CN114139301B - Hemispherical harmonic oscillator processing error standard formulation method based on frequency splitting - Google Patents

Abstract

A hemispherical resonator machining error standard making method based on frequency splitting relates to the technical field of hemispherical resonator machining errors and aims to solve the problem that the hemispherical resonator machining error standard is not made based on frequency splitting angles in the prior art so as to improve working accuracy of the hemispherical resonator. The method comprises the steps of establishing a hemispherical resonator simulation three-dimensional model by using finite element analysis software, setting model boundary conditions as fixed constraints of upper and lower surfaces of a supporting rod, carrying out finite element grid division by adopting extremely-thin free tetrahedron grids to obtain a first working frequency and a second working frequency of hemispherical resonator operation, and obtaining a frequency cracking value by differentiating the first working frequency and the second working frequency, thereby obtaining a simulation result of influence of a plurality of processing errors on frequency cracking; and respectively analyzing the simulation result of the influence of each machining error on the frequency splitting, and finally obtaining the hemispherical resonator machining error standard. The invention improves the processing precision of the hemispherical harmonic oscillator and gives consideration to the processing efficiency and the working performance.

Description

A method for formulating the machining error standard of hemispherical harmonic oscillator based on frequency cracking

technical field

The invention relates to the technical field of hemispherical harmonic oscillator processing, in particular to a method for formulating a processing error standard for hemispherical harmonic oscillators based on frequency splitting.

Background technique

With the increasing development of modern science and technology, various high-performance gyroscopes are needed to ensure accurate navigation and positioning capabilities in many fields such as aerospace, military defense, and marine exploration. As a new type of high-precision gyroscope, the hemispherical resonant gyroscope has a relatively simple structure and unique working principle. It has been widely used due to its advantages in impact resistance, strong radiation resistance, small size, low energy consumption, high reliability, and long working life. application. The hemispherical resonator is the core component of the hemispherical resonant gyroscope, and its machining accuracy and surface quality directly determine the performance of the gyroscope.

At present, for the ultra-precision machining of the hemispherical resonator, it is necessary to use a special small-sized polishing head and realize it on a dedicated multi-axis linkage ultra-precision machine tool. The machining error generated during the processing of the hemispherical resonator, such as: the alignment error of the hemispherical shell (the coaxiality error between the hemispherical shell and the symmetry axis of the support rod, the center of the sphere on the surface of the inner and outer hemispherical shells in the axial direction and radial direction Concentricity error) and surface processing error of the hemispherical shell (roundness error near the bottom lip and true sphericity error on the surface of the hemispherical shell), etc. will cause the frequency cracking of the operating frequency of the harmonic oscillator, causing the angular drift of the harmonic oscillator and affecting the performance of the harmonic oscillator. Working precision. Therefore, how to control the processing error of the hemispherical resonator in practical engineering applications needs to be solved urgently.

Contents of the invention

In view of the above problems, the present invention proposes a hemispherical harmonic oscillator processing error standard formulation method based on frequency splitting to solve the problem in the prior art that the processing error standard of the hemispherical harmonic oscillator is not formulated based on the frequency splitting angle to improve its working accuracy.

A method for formulating a processing error standard of a hemispherical harmonic oscillator based on frequency cracking, the structure of the hemispherical harmonic oscillator includes a hemispherical shell and a support rod; the method comprises the following steps:

Step 1, using finite element analysis software to establish a simulated three-dimensional model of the hemispherical harmonic oscillator, and define the material properties of the hemispherical harmonic oscillator;

Step 2. Set the boundary conditions of the simulated three-dimensional model in the finite element analysis software as fixed constraints on the upper and lower surfaces of the support rods, and use extremely fine free tetrahedral meshes for finite element meshing to obtain hemispherical resonance The sub-work is the first working frequency and the second working frequency under the four-amplitude mode shape, and the difference between the first working frequency and the second working frequency is obtained to obtain the frequency cracking value, so as to obtain the simulation results of the influence of multiple processing errors on the frequency cracking, The processing error includes coaxiality error, inner and outer hemisphere surface radial concentricity error, inner and outer hemisphere surface spherical center axial concentricity error, true sphericity error and roundness error; the specific steps include:

Step 21. The axis of the hemispherical shell of the hemispherical resonator deviates from the axis of the support rod by a first minute distance, the value of the first minute distance is equal to the coaxiality error, and the value of the first minute distance is changed to obtain multiple coaxial Accuracy errors affect the simulation results of frequency splitting, and the simulation results of the impact of multiple coaxiality errors on frequency splitting include the first operating frequency, the second operating frequency, and the frequency splitting value corresponding to each coaxiality error;

Step 22. Deviate the center of the inner and outer hemisphere surfaces of the hemispherical resonator by a second minute distance in the radial direction, the value of the second minute distance is equal to the radial concentricity error of the center of the inner and outer hemisphere surfaces, and change the second minute distance The value of the distance, the simulation results of the influence of multiple radial concentricity errors on the frequency splitting are obtained, and the simulation results of the influence of the multiple radial concentricity errors on the frequency splitting include the first operating frequency, the first operating frequency, and the second corresponding to each radial concentricity error 2. Working frequency, frequency cracking value;

Step 23: Deviate the sphere center of the inner and outer hemispherical surfaces of the hemispherical resonator along the axis of rotation of the workpiece by a third minute distance, the value of the third minute distance is equal to the axial concentricity error of the inner and outer hemispherical surfaces, and change the third The value of the small distance is used to obtain the simulation results of the influence of multiple axial concentricity errors on the frequency splitting. The simulation results of the influence of the multiple axial concentricity errors on the frequency splitting include the first operating frequency corresponding to each axial concentricity error, Second working frequency, frequency cracking value;

Step 24: Add sinusoidal function fluctuations to the surface of the inner hemispherical shell of the hemispherical harmonic oscillator to form a curved spherical shell, and the wall thickness of the curved spherical shell is distributed along the direction of the semicircular arc to present an uneven sinusoidal function shape, thereby forming multiple surface corrugations Shaped true sphericity errors, to obtain a plurality of true sphericity errors on frequency cracking simulation results, the simulation results of the multiple true sphericity errors on frequency splitting include the first operating frequency, the second 2. Working frequency, frequency cracking value;

Step 25: Divide the surface of the inner hemispherical shell of the hemispherical harmonic oscillator into two with the center plane of symmetry, set one half as a hemispherical surface, and the other half as a semi-ellipsoidal surface, the minor axis of the semi-ellipsoid is the same as the radius of the hemisphere, and the length of the semi-ellipsoid The difference between the shaft and the radius of the hemisphere is the fifth micro-distance, the value of the fifth micro-distance is equal to the roundness error, changing the value of the fifth micro-distance, and obtaining the simulation results of the impact of multiple roundness errors on the frequency splitting, so The simulation results of the impact of multiple roundness errors on frequency cracking include the first working frequency, the second working frequency, and the frequency cracking value corresponding to each roundness error;

Step 3. The simulation results of the influence of multiple coaxiality errors on the frequency cracking, the simulation results of the influence of multiple radial concentricity errors on the frequency cracking, the simulation results of the influence of multiple axial concentricity errors on the frequency cracking, and the simulation results of multiple true spheres The simulation results of the influence of roundness errors on the frequency splitting and the simulation results of the influence of multiple roundness errors on the frequency splitting are analyzed to obtain the processing error standard of the hemispherical harmonic oscillator.

Further, the material properties of the hemispherical harmonic oscillator include Young's modulus, density and Poisson's ratio.

Further, the surface function corresponding to the curved spherical shell described in step two or four is:

In the formula, α and β represent angle variables; Δd represents the size of the sinusoidal fluctuation of true sphericity.

Furthermore, the result of analyzing the simulation results of multiple coaxiality errors on frequency splitting in step three is: when the coaxiality error of the hemispherical harmonic oscillator gradually increases, the distribution of the radius of the hemispherical shell in the circumferential direction is uneven Intensified, causing the frequency splitting of the harmonic oscillator to fluctuate and increase; as the coaxiality error gradually increases in the range of 0.1 to 0.5 μm, the frequency splitting of the harmonic oscillator does not increase significantly; therefore, the standard value of the coaxiality error of the hemispherical harmonic oscillator 0.5 μm.

Further, the result of analyzing the simulation results of the influence of multiple radial concentricity errors on the frequency splitting in step 3 is: with the increase of the radial concentricity error, the frequency splitting of the harmonic oscillator fluctuates and increases, but from the numerical point of view , the radial concentricity error does not increase significantly in the range of 0.1-0.5 μm; therefore, the radial concentricity error of the inner and outer hemisphere surfaces of the hemispherical resonator is 0.5 μm.

Further, the result of analyzing the simulation results of multiple axial concentricity errors on the frequency splitting in step 3 is: when there is a concentricity error of the hemispherical shell in the axial direction, the frequency splitting of the working mode shape of the harmonic oscillator is slightly affected. Therefore, the concentricity error of the inner and outer hemispherical surfaces of the hemispherical harmonic oscillator ranges from 0 to 0.5 mm.

Further, the result of analyzing the simulation results of multiple sphericity errors on the frequency splitting in step 3 is: as the sphericity error of the hemispherical shell surface of the hemispherical harmonic oscillator increases from 0 to 10 μm, the working mode of the hemispherical harmonic oscillator The frequency splitting of the frequency increases significantly in a proportional trend. Therefore, the true sphericity error of the hemispherical harmonic oscillator is 0.5 μm.

Further, the result of analyzing the simulation results of multiple roundness errors on the frequency splitting in step 3 is: as the roundness error of the bottom surface of the hemispherical resonator increases, the frequency splitting of the hemispherical resonator presents a fluctuating upward trend. Therefore, the hemispherical resonant The roundness error of the sub is 0.5μm.

The beneficial technical effect of the present invention is:

The present invention uses finite element software to analyze the degree of influence of different processing errors on the frequency cracking of the hemispherical resonator, and combines the finite element analysis results to formulate a highly credible processing accuracy index to provide theoretical guidance for the processing accuracy of the actual hemispherical resonator; through Reasonably select the processing equipment and process parameters to reduce the true sphericity error that affects the working accuracy of the hemispherical harmonic oscillator, and take into account the processing efficiency and the working performance of the hemispherical harmonic oscillator. The method of the invention has certain universality, and can be extended to analyze and formulate the method for formulating processing error control standards of various parts.

Description of drawings

The present invention can be better understood by reference to the following description given in conjunction with the accompanying drawings, which together with the following detailed description are incorporated in and form a part of this specification, and are used to further illustrate A preferred embodiment of the invention and an explanation of the principles and advantages of the invention.

Fig. 1 is a structural schematic diagram of a hemispherical harmonic oscillator in the present invention; wherein, Figure (a) is a schematic diagram of the size parameters of a hemispherical harmonic oscillator, in which 1 is a hemispherical shell, and 2 is a support rod; Figure (b) is a hemispherical harmonic oscillator finite element network Schematic diagram of grid division;

Fig. 2 is a schematic diagram of coaxiality error in the present invention;

Fig. 3 is a schematic diagram of the radial concentricity error of the hemispherical shell in the present invention;

Fig. 4 is a schematic diagram of the axial concentricity error of the hemispherical shell in the present invention;

Fig. 5 is a schematic diagram of the sphericity error surface in the present invention;

Fig. 6 is a schematic diagram of roundness error in the present invention.

Detailed ways

In order to enable those skilled in the art to better understand the solutions of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Apparently, the described embodiments or examples are only part of the embodiments or embodiments of the present invention, not all of them. Based on the implementation modes or examples in the present invention, all other implementation modes or examples obtained by persons of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Since there is no scientific standard for the processing accuracy index of the hemispherical resonator in the prior art, unreasonable processing accuracy will not only bring a certain degree of processing difficulty, but also greatly reduce the processing efficiency. Therefore, the present invention provides a frequency cracking-based Hemispherical harmonic oscillator processing error standard formulation method, simulated research on the influence of various processing errors on harmonic oscillator frequency splitting, explored hemispherical harmonic oscillator error control standards, and established an evaluation system for harmonic oscillator processing accuracy. This method of formulating the machining error standard of hemispherical harmonic oscillator based on frequency splitting can reasonably formulate the range of machining error.

As shown in Figure 1(a), the Ψ-shaped hemispherical harmonic oscillator is composed of a hemispherical shell and a support rod, and the hemispherical shell and the support rod are transitioned by a transition fillet. The boundary conditions of the model are fixed constraints on the upper and lower surfaces of the support rods, and a very fine free tetrahedron mesh is used for finite element mesh division, as shown in Fig. 1(b).

Table 1 Dimension parameters of a certain model Ψ-type hemispherical harmonic oscillator

The machining error of the hemispherical resonator refers to the error caused by factors such as machine tool accuracy or machining environment interference during the machining process, including the alignment error of the hemispherical shell (the coaxiality error of the hemispherical shell and the symmetry axis of the support rod, the internal , the concentricity error of the center of the outer hemispherical shell in the axial direction and radial direction) and the surface processing error of the hemispherical shell (the roundness error near the bottom lip and the true sphericity error of the hemispherical shell surface). Using the single factor method, the influence of different machining errors on the frequency splitting of the hemispherical harmonic oscillator is analyzed, and according to the analysis results, the machining error standard of the harmonic oscillator is established.

The specific steps involved are as follows:

Step 1: Use the finite element analysis software COMSOL to establish a simulated 3D model of the hemispherical harmonic oscillator. COMSOL software is a finite element analysis software widely used for modal analysis of materials and multi-physics field coupling solutions. Define Young’s modulus E=7.67×10 ¹⁰ Pa, density ρ=2.2×10 ³ kg/m3, Poisson’s ratio μ=0.17 of the fused silica material used;

Step 2: Set the upper and lower surfaces of the support rods as fixed constraints, use extremely fine free tetrahedral grids for finite element mesh division, and analyze the eigenfrequency of the hemispherical harmonic oscillator to obtain the hemispherical harmonic oscillator working in the four-amplitude vibration The first and second operating frequencies under the model are 5078.865Hz and 5078.929Hz respectively, and the difference between the two frequencies gives a frequency split value of 0.063Hz.

Step 3: Analyze the influence law of the coaxiality error of the harmonic oscillator on the frequency splitting.

Step 31: Establish the model of the coaxiality error of the harmonic oscillator, and set the distance between the axis of the hemispherical shell and the axis of the support rod by the distance △x of the support rod, that is, the first minute distance, and set the coaxiality error between the axis of the hemispherical shell and the axis of the support rod, as shown in Figure 2 shown.

Step 32: Change the value of the first tiny distance in step 31, and follow step 2 to obtain the first operating frequency, the second operating frequency and the frequency splitting value of the harmonic oscillator corresponding to different coaxiality errors.

Step 33: Analyze the influence of the coaxiality error on the frequency splitting. The simulation results show that when the coaxiality error of the hemispherical harmonic oscillator gradually increases, the uneven distribution of the radius of the hemispherical shell in the circumferential direction will increase, which will cause the frequency splitting of the harmonic oscillator to be Increased volatility trend. However, with the increase of the coaxiality error in the range of 0.1-0.5μm, the frequency splitting of the harmonic oscillator does not increase significantly. If only the frequency splitting of the hemispherical resonator is considered, further increasing the error requirements will greatly increase the processing difficulty of the resonator. Therefore, from the simulation results, there is no need to increase the requirement on the coaxiality error.

Step 4: Analyze the influence law of the radial concentricity error of the hemispherical shell of the harmonic oscillator on the frequency splitting.

Step 41: Establish the model of the radial concentricity error of the hemispherical shell of the harmonic oscillator, and set the center diameter of the inner and outer hemisphere surfaces by the distance from △y in the radial direction, which is the second minute distance. Concentricity error, as shown in Figure 3.

Step 42: Change the value of the second tiny distance in step 41, and follow step 2 to obtain the first operating frequency, the second operating frequency and the frequency splitting value of the harmonic oscillator corresponding to different radial coaxiality errors.

Step 43: Analyze the influence of the radial concentricity error on the frequency splitting. The simulation results show that with the increase of the radial concentricity error, the frequency splitting of the resonator shows a trend of increasing fluctuations, but the radial concentricity error is numerically There is no obvious increase in the range of 0.1-0.5 μm. Therefore, the radial concentricity error within 0.5 μm will not have a great impact on the drift of the harmonic oscillator.

Step 5: Analyze the influence law of the axial concentricity error of the hemispherical shell of the harmonic oscillator on the frequency splitting.

Step 51: Establish the model of the axial concentricity error of the harmonic oscillator, deviate the center of the inner and outer hemispheres along the axis of rotation of the workpiece by a distance of △z, which is the third minute distance, and set the axis of the center of the inner and outer hemispheres Concentricity error, as shown in Figure 4.

Step 52: Change the value of the third tiny distance in step 51, and follow step 2 to obtain the first operating frequency, the second operating frequency and the frequency splitting value of the harmonic oscillator corresponding to different axial coaxiality errors.

Step 53: Analyze the influence of the axial concentricity error on the frequency cracking. The simulation results show that when there is a concentricity error of the hemispherical shell in the axial direction, the frequency cracking of the working mode shape of the harmonic oscillator decreases slightly. The reason may be that the axis The concentricity error will only cause the thickness of the hemispherical shell to be uneven in the axial direction, and the thickness and radius of the resonator to be uniform in the circumferential direction. The increase in the wall thickness near the rounded corners will reduce the vibration amplitude of the resonator but make it more stable. The existence of the axial concentricity error has a certain inhibitory effect on the frequency splitting.

Step 6: Analyze the influence law of the sphericity error of the harmonic oscillator on the frequency cracking.

Step 61: Establish the model of the true sphericity error of the harmonic oscillator, replace the original hemispherical shell with the parametric surface controlled by formula (1), add sinusoidal function fluctuations on the basis of the inner hemispherical shell surface, and form as The curved spherical shell shown in Figure 5 makes the wall thickness of the hemispherical shell distributed along the direction of the semicircular arc to present an uneven sinusoidal function shape, forming a corrugated surface true sphericity error.

In the formula, α and β represent angle variables; Δd represents the magnitude of the sinusoidal fluctuation of true sphericity, that is, the fourth tiny distance.

Step 62: Change the value of the fourth tiny distance in step 61, and follow step 2 to obtain the first operating frequency, the second operating frequency and the frequency cracking value of the harmonic oscillator corresponding to different true sphericity errors.

Step 63: Analyze the effect of sphericity error on frequency cracking. The simulation results show that as the sphericity error on the surface of the hemispherical shell of the hemispherical harmonic oscillator increases from 0 to 10 μm, the frequency cracking of the working mode shape of the hemispherical harmonic oscillator has a direct proportional trend. The increase of , indicating that compared with other processing errors, the existence of surface fluctuations of the hemispherical shell will have a greater impact on the working accuracy of the hemispherical harmonic oscillator. Therefore, in order to ensure the normal operation of the hemispherical resonator, it is necessary to improve the clamping accuracy when machining the hemispherical shell, and choose a tool with a higher rigidity to minimize the surface true sphericity error caused by the vibration of the machine tool or the tool.

Step 7: Analyze the law of the influence of the roundness error of the harmonic oscillator on the frequency splitting.

Step 71: Establish a model of the roundness error of the harmonic oscillator, divide the surface of the inner hemispherical shell of the hemispherical harmonic oscillator into two with the symmetrical central plane, set one half as the hemispherical surface, and the other half as the semi-ellipsoidal surface, and the minor axis of the semi-ellipsoid Same as the radius of the hemisphere, the difference △h between the major axis of the semi-ellipsoid and the radius of the hemisphere is the fifth minute distance, forming a roundness error, as shown in Figure 6.

Step 72: Change the value of the fifth tiny distance in step 71, and follow step 2 to obtain the first operating frequency, the second operating frequency and the frequency splitting value of the harmonic oscillator corresponding to different roundness errors.

Step 73: Analyze the effect of roundness error on frequency cracking. The simulation results show that with the increase of the roundness error of the bottom surface of the hemispherical harmonic oscillator, the frequency cracking of the hemispherical harmonic oscillator shows a fluctuating upward trend. Only considering the frequency cracking, continue to improve the roundness error The accuracy requirements will not only consume processing resources but also will not reduce the workload of subsequent frequency adjustment.

Step 8: Comprehensively analyze the influence of various types of errors in steps 3 to 7 on the frequency cracking of the harmonic oscillator. Under the premise that the frequency cracking of the harmonic oscillator is as small as possible, after considering the processing technology and processing efficiency of the hemispherical harmonic oscillator, formulate the hemispherical The precision index of the ultra-precision machining of the harmonic oscillator is shown in Table 2.

Table 2 Machining accuracy index of hemispherical harmonic oscillator

The present invention uses finite element software to analyze the degree of influence of different processing errors on the frequency cracking of hemispherical harmonic oscillators. The simulation analysis method can reduce the experimental workload and improve the research and development efficiency of high-quality harmonic oscillators; combined with the results of finite element analysis, a credible High precision machining accuracy index, control the machining error at about 0.5μm, provide theoretical guidance for the machining accuracy of the actual hemispherical harmonic oscillator; through the reasonable selection of processing equipment and process parameters, reduce the impact of the hemispherical harmonic oscillator. Sphericity error (when the true sphericity error is reduced from 10μm to 0.5μm, the frequency cracking of the harmonic oscillator is reduced from 3.540Hz to 0.221Hz), taking into account the processing efficiency and the working performance of the hemispherical harmonic oscillator; this method has certain universality, The method can be popularized for analyzing and formulating the standard formulation method of machining error control for various parts.

While the invention has been described in terms of a limited number of embodiments, it will be apparent to a person skilled in the art having the benefit of the above description that other embodiments are conceivable within the scope of the invention thus described. With respect to the scope of the present invention, the disclosure of the present invention is intended to be illustrative rather than restrictive, and the scope of the present invention is defined by the appended claims.

Claims (8)

1. The hemispherical resonator processing error standard making method based on frequency splitting is characterized in that the hemispherical resonator structure comprises a hemispherical shell and a supporting rod, and the method comprises the following steps:

step one, establishing a simulation three-dimensional model of a hemispherical resonator by finite element analysis, and defining the material properties of the hemispherical resonator;

setting boundary conditions of the simulation three-dimensional model as fixed constraints of the upper surface and the lower surface of a supporting rod in finite element analysis, carrying out finite element grid division by adopting extremely-thinned free tetrahedron grids to obtain a first working frequency and a second working frequency of a hemispherical resonator working under a four-wave amplitude vibration mode, and carrying out difference between the first working frequency and the second working frequency to obtain a frequency cracking value, thereby obtaining simulation results of influence of a plurality of processing errors on the frequency cracking, wherein the processing errors comprise coaxiality errors, inner and outer hemispherical surface spherical center radial concentricity errors, inner and outer hemispherical surface spherical center axial concentricity errors, true sphericity errors and roundness errors; the method comprises the following specific steps:

step two, deviating the axis of the hemispherical shell of the hemispherical resonator from the axis of the supporting rod by a first tiny distance, wherein the value of the first tiny distance is equal to the coaxiality error, changing the value of the first tiny distance, and obtaining a simulation result of the influence of a plurality of coaxiality errors on frequency splitting, wherein the simulation result of the influence of the plurality of coaxiality errors on frequency splitting comprises a first working frequency, a second working frequency and a frequency splitting value corresponding to each coaxiality error;

step two, deviating the sphere centers of the inner hemispherical surface and the outer hemispherical surface of the hemispherical harmonic oscillator by a second tiny distance in the radial direction, wherein the value of the second tiny distance is equal to the radial concentricity error of the sphere centers of the inner hemispherical surface and the outer hemispherical surface, changing the value of the second tiny distance, and obtaining a simulation result of the influence of a plurality of radial concentricity errors on frequency splitting, wherein the simulation result of the influence of the plurality of radial concentricity errors on frequency splitting comprises a first working frequency, a second working frequency and a frequency splitting value corresponding to each radial concentricity error;

step two, deviating the sphere centers of the inner hemispherical surface and the outer hemispherical surface of the hemispherical harmonic oscillator by a third tiny distance along the direction of the rotation axis of the workpiece, wherein the value of the third tiny distance is equal to the axial concentricity error of the sphere centers of the inner hemispherical surface and the outer hemispherical surface, changing the value of the third tiny distance, and obtaining a simulation result of the influence of a plurality of axial concentricity errors on frequency splitting, wherein the simulation result of the influence of the plurality of axial concentricity errors on frequency splitting comprises a first working frequency, a second working frequency and a frequency splitting value corresponding to each axial concentricity error;

step two, sinusoidal function fluctuation is added on the basis of the surface of a hemispherical shell in a hemispherical resonator to form a curve spherical shell, the wall thickness of the curve spherical shell is distributed along the direction of a semicircle arc to form a plurality of surface corrugated true sphericity errors, a frequency cracking influence simulation result of the plurality of true sphericity errors is obtained, and the frequency cracking influence simulation result of the plurality of true sphericity errors comprises a first working frequency, a second working frequency and a frequency cracking value corresponding to each true sphericity error;

fifthly, dividing the surface of a hemispherical shell in the hemispherical harmonic oscillator into two parts by a symmetrical center plane, wherein half of the hemispherical shell is set as a hemispherical surface, the other half of the hemispherical shell is set as a semi-ellipsoidal surface, the semi-ellipsoidal minor axis is identical to the hemispherical radius, the difference value between the semi-ellipsoidal major axis and the hemispherical radius is a fifth tiny distance, the value of the fifth tiny distance is equal to the roundness error, the value of the fifth tiny distance is changed, a simulation result of the influence of a plurality of roundness errors on frequency splitting is obtained, and the simulation result of the influence of the plurality of roundness errors on frequency splitting comprises a first working frequency, a second working frequency and a frequency splitting value corresponding to each roundness error;

and thirdly, analyzing the frequency cracking influence simulation result by a plurality of coaxiality errors, the frequency cracking influence simulation result by a plurality of radial concentricity errors, the frequency cracking influence simulation result by a plurality of axial concentricity errors, the frequency cracking influence simulation result by a plurality of true sphericity errors and the frequency cracking influence simulation result by a plurality of roundness errors respectively to obtain a hemispherical resonator processing error standard.

2. The method for formulating the hemispherical resonator processing error standard based on frequency splitting according to claim 1, wherein the hemispherical resonator material properties comprise young's modulus, density and poisson's ratio.

3. The method for formulating the hemispherical resonator processing error standard based on frequency splitting as claimed in claim 1, wherein the curved surface function corresponding to the curved spherical shell in the second and fourth steps is:

wherein, alpha and beta represent angle variables; Δd represents the magnitude of the sinusoidal waviness of the true sphericity.

4. The method for formulating the hemispherical resonator processing error standard based on frequency splitting according to claim 1, wherein the result of analyzing the simulation result of the influence of the plurality of coaxiality errors on the frequency splitting in the third step is as follows: the standard value of coaxiality error of the hemispherical harmonic oscillator is 0.5 mu m.

5. The method for formulating the hemispherical resonator processing error standard based on frequency splitting according to claim 1, wherein the result of analyzing the simulation result of the influence of the plurality of radial concentricity errors on the frequency splitting in the third step is as follows: the radial concentricity error of the sphere centers of the inner hemispherical surface and the outer hemispherical surface of the hemispherical harmonic oscillator is 0.5 mu m.

6. The method for formulating the hemispherical resonator processing error standard based on frequency splitting according to claim 1, wherein the result of analyzing the simulation result of the influence of the plurality of axial concentricity errors on the frequency splitting in the third step is as follows: the error value range of the axial concentricity of the spherical centers of the inner hemispherical surface and the outer hemispherical surface of the hemispherical harmonic oscillator is 0-0.5 mm.

7. The method for formulating the hemispherical resonator processing error standard based on frequency splitting according to claim 1, wherein the result of analyzing the simulation result of the influence of the plurality of true sphericity errors on the frequency splitting in the third step is as follows: as the true sphericity error of the hemispherical shell surface of the hemispherical resonator increases from 0 to 10 mu m, the true sphericity error of the hemispherical resonator takes a value of 0.5 mu m.

8. The method for formulating the hemispherical resonator processing error standard based on frequency splitting according to claim 1, wherein the result of analyzing the simulation result of the influence of the plurality of roundness errors on the frequency splitting in the third step is: the roundness error of the hemispherical harmonic oscillator is 0.5 mu m.