Method for identifying the first three harmonics of the unbalance mass of a hemispherical resonator based on vibration excitation

Abstract

This invention, based on vibration excitation, describes a method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator, belonging to the field of hemispherical harmonic gyroscope parameter identification. It solves the problems of existing methods for identifying the first three harmonics of the unbalanced mass, such as difficulties in data identification and long measurement times, leading to low leveling efficiency and accuracy. Under vibration excitation, the vibration amplitude and standing wave azimuth of the hemispherical harmonic oscillator are correlated with the first and third harmonics of the unbalanced mass; under vibration excitation, the vibration amplitude and standing wave azimuth are correlated with the second harmonic of the unbalanced mass. The amplitude and azimuth of the first three harmonics are solved by constructing the corresponding coupling relationships. This invention is mainly used for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator.

Description

Technical Field

[0001] This invention belongs to the field of parameter identification of hemispherical resonant gyroscopes. Background Technology

[0002] As a novel solid-state inertial device, the accuracy of a hemispherical resonator gyroscope is directly determined by the uniformity of its mass distribution in its core sensitive component—the hemispherical resonator. Due to limitations in existing material properties and manufacturing processes, the hemispherical resonator exhibits an unbalanced mass distribution along its circumference. This unbalanced mass can be expanded into harmonic forms using Fourier transform. Among these, the first four harmonics of the unbalanced mass have the most significant impact on the resonator's vibration performance. The first three harmonics of the unbalanced mass cause the hemispherical resonator's center of mass to vibrate, resulting in energy dissipation due to modal coupling and significantly affecting the gyroscope's performance. The fourth harmonic of the unbalanced mass causes frequency fragmentation in the resonator, leading to periodic drift of the standing wave. However, current leveling techniques primarily focus on correcting the fourth harmonic defect, while significant technical bottlenecks remain in the identification and leveling of the first three harmonics. Existing methods for identifying the first three harmonics of unbalanced mass mainly rely on laser Doppler vibration meters or piezoelectric displacement sensors to measure the displacement of the upper rod of the resonator. However, these methods suffer from high equipment costs, difficulties in data identification due to the small vibration displacement of the upper rod, long measurement times, and low identification efficiency and accuracy, making it difficult to meet the microgram-level mass adjustment requirements of the first three harmonics of unbalanced mass. For the development of high-precision hemispherical resonator gyroscopes, there is an urgent need for a high-precision and high-efficiency method and system for identifying the first three harmonics of unbalanced mass. Summary of the Invention

[0003] To address the problems of existing methods for identifying the first three harmonics of unbalanced mass, such as difficulties in data identification and long measurement times, resulting in low leveling efficiency and accuracy, this invention provides a method for identifying the first three harmonics of unbalanced mass of a hemispherical harmonic oscillator based on vibration excitation.

[0004] A method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator based on vibration excitation. This method includes:

[0005] In a vacuum environment, the hemispherical resonant gyroscope is subjected to measurements along its coordinate system. Vibration excitation in three directions of the axis, the lower hemispherical resonant gyroscope in each vibration direction starts from rest to the target amplitude and remains stable;

[0006] The vibration signals of the hemispherical harmonic oscillator of the lower hemispherical resonant gyroscope in each vibration direction after stabilization are collected and processed to obtain the amplitude control quantity and standing wave azimuth angle of the lower hemispherical resonant gyroscope in the corresponding vibration direction.

[0007] Combination and Amplitude control quantity and standing wave azimuth angle in the direction of shaft vibration, and energy of the target amplitude. The first and third harmonics are decoupled to obtain the amplitude and azimuth of the first and third harmonics of the hemispherical harmonic oscillator.

[0008] right Amplitude control quantity, standing wave azimuth angle, and energy of target amplitude in the direction of shaft vibration By performing second-order harmonic decoupling, the amplitude and azimuth of the second-order harmonic of the hemispherical harmonic oscillator are obtained.

[0009] Preferably, it combines and Amplitude control quantity and standing wave azimuth angle in the direction of shaft vibration, and energy of the target amplitude. The methods for decoupling the first and third harmonics to obtain the amplitude and azimuth angle of the first and third harmonics of the hemispherical harmonic oscillator include:

[0010] according to Amplitude control quantity in the direction of shaft vibration, energy of target amplitude And the amplitude and azimuth of the first and third harmonics to be determined, and construct the first coupling relationship expression;

[0011] according to The standing wave azimuth angle under the axial vibration direction, and the amplitude and azimuth angle of the first and third harmonics to be determined, are used to construct the second coupling relationship expression;

[0012] according to Amplitude control quantity in the direction of shaft vibration, energy of target amplitude And the amplitude and azimuth of the first and third harmonics to be determined, and construct the third coupling relationship expression;

[0013] according to The standing wave azimuth angle under the axial vibration direction, and the amplitude and azimuth angle of the first and third harmonics to be determined, are used to construct the fourth coupling relationship expression;

[0014] A system of equations is constructed from the first to fourth coupling relationship expressions, and the amplitude and azimuth of the first and third harmonics are calculated.

[0015] The preferred expression for the first coupling relationship is:

[0016] ;

[0017] ;

[0018] in, As an intermediate variable, This is the gain coefficient. The time constant of the hemispherical harmonic oscillator is... The natural frequency of the hemispherical harmonic oscillator. for Amplitude control quantity in the direction of shaft vibration Let the amplitude of the first harmonic be the value to be determined. Let the amplitude of the third harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined. The azimuth angle of the third harmonic to be determined.

[0019] Preferably, the expression for the second coupling relationship is:

[0020] ;

[0021] in, for The azimuth angle of the standing wave in the direction of vibration. Let the amplitude of the first harmonic be the value to be determined. Let the amplitude of the third harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined. The azimuth angle of the third harmonic to be determined.

[0022] Preferably, the expression for the third coupling relationship is:

[0023] ;

[0024] ;

[0025] in, As an intermediate variable, This is the gain coefficient. Let be the time constant of the hemispherical harmonic oscillator. The natural frequency of the hemispherical harmonic oscillator. for Amplitude control quantity in the direction of shaft vibration Let the amplitude of the first harmonic be the value to be determined. Let the amplitude of the third harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined. The azimuth angle of the third harmonic to be determined.

[0026] Preferably, the expression for the fourth coupling relationship is:

[0027] ;

[0028] in, for The azimuth angle of the standing wave in the direction of shaft vibration. Let the amplitude of the first harmonic be the value to be determined. Let the amplitude of the third harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined. The azimuth angle of the third harmonic to be determined.

[0029] Preferably, for Amplitude control quantity, standing wave azimuth angle, and energy of target amplitude in the direction of shaft vibration The methods for achieving second-order harmonic decoupling to obtain the amplitude and azimuth angle of the second-order harmonic of the hemispherical harmonic oscillator include:

[0030] according to Amplitude control quantity in the direction of shaft vibration, energy of target amplitude And the amplitude and azimuth of the second and third harmonics to be determined, to construct the fifth coupling relationship expression;

[0031] Based on the fifth coupling relationship expression, the amplitude and azimuth of the second harmonic are calculated.

[0032] Preferably, the fifth coupling relationship expression includes:

[0033] ;

[0034] ;

[0035] ;

[0036] in, for The azimuth angle of the standing wave in the direction of shaft vibration. As an intermediate variable, This is the gain coefficient. Let be the time constant of the hemispherical harmonic oscillator. The natural frequency of the hemispherical harmonic oscillator. for Amplitude control quantity in the direction of shaft vibration Let the amplitude of the second harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined.

[0037] Preferably, the vacuum environment has a vacuum level of less than 1×10⁻⁶. -4 Pa's environment.

[0038] Preferably, the control method for vibration excitation in each direction is as follows:

[0039] The controller provides a sinusoidal signal to the piezoelectric exciter, causing it to vibrate in the corresponding direction, thereby driving the hemispherical resonant gyroscope located on the piezoelectric exciter to vibrate synchronously. At the same time, the controller applies an orthogonal control force to the plate electrode of the hemispherical resonant gyroscope to suppress the orthogonal wave of the hemispherical resonant gyroscope.

[0040] The beneficial effects of this invention are:

[0041] The method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator based on vibration excitation has the following advantages:

[0042] (1) The method of the present invention only needs to detect the vibration amplitude control quantity and standing wave azimuth angle of the harmonic oscillator to achieve identification, and the main control loop is compatible with the existing control scheme;

[0043] (2) The measurement cost is low. The system does not require additional sensors for measurement. It can achieve control and signal detection by relying solely on the structure of the hemispherical resonant gyroscope itself.

[0044] (3) High measurement accuracy: The piezoelectric vibration table excites the first three harmonics of the unbalanced mass of the hemispherical harmonic oscillator to drive the spherical shell vibration of the hemispherical harmonic oscillator. The amplitude and azimuth of the harmonics are calculated by detecting the dynamic response of the hemispherical harmonic oscillator. The vibration amplitude of the hemispherical harmonic oscillator shell is on the order of micrometers. Compared with the traditional method of identifying the first three harmonics by measuring the nanometer-level amplitude of the top rod, the measurement accuracy of this method is significantly improved.

[0045] (4) The measurement time is shorter. Under the control of the controller, the vibration of the hemispherical harmonic oscillator will converge to the steady state more quickly. The steady state value is recorded for calculation. The measurement time is shortened to less than 5 minutes, which is significantly improved compared to the traditional top rod test method which takes more than 10 hours. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of a hemispherical resonant gyroscope subjected to vibration excitation.

[0047] Figure 2 It is a rectangular coordinate system of a hemispherical harmonic oscillator spherical coordinate system and the surface of the spherical shell A schematic diagram of the local coordinate system of a point;

[0048] Figure 3 This is a diagram showing the effect of first-order harmonic leveling;

[0049] Figure 4 This is a diagram showing the effect of third-order harmonic leveling;

[0050] Figure 5 This is a diagram showing the effect of second-order harmonic leveling;

[0051] Figure 6This is a comparison chart of the quality factors before and after leveling the first three harmonics; among them, Figure 6 In This represents the mean of the quality factor. This indicates the uniformity of the quality factor. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0054] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0055] Theoretical derivation:

[0056] like Figure 2 As shown, the hemispherical harmonic oscillator can be simplified to a hemispherical shell model as shown in the figure, and a rectangular coordinate system can be established. spherical coordinate system and the surface of the spherical shell Local coordinate system of a point , Let be the radius of the hemispherical shell. and These represent the polar angle and azimuth angle, respectively. These are the first to third coordinate variables of the local coordinate system. The thickness of the hemispherical shell, The coordinate axes of the hemispherical shell in the local coordinate system are respectively. The displacement below;

[0057] To characterize the circumferential mass distribution of the resonator shell of the hemispherical resonator gyroscope while also improving the convenience of mathematical modeling of the resonator, a density parameter is chosen here. As the independent variable, the circumferential mass of the spherical shell is expanded into a function of the circumferential angle of the spherical shell. The Fourier series, i.e.:

[0058] (1);

[0059] in, The mean circumferential density of the spherical shell of the harmonic oscillator; and These represent the first and second circumferential density distributions caused by the non-uniform circumferential density distribution of the harmonic oscillator shell. The amplitude and azimuth of the first harmonic.

[0060] The vibrational excitation displacement along the x-axis of the harmonic oscillator is:

[0061] (2);

[0062] in, and These represent the vibration amplitude and frequency of the resonator caused by the linear vibration exciter. It is a time variable.

[0063] The acceleration of the harmonic oscillator along the x-axis is expressed as:

[0064] (3);

[0065] This acceleration In the local coordinate system The Chinese character is represented as:

[0066] (4);

[0067] (5);

[0068] Cartesian coordinate system With local coordinate system Coordinate transformation matrix between;

[0069] Under vibration excitation in the x-axis direction, neglecting the asymmetry between damping and stiffness, the principal modal motion equations of the harmonic oscillator shell are expressed as:

[0070] (6);

[0071] in, and These are the generalized displacements under the first and second principal modes, respectively. The mass of the first mode of the second-order vibration of the hemispherical harmonic oscillator. For the natural frequency, It is a time constant. for The first derivative with respect to time, in physical terms, represents the first generalized velocity. for The second derivative with respect to time, in physical terms, represents the first generalized acceleration. for The first derivative with respect to time, in physical terms, represents the second generalized velocity. for The second derivative with respect to time, in physical terms, represents the second generalized acceleration. Local coordinate system The acceleration matrix of the lower harmonic oscillator For transpose, and Rectangular coordinate system The coordinate transformation matrices between the first and second principal modal coordinates can be expressed as:

[0072] (7);

[0073] in,

[0074] (8);

[0075] , and They are the edges of the harmonic oscillator. The first to third amplitude gain functions in the axial direction;

[0076] Substituting formulas (1), (4), and (7) into formula (6), we get:

[0077] (9);

[0078] in, These are the coefficients related to the first through third quality levels, respectively.

[0079] (10);

[0080] From equation (10), we can obtain:

[0081] (11);

[0082] Substituting equations (3) and (11) into equation (9), we can obtain

[0083] (12);

[0084] in,

[0085] (13);

[0086] This is the gain coefficient;

[0087] When the vibration of the spherical shell of the harmonic oscillator reaches a steady state, the solution of equation (12) is expressed in the form of:

[0088] (14);

[0089] Where e, g, m, and n represent the values ​​of the harmonic oscillator when it reaches a steady state. The amplitude of the cosine component, The amplitude of the sine component, The amplitude of the cosine component and The amplitude of the sinusoidal component.

[0090] Substituting equation (13) into equation (11), when the external excitation frequency is equal to the natural frequency of the harmonic oscillator, the amplitude parameter of the steady-state response of the spherical shell of the harmonic oscillator is expressed as:

[0091] (15);

[0092] When the amplitude of the spherical shell vibration of the harmonic oscillator reaches a steady state, in the local coordinate system Below, the edge of the harmonic oscillator shell The expression for displacement in the axial direction is:

[0093] (16);

[0094] in, For time Polar angle Azimuth For the independent variable Displacement in the axial direction, for Standing wave azimuth angle in the direction of vibration;

[0095] The standing wave azimuth angle of the harmonic oscillator is:

[0096] (17);

[0097] Substituting equation (14) into equation (16), the standing wave azimuth angle of the harmonic oscillator is:

[0098] (18);

[0099] Equation (17) illustrates that the harmonic oscillator in Under the excitation of vibration in the direction, the azimuth of the standing wave will be locked at the azimuth of the first and third harmonics of the quality defect acting together.

[0100] Substituting equation (15) into equation (16), we can obtain the hemispherical harmonic oscillator in... The expression for the displacement of the edge of the spherical shell along the n-axis direction under vibration excitation in the directional direction is:

[0101] (19);

[0102] Equation (19) shows that the hemispherical harmonic oscillator in The displacement of the edge of the spherical shell along the n-axis under vibration excitation is proportional to the amplitudes of the first and third harmonics of the unbalanced mass.

[0103] The energy of a vibration signal is defined as:

[0104] (19-1);

[0105] exist Steady-state energy under directional vibration excitation Represented as:

[0106] (19-2);

[0107] Similarly, along the harmonic oscillator When excited by vibration in the axial direction, the equation of motion of the harmonic oscillator is expressed as:

[0108] (20);

[0109] in, and These represent the vibration amplitude and frequency of the resonator acted upon by the linear vibration exciter, respectively.

[0110] harmonic oscillator along The linear acceleration in the axial direction can be expressed as:

[0111] (twenty one);

[0112] harmonic oscillator along Linear acceleration in the axial direction in the local coordinate system The Chinese character is represented as:

[0113] (twenty two);

[0114] exist Under axial linear vibration excitation, the equation of motion of the harmonic oscillator is expressed as:

[0115] (twenty three);

[0116] Substituting equations (1), (7), and (22) into equation (23), we get:

[0117] (twenty four);

[0118] Substituting equation (14) into equation (24), when the external excitation frequency is the natural frequency of the resonator shell, the amplitude parameter of the steady-state response of the resonator is expressed as:

[0119] (25);

[0120] Substituting equation (25) into equation (17), the harmonic oscillator The azimuth angle of the standing wave in the direction of vibration can be expressed as:

[0121] (26);

[0122] Equation (26) illustrates that the harmonic oscillator in Under linear vibration excitation in the direction of the wave, the azimuth of the standing wave will also be bound to the azimuth of the first and third harmonics of the quality defect acting together.

[0123] Substituting equation (25) into equation (16), we can obtain the hemispherical harmonic oscillator in... Vibration excitation in the direction of the spherical shell edge The expression for displacement in the axial direction is:

[0124] (27);

[0125] Equation (27) shows that the hemispherical harmonic oscillator in Vibration excitation in the direction of the spherical shell edge The displacement in the axial direction is also proportional to the amplitude of the first and third harmonics of the unbalanced mass.

[0126] Therefore, from equation (19-1), we can know that Under directional vibration excitation, the energy expression is:

[0127] (19-3);

[0128] harmonic oscillator along The vibration excitation form in the axial direction is expressed as:

[0129] (28);

[0130] in, and These represent the vibration amplitude and frequency of the resonator acted upon by the linear vibration exciter, respectively.

[0131] harmonic oscillator along The linear acceleration in the axial direction is expressed as:

[0132] (29);

[0133] harmonic oscillator along Linear acceleration in the axial direction in the local coordinate system The Chinese character is represented as:

[0134] (30);

[0135] exist The equation of motion of the harmonic oscillator under axial linear vibration excitation is expressed as:

[0136] (31);

[0137] Substituting equations (1), (7), and (30) into equation (31), we get:

[0138] (32);

[0139] in, The second modal mass of the second-order vibration of the hemispherical harmonic oscillator;

[0140] (33);

[0141] exist The final equation of motion for the harmonic oscillator under axial linear vibration excitation is:

[0142] (34);

[0143] in,

[0144] (35);

[0145] This is the gain coefficient;

[0146] Substituting equation (14) into equation (34), and when the external excitation frequency is equal to the natural frequency of the resonator shell, the vibration amplitude parameter of the steady-state response of the resonator is expressed as:

[0147] (36);

[0148] Substituting equation (36) into equation (17), the harmonic oscillator in The azimuth angle of the standing wave in the direction of shaft vibration is:

[0149] (37);

[0150] Equation (37) illustrates that the harmonic oscillator in Under linear vibration excitation in the direction, the standing wave azimuth will be bound to the azimuth of the second harmonic of the quality defect.

[0151] Substituting equation (36) into equation (16), we can obtain the hemispherical harmonic oscillator in... Vibration excitation in the direction of the spherical shell edge The expression for displacement in the axial direction is:

[0152] (38);

[0153] Equation (38) shows that the hemispherical harmonic oscillator in Vibration excitation in the direction of the spherical shell edge The displacement in the axial direction is also proportional to the amplitude of the second harmonic of the unbalanced mass.

[0154] From equation (19-1), it can be seen that in When subjected to directional vibration excitation, the energy expression is:

[0155] (19-4);

[0156] By establishing a vibration response model of a hemispherical harmonic oscillator under vibration excitation, it can be known that... Under vibrational excitation, the vibration amplitude and standing wave azimuth of the hemispherical harmonic oscillator are correlated with the first and third harmonics of the unbalanced mass. Under vibration excitation, the vibration amplitude and standing wave azimuth of the hemispherical harmonic oscillator are related to the second harmonic of the unbalanced mass.

[0157] Therefore, in order to obtain the amplitude and azimuth of the first to third harmonics of the unbalanced mass of the hemispherical harmonic oscillator, the gyroscope's control circuit can directly detect and output the system energy. Thus, based on energy... Construct an amplitude controller so that the energy of the harmonic oscillator converges rapidly to the target amplitude. The equations (19-2) and (19-3) are... Rewritten as Consider establishing a system of equations to solve for the four unknowns: the amplitude and azimuth of the first and third harmonics. .

[0158] Similarly, in equation 19-4) Rewritten as Consider establishing a system of equations to solve for the two unknowns: the amplitude and azimuth of the second harmonic. .

[0159] The above theoretical derivation shows that under vibration excitation, the first three harmonics of the unbalanced mass will excite the hemispherical harmonic oscillator to generate standing waves in a specific direction, and the amplitude of the standing waves is proportional to the amplitude of the first three harmonics. Utilizing this characteristic, this invention further proposes a method for identifying the amplitude and azimuth of the first three harmonics of the mass defect in a hemispherical harmonic gyroscope by analyzing the steady-state response of the hemispherical harmonic oscillator under vibration in the x, y, and z directions.

[0160] Specific Implementation Method 1: Combination Figure 1 This embodiment describes the method for identifying the first three harmonics of the unbalanced mass of a vibrating hemispherical harmonic oscillator based on vibration excitation. This method includes:

[0161] In a vacuum environment, the hemispherical resonant gyroscope is subjected to measurements along its coordinate system. Vibration excitation in three directions of the axis, the lower hemispherical resonant gyroscope in each vibration direction starts from rest to the target amplitude and remains stable;

[0162] The vibration signals of the hemispherical harmonic oscillator of the lower hemispherical resonant gyroscope in each vibration direction after stabilization are collected and processed to obtain the amplitude control quantity and standing wave azimuth angle of the lower hemispherical resonant gyroscope in the corresponding vibration direction.

[0163] Combination and Amplitude control quantity and standing wave azimuth angle in the direction of shaft vibration, and energy of the target amplitude. The first and third harmonics are decoupled to obtain the amplitude and azimuth of the first and third harmonics of the hemispherical harmonic oscillator.

[0164] right Amplitude control quantity, standing wave azimuth angle, and energy of target amplitude in the direction of shaft vibration By performing second-order harmonic decoupling, the amplitude and azimuth of the second-order harmonic of the hemispherical harmonic oscillator are obtained.

[0165] This embodiment utilizes the characteristic that under vibration excitation, the first three harmonics of the unbalanced mass excite a hemispherical harmonic oscillator to generate a standing wave in a specific direction, and that the amplitude of the standing wave is proportional to the amplitude of the first three harmonics. Based on this characteristic, a method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator is derived, which involves applying... The vibration excitation direction is used to obtain the response vibration signal of the harmonic oscillator under the excitation. The response signal is calculated to obtain the amplitude control quantity and standing wave azimuth of the hemispherical resonant gyroscope in the corresponding vibration direction. The amplitude and azimuth of the first three harmonics can be obtained by decoupling.

[0166] In practical applications, the vacuum level is less than 1×10⁻⁶. -4 Pa's environment.

[0167] Furthermore, combining and Amplitude control quantity and standing wave azimuth angle in the direction of shaft vibration, and energy of the target amplitude. The methods for decoupling the first and third harmonics to obtain the amplitude and azimuth angle of the first and third harmonics of the hemispherical harmonic oscillator include:

[0168] according to Amplitude control quantity in the direction of shaft vibration, energy of target amplitude And the amplitude and azimuth of the first and third harmonics to be determined, and construct the first coupling relationship expression;

[0169] Specifically, the first coupling relationship expression is:

[0170] (39);

[0171] (40);

[0172] in, As an intermediate variable, This is the gain coefficient. The time constant of the hemispherical harmonic oscillator is... The natural frequency of the hemispherical harmonic oscillator. for Amplitude control quantity in the direction of shaft vibration Let the amplitude of the first harmonic be the value to be determined. Let the amplitude of the third harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined. The azimuth angle of the third harmonic to be determined.

[0173] according to The standing wave azimuth angle under the axial vibration direction, and the amplitude and azimuth angle of the first and third harmonics to be determined, are used to construct the second coupling relationship expression;

[0174] Specifically, the expression for the second coupling relationship is:

[0175] (41);

[0176] in, for Standing wave azimuth angle in the direction of vibration;

[0177] according to Amplitude control quantity in the direction of shaft vibration, energy of target amplitude And the amplitude and azimuth of the first and third harmonics to be determined, and construct the third coupling relationship expression;

[0178] Specifically, the expression for the third coupling relationship is:

[0179] (42);

[0180] in, for Amplitude control quantity in the direction of shaft vibration;

[0181] according to The standing wave azimuth angle under the axial vibration direction, and the amplitude and azimuth angle of the first and third harmonics to be determined, are used to construct the fourth coupling relationship expression;

[0182] Specifically, the expression for the fourth coupling relationship is:

[0183] (43);

[0184] in, for Standing wave azimuth angle in the direction of shaft vibration;

[0185] Finally, a system of equations is constructed from the first to fourth coupling relationship expressions to calculate the amplitude and azimuth of the first and third harmonics.

[0186] In this preferred embodiment, the energy of the harmonic oscillator converges rapidly to the target amplitude in practical applications. By constructing the first to fourth coupling relationships, and by outputting... The energy control quantity and azimuth of the standing wave under vibration can be used to directly decouple the four unknown quantities of the first and third harmonics: amplitude and azimuth. .

[0187] Furthermore, regarding Amplitude control quantity, standing wave azimuth angle, and energy of target amplitude in the direction of shaft vibration The methods for achieving second-order harmonic decoupling to obtain the amplitude and azimuth angle of the second-order harmonic of the hemispherical harmonic oscillator include:

[0188] according to Amplitude control quantity in the direction of shaft vibration, energy of target amplitude And the amplitude and azimuth of the second and third harmonics to be determined, to construct the fifth coupling relationship expression;

[0189] Based on the fifth coupling relationship expression, the amplitude and azimuth of the second harmonic are calculated.

[0190] Specifically, the fifth coupling relationship expression includes:

[0191] (44);

[0192] (45);

[0193] in, for The azimuth angle of the standing wave in the direction of shaft vibration. As an intermediate variable, This is the gain coefficient. Let be the time constant of the hemispherical harmonic oscillator. The natural frequency of the hemispherical harmonic oscillator. for Amplitude control quantity in the direction of shaft vibration Let the amplitude of the second harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined.

[0194] In this preferred embodiment, the energy of the harmonic oscillator converges rapidly to the target amplitude in practical applications. By constructing the fifth coupling equation, the amplitude and azimuth of the second harmonic can be directly calculated.

[0195] Further, see Figure 1 The control methods for vibration excitation in each direction are as follows:

[0196] The controller provides a sinusoidal signal to the piezoelectric exciter, causing it to vibrate in the corresponding direction, thereby driving the hemispherical resonant gyroscope located on the piezoelectric exciter to vibrate synchronously. At the same time, the controller applies an orthogonal control force to the plate electrode of the hemispherical resonant gyroscope to suppress the orthogonal wave of the hemispherical resonant gyroscope.

[0197] Verification experiment:

[0198] To verify the accuracy of the identification method of the present invention, corresponding experiments were conducted. The hemispherical harmonic oscillator with the first three harmonics of unbalanced mass obtained after identification was adjusted using the amplitude and azimuth angle of the first three harmonics obtained by the identification method of the present invention, and then adjusted using the existing adjustment method (ion beam adjustment). After adjustment, the harmonic amplitude decreased significantly, which verified the accuracy of the method.

[0199] Figure 3 The changes in amplitude and azimuth of the first harmonic during the tuning process are shown. Experimental results show that the harmonic amplitude after tuning significantly decreased from the initial 1.96 to 0.65, a decrease of 66.84%. Simultaneously, the fluctuation of the harmonic azimuth was less than 10°, indicating that the identification method of this invention accurately obtains the amplitude and azimuth of the first harmonic, resulting in good stability during the tuning process.

[0200] Figure 4 The results show that the amplitude of the third harmonic decreased from 1.2 to 0.65 after adjustment, a reduction of 45.83%. The fluctuation of the harmonic azimuth angle was less than 3°. This indicates that the identification method of the present invention accurately obtains the amplitude and azimuth angle of the third harmonic, resulting in good stability of the adjustment process.

[0201] Figure 5 shows that after adjustment, the amplitude of the second harmonic decreased from 0.85 to 0.58, a reduction of 31.76%, and the azimuth fluctuation was less than 3°. This indicates that the identification method of the present invention accurately obtains the amplitude and azimuth of the second harmonic, resulting in good stability of the adjustment process.

[0202] Figure 6 The quality factor of the hemispherical resonator before and after eliminating first, second, and third harmonics was compared. The results show that the average quality factor increases from 9.67 × 10⁻⁶. 7 Slightly decreased to 9.59 × 10 7 However, the uniformity of the quality factor was significantly improved, with the non-uniformity decreasing from 17.57% to 0.48%.

[0203] These experimental results demonstrate that the proposed method for identifying the first three harmonics of the unbalanced mass of a hemispherical resonator based on vibration excitation is accurate in obtaining the amplitude and azimuth of the first, second, and third harmonics. This method is effective in identifying and balancing the unbalanced mass, improving the uniformity of the quality factor of the hemispherical resonator, and is applicable to the development of high-precision hemispherical resonator gyroscopes.

[0204] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator based on vibration excitation, characterized in that, The identification method includes: In a vacuum environment, the hemispherical resonant gyroscope is subjected to measurements along its coordinate system. Vibration excitation in three directions of the axis, the lower hemispherical resonant gyroscope in each vibration direction starts from rest to the target amplitude and remains stable; The vibration signals of the hemispherical harmonic oscillator of the lower hemispherical resonant gyroscope in each vibration direction after stabilization are collected and processed to obtain the amplitude control quantity and standing wave azimuth angle of the lower hemispherical resonant gyroscope in the corresponding vibration direction. Combination and Amplitude control quantity and standing wave azimuth angle in the direction of shaft vibration, and energy of the target amplitude. By decoupling the first and third harmonics, the amplitudes and azimuths of the first and third harmonics of the hemispherical harmonic oscillator are obtained, specifically: according to Amplitude control quantity in the direction of shaft vibration, energy of target amplitude The amplitudes and azimuths of the first and third harmonics to be determined are used to construct the first coupling relationship expression; wherein, the first coupling relationship expression is: ； ； in, As an intermediate variable, This is the gain coefficient. The time constant of the hemispherical harmonic oscillator is... The natural frequency of the hemispherical harmonic oscillator. for Amplitude control quantity in the direction of shaft vibration Let the amplitude of the first harmonic be the value to be determined. Let the amplitude of the third harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined. The azimuth angle of the third harmonic to be determined; according to The standing wave azimuth angle under the axial vibration direction, and the amplitude and azimuth angle of the first and third harmonics to be determined, are used to construct the second coupling relationship expression; according to Amplitude control quantity in the direction of shaft vibration, energy of target amplitude And the amplitude and azimuth of the first and third harmonics to be determined, and construct the third coupling relationship expression; according to The standing wave azimuth angle under the axial vibration direction, and the amplitude and azimuth angle of the first and third harmonics to be determined, are used to construct the fourth coupling relationship expression; A system of equations is constructed from the first to fourth coupling relationship expressions, and the amplitude and azimuth of the first and third harmonics are calculated. right Amplitude control quantity, standing wave azimuth angle, and energy of target amplitude in the direction of shaft vibration By performing second-order harmonic decoupling, the amplitude and azimuth of the second-order harmonic of the hemispherical harmonic oscillator are obtained.

2. The method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator based on vibration excitation according to claim 1, characterized in that, The second coupling relationship expression is: ； in, for The azimuth angle of the standing wave in the direction of vibration. Let the amplitude of the first harmonic be the value to be determined. Let the amplitude of the third harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined. The azimuth angle of the third harmonic to be determined.

3. The method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator based on vibration excitation according to claim 1, characterized in that, The third coupling relationship expression is: ； ； in, As an intermediate variable, This is the gain coefficient. Let be the time constant of the hemispherical harmonic oscillator. The natural frequency of the hemispherical harmonic oscillator. for Amplitude control quantity in the direction of shaft vibration Let the amplitude of the first harmonic be the value to be determined. Let the amplitude of the third harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined. The azimuth angle of the third harmonic to be determined.

4. The method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator based on vibration excitation according to claim 1, characterized in that, The fourth coupling relationship expression is: ； in, for The azimuth angle of the standing wave in the direction of shaft vibration. Let the amplitude of the first harmonic be the value to be determined. Let the amplitude of the third harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined. The azimuth angle of the third harmonic to be determined.

5. The method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator based on vibration excitation according to claim 1, characterized in that, right Amplitude control quantity, standing wave azimuth angle, and energy of target amplitude in the direction of shaft vibration The methods for achieving second-order harmonic decoupling to obtain the amplitude and azimuth angle of the second-order harmonic of the hemispherical harmonic oscillator include: according to Amplitude control quantity in the direction of shaft vibration, energy of target amplitude And the amplitude and azimuth of the second and third harmonics to be determined, to construct the fifth coupling relationship expression; Based on the fifth coupling relationship expression, the amplitude and azimuth of the second harmonic are calculated.

6. The method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator based on vibration excitation according to claim 5, characterized in that, The fifth coupling relationship expression includes: ； ； ； in, for The azimuth angle of the standing wave in the direction of shaft vibration. As an intermediate variable, This is the gain coefficient. Let be the time constant of the hemispherical harmonic oscillator. The natural frequency of the hemispherical harmonic oscillator. for Amplitude control quantity in the direction of shaft vibration Let the amplitude of the second harmonic be the value to be determined. Let be the azimuth angle of the first harmonic to be determined.

7. The method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator based on vibration excitation according to claim 1, characterized in that, In a vacuum environment, the vacuum level is less than 1×10⁻⁶. -4 Pa's environment.

8. The method for identifying the first three harmonics of the unbalanced mass of a hemispherical harmonic oscillator based on vibration excitation according to claim 1, characterized in that, The control methods for vibration excitation in each direction are as follows: The controller provides a sinusoidal signal to the piezoelectric exciter, causing it to vibrate in the corresponding direction, thereby driving the hemispherical resonant gyroscope located on the piezoelectric exciter to vibrate synchronously. At the same time, the controller applies an orthogonal control force to the plate electrode of the hemispherical resonant gyroscope to suppress the orthogonal wave of the hemispherical resonant gyroscope.

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