A mass trimming method of a hemispherical resonator, a hemispherical resonator gyroscope, an electronic device and a computer readable storage medium

Abstract

The application discloses a kind of mass trimming method of hemispherical resonator, hemispherical resonator gyro, electronic equipment and computer readable storage medium, mass trimming method includes the following steps: S1: according to the design size of hemispherical resonator, and the frequency crack value measured after processing of hemispherical resonator, construct hemispherical resonator model, and simulation calculation is carried out after loading spiral model thereon, until the frequency crack simulation calculation value meets the set requirement, and the optimized spiral model is obtained;S2: using the optimized spiral model to carry out mass trimming to the hemispherical resonator after processing.The application can achieve the frequency crack trimming of hemispherical resonator in one step, improve the time-consuming and labor-consuming and the problem that trimming result is not ideal caused by the existing repeated test iteration trimming of hemispherical resonator.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of inertial navigation, in particular to a mass trimming method of a hemispherical resonator, a hemispherical resonator gyroscope, an electronic device and a computer readable storage medium. BACKGROUND

[0002] As a high-performance inertial sensor, the hemispherical resonator gyroscope measures angular velocity by detecting the change of vibration mode of the hemispherical resonator. However, the precision and stability of the hemispherical resonator gyroscope are easily affected by the uniformity of the mass distribution of the resonator. Ideally, a hemispherical resonator should have a completely symmetrical mass distribution, and the two modal frequencies of the second-order normal vibration mode during operation should be equal. However, due to factors such as material defects, machining errors and uneven plating, the actual manufactured hemispherical resonator has a certain degree of mass unevenness, resulting in unequal two modal frequencies of the two normal vibration modes, forming frequency splitting, thereby introducing zero bias and scale factor errors, and reducing the precision of the gyroscope. In order to eliminate or reduce the precision reduction of the gyroscope caused by mass unevenness, high-precision mass trimming of the hemispherical resonator is required. The goal of mass trimming is to adjust the mass distribution of the resonator to restore the ideal symmetry as much as possible, thereby reducing the frequency split and improving the mode orthogonality, thereby improving the performance of the gyroscope. Conventionally, the azimuth of the high-frequency axis and the low-frequency axis generated by the mass unevenness and the size of the frequency split value are determined by a laser vibration tester, and then the mass is removed at the position of the low-frequency axis. However, the amount of mass removal at each time is difficult to determine, and after multiple mass removal and multiple measurements, the ideal value to be trimmed can be reached. SUMMARY

[0003] In view of the problems in the background art, the present application provides a mass trimming method of a hemispherical resonator, which can achieve frequency split trimming of the hemispherical resonator in one step, and improve the problem of time-consuming and laborious and unsatisfactory trimming results caused by repeated testing and iterative trimming of the hemispherical resonator.

[0004] The present application adopts the following technical solutions:

[0005] A mass trimming method of a hemispherical resonator, comprising the following steps:

[0006] S1: According to the design size of the hemispherical resonator and the frequency split value measured after processing, a hemispherical resonator model is constructed, and after loading a spiral model on it, simulation calculation is performed until the frequency split simulation calculation value meets the set requirements, and an optimized spiral model is obtained;

[0007] S2: The optimized spiral model is used for mass trimming of the processed hemispherical resonator.

[0008] Optionally, step S1 specifically comprises:

[0009] S1.1: constructing a half-sphere model according to the design size of the half-sphere resonator,

[0010] S1.2: loading a spiral line model on the half-sphere model and performing a first simulation calculation to obtain a first frequency split simulation calculation value,

[0011] S1.3: determining whether the first frequency split simulation calculation value meets the set requirement, if yes, forming a first optimized spiral line model and turning to step S1.5; if no, turning to step S1.4,

[0012] S1.4: adjusting the spiral line model and turning to step S1.2,

[0013] S1.5: constructing a half-sphere resonator model according to the design size of the half-sphere resonator and the measured frequency split value of the half-sphere resonator after processing, loading the first optimized spiral line model on the half-sphere resonator model and performing a second simulation calculation to obtain a second frequency split simulation calculation value, determining whether the second frequency split simulation calculation value meets the set requirement, if no, turning to S1.4, if yes, obtaining an optimized spiral line model.

[0014] Optionally, the spiral line model comprises a spiral trace parameterization equation and a cross-section parameter equation of each spiral trace, the spiral trace parameterization equation is:

[0015] ,

[0016] ,

[0017] ,

[0018] ,

[0019] wherein R is the outer sphere radius of the half-sphere resonator, t is the polar angle, is the phase angle, i is the i-th spiral line, is the x-axis coordinate of the i-th spiral line at the polar angle t and the phase angle , is the y-axis coordinate of the i-th spiral line at the polar angle t and the phase angle , is the z-axis coordinate of the i-th spiral line at the polar angle t and the phase angle , is the phase angle of the i-th spiral line, n is the pitch coefficient, and N is the total number of spiral lines on the outer sphere surface, is the starting phase angle;

[0020] the cross-section parameter equation of each spiral trace is:

[0021] ,

[0022] ,

[0023] wherein, is the etching depth of the spiral line at polar angle t, is the etching width of the spiral line at polar angle t, is the reference depth, is the reference width, a is the depth modulation amplitude coefficient, β is the depth modulation frequency coefficient, γ is the width modulation amplitude coefficient, δ is the width modulation frequency coefficient.

[0024] Optionally, in the S1.2, the first simulation calculation is performed to obtain a first frequency splitting simulation calculation value, and specifically includes:

[0025] Each spiral line is divided into several equal parts along the spiral direction, the microelement mass of each equal part is calculated, and the phase angle of each equal part on the equator of the hemisphere is calculated. The microelement mass corresponding to each phase angle on the equator of the hemisphere is accumulated to obtain the angular mass corresponding to the phase angle.

[0026] The average value of the angular mass corresponding to all phase angles is solved to obtain the angular average mass,

[0027] The angular mass corresponding to each phase angle is subtracted from the angular average mass to obtain the angular alternating current mass corresponding to the phase angle. The angular alternating current mass corresponding to a plurality of phase angles forms an angular alternating current mass distribution. The fourth harmonic component corresponding to the angular alternating current mass distribution is solved , and the first frequency splitting simulation calculation value is calculated according to the fourth harmonic component .

[0028] Optionally, in the step S1.3, the first frequency splitting simulation calculation value is judged whether it meets the set requirement, and specifically includes:

[0029] The frequency splitting value of the actual processed hemispherical resonator is subtracted from the first frequency splitting simulation calculation value, and it is judged whether the square of the difference between the obtained difference and the target frequency splitting value is less than or equal to the set convergence tolerance.

[0030] Optionally, in the step S1.3, after it is judged that the first frequency splitting simulation calculation value meets the set requirement, it further includes:

[0031] It is judged whether the set constraint condition is met. If it is met, a first optimized spiral line model is formed and the step S1.5 is turned. If it is not met, the step S1.4 is turned.

[0032] Optionally, in the step S1.4, the spiral line model is adjusted, and specifically includes:

[0033] The differential evolution algorithm or NAGA-II algorithm is used to sample the parameters in the parameterized equation of the spiral pattern and the cross-sectional parameter equation of each spiral pattern. The spiral model is adjusted according to the sampling results to generate the spiral model for the next round of simulation calculation.

[0034] As a general inventive concept, the present invention also provides a hemispherical resonant gyroscope, the hemispherical resonant gyroscope comprising a hemispherical resonator, the hemispherical resonator being mass-adjusted using the mass-adjustment method for the hemispherical resonator as described above.

[0035] As a general inventive concept, the present invention also provides an electronic device, the device comprising:

[0036] Memory, used to store computer programs:

[0037] A processor is used to implement the steps of the mass adjustment method for the hemispherical harmonic oscillator as described above when executing the computer program.

[0038] As a general inventive concept, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the mass adjustment method for the hemispherical harmonic oscillator described above.

[0039] Compared with the prior art, the advantages of the present invention are as follows:

[0040] This invention presents a parametric modeling method combining helical pattern geometric design with the dynamic performance of hemispherical harmonic oscillators. By loading a helical model onto a hemispherical harmonic oscillator model and performing simulation optimization, the optimal helical model is obtained. This optimal helical model is then used to perform mass adjustment on the actually manufactured hemispherical harmonic oscillator, assisting in establishing an effective mass adjustment model and parameters. Results show that the helical pattern design method can create a mass redistribution effect, thereby improving the uniformity of mass distribution. Furthermore, the helical pattern provides more controllable mass adjustment compared to random patterns. The ordered thread pattern design can release machining stress, similar to a stress relief groove. Therefore, this invention can achieve frequency-splitting adjustment of hemispherical harmonic oscillators in one step, improving upon the problems of time-consuming, labor-intensive, and unsatisfactory adjustment results caused by repeated testing and iterative adjustment of hemispherical harmonic oscillators in existing methods. Attached Figure Description

[0041] To facilitate understanding of the invention, it will be described in more detail with reference to the specific embodiments shown in the accompanying drawings. These drawings depict only typical embodiments of the invention and should not be considered as limiting the scope of protection of the invention.

[0042] Figure 1A flow chart of the mass trimming method of the hemispherical resonator of the embodiment of the present application.

[0043] Figure 2 A schematic diagram of constructing the hemispherical model loaded with the spiral model in the python or matlab software of the embodiment of the present application.

[0044] Figure 3 A schematic diagram of constructing the hemispherical resonator model loaded with the spiral model in the COMSOL software of the embodiment of the present application.

[0045] Figure 4 A hemispherical resonator model with an initial frequency split of 0.02 Hz simulated in the COMSOL software.

[0046] Figure 5 A hemispherical resonator model with a trimmed frequency split of 0.007 Hz simulated in the COMSOL software after loading the spiral model. DETAILED DESCRIPTION

[0047] Embodiments of the present application are described below with reference to the accompanying drawings, so that those skilled in the art can better understand the present application and implement it, but the listed embodiments are not intended to limit the present application, and the embodiments described below and the technical features in the embodiments can be combined with each other without conflict, wherein the same components are denoted by the same reference numerals.

[0048] As shown in Figure 1 The present embodiment provides a mass trimming method of a hemispherical resonator, comprising the following steps:

[0049] S1: according to the design size of the hemispherical resonator and the frequency split value of the hemispherical resonator measured after processing, a hemispherical resonator model is constructed, and simulation calculation is performed after loading a spiral model thereon, until the frequency split simulation calculation value meets the set requirement, to obtain an optimized spiral model;

[0050] S2: the optimized spiral model is used to trim the mass of the processed hemispherical resonator.

[0051] The parameterized modeling method combining the above-mentioned spiral thread-based geometric design and hemispherical resonator dynamic performance, by loading the spiral line model on the hemispherical resonator model and performing simulation optimization, solves the optimal spiral line model, and uses the solved optimal spiral line model to perform mass adjustment on the actual processed hemispherical resonator, to assist in establishing an effective mass adjustment model and parameters of the actual processed hemispherical resonator. The results show that the spiral thread design method can create a mass redistribution effect, thereby improving the uniformity of the mass distribution. In addition, the spiral pattern can provide more controllable mass adjustment than random threads. The ordered thread design can release the machining stress, similar to a stress relief groove. Therefore, the present application can realize the frequency split adjustment of the hemispherical resonator in one step, and improve the problem of time-consuming and laborious and unsatisfactory adjustment results caused by the existing repeated test iteration adjustment of the hemispherical resonator.

[0052] In the embodiment, step S1 specifically comprises:

[0053] S1.1: constructing a hemispherical model according to the design size of the hemispherical resonator,

[0054] S1.2: loading a spiral line model on the hemispherical model and performing first simulation calculation to obtain a first frequency split simulation calculation value,

[0055] S1.3: judging whether the first frequency split simulation calculation value meets the set requirement, if yes, forming a first optimized spiral line model and outputting; if not, turning to step S1.4,

[0056] S1.4: adjusting the spiral line model, and turning to step S1.2,

[0057] S1.5: constructing a hemispherical resonator model according to the design size of the hemispherical resonator and the measured frequency split value of the hemispherical resonator after processing, loading the first optimized spiral line model on the hemispherical resonator model and performing second simulation calculation to obtain a second frequency split simulation calculation value, judging whether the second frequency split simulation calculation value meets the set requirement, if not, turning to S1.4, if yes, obtaining an optimized spiral line model.

[0058] Specifically, the application firstly constructs a semi-sphere model (i.e. simplifies the semi-sphere harmonic oscillator with a belt anchor by using a semi-sphere) in python or matlab software, and loads a spiral line model on the constructed semi-sphere model, solves the optimal spiral line model through simulation optimization, so that the square of the frequency crack value of the semi-sphere harmonic oscillator after actual processing minus the frequency crack value after loading the spiral line model is minimized, then a semi-sphere harmonic oscillator model loaded with an actual frequency crack value is constructed in COMSOL software, and the optimal spiral line model solved above is loaded to perform simulation verification. Finally, the optimal spiral line model verified through simulation is used to adjust the mass of the semi-sphere harmonic oscillator after actual processing. Thus, the problems such as large amount of calculation and program crash caused by the spiral line model loading-simulation iteration operation process of the semi-sphere harmonic oscillator model in COMSOL software can be avoided.

[0059] In the embodiment, the spiral line model comprises a spiral line parameterization equation and a cross section parameter equation of each spiral line, the spiral line parameterization equation is:

[0060] ,

[0061] ,

[0062] ,

[0063] ,

[0064] wherein R is the outer sphere radius of the semi-sphere harmonic oscillator, t is the polar angle, is the phase angle, i is the i-th spiral line, is the x-axis coordinate of the i-th spiral line at the polar angle t and the phase angle is the y-axis coordinate of the i-th spiral line at the polar angle t and the phase angle is the z-axis coordinate of the i-th spiral line at the polar angle t and the phase angle is the phase angle of the i-th spiral line, n is the pitch coefficient, N is the total number of spiral lines on the outer sphere surface, is the starting phase angle; The cross section parameter equation of each spiral line is:

[0065]

[0066] ,

[0067] ,

[0068] wherein, is the etching depth of the spiral line at the polar angle t, ​​​is the etching width of the helix line at the polar angle t, is the reference depth, is the reference width, a is the depth modulation amplitude coefficient, β is the depth modulation frequency coefficient, γ is the width modulation amplitude coefficient, and δ is the width modulation frequency coefficient.

[0069] The helix line is parameterized and modeled, and the differential evolution algorithm or the NSGA-II algorithm is used to optimize the parameters of the helix line, such as the number of helixes, the pitch coefficient, the etching depth, the etching width, and the polar angle of the helix line. The manufacturing constraints, such as the maximum etching depth and width and the maximum number of helixes, are superimposed. While the parameters of the helix line are optimized, the machinability of quality leveling is ensured.

[0070] In the embodiment, in the S1.2, the first simulation calculation is performed to obtain a first frequency splitting simulation calculation value, and specifically includes:

[0071] Each helical path is divided into several equal parts along the helical direction, the microelement mass of each equal part is calculated, and the phase angle of each equal part on the equator of the hemisphere is calculated. The microelement mass corresponding to each phase angle on the equator of the hemisphere is accumulated to obtain the angular mass corresponding to the phase angle.

[0072] The average value of the angular mass corresponding to all phase angles is obtained, and the angular average mass is obtained.

[0073] The angular average mass is subtracted from the angular mass corresponding to each phase angle to obtain the angular alternating current mass corresponding to the phase angle. The angular alternating current mass corresponding to a plurality of phase angles forms an angular alternating current mass distribution. The fourth harmonic component corresponding to the angular alternating current mass distribution is solved , and the first frequency splitting simulation calculation value is calculated according to the fourth harmonic component .

[0074] In the embodiment, in the step S1.3, the judgment whether the first frequency splitting simulation calculation value meets the set requirement specifically includes:

[0075] The frequency splitting value of the actual processed hemispherical resonator is subtracted from the first frequency splitting simulation calculation value, and it is judged whether the square of the difference between the obtained difference and the target frequency splitting value is less than or equal to the set convergence tolerance.

[0076] In the embodiment, in the step S1.3, after it is judged that the first frequency splitting simulation calculation value meets the set requirement, the step further includes:

[0077] It is judged whether the set constraint condition is met. If yes, a first optimized helix line model is formed and the step S1.5 is performed. If not, the step S1.4 is performed.

[0078] In the embodiment, in the step S1.4, the helix line model is adjusted, and specifically includes:

[0079] The differential evolution algorithm or NAGA-II algorithm is used to sample the parameterized equation of the spiral thread and each parameter in the cross-section parameter equation of the spiral thread, and the spiral line model is adjusted according to the sampling result to generate the spiral line model of the next round.

[0080] The above steps S1.1-S1.4 are executed in python or matlab software, and step 1.5 is executed in COMSOL software.

[0081] Specifically, the implementation steps of the hemispherical harmonic oscillator outer sphere spiral line optimization method using python or matlab are as follows:

[0082] The basic parameters of the hemispherical harmonic oscillator are constructed, including the hemispherical radius, the harmonic oscillator shell thickness, the fused quartz density, and the 4th harmonic mass sensitivity.

[0083] The spiral line optimization parameters are constructed.

[0084] A spiral thread geometric parameterization model is built to describe the basic equation of the spiral thread path on the outer surface of the hemispherical harmonic oscillator. For a hemispherical harmonic oscillator (radius R), the parameterization equation of the spiral thread is expressed in the direction of the spiral center line of the spherical surface as:

[0085] ,

[0086] ,

[0087] ,

[0088] ,

[0089] Wherein:

[0090] R is the outer spherical radius of the hemispherical harmonic oscillator,

[0091] t ∈ [0, π / 2] (polar angle, along the Z-axis direction from the top of the hemispherical harmonic oscillator to the hemispherical harmonic oscillator lip),

[0092] : phase angle,

[0093] i: the i-th spiral line,

[0094] : the x-axis coordinate of the i-th spiral line at the polar angle t and the phase angle ,

[0095] : the y-axis coordinate of the i-th spiral line at the polar angle t and the phase angle ,

[0096] : z-coordinate of the i-th spiral line at polar angle t, phase angle

[0097] : phase angle of the i-th spiral line,

[0098] n: pitch factor,

[0099] N: total number of spiral lines on the outer sphere,

[0100] : initial phase angle.

[0101] The spiral thread cross-section is parameterized, and two modulation functions, the thread removal depth function and the thread removal width function, are used for modulation, allowing the depth and width of thread removal to vary along the spiral path, achieving more precise and local quality adjustment.

[0102] Thread removal depth function:

[0103] ,

[0104] Thread removal width function:

[0105] ,

[0106] where:

[0107] : etching depth of the spiral line at polar angle t,

[0108] : etching width of the spiral line at polar angle t,

[0109] reference depth,

[0110] reference width,

[0111] α depth modulation amplitude coefficient,

[0112] β depth modulation frequency coefficient,

[0113] γ width modulation amplitude coefficient,

[0114] δ width modulation frequency coefficient.

[0115] Therefore, the constructed spiral line optimization parameters are the number of spiral lines N on the outer sphere of the hemispherical resonator, the pitch factor n, the etching depth , the etching width , and the spiral line polar angle t.

[0116] Construct a frequency splitting optimizer:​

[0117] Set the target frequency crack value of optimization, the above spiral formula, depth and width formula, and the initial value of the parameters in each formula (that is: first according to experience, the parameters that need to be optimized, such as the number of spiral lines N on the outer sphere of the hemispherical resonator, the pitch coefficient n, the etching depth , the etching width , the spiral line polar angle t are initially assigned) implanted into the optimizer, each spiral line is divided into multiple equal small segments according to its spiral direction, and the mass removal of each equal small segment of each spiral line (i.e. microelement mass) is calculated. The removal cross section of the spiral line is simplified as the area of the pipeline, and the volume of the spiral pipeline is the product of the cross-sectional area and the microelement length, and then multiplied by the density of the hemispherical resonator material to obtain the microelement mass; the specific calculation process is: along the spiral direction of each spiral line, it is divided into several equal parts, such as 100~200 equal parts, the x, y and z coordinate values of the center point of each equal small segment on the i-th spiral line among the total number of N spiral lines are found through the spiral line parameter equation, the removal depth and width of the equal small segment are found according to the depth and width modulation function, the microelement arc length of each equal part is calculated, the microelement arc length is multiplied by the removal depth and removal width to obtain the microelement volume, and then multiplied by the density to obtain the microelement mass. At the same time, the circumferential angle of each equal small segment relative to the starting phase angle of the hemispherical resonator is calculated through the trigonometric relationship of the x and y coordinate values, that is, the phase angle; then the microelement mass of each equal small segment corresponding to each phase angle is accumulated (for example, as shown in Figure 2 , a phase angle corresponds to three equal small segments of three spiral lines, the microelement masses of the three equal small segments are accumulated), and the angular mass corresponding to the phase angle is obtained. Thus, by performing equal grid processing on N spiral lines and calculating the microelement mass and the microelement phase angle, the angular mass distribution of the hemispherical resonator along the equatorial circumference can be obtained, that is, the angular mass distribution.

[0118] The next frequency crack distribution calculation step is: adding all the angular mass in the angular mass distribution and solving the average value to obtain the angular average mass, and then subtracting the angular average mass from all the angular mass in the angular mass distribution to obtain the angular alternating mass distribution; the angular alternating mass distribution is subjected to Fourier transform according to the following formula to obtain the 4th harmonic component .

[0119] ,

[0120] Wherein:

[0121] : angular alternating mass distribution,

[0122] k: harmonic order,

[0123] , : the cosine coefficient corresponding to the k-th order mass non-uniformity,

[0124] : the phase angle.

[0125] where the 4th order harmonic component has the greatest impact on the frequency split, k takes 4, and the solution is obtained as and .

[0126] Frequency split caused by the removal of helical lines (i.e. the frequency split value caused by loading the helical line model on the hemisphere model) calculation formula:

[0127] ,

[0128] where:

[0129] , : the first and second frequency axes of the hemisphere resonator,

[0130] : the mass sensitivity coefficient ≈ 3.91 Hz / mg,

[0131] : the sine coefficient corresponding to the 4th order mass non-uniformity.

[0132] After the calculation of the frequency split caused by the removal of the helical line mass, the difference between the frequency split value of the hemisphere resonator after actual processing and the frequency split value caused by loading the helical line model is solved, and the multi-objective optimization function is set as the square of the difference between the target frequency split value and the difference. The final convergence condition is that the square of the difference is less than or equal to the convergence tolerance 1e-6, which represents that the calculated frequency split value is basically consistent with the target frequency split value, i.e. the optimal helical line model is obtained.

[0133] If the square of the difference between the initial round calculation frequency split value and the target frequency split value is greater than the set convergence tolerance, the program will sample the next round of parameters in the helical line parameterization equation and the cross-sectional parameter equation of each helical line, and construct the next round of frequency split optimizer until the square of the difference between the calculated frequency split value and the target frequency split value is less than or equal to the set convergence tolerance.

[0134] Before iterative calculation, the following constraints need to be established:

[0135] 1) The depth h is much smaller than the shell thickness, such as not more than 5-10 um;

[0136] 2) The width w is much smaller than the distance between adjacent lines, such as not more than 5-10 um;

[0137] 3) The number of threads is not more than 30;

[0138] 4) The total amount of mass removal < 0.2%~0.4% total mass.

[0139] The above constraints can avoid the algorithm to sample calculation outside the constraint condition, prevent the appearance of too deep, too wide and too much lines.

[0140] 5) At the same time, the increase of the spiral line etching area is included in the punishment mechanism. If the calculated increase of the spiral line etching area is greater than the value of the last round, the program will change the direction in the next round of parameter sampling, so that the increase of the spiral line etching area obtained by the next round of optimization calculation is less than the calculated value of this round, so as to optimize the result to reduce the frequency splitting of the hemispherical resonator, and the increase of the etching area of the outer surface of the hemispherical resonator is minimized, so as to avoid the loss of the vibration Q value of the hemispherical resonator. That is, the etching area of the spiral line is increased as little as possible to achieve the goal of reducing the frequency splitting.

[0141] The influence model of surface topography evolution on Q value change can be described as:

[0142] ,

[0143] : the surface Q value of the hemispherical resonator,

[0144] is the frequency of the frequency axis of the hemispherical resonator,

[0145] is the surface loss rate,

[0146] is the density of the hemispherical resonator,

[0147] is the volume of the hemispherical resonator,

[0148] wherein, is directly related to the surface topography, and the surface area increase rate is used to represent the surface loss rate in the program for optimization.

[0149] 6) In addition, the total harmonic component sum is also included in the punishment mechanism, and the punishment mechanism refers to the processing method of the total increase of the spiral line etching area.

[0150] An ideal state of the hemispherical resonator three-dimensional model is constructed in COMSOL software, and the frequency splitting value of the actual processed hemispherical resonator is loaded to the ideal state of the hemispherical resonator three-dimensional model. The specific loading method is as follows:

[0151] The density of the hemispherical resonator on the entire circumferential surface The Fourier coefficients are used for characterization:

[0152] ,

[0153] In the formula: is a constant term, representing the density of the material used by the hemispherical resonator, usually fused quartz, with a density of about 2200 kg / m 3 ;

[0154] , is the coefficient corresponding to the mass unevenness of the nth order mode, and generally the larger the frequency splitting of the nth order mode, , the value of is also larger;

[0155] is a certain position on the circumferential surface of the hemispherical resonator (it can be understood that the loading module will grid the circumferential surface of the hemispherical resonator, and each node corresponds to a position , the loading module calculates the density , of each position node according to the user-given ;

[0156] Given the value of , , load the obtained to the three-dimensional model of the hemispherical resonator in the ideal state, call the simulation module for simulation, obtain the frequency splitting calculation value of the second order mode, and compare it with the frequency splitting value of the hemispherical resonator after actual processing. If they are not equal, change the value of , , repeat the above calculation-loading-frequency splitting calculation process until the frequency splitting calculation value is equal to the frequency splitting value of the hemispherical resonator after actual processing; load the finally determined to the three-dimensional model of the hemispherical resonator in the ideal state to obtain the mass uneven hemispherical resonator three-dimensional model corresponding to the frequency splitting value of the hemispherical resonator after actual processing.

[0157] Then load the above optimal spiral model on the mass uneven hemispherical resonator three-dimensional model and perform simulation to calculate the frequency value, and determine whether the calculated simulation frequency value is less than or equal to the target value. If yes, output the spiral model; if no, perform a new round of spiral model parameter sampling-simulation iteration in python or matlab software to obtain the optimal spiral model, and then load it to the mass uneven hemispherical resonator three-dimensional model in COMSOL software for simulation verification until the calculated simulation frequency value is less than or equal to the target value.

[0158] The following is an example of mass adjustment of a hemispherical resonator for a certain process using the present application:

[0159] A hemispherical resonator with an outer diameter of 15 mm and a wall thickness of 0.8 mm is processed using fused quartz (density 2200 kg / m 3 ). The initial frequency split of the hemispherical resonator caused by processing and other reasons is measured to be 0.02 Hz, and the target frequency split after adjustment is ≤0.008 Hz.

[0160] Using the differential evolution algorithm, the number of spiral lines is calculated to be 24, the polar angle range is [π / 9, 49π / 100], the pitch coefficient is 3, the phase angle of the first spiral line is about 0.5°, the spiral line width is about 0.05 mm, and the depth is about 0.025 mm.

[0161] A hemispherical resonator with a spiral line model constructed using three-dimensional modeling software is shown in Figure 3 . Using COMSOL for hemispherical simulation, mass defects can be created by increasing or decreasing mass near the lip of the hemispherical resonator to create a frequency split of 0.02 Hz, as shown in Figure 4 . The initial frequency split of 0.02 Hz is Figure 4 The difference between the first frequency axis frequency 5088.86534 and the second frequency axis frequency 5088.84690 of the hemispherical resonator obtained by simulation calculation in the lower left corner. According to the above steps, an optimized spiral line adjustment model is constructed on the outer surface of the hemispherical resonator with a frequency split of 0.02 Hz, with parameters calculated using the differential evolution algorithm, and finally an adjusted frequency split of 0.007 Hz is obtained, as shown in Figure 5 . The adjusted frequency split of 0.007 Hz is Figure 5 The difference between the first frequency axis frequency 5084.669259 and the second frequency axis frequency 5084.662013 of the hemispherical resonator obtained by simulation calculation in the lower left corner.

[0162] The above embodiments are only preferred specific embodiments of the present application. The phrases "in one embodiment", "in another embodiment", "in yet another embodiment" or "in other embodiments" used in this specification can refer to one or more of the same or different embodiments according to the present disclosure. Common changes and substitutions made by those skilled in the art within the scope of the technical solutions of the present application should be included in the protection scope of the present application.

Claims

1. A method of mass trimming of a hemispherical resonator, characterized by, The method comprises the following steps: S1: according to the design size of the hemispherical resonator and the frequency split value measured after processing, a hemispherical resonator model is constructed, and simulation calculation is performed after loading the spiral line model thereon, until the frequency split simulation calculation value meets the set requirement, and an optimized spiral line model is obtained; S2: the optimized spiral line model is used for mass adjustment of the processed hemispherical resonator; Step S1 specifically comprises: S1.1: a hemispherical model is constructed according to the design size of the hemispherical resonator, S1.2: a spiral line model is loaded on the hemispherical model, and first simulation calculation is performed to obtain a first frequency split simulation calculation value, S1.3: whether the first frequency split simulation calculation value meets the set requirement is judged, if yes, a first optimized spiral line model is formed and step S1.5 is transferred; if no, step S1.4 is transferred, S1.4: the spiral line model is adjusted, and step S1.2 is transferred, S1.5: according to the design size of the hemispherical resonator and the frequency split value measured after processing, a hemispherical resonator model is constructed, a first optimized spiral line model is loaded on the hemispherical resonator model, and second simulation calculation is performed to obtain a second frequency split simulation calculation value, whether the second frequency split simulation calculation value meets the set requirement is judged, if no, step S1.4 is transferred, and if yes, an optimized spiral line model is obtained; The spiral line model comprises a spiral thread parameterization equation and a cross section parameter equation of each spiral thread, and the spiral thread parameterization equation is: ， ， ， ， wherein R is the outer sphere radius of the hemispherical resonator, t is the polar angle, is the phase angle, i is the i-th spiral, is the x-axis coordinate of the i-th spiral at the polar angle t, the phase angle , is the y-axis coordinate of the i-th spiral at the polar angle t, the phase angle , is the z-axis coordinate of the i-th spiral at the polar angle t, the phase angle , is the phase angle of the i-th spiral, n is the pitch coefficient, N is the total number of spirals on the outer sphere surface, is the initial phase angle; The cross section parameter equation of each spiral thread is: ， ， wherein, is the spiral line etch depth at polar angle t, is the spiral line etch width at polar angle t, is the reference depth, is the reference width, a is the depth modulation amplitude coefficient, β is the depth modulation frequency coefficient, γ is the width modulation amplitude coefficient, and δ is the width modulation frequency coefficient.

2. The method of mass trim of a hemispherical resonator according to claim 1, characterized in that, In S1.2, the first simulation calculation is performed to obtain the first frequency split simulation calculation value, which specifically comprises: Each spiral thread is divided into several equal parts along the spiral direction, the microelement mass of each equal part and the phase angle of each equal part on the hemispherical equator are calculated, and the microelement mass corresponding to each phase angle on the hemispherical equator is accumulated to obtain the angular mass corresponding to the phase angle; The average value of the angular mass corresponding to all phase angles is solved to obtain the angular average mass, Subtracting the angular average quality from the angular quality corresponding to each phase angle, an angular alternating-current quality corresponding to the phase angle is obtained, and angular alternating-current qualities corresponding to multiple phase angles form an angular alternating-current quality distribution; solving a fourth harmonic component corresponding to the angular alternating-current quality distribution According to the fourth harmonic component , a first frequency split simulation calculation value is calculated.

3. The method of mass trim of a hemispherical resonator according to claim 1, characterized in that, In step S1.3, whether the first frequency split simulation calculation value meets the set requirement is judged, which specifically comprises: The frequency split value of the actually processed hemispherical resonator is subtracted from the first frequency split simulation calculation value, and whether the square of the difference between the obtained difference and the target frequency split value is less than or equal to the set convergence tolerance is judged.

4. The method of mass trim of a hemispherical resonator according to claim 1, characterized in that, In step S1.3, after it is judged that the first frequency split simulation calculation value meets the set requirement, it further comprises: Whether the set constraint condition is met is judged, if yes, a first optimized spiral line model is formed and step S1.5 is transferred; if no, step S1.4 is transferred.

5. The method of mass trim of a hemispherical resonator according to claim 1, characterized in that, In step S1.4, the spiral line model is adjusted, which specifically comprises: A difference evolution algorithm or NAGA-II algorithm is used to sample each parameter in the spiral thread parameterization equation and the cross section parameter equation of each spiral thread, the spiral line model is adjusted according to the sampling result to generate a spiral line model for next round simulation calculation.

6. A hemispherical resonator gyroscope comprising a hemispherical resonator, characterized in that, The hemispherical resonator is mass adjusted by using the mass adjustment method of the hemispherical resonator according to any one of claims 1-5.

7. An electronic device, comprising: The device comprises: A memory for storing a computer program: A processor for implementing the steps of the method for mass trimming of a hemispherical resonator as claimed in any one of claims 1 to 5 when executing the computer program.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program which, when executed by the processor, implements the steps of the method for mass trimming of a hemispherical resonator as claimed in any one of claims 1 to 5.

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