A high-precision, equal-mass-density shaping method for hemispherical harmonic oscillators

Abstract

This invention discloses a high-precision, equal-mass-density shaping method for hemispherical resonators, comprising the following steps: determining the axial orientation of the central anchor of the hemispherical resonator through multi-position detection and analysis, serving as a measurement reference; measuring the three-dimensional contour point cloud coordinates and eccentric coordinates relative to the axial reference of the outer and inner spheres to establish actual contour models of the outer and inner spheres; determining the shaping area and corresponding removal thickness to establish a three-dimensional shaping removal model; performing three-dimensional continuous shaping removal processing on the areas to be shaped on the outer and inner spheres using an etching method; and evaluating the shaping results based on the mid-surface diameter and thickness distribution of the cross-sectional circles of the outer and inner spheres. This invention can achieve mass adjustment of the three-dimensional spherical shell of the hemispherical resonator. By jointly shaping the outer and inner spheres, a relatively symmetrical hemispherical resonator with a mass density distribution can be obtained, which is beneficial for improving the accuracy of the hemispherical resonator gyroscope.

Description

Technical Field

[0001] This invention belongs to the field of hemispherical resonator gyroscope technology, and in particular relates to a high-precision equal mass density shaping method for hemispherical resonators. Background Technology

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

[0003] The working principle of a hemispherical resonator gyroscope is based on detecting the rotation angle of the surrounding environment according to the precession of the standing wave of the hemispherical resonator. Therefore, the hemispherical resonator needs to have extremely high circumferential symmetry. However, errors exist in the actual manufacturing process of the hemispherical resonator, leading to mass imbalance, which directly affects the accuracy of the hemispherical resonator gyroscope. 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 significant impact on the damping non-uniformity of the hemispherical resonator, and the fourth harmonic defect has a significant impact on the frequency fragmentation of the hemispherical resonator. In order to reduce the mass defects of the hemispherical resonator, mass leveling is required. At present, various domestic mass leveling methods are effective in dealing with the fourth harmonic defect of the hemispherical resonator, but they 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 gyroscope. Therefore, it is necessary to explore and develop a mass adjustment method for the three-dimensional spherical shell of the hemispherical resonator to improve the accuracy of the hemispherical resonator gyroscope. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a high-precision equal-mass-density shaping method for hemispherical resonators, which can achieve mass adjustment of the three-dimensional spherical shell of the hemispherical resonator, resulting in a relatively symmetrical hemispherical resonator with equal mass density distribution centered on the anchor axis, which is beneficial for improving the accuracy of hemispherical resonant gyroscopes.

[0005] The technical solution of this invention:

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

[0007] Step 1: Perform multi-position detection and analysis on the central anchor of the hemispherical harmonic oscillator to determine the axial orientation of the central anchor of the hemispherical harmonic oscillator, and use it as the axial reference for the contour measurement of the hemispherical harmonic oscillator.

[0008] Step 2: Measure the three-dimensional contours of the outer and inner spheres to obtain the three-dimensional point cloud coordinates of the outer sphere of the hemispherical harmonic oscillator. 3D point cloud coordinates of the inner sphere ;

[0009] Step 3: Based on the point cloud coordinates, perform interpolation fitting on the outer and inner spherical contours, and divide the point cloud data into multi-section circles according to different cross-sectional circle angles;

[0010] Determine the measurement profile coordinates of the outer spherical surface at different angles of the cross-sectional circles. Measurement profile coordinates of the inner sphere at different cross-sectional circles ;

[0011] Determine the eccentric coordinates of the center of the outer spherical section relative to the central anchor axis reference. The eccentric coordinates of the center of the inner spherical cross section relative to the central anchor axis reference ;

[0012] Step 4: Based on the contour coordinates of the outer and inner spheres, and the eccentric coordinates of the outer and inner spheres relative to the central anchor axis reference, establish the actual contour coordinates of the outer sphere centered on the anchor axis. and the actual contour coordinates of the inner sphere ;

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

[0014] ,

[0015] in ,

[0016] Step 6: Determine the starting position for reshaping and removing circles with different cross-sections on the inner and outer spheres based on the thickness distribution of the outer and inner spheres, and determine the removal thickness corresponding to the circles with different cross-sections on the outer sphere based on the set threshold. The thickness removed corresponding to the different cross-sections of the inner sphere :

[0017] ,

[0018] Step 7: Perform splicing and fitting on the starting position and removal thickness of the shaping in each cross-sectional circle to establish a three-dimensional shaping removal model for the outer sphere. and the three-dimensional shape removal model of the inner sphere ;

[0019] Step 8: Use an etching method to perform three-dimensional continuous shaping and removal processing on the areas to be shaped on the outer and inner spherical surfaces to obtain the shaped and removed hemispherical harmonic oscillator.

[0020] Step 9: Repeat steps 2-7 until the mid-surface diameter and thickness distribution of the modified outer and inner spherical cross-sections meet the set threshold, and evaluate the vibration performance of the hemispherical harmonic oscillator.

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

[0022] Furthermore, in step 2, the three-dimensional contours of the outer and inner spheres are used to generate point cloud coordinate data through point, line, or surface measurements, and the point cloud coordinate data are the absolute coordinate positions or relative error contours of the outer and inner spheres.

[0023] Furthermore, in step 3, the outer and inner spherical contours are interpolated and fitted, and the interpolation and fitting are performed along the latitude and longitude directions based on the point cloud coordinates.

[0024] Furthermore, in step 5, during the process of dividing the actual contours of the outer and inner spheres into multi-section circles, the dividing interval range is 0.1mm-4mm.

[0025] Furthermore, in step 6, the starting position for the shaping and removal of the outer sphere is the position with the smallest 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 shaping and removal of the inner sphere is the position with the largest radius of the first cross-sectional circle.

[0026] Furthermore, in steps 6 and 7, the shaping thicknesses of the outer and inner spherical surfaces with different cross-sectional circles are distributed at equal phase intervals on the cross-sectional circles, with a phase interval of [missing information]. , m Integer and .

[0027] Furthermore, in step 8, the outer and inner spherical surfaces are modified by a machining tool using a spiral path for controllable modification, or the modification areas of the outer and inner spherical surfaces 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] Based on the performance requirements of gyroscopes, this invention proposes a surface mass removal shaping method. Compared to traditional point mass removal leveling (four-point leveling), this method more easily approximates the uniformity and balance of the resonator's profile. This invention also proposes a method for joint mass shaping of the inner and outer spherical surfaces, which can obtain a relatively symmetrical hemispherical resonator with equal mass density centered on the anchor axis, thereby improving the vibration performance of the hemispherical resonator. Furthermore, this invention proposes a three-dimensional profile error modeling method for the hemispherical resonator. By measuring the outer spherical profile, the inner spherical profile, and the eccentricity relative to the anchor axis, a three-dimensional error model of the hemispherical resonator can be established, thereby enabling the evaluation of the hemispherical resonator's machining accuracy. This invention adopts the minimum radius principle for outer spherical surface shaping and the maximum radius principle for inner spherical surface shaping, enabling the establishment of an accurate three-dimensional shaping model while ensuring minimum... This invention improves shaping efficiency by removing defects and using a combination of the mid-diameter and thickness values ​​of different cross-sections of the hemispherical harmonic oscillator to evaluate the shaping effect. This approach reasonably balances the radius and relative contour error of the hemispherical harmonic oscillator, ensuring shaping accuracy. Furthermore, by calibrating the anchor column's central axis through multi-position detection, this invention improves the accuracy of the axis reference, thereby ensuring the accuracy of the error model. By performing bidirectional interpolation fitting along parallels and meridians based on the measured contours of the outer and inner spheres, this invention smooths the shaping error model and improves the dynamic performance of three-dimensional shaping. By setting different processing times based on the contour errors of the outer and inner spheres, this invention enables deterministic shaping, improving the shaping accuracy of the hemispherical harmonic oscillator. Finally, by optimizing and matching the processing tools, processing pitch, and processing path to determine processing parameters, this invention reasonably allocates processing errors, improving the three-dimensional shaping accuracy of the hemispherical harmonic oscillator. Attached Figure Description

[0030] Figure 1 A flowchart of a high-precision, equal-mass-density shaping method for a hemispherical harmonic oscillator;

[0031] Figure 2 A schematic diagram showing the contours of the outer and inner spherical surfaces of a hemispherical harmonic oscillator before and after modification;

[0032] Figure 3 A schematic diagram of the three-dimensional shape removal model of the outer or inner spherical surface of a hemispherical harmonic oscillator;

[0033] In the diagram: 1 - Outer spherical outline before shaping, 2 - Outer spherical outline after shaping, 3 - Inner spherical outline after shaping, 4 - Inner spherical outline before shaping, 5 - Area removed during outer spherical shaping, 6 - Area removed during inner spherical shaping. Detailed Implementation

[0034] The present invention will now be clearly and specifically described in conjunction with the accompanying drawings and specific implementation methods.

[0035] refer to Figure 1This invention provides a high-precision, equal-mass-density shaping method for a hemispherical harmonic oscillator, comprising the following steps:

[0036] Step 1) Perform multi-position detection and analysis on the central anchor of the hemispherical harmonic oscillator to determine the axial orientation of the central anchor of the hemispherical harmonic oscillator, and use it as the axial reference for the contour measurement of the hemispherical harmonic oscillator.

[0037] Step 2) Measure the three-dimensional contours of the outer and inner spheres to obtain the three-dimensional point cloud coordinates of the outer sphere of the hemispherical harmonic oscillator. 3D point cloud coordinates of the inner sphere ;

[0038] Step 3) Based on the point cloud coordinates, interpolate and fit the outer and inner spherical contours, and divide the point cloud data into multi-section circles according to different cross-sectional circle angles; whereby... , representing the angle of circles with different cross sections;

[0039] Determine the measurement profile coordinates of the outer spherical surface at different angles of the cross-sectional circles. Measurement profile coordinates of the inner sphere at different cross-sectional circles ;

[0040] Determine the eccentric coordinates of the center of the outer spherical section relative to the central anchor axis reference. The eccentric coordinates of the center of the inner spherical cross section relative to the central anchor axis reference ;

[0041] Step 4) Based on the contour coordinates of the outer and inner spheres, and the eccentric coordinates of the outer and inner spheres relative to the central anchor axis reference, establish the actual contour coordinates of the outer sphere centered on the anchor axis. and the actual contour coordinates of the inner sphere ;

[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 of each cross-sectional circle. and thickness distribution ,

[0043] ,

[0044] in ,

[0045] Step 6), refer to Figure 2 The starting positions for reshaping and removing circles with different cross-sections on the inner and outer spheres are determined based on the thickness distribution of the outer and inner spheres. The removal thickness corresponding to the circles with different cross-sections on the outer sphere is determined based on a set threshold. The thickness removed corresponding to the different cross-sections of the inner sphere :

[0046] ,

[0047] Step 7), refer to Figure 3 By stitching and fitting the starting position and removal thickness of the shaping in each cross-sectional circle, a three-dimensional shaping removal model for the outer sphere is established. and the three-dimensional shape removal model of the inner sphere ;

[0048] Step 8) Use an etching method to perform three-dimensional continuous shaping and removal processing on the areas to be shaped on the outer and inner spherical surfaces; to obtain the shaped and removed hemispherical harmonic oscillator.

[0049] Step 9) Repeat steps 2)-7) until the mid-surface diameter and thickness distribution of the modified outer and inner spherical cross-sections meet the set threshold, and evaluate the vibration performance of the hemispherical harmonic oscillator.

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

[0051] In step 2), the three-dimensional contours of the outer and inner spheres are used to generate point cloud coordinate data through point, line or surface measurements, and the point cloud coordinate data are the absolute coordinate positions or relative error contours of the outer and inner spheres.

[0052] In step 3), the outer and inner spherical contours are interpolated and fitted, and the interpolation and fitting are performed along the latitude and longitude directions based on the point cloud coordinates.

[0053] In step 5), during the process of dividing the actual contours of the outer and inner spherical surfaces into multi-section circles, the dividing interval range is 0.1mm-4mm.

[0054] In step 6), the starting position for the shaping and removal of the outer spherical surface is at the position with 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 shaping and removal of the inner sphere is at the position of the maximum radius of the first cross-section circle, i.e. ;

[0055] In steps 6) and 7), the shaping thicknesses of the outer and inner spherical surfaces with different cross-sectional circles are distributed at equal phase intervals on the cross-sectional circles, with a phase interval of [missing information]. , m Integer and ;

[0056] In step 8), the outer and inner spherical surfaces are reshaped using a controllable spiral path with a machining tool, or by masking the reshaped areas of the outer and inner spherical surfaces. Effective reshaping is achieved by setting different machining times for different reshaped areas. During the spiral path reshaping of the outer spherical surface, the machining tool follows the changes in the steepness of the outer spherical surface at different heights to ensure uniform machining. Simultaneously, machining time compensation is performed based on the changes in the diameter of the cross-section circle under different steepnesses of the outer spherical surface to ensure uniform point density machining. During the spiral path reshaping of the inner spherical surface, the angle between the normal direction of the inner spherical surface and the axis of the machining tool is adjusted in real time to ensure perpendicular machining. Furthermore, the spiral path is geometrically optimized based on the occlusion of the inner spherical surface reshaping area by the central anchor post to ensure unobstructed machining of the inner spherical surface.

[0057] To address the problem that existing hemispherical resonator mass leveling techniques only perform localized mass removal for fourth harmonic defects, this invention provides a high-precision equal-mass-density shaping method for hemispherical resonators. This method enables mass leveling of the three-dimensional spherical shell of the hemispherical resonator. By jointly shaping the outer and inner spherical surfaces, a completely symmetrical hemispherical resonator with equal mass density distribution can be obtained, which is beneficial for improving the accuracy of hemispherical resonator gyroscopes.

[0058] Example 1

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

[0060] Step 1) Use a roundness meter to perform four-section circularity tests on the central anchor of the hemispherical harmonic oscillator to determine the axial orientation of the central anchor of the hemispherical harmonic oscillator, and use it as the axial reference for measuring the relative error profile of the hemispherical harmonic oscillator.

[0061] Step 2) Use a roundness meter to measure the three-dimensional roundness error of the outer sphere 1 and the inner sphere 4 to obtain the three-dimensional error point cloud coordinates of the outer sphere of the hemispherical harmonic oscillator. 3D error point cloud coordinates of the inner sphere ;

[0062] Step 3) Based on the error point cloud coordinates, interpolate and fit the error profiles of outer sphere 1 and inner sphere 4 along the latitude and longitude directions. Divide the error point cloud data into multiple cross-sectional circles with a pitch of 0.1 mm between the cross-sectional circles. Determine the eccentric coordinates of the center of the cross-sectional circle of the outer sphere relative to the central anchor axis reference. The eccentric coordinates of the center of the inner spherical cross section relative to the central anchor axis reference ;

[0063] Step 4) Based on the relative error profile coordinates of outer spherical surface 1 and inner spherical surface 4, and the eccentric coordinates of the outer and inner spherical surfaces relative to the central anchor axis reference, establish the actual error profile coordinates of the outer spherical surface centered on the anchor axis. And the actual error profile coordinates of the inner sphere ;

[0064] Step 5) Divide the actual error profiles of outer sphere 1 and inner sphere 4 into multiple cross-section circles. The pitch between the cross-section circles is 0.1 mm, and the phase interval on the cross-section circles is... Calculate the mid-surface diameter of each cross-section circle. and thickness distribution ;

[0065] Step 6) The starting position for reshaping and removing circles with different cross-sections on the outer sphere is the position with the smallest radius, and the starting position for reshaping and removing circles with different cross-sections on the inner sphere is the position with the largest radius. The reshaping area 5 and the corresponding removal thickness of the circles with different cross-sections on the outer sphere are determined according to the set threshold. The shaping area 6 and the corresponding thickness removal of the circle with different cross-sections from the inner sphere. :

[0066] Step 7) By splicing and fitting the starting position and removal thickness of the shaping in each cross-sectional circle, a three-dimensional shaping removal model of the outer sphere is established. and the three-dimensional shape removal model of the inner sphere ;

[0067] Step 8) Calculate the processing time based on the areas to be modified on the outer and inner spherical surfaces, and use the ion beam etching method to directly perform three-dimensional spiral continuous modification and removal processing on the areas to be modified.

[0068] Step 9) Repeat steps 2)-7) until the mid-surface diameter and thickness distribution of the modified outer spherical surface 2 and inner spherical surface 3 cross-section circles meet the set threshold, and evaluate the vibration performance of the hemispherical harmonic oscillator.

[0069] Example 2

[0070] The high-precision equal-mass-density shaping method for the hemispherical harmonic oscillator in this embodiment is basically the same as steps 5)-9) in embodiment 1, except that in this embodiment:

[0071] Step 1) Use a coordinate measuring machine to perform four-point detection on two or more sections of the central anchor of the hemispherical harmonic oscillator. Determine the axial orientation of the central anchor of the hemispherical harmonic oscillator by center fitting, and use it as the axial reference for the absolute profile measurement of the hemispherical harmonic oscillator.

[0072] Step 2) Use a linear displacement sensor to measure the three-dimensional contours of the outer sphere 1 and the inner sphere 4 to obtain the three-dimensional point cloud coordinates of the outer sphere of the hemispherical harmonic oscillator. 3D point cloud coordinates of the inner sphere ;

[0073] Step 3) Based on the absolute point cloud coordinates, interpolate and fit the contours of outer sphere 1 and inner sphere 4 along the latitudinal and longitudinal directions. Divide the contour point cloud data into multiple cross-sectional circles with a pitch of 0.1 mm between the cross-sectional circles. Determine the eccentric coordinates of the center of the cross-sectional circle of the outer sphere relative to the central anchor axis reference. The eccentric coordinates of the center of the inner spherical cross section relative to the central anchor axis reference ;

[0074] Step 4) Based on the absolute contour coordinates of the outer sphere 1 and the inner sphere 4, and the eccentric coordinates of the outer and inner spheres relative to the central anchor axis reference, establish the actual contour coordinates of the outer sphere centered on the anchor axis. and the actual contour coordinates of the inner sphere ;

[0075] Example 3

[0076] The high-precision equal-mass-density shaping method for the hemispherical harmonic oscillator 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 sphere 1 and the inner sphere 4 into multiple cross-section circles. Set the pitch between the cross-section circles to 0.5 mm based on the diameter of the machining tool, and the phase interval on the cross-section circles is... Calculate the mid-surface diameter of each cross-section circle. and thickness distribution ;

[0078] Step 8) Calculate the processing time based on the areas to be shaped on the outer and inner spheres, mask the areas to be shaped on the outer and inner spheres, and use chemical etching to achieve effective shaping by controlling the processing time.

Claims

1. A high-precision, equal-mass-density shaping method for a hemispherical harmonic oscillator, characterized in that, The method includes the following steps: Step 1: Perform multi-position detection and analysis on the central anchor of the hemispherical harmonic oscillator to determine the axial orientation of the central anchor of the hemispherical harmonic oscillator, and use it as the axial reference for the contour measurement of the hemispherical harmonic oscillator. Step 2: Measure the three-dimensional contours of the outer and inner spheres to obtain the three-dimensional point cloud coordinates of the outer sphere of the hemispherical harmonic oscillator. 3D point cloud coordinates of the inner sphere ; Step 3: Based on the point cloud coordinates, perform interpolation fitting on the outer and inner spherical contours, and divide the point cloud data into multi-section circles according to different cross-sectional circle angles; Determine the measurement profile coordinates of the outer spherical surface at different angles of the cross-sectional circles. Measurement profile coordinates of the inner sphere at different cross-sectional circles ; Determine the eccentric coordinates of the center of the outer spherical section relative to the central anchor axis reference. The eccentric coordinates of the center of the inner spherical cross section relative to the central anchor axis reference ; Step 4: Based on the contour coordinates of the outer and inner spheres, and the eccentric coordinates of the outer and inner spheres relative to the central anchor axis reference, establish the actual contour coordinates of the outer sphere centered on the anchor axis. and the actual contour coordinates of the inner sphere ; Step 5: Calculate the mid-surface diameter of each cross-sectional circle. and thickness distribution , ， in , Step 6: Determine the starting position for reshaping and removing circles with different cross-sections on the inner and outer spheres based on the thickness distribution of the outer and inner spheres, and determine the removal thickness corresponding to the circles with different cross-sections on the outer sphere based on the set threshold. The thickness removed corresponding to the different cross-sections of the inner sphere : ， Step 7: Perform splicing and fitting on the starting position and removal thickness of the shaping in each cross-sectional circle to establish a three-dimensional shaping removal model for the outer sphere. and the three-dimensional shape removal model of the inner sphere ; Step 8: Use an etching method to perform three-dimensional continuous shaping and removal processing on the areas to be shaped on the outer and inner spherical surfaces to obtain the shaped and removed hemispherical harmonic oscillator. Step 9: Repeat steps 2-7 until the mid-surface diameter and thickness distribution of the modified outer and inner spherical cross-sections meet the set threshold, and evaluate the vibration performance of the hemispherical harmonic oscillator.

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

3. The high-precision equal-mass-density shaping method for a hemispherical harmonic oscillator according to claim 1, characterized in that, In step 2, the three-dimensional contours of the outer and inner spheres are generated by point cloud coordinate data through point, line or surface measurements, and the point cloud coordinate data are the absolute coordinate positions or relative error contours of the outer and inner spheres.

4. The high-precision equal-mass-density shaping method for a hemispherical harmonic oscillator according to claim 1, characterized in that, In step 3, the outer and inner spherical contours are interpolated and fitted, and the interpolation and fitting are performed along the latitude and longitude directions based on the point cloud coordinates.

5. The high-precision equal-mass-density shaping method for a hemispherical harmonic oscillator according to claim 1, characterized in that, In step 5, during the process of dividing the actual contours of the outer and inner spheres into multi-section circles, the dividing interval range is 0.1mm-4mm.

6. The high-precision equal-mass-density shaping method for a hemispherical harmonic oscillator according to claim 1, characterized in that, In step 6, the starting position for the shaping and removal of the outer sphere is the position with 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 shaping and removal of the inner sphere is the position with the largest radius of the first cross-sectional circle.

7. The high-precision equal-mass-density shaping method for a hemispherical harmonic oscillator according to claim 1, characterized in that, In steps 6 and 7, the shaping thicknesses of the outer and inner spherical surfaces with different cross-sectional circles are distributed at equal phase intervals on the cross-sectional circles, with a phase interval of [missing information]. , m Integer and .

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

Images