CN109084741B - Method and system for cracking harmonic oscillator frequency of cylindrical shell vibrating gyroscope - Google Patents
Method and system for cracking harmonic oscillator frequency of cylindrical shell vibrating gyroscope Download PDFInfo
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- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
- G01C19/56—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
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Abstract
The invention discloses a method and a system for cracking harmonic oscillator frequency of a cylindrical shell vibrating gyroscope, wherein the method comprises the following steps of A, measuring roundness error of a harmonic oscillator of the cylindrical shell vibrating gyroscope; B. calculating the wall thickness error of the harmonic oscillator according to the roundness error of the harmonic oscillator; C. carrying out harmonic fitting on the wall thickness error of the harmonic oscillator to obtain a Fourier coefficient of the wall thickness error; D. and establishing a finite element simulation model, and substituting the finite element simulation model into the Fourier coefficient of the wall thickness error to obtain the frequency cracking of the harmonic oscillator. The circular distribution of the roundness error of the harmonic oscillator is obtained through harmonic fitting, finite element simulation modeling is carried out, frequency cracking components caused by geometric errors are separated independently, and the frequency cracking components of the harmonic oscillator can be analyzed specifically.
Description
Technical Field
The invention relates to the field of vibrating gyroscopes, in particular to a method and a system for cracking harmonic oscillator frequency of a vibrating gyroscope with a cylindrical shell.
Background
The cylindrical shell vibrating gyroscope is one kind of solid wave gyroscope, and utilizes the inertia effect of elastic waves in the cylindrical shell structure to realize angular speed measurement. The working principle of the cylindrical shell vibrating gyroscope is as follows: when the driving frequency of the piezoelectric electrode is consistent with the second-order mode inherent working frequency of the harmonic oscillator, standing wave vibration is excited. The working mode pairs of the cylindrical shell vibration gyro harmonic oscillator are respectively called as a driving mode and a detection mode and form an included angle of 45 degrees with each other. When no angular velocity is input, the harmonic oscillator only works in the driving mode, and the output is zero at the position of the standing wave node. When the angular velocity is input, the mass unit of the harmonic oscillator is excited under the action of the Coriolis force along the 45-degree direction of a detection mode. The amplitude of the detection mode standing wave is in a direct proportion relation with the angular speed, and the input angular speed is obtained through circuit demodulation. The frequency cracking is the frequency difference value of the driving mode and the detection mode of the cylindrical shell vibration gyro harmonic oscillator, and reflects the mass and rigidity error of the harmonic oscillator. In the prior art, frequency cracking is caused by geometric errors of harmonic oscillators and material unevenness, but the frequency cracking component caused by the geometric errors is usually difficult to separate.
Accordingly, the prior art is yet to be improved and developed.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a method and a system for frequency splitting of a resonator of a vibrating gyroscope with a cylindrical shell, aiming at solving the problem that frequency splitting components are difficult to separate due to geometric errors in the prior art.
The technical scheme adopted by the invention for solving the technical problem is as follows:
a method for cracking the harmonic oscillator frequency of a cylindrical shell vibrating gyroscope comprises the following steps:
A. measuring the roundness error of a harmonic oscillator of the cylindrical shell vibrating gyroscope;
B. calculating the wall thickness error of the harmonic oscillator according to the roundness error of the harmonic oscillator;
C. carrying out harmonic fitting on the wall thickness error of the harmonic oscillator to obtain a Fourier coefficient of the wall thickness error;
D. and establishing a finite element simulation model, and substituting the finite element simulation model into the Fourier coefficient of the wall thickness error to obtain the frequency cracking of the harmonic oscillator.
The frequency cracking method of the cylindrical shell vibrating gyroscope harmonic oscillator comprises the following steps: and measuring the inner circle radius and the outer circle radius of the harmonic oscillator by using a roundness meter to obtain the inner circle roundness error and the outer circle roundness error of the harmonic oscillator.
The frequency cracking method of the cylindrical shell vibrating gyroscope harmonic oscillator comprises the following steps: and measuring the inner circle eccentricity and the outer circle eccentricity of the harmonic oscillator by using a roundness measuring instrument.
The frequency cracking method of the cylindrical shell vibrating gyro harmonic oscillator comprises the following steps:
c1, fitting the first i-th harmonic to obtain a change rule of the wall thickness error along with the harmonic frequency;
and C2, obtaining Fourier coefficients of the wall thickness error by performing j-order harmonic fitting on the wall thickness error of the harmonic oscillator, wherein i and j are positive integers, and j < i.
The frequency cracking method of the cylindrical shell vibrating gyroscope harmonic oscillator comprises the following steps:
d1, establishing a finite element simulation model, and substituting the finite element simulation model into a Fourier coefficient of the wall thickness error to obtain the working frequency of the harmonic oscillator;
d2, calculating frequency cracking.
A cylindrical shell vibratory gyroscope harmonic oscillator frequency splitting system, comprising: a processor, and a memory coupled to the processor,
the memory stores a cylindrical shell vibrating gyro harmonic oscillator frequency cracking program, and the cylindrical shell vibrating gyro harmonic oscillator frequency cracking program realizes the following steps when executed by the processor:
A. measuring the roundness error of a harmonic oscillator of the cylindrical shell vibrating gyroscope;
B. calculating the wall thickness error of the harmonic oscillator according to the roundness error of the harmonic oscillator;
C. carrying out harmonic fitting on the wall thickness error of the harmonic oscillator to obtain a Fourier coefficient of the wall thickness error;
D. and establishing a finite element simulation model, and substituting the finite element simulation model into the Fourier coefficient of the wall thickness error to obtain the frequency cracking of the harmonic oscillator.
The frequency cracking system for the cylindrical shell vibrating gyroscope harmonic oscillator comprises the following steps: and measuring the inner circle radius and the outer circle radius of the harmonic oscillator by using a roundness meter to obtain the inner circle roundness error and the outer circle roundness error of the harmonic oscillator.
The frequency cracking system for the cylindrical shell vibrating gyroscope harmonic oscillator comprises the following steps: and measuring the inner circle eccentricity and the outer circle eccentricity of the harmonic oscillator by using a roundness measuring instrument.
The frequency cracking system for the cylindrical shell vibrating gyro harmonic oscillator comprises the following steps:
c1, fitting the first i-th harmonic to obtain a change rule of the wall thickness error along with the harmonic frequency;
and C2, obtaining Fourier coefficients of the wall thickness error by performing j-order harmonic fitting on the wall thickness error of the harmonic oscillator, wherein i and j are positive integers, and j < i.
The frequency cracking system for the cylindrical shell vibrating gyro harmonic oscillator comprises the following steps:
d1, establishing a finite element simulation model, substituting the finite element simulation model into the Fourier coefficient of the wall thickness error to obtain the working frequency of the harmonic oscillator
D2, calculating frequency cracking.
Has the advantages that: the circular distribution of the roundness error of the harmonic oscillator is obtained through harmonic fitting, finite element simulation modeling is carried out, frequency cracking components caused by geometric errors are separated independently, and the frequency cracking components of the harmonic oscillator can be analyzed specifically.
Drawings
FIG. 1 is a flow chart of a preferred embodiment of a method for frequency-cracking cylindrical shell vibratory gyroscope harmonic oscillators according to the present invention;
FIG. 2 is a circular distribution diagram of the inner roundness error of the harmonic oscillator according to the present invention;
FIG. 3 is a circumferential distribution diagram of the outer roundness error of the harmonic oscillator according to the present invention;
FIG. 4 is a circumferential distribution diagram of the wall thickness error of the harmonic oscillator according to the present invention;
FIG. 5 is a graph showing the wall thickness error as a function of harmonic order for the first 100 harmonics of the present invention;
FIG. 6 is a circumferential distribution diagram of wall thickness error of harmonic oscillators fitted in the present invention;
FIG. 7 is a circumferential distribution diagram of wall thickness error of a harmonic oscillator of the finite element simulation of the present invention;
FIG. 8 is a graph of frequency cracking of different secondary harmonic components in the present invention;
fig. 9 is a gyro resonator employed in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer and clearer, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 9, the gyro resonator employed in the present invention includes: resonator chassis 10, piezoelectric electrode 20, mount 30, support structure 40, and resonating structure 50. The resonator chassis 10 is disposed on the mount 30, the support structure 40 is disposed on an edge of the resonator chassis 10, the resonant structure 50 is disposed on the support structure 40, and the piezoelectric electrode 20 is bonded on a surface of the resonator chassis 10. The resonator chassis 10 is circular, the resonant structure 50 and the supporting structure 40 are both in a circular tube shape, and the tube diameter of the supporting structure 40 is smaller than that of the resonant structure 50. The resonator chassis 10 is a circular disc with a diameter equal to the outer diameter of the support structure 40. The mounting seat 30 is in a shape of a circular tube, and the diameter of the mounting seat 30 is smaller than that of the resonator chassis 10. The axial lines of the resonator chassis 10, the piezoelectric electrode 20, the mount 30, the support structure 40, and the resonant structure 50 all coincide. The piezoelectric electrode 20 is bonded to the resonator chassis 10. For the gyro resonator of the present invention, the geometric error refers to a wall thickness error.
Referring to fig. 1-9, as shown in fig. 1, a flow chart of a preferred embodiment of a method for frequency cracking of a resonator of a cylindrical shell vibrating gyroscope according to the present invention is provided, which includes the steps of:
and S100, measuring the roundness error of the harmonic oscillator of the cylindrical shell vibration gyro.
Specifically, the radius of the resonator (i.e., the resonant structure 50) is measured using a roundness meter, and the inner circle radius and the outer circle radius of the resonator, both of which are functions with respect to the circumferential angle variable θ, are obtained. As shown in fig. 2 to 3, the inner roundness error and the outer roundness error of the harmonic oscillator can be obtained.
Of course, besides the roundness of the harmonic oscillator, the inner circle eccentricity and the outer circle eccentricity of the harmonic oscillator can be measured through a roundness meter, and the inner circle eccentricity and the outer circle eccentricity can be obtained. The wall thickness error caused by eccentricity corresponds to the size of 1 st harmonic, and the 1 st harmonic can correspond to a certain amount of frequency cracking. Frequency cracking due to eccentricity is small and is generally not considered, if it is to be very accurate.
And step S200, calculating the wall thickness error of the harmonic oscillator according to the roundness error of the harmonic oscillator.
Specifically, the wall thickness error of the harmonic oscillator is the difference of the excircle roundness error minus the inner roundness error of the harmonic oscillator. And after the roundness error of the harmonic oscillator is measured, fitting the circumferential distribution of the wall thickness error of the harmonic oscillator based on Matlab. The circumferential distribution graph of the wall thickness error of the harmonic oscillator shown in fig. 4 shows the thickness variation law of the harmonic oscillator along different axes.
And step S300, carrying out harmonic fitting on the wall thickness error of the harmonic oscillator to obtain a Fourier coefficient of the wall thickness error.
The method specifically comprises the following steps:
and S301, fitting the first i-th harmonic to obtain a change rule of the wall thickness error along with the harmonic frequency.
Specifically, i is usually 100, i.e. the first 100 harmonics are fitted to obtain the law of variation of wall thickness error with harmonic order. The radius of the harmonic oscillator is as follows:
wherein r is0Is the average radius, theta is the variation of the circumferential angle, n is the harmonic order, anAnd bnThe coefficients are Fourier coefficients of reaction errors, and r (theta) is the radius of the harmonic oscillator, wherein the radius of the harmonic oscillator comprises the outer circle radius of the harmonic oscillator and the inner circle radius of the harmonic oscillator, and the outer circle radius and the inner circle radius are calculated by the formula (1). They can be determined by the following system of equations:
the radius r (theta) of the harmonic oscillator and the average radius r can be obtained in step S1000It can also be calculated, of course, the average radius of the harmonic oscillator is calculated for the inner circle and the outer circle of the harmonic oscillator respectively, and then a is calculated by fitting the equation (1) and the equation set (2)nAnd bn。
If eccentricity is taken into account, equation (1) is extended to
Wherein e isx，eyIs the amount of eccentricity. Similarly, the radius r (θ) of the harmonic oscillator and the average radius r can be obtained in step S1000Then combining the formula (1) and the formula (3) to calculate anAnd bn。
Step S302, j harmonic fitting is carried out on the wall thickness error of the harmonic oscillator to obtain a Fourier coefficient of the wall thickness error, wherein i and j are positive integers, and j is less than i.
The first 100 harmonics as shown in fig. 5 show a graph of the variation rule of the wall thickness error with the harmonic number, and by fitting the first 100 harmonics showing the variation rule of the wall thickness error with the harmonic number, it can be found that the first 20 harmonics have a large influence on the wall thickness error of the harmonic oscillator, for example, the fourth harmonic component is 0.107 μm. Then 80 th harmonic changes have less influence on the wall thickness error of the harmonic oscillator. Therefore, j is set to 20, but j may be set to 4.
Specifically, as shown in fig. 6, the circumferential wall thickness error distribution diagram of the harmonic oscillator is fitted, and the circumferential wall thickness error distribution of the harmonic oscillator is fitted through the change of the first 100 harmonic components. The fourth harmonic component is analyzed using a harmonic fitting method, where the fourth harmonic causes most of the frequency cracking, and generally only the fourth harmonic is analyzed, and other orders can be analyzed with little effect.
And S400, establishing a finite element simulation model, and substituting the finite element simulation model into a Fourier coefficient of the wall thickness error to obtain the frequency cracking of the harmonic oscillator.
Specifically, an，bnSubstituting the numerical value into finite element simulation to calculate the corresponding frequency cracking. Thereby determining the magnitude of the frequency cracking caused by the geometric error.
Step S400 specifically includes:
and S401, establishing a finite element simulation model, and substituting the finite element simulation model into a Fourier coefficient of the wall thickness error to obtain the working frequency of the harmonic oscillator.
Specifically, the modeling can be realized by using finite element simulation software, and the programming calculation can also be realized by using a general finite element algorithm. The working frequency of the harmonic oscillator can be obtained through a finite element modeling simulation result, and the simulation model already contains geometric error information.
The finite element calculation comprises the following specific steps:
1. a is an，bnThe numerical value of (2) is substituted into the formula (1) or the formula (3) to obtain an r (theta) function, and the inner and outer diameter node coordinates are calculated by the r (theta) function, that is, the inner and outer diameter node coordinates are calculated by taking different theta values within the range of 0 to 360 degrees, for example, taking one value every 0.1 degrees. Of course, the circumferential distribution diagram of the wall thickness error of the harmonic oscillator of the finite element simulation shown in fig. 7 can also be obtained, and the change rule of the wall thickness error along with different positions of the harmonic oscillator is regular.
2. And inputting the obtained coordinates of the inner and outer diameter nodes into finite element software to establish the nodes. The finite element software may be ANSYS finite element software.
3. And connecting the nodes to establish a 3-dimensional cylindrical shell vibration gyro model with a wall thickness error.
4. And (3) dividing the 3-dimensional cylindrical shell vibration gyro model with the wall thickness error into grids, and inputting the density and elastic modulus parameters of the harmonic oscillator material.
5. And performing modal calculation, and outputting modal frequency, namely outputting the working frequency of the harmonic oscillator. The modal frequencies herein include the frequencies of the driving mode and the frequencies of the detecting mode.
Step S402, calculating frequency cracking.
Specifically, the simulation result shows that the operating frequencies of the harmonic oscillator are 4034.4Hz (the frequency of the driving mode) and 4035Hz (the frequency of the detection mode), respectively, i.e., the frequency splitting is 0.6Hz (4035Hz-4034.4Hz ═ 0.6 Hz).
Further, as shown in fig. 8, the frequency cracking diagram of different secondary harmonic components is specifically the frequency cracking size corresponding to each 10 μm error of each order harmonic. It can be seen that the fourth harmonic component has a greater effect on the harmonic elements. The corresponding fourth harmonic component (0.107 μm) can result in frequency cracking at 0.47 Hz. Since it is in FIG. 8 that each order harmonic corresponds to a 43Hz frequency split every 10 μm fourth harmonic, a frequency split of 0.107 μm can be calculated as 0.107X 4.33 ≈ 0.47.
Therefore, the method for cracking the harmonic oscillator frequency of the vibrating gyroscope with the cylindrical shell can separate the frequency cracking component caused by geometric errors independently, and can analyze the frequency cracking component of the harmonic oscillator specifically, thereby being beneficial to preparing the harmonic oscillator with better performance.
The embodiment of the invention also provides a frequency cracking system for the cylindrical shell vibrating gyroscope harmonic oscillator, which comprises the following components:
a processor, and a memory coupled to the processor,
the memory stores a cylindrical shell vibrating gyro harmonic oscillator frequency cracking program, and the cylindrical shell vibrating gyro harmonic oscillator frequency cracking program realizes the following steps when executed by the processor:
s100, measuring the roundness error of a harmonic oscillator of the cylindrical shell vibrating gyroscope;
s200, calculating a wall thickness error of the harmonic oscillator according to the roundness error of the harmonic oscillator;
step S300, carrying out harmonic fitting on the wall thickness error of the harmonic oscillator to obtain a Fourier coefficient of the wall thickness error;
and S400, establishing a finite element simulation model, and substituting the finite element simulation model into a Fourier coefficient of the wall thickness error to obtain the frequency cracking of the harmonic oscillator.
The step S100 includes: the roundness error of the inner circle and the roundness error of the outer circle of the harmonic oscillator are measured by using the roundness measuring instrument, which is specifically described above.
The step S100 further includes: the roundness measuring instrument is used for measuring the inner circle eccentricity and the outer circle eccentricity of the harmonic oscillator, and is specifically as described above.
The step S300 includes:
s301, fitting the first i-th harmonic to obtain a change rule of the wall thickness error along with the harmonic frequency;
step S302, performing j-order harmonic fitting on the wall thickness error of the harmonic oscillator to obtain a fourier coefficient of the wall thickness error, where i and j are positive integers, and j < i, as described above.
The step S400 includes:
step S401, establishing a finite element simulation model, and substituting the finite element simulation model into a Fourier coefficient of a wall thickness error to obtain the working frequency of the harmonic oscillator;
step S402, calculating frequency cracking, as described above.
In summary, the invention provides a method and a system for frequency cracking of a cylindrical shell vibrating gyroscope harmonic oscillator, wherein the method comprises the following steps: A. measuring the roundness error of a harmonic oscillator of the cylindrical shell vibrating gyroscope; B. calculating the wall thickness error of the harmonic oscillator according to the roundness error of the harmonic oscillator; C. carrying out harmonic fitting on the wall thickness error of the harmonic oscillator to obtain a Fourier coefficient of the wall thickness error; D. and establishing a finite element simulation model, and substituting the finite element simulation model into the Fourier coefficient of the wall thickness error to obtain the frequency cracking of the harmonic oscillator. The circular distribution of the roundness error of the harmonic oscillator is obtained through harmonic fitting, finite element simulation modeling is carried out, frequency cracking components caused by geometric errors are separated independently, and the frequency cracking components of the harmonic oscillator can be analyzed specifically.
It is to be understood that the invention is not limited to the examples described above, but that modifications and variations may be effected thereto by those of ordinary skill in the art in light of the foregoing description, and that all such modifications and variations are intended to be within the scope of the invention as defined by the appended claims.
Claims (6)
1. A method for cracking harmonic oscillator frequency of a cylindrical shell vibrating gyroscope is characterized by comprising the following steps:
A. measuring the roundness error of a harmonic oscillator of the cylindrical shell vibrating gyroscope;
B. calculating the wall thickness error of the harmonic oscillator according to the roundness error of the harmonic oscillator;
C. carrying out harmonic fitting on the wall thickness error of the harmonic oscillator to obtain a Fourier coefficient of the wall thickness error;
D. establishing a finite element simulation model, and substituting the finite element simulation model into a Fourier coefficient of a wall thickness error to obtain the frequency cracking of the harmonic oscillator;
the step A comprises the following steps: measuring the inner circle roundness error and the outer circle roundness error of the harmonic oscillator by using a roundness meter; the wall thickness error of the harmonic oscillator is the difference value of the excircle roundness error minus the inner roundness error of the harmonic oscillator;
the step C comprises the following steps:
c1, fitting the first i-th harmonic to obtain a change rule of the wall thickness error along with the harmonic frequency;
and C2, obtaining Fourier coefficients of the wall thickness error by performing j-order harmonic fitting on the wall thickness error of the harmonic oscillator, wherein i and j are positive integers, and j < i.
2. The method for frequency-splitting a cylindrical shell vibratory gyroscope harmonic oscillator of claim 1, wherein the step a further comprises: and measuring the inner circle eccentricity and the outer circle eccentricity of the harmonic oscillator by using a roundness measuring instrument.
3. The method for frequency-splitting a cylindrical shell vibratory gyroscope harmonic oscillator of claim 1, wherein the step D comprises:
d1, establishing a finite element simulation model, and substituting the finite element simulation model into a Fourier coefficient of the wall thickness error to obtain the working frequency of the harmonic oscillator;
d2, calculating frequency cracking.
4. The utility model provides a cylinder casing vibrating top harmonic oscillator frequency schizolysis system which characterized in that includes: a processor, and a memory coupled to the processor,
the memory stores a cylindrical shell vibrating gyro harmonic oscillator frequency cracking program, and the cylindrical shell vibrating gyro harmonic oscillator frequency cracking program realizes the following steps when executed by the processor:
A. measuring the roundness error of a harmonic oscillator of the cylindrical shell vibrating gyroscope;
B. calculating the wall thickness error of the harmonic oscillator according to the roundness error of the harmonic oscillator;
C. carrying out harmonic fitting on the wall thickness error of the harmonic oscillator to obtain a Fourier coefficient of the wall thickness error;
D. establishing a finite element simulation model, and substituting the finite element simulation model into a Fourier coefficient of a wall thickness error to obtain the frequency cracking of the harmonic oscillator;
the step A comprises the following steps: measuring the inner circle roundness error and the outer circle roundness error of the harmonic oscillator by using a roundness meter; the wall thickness error of the harmonic oscillator is the difference value of the roundness error of the outer circle of the harmonic oscillator minus the roundness error of the inner circle of the harmonic oscillator;
the step C comprises the following steps:
c1, fitting the first i-th harmonic to obtain a change rule of the wall thickness error along with the harmonic frequency;
and C2, obtaining Fourier coefficients of the wall thickness error by performing j-order harmonic fitting on the wall thickness error of the harmonic oscillator, wherein i and j are positive integers, and j < i.
5. The cylindrical shell vibratory gyroscope harmonic oscillator frequency splitting system of claim 4, wherein the step A further comprises: and measuring the inner circle eccentricity and the outer circle eccentricity of the harmonic oscillator by using a roundness measuring instrument.
6. The cylindrical shell vibratory gyroscope harmonic oscillator frequency splitting system of claim 4, wherein the step D comprises:
d1, establishing a finite element simulation model, and substituting the finite element simulation model into a Fourier coefficient of the wall thickness error to obtain the working frequency of the harmonic oscillator;
d2, calculating frequency cracking.
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