis orientation of the central anchor column of the hemispherical resonator by circle center fitting, and use it as the axis reference for absolute profile measurement of the hemispherical resonator;

[0072] Step 2) Use a linear displacement sensor to measure the three-dimensional contours of the outer spherical surface 1 and the inner spherical surface 4 to obtain the three-dimensional point cloud coordinates (x w ,y w ,z w ) and the 3D point cloud coordinates of the inner sphere (x n ,y n ,z n );

[0073] Step 3) According to the absolute point cloud coordinates, the contours of the outer sphere 1 and the inner sphere 4 are interpolated and fitted along the latitude and longitude directions, and the contour point cloud data is divided into multiple cross-sectional circles. The pitch between the cross-sectional circles is 0.1 mm, and the eccentric coordinates (x wΦ ',y wΦ ') and the eccentric coordinate (x nΦ ',y nΦ ');

[0074] Step 4) According to the absolute contour coordinates of the outer spherical surface 1 and the inner spherical surface 4, and the eccentric coordinates of the outer spherical surface and the inner spherical surface relative to the central anchor column axis, the actual contour coordinates (x wΦ -x wΦ ',y wΦ -y wΦ ') and the actual contour coordinates of the inner sphere (x nΦ -x nΦ ',y nΦ -y nΦ ');

[0075] Example 3

[0076] The high-precision equal-mass density shaping method of the hemispherical resonator in this embodiment is basically the same as that in Embodiment 1, except that in this embodiment:

[0077] Step 5) Divide the actual contours of the outer spherical surface 1 and the inner spherical surface 4 into multiple cross-sectional circles. Set the pitch between the cross-sectional circles to 0.5 mm according to the diameter of the machining tool, and the phase interval on the cross-sectional circles to 2π / 50. Calculate the mid-surface diameter R of each cross-sectional circle. Φ and thickness distribution h Φ ;

[0078] Step 8) Calculate the processing time according to the areas to be modified on the outer spherical surface and the inner spherical surface, mask the modification areas on the outer spherical surface and the inner spherical surface, and use a chemical etching method to control the processing time to achieve effective modification processing.

Claims

1. A high-precision equal-mass density shaping method for a hemispherical resonator, characterized in that: The method comprises the following steps: Step 1: Perform multi-position detection and analysis on the central anchor column of the hemispherical resonator to determine the axis orientation of the central anchor column of the hemispherical resonator and use it as the axis reference for the contour measurement of the hemispherical resonator; Step 2: Measure the three-dimensional contours of the outer sphere and the inner sphere to obtain the three-dimensional point cloud coordinates (x w ,y w ,z w ) and the 3D point cloud coordinates of the inner sphere (x n ,y n ,z n ); Step 3: interpolate and fit the outer spherical surface and the inner spherical surface contours according to the point cloud coordinates, and divide the point cloud data into multiple cross-sectional circles according to different cross-sectional circle angles; Determine the measured contour coordinates (x wΦ ′,y wΦ ′) and the measured contour coordinates (x nΦ ′,y nΦ ′); Determine the eccentric coordinate (x wΦ ′,y wΦ ′) and the eccentric coordinate (x nΦ ′,y nΦ ′); Step 4: According to the contour coordinates of the outer sphere and the inner sphere, and the eccentric coordinates of the outer sphere and the inner sphere relative to the central anchor column axis, the actual contour coordinates (x wΦ -x wΦ ′,y wΦ -y wΦ ′) and the actual contour coordinates of the inner sphere (x nΦ -x nΦ ′,y nΦ -y nΦ ′); Step 5: Calculate the mid-surface diameter R of each cross-sectional circle Φ and thickness distribution h Φ , h Φ =R wΦ '-R nΦ ' in Step 6: Determine the starting position of the modification and removal of the different cross-section circles of the inner and outer spheres according to the thickness distribution of the outer sphere and the inner sphere, and determine the removal thickness h corresponding to the different cross-section circles of the outer sphere according to the set threshold. wΦ The removal thickness h corresponding to the different cross-section circles of the inner sphere nΦ : h wΦ =R wΦ '-min(R wΦ '),h nΦ =max(R nΦ ')-R nΦ ' Step 7: Perform splicing and fitting of the trimming starting position and trimming removal thickness in each cross-sectional circle to establish a three-dimensional trimming removal model for the outer spherical surface [h wΦ1 ;h wΦ2 ;h wΦ3 …] and the three-dimensional shape removal model of the inner sphere [h nΦ1 ;h nΦ2 ;h nΦ3 …]; Step 8, performing three-dimensional continuous shaping and removing processing on the areas to be modified on the outer spherical surface and the inner spherical surface by etching method, so as to obtain a hemispherical resonator after shaping and removal; Step 9, repeat steps 2 to 7 until the mid-surface diameter and thickness distribution of the outer spherical surface and the inner spherical surface cross-section circle after modification meet the set threshold value, and evaluate the vibration performance of the hemispherical resonator.

2. A high-precision equal-mass density shaping method for a hemispherical resonator according to claim 1, characterized in that: In step 1, the axis orientation of the central anchor column is determined by measuring the cross-sectional profiles of the central anchor column at different heights, fitting the center of each cross-sectional profile, and determining the reference axis according to the line connecting all the center points.

3. The high-precision equal-mass density shaping method of a hemispherical resonator according to claim 1, characterized in that: In step 2, the three-dimensional contours of the outer spherical surface and the inner spherical surface are measured by points, lines or surfaces to generate point cloud coordinate data, and the point cloud coordinate data are the absolute coordinate positions or relative error contours of the outer spherical surface and the inner spherical surface.

4. The high-precision equal-mass density shaping method of a hemispherical resonator according to claim 1, characterized in that: In step 3, the outer spherical surface and the inner spherical surface contours are interpolated and fitted, and interpolated and fitted along the latitude direction and the longitude direction according to the point cloud coordinates.

5. The high-precision equal-mass density shaping method of a hemispherical resonator according to claim 1, characterized in that: In step 5, during the multi-section circle division of the actual contours of the outer spherical surface and the inner spherical surface, the division interval range is 0.1 mm-4 mm.

6. The high-precision equal-mass density shaping method of a hemispherical resonator according to claim 1, characterized in that: In step 6, the starting position for the outer spherical surface modification and removal is the position of the smallest radius of the first cross-sectional circle, which is the circle with the largest radius among all cross-sectional circles; the starting position for the inner spherical surface modification and removal is the position of the largest radius of the first cross-sectional circle.

7. The high-precision equal-mass density shaping method of a hemispherical resonator according to claim 1, characterized in that: In step 6 and step 7, the modified thicknesses of different cross-sectional circles of the outer spherical surface and the inner spherical surface are distributed at equal phase intervals on the cross-sectional circles, and the phase interval is 2π / m, where m is an integer and m≥10.

8. The high-precision equal-mass density shaping method of a hemispherical resonator according to claim 1, characterized in that: In step 8, the outer spherical surface and the inner spherical surface are modified by a processing tool in a spiral path to perform controllable modification processing, or the modification areas of the outer spherical surface and the inner spherical surface are masked, and different processing times are set for different modification areas to achieve effective modification processing.

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