CN114139301B - Hemispherical harmonic oscillator processing error standard formulation method based on frequency splitting - Google Patents
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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
Technical Field
The invention relates to the technical field of hemispherical harmonic oscillator processing, in particular to a hemispherical harmonic oscillator processing error standard formulation method based on frequency splitting.
Background
With the increasing development of modern science and technology, in many fields such as aerospace, military national defense, navigation exploration and the like, various high-performance gyroscopes are required to ensure accurate navigation positioning capability. The hemispherical resonator gyroscope has a simple structure and a unique working principle as a novel high-precision gyroscope, and is widely applied by virtue of the advantages of impact resistance, strong radiation resistance, small size, low energy consumption, high reliability, long working life and the like. The hemispherical harmonic oscillator is used as a core component of the hemispherical resonant gyroscope, and the working performance of the gyroscope is directly determined by the processing precision and the surface quality of the hemispherical harmonic oscillator.
At present, ultra-precision machining of hemispherical resonators is realized on a special multi-axis linkage ultra-precision machine tool by adopting a special small-size polishing head. Machining errors generated in the machining process of the hemispherical harmonic oscillator are as follows: the alignment error of the hemispherical shell (the coaxiality error of the hemispherical shell and the symmetry axis of the supporting rod, the concentricity error of the spherical centers of the inner hemispherical shell surface and the outer hemispherical shell surface in the axial direction and the radial direction) and the processing error of the hemispherical shell surface (the roundness error near the bottom lip and the true sphericity error of the hemispherical shell surface) and the like can cause the frequency splitting of the working frequency of the harmonic oscillator, so that the harmonic oscillator generates angular drift and the working precision of the harmonic oscillator is influenced. Therefore, how to control the processing error of the hemispherical resonator in engineering practical application needs to be solved.
Disclosure of Invention
In view of the above problems, the invention provides a hemispherical resonator processing error standard formulation method based on frequency splitting, which is used for solving the problem that the processing error standard of the hemispherical resonator is not formulated based on the frequency splitting angle so as to improve the working accuracy of the hemispherical resonator in the prior art.
A hemispherical resonator processing error standard formulation method based on frequency splitting is provided, wherein the hemispherical resonator structure comprises a hemispherical shell and a supporting rod; the method comprises the following steps:
step one, establishing a simulation three-dimensional model of a hemispherical resonator by using finite element analysis software, 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 software, carrying out finite element mesh division by adopting extremely-thinned free tetrahedron meshes, obtaining 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.
Further, the hemispherical resonator material properties include young's modulus, density, and poisson's ratio.
Further, 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.
Further, in the third step, the result of analyzing the simulation result of the influence of the plurality of coaxiality errors on the frequency splitting is: when the coaxiality error of the hemispherical harmonic oscillator is gradually increased, the distribution nonuniformity of the radius of the hemispherical shell in the circumferential direction is aggravated, so that the frequency cracking of the harmonic oscillator is caused to be in a fluctuation increasing trend; along with the gradual increase of coaxiality errors within the range of 0.1-0.5 mu m, the frequency splitting of the harmonic oscillator is not obviously increased; therefore, the coaxiality error standard value of the hemispherical harmonic oscillator is 0.5 μm.
Further, in the third step, the result of analyzing the simulation result of the influence of the plurality of radial concentricity errors on the frequency splitting is: along with the increase of the radial concentricity error, the frequency splitting of the harmonic oscillator is in a fluctuation increasing trend, but the radial concentricity error is not obviously increased within the range of 0.1-0.5 mu m from the numerical point of view; therefore, the radial concentricity error of the sphere centers of the inner hemispherical surface and the outer hemispherical surface of the hemispherical resonator is 0.5 μm.
Further, in the third step, the result of analyzing the simulation result of the influence of the plurality of axial concentricity errors on the frequency splitting is: when the concentricity error of the hemispherical shell in the axis direction exists, the frequency splitting of the working vibration mode of the harmonic oscillator is slightly reduced, so that the value range of the axial concentricity error of the spherical centers of the inner hemispherical surface and the outer hemispherical surface of the hemispherical harmonic oscillator is 0-0.5 mm.
Further, in the third step, the result of analyzing the simulation result of the influence of the plurality of true sphericity errors on the frequency splitting is: along with the increase of the true sphericity error of the hemispherical shell surface of the hemispherical resonator from 0 to 10 mu m, the frequency splitting of the working vibration mode of the hemispherical resonator has a remarkable increase in a proportional trend, so that the true sphericity error of the hemispherical resonator takes a value of 0.5 mu m.
Further, in the third step, the result of analyzing the simulation result of the influence of the plurality of roundness errors on the frequency splitting is: as the roundness error of the bottom surface of the hemispherical resonator increases, the frequency splitting of the hemispherical resonator tends to rise, so that the roundness error of the hemispherical resonator takes a value of 0.5 μm.
The beneficial technical effects of the invention are as follows:
according to the method, finite element software is adopted to analyze the influence degree of different processing errors on the frequency splitting of the hemispherical harmonic oscillator, and a processing precision index with high reliability is formulated by combining a finite element analysis result, so that theoretical guiding significance is provided for the processing precision of the actual hemispherical harmonic oscillator; by reasonably selecting processing equipment and process parameters, the true sphericity error affecting the working accuracy of the hemispherical harmonic oscillator is reduced, and the processing efficiency and the working performance of the hemispherical harmonic oscillator are both considered. The method has certain universality and can be popularized to a processing error control standard making method for analyzing and making various parts.
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The invention may be better understood by reference to the following description taken in conjunction with the accompanying drawings, which are included to provide a further illustration of the preferred embodiments of the invention and to explain the principles and advantages of the invention, together with the detailed description below.
FIG. 1 is a schematic diagram of a hemispherical resonator according to the present invention; wherein, the figure (a) is a schematic diagram of the dimension parameter of a hemispherical resonator, 1 is a hemispherical shell in the figure, and 2 is a supporting rod; fig. (b) is a diagram of hemispherical resonator finite element meshing;
FIG. 2 is a schematic diagram of coaxiality error in the present invention;
FIG. 3 is a graph of radial concentricity error of a hemispherical shell according to the present invention;
FIG. 4 is a graph showing the axial concentricity error of the hemispherical shell according to the present invention;
FIG. 5 is a schematic representation of true sphericity error surfaces in accordance with the present invention;
fig. 6 is a schematic diagram of roundness error in the present invention.
Detailed Description
In order that those skilled in the art will better understand the present invention, exemplary embodiments or examples of the present invention will be described below with reference to the accompanying drawings. It is apparent that the described embodiments or examples are only implementations or examples of a part of the invention, not all. All other embodiments or examples, which may be made by one of ordinary skill in the art without undue burden, are intended to be within the scope of the present invention based on the embodiments or examples herein.
Because the hemispherical resonator machining precision index in the prior art has no scientific standard, the unreasonable machining precision not only brings certain machining difficulty, but also greatly reduces machining efficiency, the invention provides a hemispherical resonator machining error standard formulation method based on frequency splitting, which is used for simulating and researching the influence degree of various machining errors on the frequency splitting of the hemispherical resonator, exploring the hemispherical resonator error control standard and establishing an evaluation system of the hemispherical resonator machining precision. The hemispherical harmonic oscillator processing error standard formulation method based on frequency splitting can reasonably formulate the range of processing errors.
As shown in fig. 1 (a), the ψ -type hemispherical resonator consists of a hemispherical shell and a supporting rod, the hemispherical shell and the supporting rod are transited by adopting a transition fillet, the structural size parameters of the hemispherical resonator are shown in table 1, the boundary condition of a three-dimensional model of the hemispherical resonator is set as the fixed constraint of the upper surface and the lower surface of the supporting rod, and the finite element mesh division is carried out by adopting a extremely-thinned free tetrahedron mesh, as shown in fig. 1 (b).
TABLE 1 structural dimension parameters of certain model ψ -type hemispherical harmonic oscillator
The machining errors of the hemispherical resonator refer to errors generated by factors such as machine tools, cutter precision or machining environment interference in the machining process, and include hemispherical shell alignment errors (coaxiality errors of hemispherical shells and symmetry axes of supporting rods), concentricity errors of spherical centers of inner and outer hemispherical shell surfaces in the axial direction and the radial direction, and hemispherical shell surface machining errors (roundness errors near a bottom lip and true sphericity errors of hemispherical shell surfaces). And analyzing the influence of different processing errors on the frequency splitting of the hemispherical harmonic oscillator by adopting a single factor method, and formulating a harmonic oscillator processing error standard according to an analysis result.
The method comprises the following specific steps:
step one: a simulation three-dimensional model of a hemispherical resonator is established by using finite element analysis software COMSOL, wherein the COMSOL software is widely used for modal analysis of materials and multi-physical field coupling solution. Definition of young's modulus of fused silica material used e=7.67×10 10 Pa, density ρ=2.2×10 3 kg/m3, poisson ratio μ=0.17；
Step two: the upper surface and the lower surface of the supporting rod are set as fixed constraint, extremely-thinned free tetrahedron grids are adopted for finite element grid division, characteristic frequency analysis is carried out on the hemispherical harmonic oscillator, the first working frequency and the second working frequency of the hemispherical harmonic oscillator working under the four-wave amplitude vibration mode are 5078.865Hz and 5078.929Hz respectively, and the difference between the two frequencies is 0.063Hz.
Step three: and analyzing the influence rule of the coaxiality error of the harmonic oscillator on frequency splitting.
Step three: and establishing a model of the coaxiality error of the harmonic oscillator, and setting the coaxiality error of the axis of the hemispherical shell and the axis of the support rod by a distance of the axis of the hemispherical shell deviating from the axis Deltax of the support rod, namely a first micro distance, as shown in figure 2.
Step three, two: and changing the value of the first micro distance in the third step, and obtaining the first working frequency, the second working frequency and the frequency splitting value of the harmonic oscillator corresponding to different coaxiality errors according to the second step.
And step three: as shown by analysis of the simulation result of the influence of the coaxiality error on the frequency splitting, when the coaxiality error of the hemispherical resonator is gradually increased, the distribution non-uniformity of the radius of the hemispherical shell in the circumferential direction is aggravated, and the frequency splitting of the hemispherical resonator is caused to be in a fluctuation increasing trend. However, along with the increase of the axiality error in the range of 0.1-0.5 μm, there is no significant increase in resonant frequency splitting. If only frequency splitting of the hemispherical harmonic oscillator is considered, the processing difficulty of the harmonic oscillator can be greatly increased by further improving the error requirement. Therefore, from the simulation result, the requirement for coaxiality errors does not need to be increased.
Step four: and analyzing the influence rule of the radial concentricity error of the hemispherical shell of the harmonic oscillator on frequency splitting.
Step four, first: and (3) establishing a model of radial concentricity errors of the hemispherical shells of the harmonic oscillator, and setting the radial concentricity errors of the spherical centers of the inner and outer hemispherical surfaces by a distance delta y, namely a second micro distance, in the radial direction, as shown in fig. 3.
Step four, two: and changing the value of the second micro distance in the fourth step, and obtaining the first working frequency, the second working frequency and the frequency splitting value of the harmonic oscillator corresponding to different radial coaxiality errors according to the second step.
And step four, three: as shown by analysis of the simulation result of the influence of the radial coaxiality error on the frequency splitting, along with the increase of the radial coaxiality error, the frequency splitting of the harmonic oscillator tends to be fluctuated, but the radial coaxiality error is not obviously increased within the range of 0.1-0.5 mu m from the numerical value. Therefore, radial concentricity errors within 0.5 μm do not have a large influence on resonator drift.
Step five: and analyzing the influence rule of the axial concentricity error of the hemispherical shell of the harmonic oscillator on frequency splitting.
Step five: and (3) establishing a model of the axial concentricity error of the harmonic oscillator, and setting the axial concentricity error of the spherical centers of the inner and outer hemispherical surfaces along the direction of the rotation axis of the workpiece by a distance delta z, namely a third micro distance, as shown in fig. 4.
Step five: and changing the value of the third micro distance in the fifth step, and obtaining the first working frequency, the second working frequency and the frequency splitting value of the harmonic oscillator corresponding to different axial coaxiality errors according to the second step.
Step five: as can be seen from simulation results of analyzing the influence of the axial concentricity error on the frequency splitting, when the concentricity error of the hemispherical shell in the axial direction exists, the frequency splitting of the working vibration mode of the harmonic oscillator is slightly reduced, and the reason is probably that the concentricity error in the axial direction only causes the uneven thickness of the hemispherical shell in the axial direction, the thickness and the radius of the harmonic oscillator are uniform in the thickness of the hemispherical shell in the circumferential direction, the increase of the wall thickness near the circular angle reduces the vibration amplitude of the harmonic oscillator but is more stable, and the existence of the axial concentricity error has a certain inhibition effect on the frequency splitting.
Step six: and analyzing the influence rule of the true sphericity error of the harmonic oscillator on frequency splitting.
Step six,: and (3) establishing a model of the true sphericity error of the harmonic oscillator, replacing the original hemispherical shell shape inner hemispherical shell with a parameterized curved surface controlled by the formula (1), adding sine function fluctuation on the basis of the inner hemispherical shell surface to form a curve spherical shell shown in fig. 5, and enabling the hemispherical shell wall thickness to be distributed along the semicircle direction to present non-uniformity of the sine function shape to form the true sphericity error of the surface ripple shape.
Wherein, alpha and beta represent angle variables; Δd represents the magnitude of the sinusoidal fluctuation of true sphericity, i.e., the fourth minute distance.
Step six, two: and changing the value of the fourth micro distance in the step six, and obtaining the first working frequency, the second working frequency and the frequency splitting value of the harmonic oscillator corresponding to different sphericity errors according to the step two.
And step six, three: as can be seen from the simulation result of analyzing the influence of the true sphericity error on the frequency splitting, as the true sphericity error of the hemispherical shell surface of the hemispherical resonator increases from 0 to 10 mu m, the frequency splitting of the working vibration mode of the hemispherical resonator has a remarkable increase in a proportional trend, which shows that compared with other processing errors, the existence of the surface fluctuation of the hemispherical shell can have a larger influence on the working precision of the hemispherical resonator. Therefore, in order to ensure the normal operation of the hemispherical resonator, clamping precision is required to be improved when the hemispherical shell is machined, a cutter with higher rigidity is selected, and the surface sphericity error generated by shaking of a machine tool or the cutter is reduced as much as possible.
Step seven, a step of performing a step of; and analyzing the influence rule of the roundness error of the harmonic oscillator on frequency splitting.
Seventhly, step seven: establishing a model of the roundness error of the harmonic oscillator, dividing the surface of the hemispherical shell in the hemispherical harmonic oscillator into two parts by a symmetrical center plane, setting half of the hemispherical shell as the hemispherical surface, setting the other half as the hemispherical surface, setting the short axis of the hemispherical surface to be the same as the radius of the hemispherical surface, and setting the difference delta h between the long axis of the hemispherical surface and the radius of the hemispherical surface as the fifth tiny distance to form the roundness error, as shown in fig. 6.
Seventhly, step two: and changing the value of the fifth micro distance in the seventh step, and obtaining the first working frequency, the second working frequency and the frequency splitting value of the harmonic oscillator corresponding to different roundness errors according to the second step.
Seventhly, step seven: according to the simulation result of analyzing the influence of the roundness error on the frequency cracking, along with the increase of the roundness error of the bottom surface of the hemispherical resonator, the frequency cracking of the hemispherical resonator is in a fluctuation rising trend, only the frequency cracking aspect is considered, the precision requirement of continuously improving the roundness error can not only consume processing resources, but also the workload of subsequent frequency modulation can not be reduced.
Step eight: and comprehensively analyzing the influence rule of various errors in the third step to the seventh step on the frequency splitting of the harmonic oscillator, and on the premise that the frequency splitting of the harmonic oscillator is as small as possible, formulating the precision index of ultra-precise machining of the hemispherical harmonic oscillator after considering the machining process and the machining efficiency of the hemispherical harmonic oscillator as shown in table 2.
Table 2 hemispherical resonator machining accuracy index
According to the invention, finite element software is adopted to analyze the influence degree of different processing errors on the frequency splitting of the half-sphere harmonic oscillator, and experimental workload can be reduced by a simulation analysis method, so that the research and development efficiency of the high-quality harmonic oscillator is improved; combining finite element analysis results, formulating a machining precision index with high reliability, controlling each machining error to be about 0.5 mu m, and providing theoretical guiding significance for the machining precision of an actual hemispherical harmonic oscillator; by reasonably selecting processing equipment and process parameters, the true sphericity error affecting the working accuracy of the hemispherical harmonic oscillator is reduced (when the true sphericity error is reduced from 10 mu m to 0.5 mu m, the frequency splitting of the harmonic oscillator is reduced from 3.540Hz to 0.221 Hz), and the processing efficiency and the working performance of the hemispherical harmonic oscillator are both considered; the method has certain universality and can be popularized to the processing error control standard formulation method for analyzing and formulating various parts.
While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of the above description, will appreciate that other embodiments are contemplated within the scope of the invention as described herein. The disclosure of the present invention is intended to be illustrative, but not limiting, of the scope of the invention, which 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.
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| CN109084741A (en) * | 2018-07-04 | 2018-12-25 | 中国人民解放军国防科技大学 | Method and system for cracking harmonic oscillator frequency of cylindrical shell vibrating gyroscope |
| CN112729159A (en) * | 2020-12-26 | 2021-04-30 | 华中光电技术研究所（中国船舶重工集团公司第七一七研究所） | Detection method for spherical surface shape of hemispherical harmonic oscillator |
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| CN109084741A (en) * | 2018-07-04 | 2018-12-25 | 中国人民解放军国防科技大学 | Method and system for cracking harmonic oscillator frequency of cylindrical shell vibrating gyroscope |
| CN112729159A (en) * | 2020-12-26 | 2021-04-30 | 华中光电技术研究所（中国船舶重工集团公司第七一七研究所） | Detection method for spherical surface shape of hemispherical harmonic oscillator |
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| 谐振子支柱偏心误差对谐振子振动特性影响分析(英文);徐泽远 等;中国惯性技术学报;第27卷(第01期);101-107页 * |
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