Electrostatic tuning optimization method and device for metal resonator gyroscope

Abstract

The invention discloses an electrostatic tuning optimization method and device for a metal resonator gyroscope. The method comprises the following steps: establishing a dynamic model based on structural symmetry disturbance and a coupling stiffness effect; based on the dynamic model, calculating modal frequency distribution of the metal resonator gyroscope under different azimuth angles to obtain modal frequency difference data, and based on the modal frequency difference data, constructing an equivalent stiffness distribution model, and quantifying stiffness nonuniformity of the resonant structure to obtain a stiffness matrix; based on the stiffness matrix, voltage control parameters corresponding to the azimuth angles are obtained, the voltage control parameters are applied to the multiple electrostatic tuning electrodes, and an optimized stiffness matrix is obtained; and recalculating the modal frequency of the metal harmonic oscillator based on the optimized stiffness matrix. The invention solves the technical problem that the prior art is mainly suitable for the inertial device before or after packaging but is difficult to effectively eliminate the frequency cracking after packaging.

Description

Technical Field

[0001] This invention relates to the field of metal resonant gyroscopes, and more specifically, to a method and apparatus for electrostatic tuning optimization of a metal resonant gyroscope. Background Technology

[0002] Metal microresonant gyroscopes, a type of Coriolis gyroscope, are characterized by high precision, high reliability, and long service life. Therefore, they are widely used in inertial navigation systems for various vehicles, including surface ships, underwater unmanned vehicles, and aerospace vehicles. The resonator, as the core component of the resonant gyroscope, primarily works by transferring energy between several vibration modes generated by the Coriolis force. The uniformity and symmetry of its structure have a significant impact on the performance of the metal resonant gyroscope.

[0003] Currently, the control modes of metal microresonator gyroscopes mainly include force balance and full-angle modes. In force balance mode, the vibration mode is controlled to a certain angle, and the rotational speed is determined by feedback control force. However, the angular velocity measurement results of the metal microresonator gyroscope under modal vibration are sensitive to various influences, including the nonlinearity of the scaling factor, temperature drift instability, and bandwidth constraints. Therefore, resonator gyroscopes in force balance mode are only suitable for high-precision measurements with limited dynamic range. Compared with force balance mode, full-angle mode allows the resonator gyroscope to precess in free vibration modes and directly measure angular position. Therefore, it has a nearly unlimited dynamic range and eliminates the cumulative error caused by integration in force balance mode. When realizing the full-angle mode of a metal microresonator gyroscope, the metal resonator must have a high degree of symmetry. In the actual manufacturing process, the manufacturing of the resonator gyroscope includes problems such as material failure, geometric parameter errors, and residual stress. These problems can all lead to quality defects in the hemispherical resonator, which can be distinguished by damping, stiffness, and mass inhomogeneity. Damping inhomogeneity leads to angular errors and velocity threshold effects, while stiffness and mass inhomogeneity cause frequency division between vibration modes, i.e., frequency differences between the excitation and detection modes. Furthermore, the design of the metallic material and the special toothed structure also affects the mass uniformity and stiffness consistency of the resonator, resulting in frequency fragmentation. Extensive research has been conducted both domestically and internationally on the formation and evolution mechanism of frequency fragmentation in hemispherical resonators, as well as tuning and testing methods, mainly focusing on the influence of resonator manufacturing errors and material anisotropy on frequency fragmentation. Existing techniques derive the vibration equation of imperfect disk resonators based on the principle of mass perturbation, and then improve the frequency distribution of the resonator in experiments. Existing techniques have also studied the influence of mass defects in slowly rotating hemispherical resonators on standing wave evolution, showing that mass anisotropy in the vibration modes of the resonator can severely degrade gyroscope performance. Existing techniques have also studied the influence of uneven mass distribution on resonator frequency fragmentation and mass defects on standing wave drift; existing techniques have also derived an analytical model of frequency fragmentation in a hemispherical shell considering defects, and derived a quantitative relationship between frequency fragmentation and these defects.

[0004] Regarding frequency splitting correction, existing technologies propose a method using directional grinding to reduce frequency splitting in micro-quartz resonators. Another existing technology proposes a chemical etching method that can reduce frequency splitting to below 0.05 Hz. While chemical etching can effectively eliminate defect mass in fused silica hemispherical resonators and achieve frequency splitting correction, this method faces difficulties such as uncontrollable chemical etching solution concentration and difficulty in locating the etching position, making high-precision frequency splitting correction challenging. Existing technologies also propose a high-precision balancing method based on a synchronous adjustment system, using focused ion beam etching experiments to reduce the frequency splitting of all resonators to below 0.0005 Hz. Furthermore, existing technologies propose an ion beam fine-tuning process that eliminates frequency splitting by fine-tuning defect mass on the low-frequency axis. The frequency splitting of the fine-tuned hemispherical resonator is below 0.001 Hz. These methods are only applicable to pre-packaging cases involving physical cutting or laser trimming and are not suitable for packaged devices.

[0005] Another attractive method is electrostatic tuning. Electrostatic stiffness tuning involves applying a DC voltage to the tuning electrodes of a hemispherical resonator gyroscope, causing a spring softening effect that aligns the circular resonant frequencies of the hemispherical resonator, thereby eliminating frequency splitting. It uses electrostatic force to selectively change the stiffness at various points in the resonant structure. This method not only compensates for mass distribution and stiffness axis deviations but also allows for dynamic adjustment after device packaging, thus improving the accuracy and stability of the hemispherical resonator gyroscope and ensuring long-term reliability. This method provides a flexible and efficient technical means to solve frequency splitting. Electrostatic tuning adjusts the operating state of the resonator by applying an external electric field, thereby correcting frequency splitting. The advantage of this method is that it can be adjusted without disassembling the packaged device. In summary, existing research methods are mainly applicable to inertial devices before or after packaging, but it is difficult to effectively eliminate frequency splitting after packaging.

[0006] There is currently no effective solution to the above problems. Summary of the Invention

[0007] This invention provides an electrostatic tuning optimization method and apparatus for a metal resonant gyroscope, which at least solves the technical problem that the prior art is mainly applicable to inertial devices before or after packaging, but it is difficult to effectively eliminate frequency fragmentation after packaging.

[0008] According to one aspect of the present invention, an electrostatic tuning optimization method for a metal resonant gyroscope is provided, comprising: establishing a multi-degree-of-freedom dynamic model based on structural symmetry perturbation and coupling stiffness effect, based on the geometric structural parameters and operating modes of the metal resonant gyroscope, as a dynamic model describing the vibration modal characteristics of the metal resonant gyroscope; and calculating the modal frequency distribution of the metal resonant gyroscope at different azimuth angles based on the dynamic model, thereby obtaining...

[0009] The modal frequency difference data is used to construct an equivalent stiffness distribution model, quantify the stiffness non-uniformity of the resonant structure, and obtain a stiffness matrix. Based on the stiffness matrix, the applied voltage distribution of the electrostatic tuning electrodes is determined, and voltage control parameters corresponding to each azimuth angle are obtained. The voltage control parameters are applied to multiple electrostatic tuning electrodes of the metal resonant gyroscope to adjust the equivalent electrostatic stiffness distribution in a local region of the metal resonator, resulting in an optimized stiffness matrix. Based on the optimized stiffness matrix, the modal frequencies of the metal resonator are recalculated to obtain the tuned modal frequency difference. Based on the tuned modal frequency difference, active suppression of frequency fragmentation is achieved.

[0010] According to another aspect of the present invention, an electrostatic tuning optimization device for a metal resonant gyroscope is also provided, comprising: a model building module configured to establish a multi-degree-of-freedom dynamic model based on the geometric structural parameters and operating modes of the metal resonant gyroscope, using structural symmetry perturbation and coupling stiffness effects as a dynamic model describing the vibration modal characteristics of the metal resonant gyroscope; and a matrix building module configured to calculate the modal frequency distribution of the metal resonant gyroscope at different azimuth angles based on the dynamic model, thereby obtaining...

[0011] The system uses modal frequency difference data and, based on this data, constructs an equivalent stiffness distribution model to quantify the stiffness non-uniformity of the resonant structure, obtaining a stiffness matrix. A matrix optimization module is configured to determine the applied voltage distribution of the electrostatic tuning electrodes based on the stiffness matrix, obtaining voltage control parameters corresponding to each azimuth angle. These voltage control parameters are then applied to multiple electrostatic tuning electrodes of the metal resonant gyroscope to adjust the equivalent electrostatic stiffness distribution in a local region of the metal resonator, resulting in an optimized stiffness matrix. A fragmentation suppression module is configured to recalculate the modal frequencies of the metal resonator based on the optimized stiffness matrix, obtaining the tuned modal frequency difference, and, based on this tuned modal frequency difference, actively suppress frequency fragmentation.

[0012] In this embodiment of the invention, based on the geometric parameters and operating modes of the metal resonant gyroscope, a multi-degree-of-freedom dynamic model based on structural symmetry perturbation and coupled stiffness effects is established as a dynamic model describing the vibration modal characteristics of the metal resonator. Based on the dynamic model, the modal frequency distribution of the metal resonant gyroscope at different azimuth angles is calculated to obtain modal frequency difference data. Based on the modal frequency difference data, an equivalent stiffness distribution model is constructed to quantify the stiffness non-uniformity of the resonant structure, resulting in a stiffness matrix. Based on the stiffness matrix, the applied voltage distribution of the electrostatic tuning electrodes is determined to obtain voltage control parameters corresponding to each azimuth angle. The voltage control parameters are applied to multiple electrostatic tuning electrodes of the metal resonant gyroscope to adjust the equivalent electrostatic stiffness distribution in a local region of the metal resonator, resulting in an optimized stiffness matrix. Based on the optimized stiffness matrix, the modal frequencies of the metal resonator are recalculated to obtain the tuned modal frequency difference. Based on the tuned modal frequency difference, active suppression of frequency fragmentation is achieved. The above solution solves the technical problem that existing technologies are mainly applicable to inertial devices before or after packaging, but it is difficult to effectively eliminate frequency fragmentation after packaging. Attached Figure Description

[0013] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0014] Figure 1 This is a flowchart of an optional electrostatic tuning optimization method for a metal resonant gyroscope according to an embodiment of the present invention;

[0015] Figure 2 This is a flowchart of another optional electrostatic tuning optimization method for a metal resonant gyroscope according to an embodiment of the present invention;

[0016] Figure 3 This is a schematic diagram of an optional metal resonant gyroscope structure and vibration characteristic analysis model according to an embodiment of the present invention, wherein (a) is a schematic diagram of the overall structure of the metal resonant gyroscope, showing the composition relationship between the resonator and the planar electrode; (b) is a vibration characteristic analysis model of the metal resonator; (c) is an equivalent model of the second-order vibration of the hemispherical resonator, showing the vibration mode distribution of the outer edge of the ring structure; (d) is an equivalent model of the resonant ring, a simplified vibration analysis model composed of N mass points (m) and a radial spring (k);

[0017] Figure 4This is a schematic diagram of an optional mass offset and frequency split simulation and a diagram of the numbering of the plate electrodes according to an embodiment of the present invention. (a) is a physical diagram of the resonator; (b) is a diagram of the simulation equivalent of the resonator's processing defects; (c) is the modeling and mesh generation in the finite element simulation; (d) is the linear relationship between mass offset and frequency split; (e) is a schematic diagram of the grouping of the plate electrodes.

[0018] Figure 5 This document presents a simulation comparison of the optimization process and schematic diagram of an optional electrostatic tuning electrode combination according to an embodiment of the present invention; wherein (a) is the attenuation process of the frequency domain subpeak amplitude as the voltage increases under single-pair electrode tuning; (b) is a comparison of the frequency domain subpeak suppression effect of multi-pair electrode combination tuning; (c) is the relationship between the electrode tuning combination voltage and the frequency domain subpeak peak value; (d) is the optimal tuning voltage of the electrode tuning combination; (e) is the relationship between the normalized tuning voltage and the frequency domain subpeak suppression ratio; (f) is the normalized tuning combination score; (g) is the data processing flow, including the steps of invalid data removal, valid data analysis and optimal combination screening; h. Schematic diagram of the electrostatic voltage distribution of the optimal tuning electrode group on the plate electrode;

[0019] Figure 6 This is an optional electrostatic tuning experiment verification result diagram according to an embodiment of the present invention, wherein (a) is the curve of the frequency domain secondary peak descent ratio of Groups 2, 5, and 7 under atmospheric conditions as a function of tuning voltage; (b) is the curve of the frequency domain secondary peak descent ratio of Groups 2, 5, and 7 under vacuum conditions as a function of tuning voltage; (c) is the energy ratio of the frequency domain secondary peaks of Groups 2, 5, and 7 relative to the main peak under atmospheric conditions; (d) is the energy ratio of the frequency domain secondary peaks of Groups 2, 5, and 7 relative to the main peak under vacuum conditions; and (e) is a schematic diagram of the tuning results under atmospheric and vacuum conditions under electrostatic tuning.

[0020] Figure 7 This is a diagram showing key equipment and steps in an optional metal resonant gyroscope packaging manufacturing process according to an embodiment of the present invention;

[0021] Figure 8 This is a diagram showing the testing platform and experimental results according to an embodiment of the present invention;

[0022] Figure 9 This is a structural diagram of an optional electrostatic tuning optimization device for a metal resonant gyroscope according to an embodiment of the present invention;

[0023] Figure 10 A schematic diagram of the structure of a computer device suitable for implementing embodiments of the present disclosure is shown. Detailed Implementation

[0024] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.

[0025] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0026] According to an embodiment of the present invention, a method embodiment of an electrostatic tuning optimization method for a metal resonant gyroscope is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0027] Metal resonant gyroscopes (MRGs) are widely used in high-performance navigation and inertial measurement systems due to their excellent structural stability and long-term reliability. However, their performance is often limited by frequency fragmentation caused by structural asymmetry or manufacturing errors. This phenomenon severely interferes with the frequency uniformity and modal coupling stability of the resonator, thereby reducing sensing accuracy and system robustness. To address this, this application proposes an electrostatic tuning optimization strategy that does not require changes to the physical structure of the device. By adjusting the equivalent stiffness distribution of the resonator, frequency fragmentation can be actively suppressed. This method is highly flexible and easy to integrate, making it suitable for multi-field control of microscale inertial devices. First, this application establishes a multi-degree-of-freedom dynamic model considering structural symmetry perturbations and coupling stiffness effects, quantitatively revealing the formation mechanism of modal frequency differences. Based on this, a tunable electrostatic control scheme is implemented to adjust the equivalent stiffness distribution of the resonator. Experimental results show that this method can significantly eliminate frequency differences and enhance modal frequency uniformity under both atmospheric pressure and vacuum environments. This application provides an effective technical path for the modal frequency uniformity control of high-quality metal resonators and provides experimental evidence for the future development of multi-physics coupling tuning mechanisms and the structural design of high-precision inertial devices.

[0028] Figure 1 This is an electrostatic tuning optimization method for a metal resonant gyroscope according to an embodiment of the present invention, such as... Figure 1 As shown, the method includes the following steps:

[0029] Step S102: Based on the geometric parameters and operating modes of the metal resonant gyroscope, a dynamic model based on structural symmetry disturbance and coupling stiffness effect is established, wherein the dynamic model is used to describe the vibration mode characteristics of the metal resonator.

[0030] The geometric parameters and operating modes of the metal resonant gyroscope are obtained, and a basic dynamic model under an ideal symmetrical structure is established. A structural symmetry perturbation term and a coupling stiffness term are introduced into the basic dynamic model. The structural symmetry perturbation term characterizes the mass deviation and geometric distortion caused by manufacturing errors, and the coupling stiffness term describes the energy coupling effect between different vibration modes. The structural symmetry perturbation term and the coupling stiffness term are superimposed and corrected with the mass matrix and stiffness matrix in the basic dynamic model to form a corrected dynamic model based on perturbation and coupling effects. Modal analysis is performed on the corrected dynamic model to obtain the natural frequencies and mode shape vectors of each mode, thus forming a dynamic model capable of describing the vibration modal characteristics of the metal resonator.

[0031] Step S104: Based on the dynamic model, calculate the modal frequency distribution of the metal resonant gyroscope at different azimuth angles to obtain modal frequency difference data, and based on the modal frequency difference data, construct an equivalent stiffness distribution model to quantify the stiffness non-uniformity of the resonant structure and obtain the stiffness matrix.

[0032] First, the modal frequency difference data is determined. For example, multiple azimuth parameters are set, and the dynamic model is solved for each azimuth angle to obtain the corresponding modal frequency distribution. Based on the modal frequency distribution, the frequency values ​​of the two degenerate modes with the closest frequencies are extracted, and their difference is calculated to obtain the modal frequency difference for the corresponding azimuth angle. The modal frequency difference is then statistically and normally processed according to the azimuth angle to form the modal frequency difference data reflecting the degree of frequency fragmentation of the metal resonator in different directions.

[0033] Next, the stiffness matrix is ​​determined. For example, based on the modal frequency difference data, a mapping relationship model between the modal frequency difference and the equivalent stiffness of the structure is established; based on the mapping relationship model, the equivalent stiffness distribution under each azimuth angle is calculated using the azimuth angle and modal frequency difference information in the modal frequency difference data, and the equivalent stiffness distribution is obtained; the equivalent stiffness distribution is then matrix-discretely processed to convert local stiffness deviations into stiffness disturbances, and the stiffness matrix is ​​formed by matrix assembly.

[0034] Step S106: Based on the stiffness matrix, determine the applied voltage distribution of the electrostatic tuning electrodes, obtain voltage control parameters corresponding to each azimuth angle, apply the voltage control parameters to the multiple electrostatic tuning electrodes of the metal resonant gyroscope, adjust the equivalent electrostatic stiffness distribution of the local region of the metal resonator, and obtain the optimized stiffness matrix.

[0035] For example, based on the stiffness matrix, the least squares method or gradient descent algorithm is used to solve for the target voltage distribution of each electrostatic tuning electrode at different azimuth angles, and the voltage control parameters corresponding to the azimuth angles are obtained; based on the voltage control parameters, corresponding voltages are applied to the multiple electrostatic tuning electrodes of the metal resonant gyroscope to adjust the equivalent electrostatic stiffness of the local region of the metal resonator, and updated equivalent stiffness distribution data is obtained; based on the updated equivalent stiffness distribution data, the stiffness matrix is ​​iteratively corrected to obtain an optimized stiffness matrix.

[0036] Step S108: Based on the optimized stiffness matrix, recalculate the modal frequencies of the metal resonator to obtain the tuned modal frequency difference, and based on the tuned modal frequency difference, actively suppress frequency fragmentation.

[0037] For example, based on the optimized stiffness matrix, the vibration characteristics of the metal resonator at multiple azimuth angles are solved to obtain the modal frequencies; the frequency values ​​of adjacent degenerate modes are extracted from the modal frequencies, and their differences are calculated to obtain the tuned modal frequency differences for each corresponding azimuth angle; based on the tuned modal frequency differences, the changing trends of the frequency differences before and after tuning are compared to determine the degree of suppression of frequency fragmentation, and the performance index results used to evaluate the tuning effect are obtained, so as to achieve active suppression of frequency fragmentation.

[0038] Figure 2 This is another electrostatic tuning optimization method for a metal resonant gyroscope according to an embodiment of the present invention, such as... Figure 2 As shown, the method includes the following steps:

[0039] Step S202: Construct a dynamic model.

[0040] The overall structure of a metal resonant gyroscope mainly includes a resonator and planar electrodes. For example... Figure 3 (a) illustrates this structural feature. The planar electrodes form the core components for electrostatic actuation and capacitive detection. Specifically, they can identify and perform mass balancing tuning of the fourth harmonic, which is not uniform in mass. The natural frequency of a metal resonant gyroscope is affected by the alloy material properties, geometric parameters, and processing; a perfect resonator will not experience frequency fragmentation. Anisotropy of the material and errors in the resonator manufacturing process can lead to two inherently rigid axes in the resonator that are at a 45° angle to each other. Figure 3 Figure (b) shows the equivalent model of the second-order vibration of a hemispherical harmonic oscillator. The outer edge of the ring model of the metal harmonic oscillator forms two natural axes spaced 45° apart, representing two modes. When the metal harmonic oscillator vibrates, the natural frequency along each of these axes reaches both a maximum and a minimum. The frequency difference between the maximum and minimum of the angular frequency is called the natural frequency split. When the azimuth of the excitation force does not coincide with the natural rigid axis, the vibration modes at the two rigid axes of the hemispherical harmonic oscillator are excited to varying degrees. Two signal peaks appear in the vibration signal, corresponding to the two vibration modes of the rigid axis of the harmonic oscillator. The frequency corresponding to the signal peak is the resonant frequency of the mode shape. The different amplitudes of the two peaks reflect the deviation between the azimuth of the excitation force and the azimuth of the natural rigid axis. This defect leads to the loss of gyroscopic effect and even the inability to detect angular motion. Therefore, the existence of frequency splitting causes standing wave drift, generates mechanical coupling error, and reduces the sensitivity of the hemispherical harmonic oscillator.

[0041] Before analyzing the frequency splitting mechanism, a dynamic model of the metal micro-hemispherical resonant gyroscope needs to be established to clarify its vibration characteristics. This model provides a theoretical basis for the derivation of frequency splitting and electrostatic tuning research, revealing the influence of manufacturing errors on modal coupling. The vibration characteristic analysis model of the metal resonator is as follows: Figure 3As shown in (c), the metal resonant gyroscope operates based on the Coriolis effect. For ease of analysis, it can be simplified as a generalized two-degree-of-freedom vibration system. and It is represented by the generalized coordinates of the motion of the large mass block in the local coordinate system of the resonant gyroscope itself.

[0042] The dynamic model of a metallic micro-hemispherical resonant gyroscope in generalized coordinates is derived using the Lagrange energy method, and its dynamic characteristics are analyzed in depth. In this process, based on the mass distribution and velocity vector of the metal shell, the kinetic energy of the resonant structure in the operating modes is systematically studied. Potential energy Energy dissipation due to damping and external electrostatic driving force The interrelationships between them. Based on the above analysis, and combined with the Lagrangian function, a dynamic model of the metal harmonic oscillator under driving conditions is constructed:

[0043]

[0044] The motion of a metal resonant gyroscope is described using inertial, rotational, and local coordinate systems. Based on the Lagrange energy method, a two-degree-of-freedom dynamic model is established, and the dynamic equations of the metal-shell resonant gyroscope in the resonant state can be simplified as follows:

[0045]

[0046] in, The equivalent mass of the shell resonant structure. For Coriolis equivalent mass.

[0047] Based on the established dynamic model, to further describe the structural characteristics and frequency response relationship of the metal resonant gyroscope, its complex three-dimensional geometry needs to be reasonably simplified and equivalently treated. Specifically, the overall structure of the metal resonator can be divided into three main units: the central support column, the resonant shell, and the sensitivity amplification structure. The resonant shell is the key component that dominates the resonant frequency, while the central support column can be considered a non-resonant unit with minimal impact on the frequency response. The sensitivity amplification structure, as a discretely distributed element, has virtually no effect on the overall stiffness distribution of the resonator. To simplify the analysis of the vibration characteristics of the metal resonator, it can be equivalent to a resonant ring model. Figure 3 As shown in (d), assuming the resonant ring is composed of It consists of 1 mass point, and the mass of each mass point is 1. Their circumferential positions are respectively In addition, [something] was arranged at the corresponding positions on the ring. There are 1 radial spring, each with a stiffness of 1. Its location is .

[0048] Due to the non-uniform distribution of mass and stiffness on the ring, the resonator will excite two modes out of phase by 45°, corresponding to the high-frequency and low-frequency rigid principal axes, respectively. Their specific circumferential positions are described by... It indicates that it conforms to the expression.

[0049] Assuming the rigid axis position is defined as the antinode position between 0° and 90°, it can be seen that the rigid axis position of the high-frequency axis satisfies

[0050]

[0051] In the formula: ; This is the ratio of radial amplitude to tangential amplitude. Let be the elastic potential energy of the harmonic oscillator in the n=2 mode. And its frequency maximum is... , and frequency minimum , respectively

[0052]

[0053]

[0054] Step S204: Construct the stiffness matrix.

[0055] To further elucidate the formation mechanism of frequency splitting, a stiffness perturbation model needs to be introduced based on the aforementioned resonant ring model to quantify the influence of non-uniform stiffness distribution on vibration modes. By analyzing the coupling effect of mass and stiffness perturbation on the high-frequency and low-frequency rigid shafts, the mathematical expression for frequency splitting can be derived, providing a theoretical basis for the subsequent design of electrostatic tuning schemes. The following will elaborate on the establishment process of the resonant oscillator stiffness perturbation model. For ease of understanding, the equivalent mass of the resonant structure is set to 0, with only radial springs present.

[0056]

[0057] The asymmetric stiffness distribution resulted in two vibration modes that differed by 45°, as shown in the equation. The maximum frequency can be obtained after adding a mass point. , and frequency minimum , respectively satisfy:

[0058]

[0059] In the formula This represents the potential energy of the harmonic oscillator when it operates in the n=2 mode.

[0060] Depend on achievable

[0061]

[0062] Assuming the resonant frequency after frequency fragmentation caused by stiffness error is very small compared to the original resonant frequency, therefore

[0063]

[0064] Therefore, the frequency fragmentation caused by uneven stiffness distribution can be expressed as:

[0065]

[0066] make

[0067]

[0068] Mode Can be transformed into

[0069]

[0070] Based on the resonant ring model, the formation mechanism of frequency fragmentation in metal resonant structures was further revealed, and the influence of non-uniform stiffness distribution on vibration modes was quantified. Assuming an equivalent mass of 0 and considering only the radial spring, the coupling effect of the 45° phase difference mode shapes and high- and low-frequency rigid shafts caused by stiffness asymmetry was analyzed. By deriving the relationship between frequency extrema and the potential energy of mode n=2, and based on the assumption that the frequency change caused by stiffness error is small, the expression for frequency fragmentation caused by stiffness non-uniformity and its simplified form were obtained.

[0071] To gain a deeper understanding and quantify this phenomenon, an equivalent second-order spring-mass model can be used as an analytical tool. This model reveals the influence of stiffness non-uniformity on frequency fragmentation by establishing a direct relationship between spring stiffness and the natural frequency of the mass. In the equivalent second-order spring-mass model of a metallic resonant structure, the following relationship exists between spring stiffness and the natural frequency of the mass:

[0072]

[0073] When considering frequency splitting, from equation The resulting matrix can be represented in the following form

[0074]

[0075] In the formula

[0076]

[0077] Step S206 yields the optimized stiffness matrix.

[0078] Analysis reveals that in a metallic micro-hemispherical resonant gyroscope, the main diagonal elements of the stiffness matrix *f* exhibit frequency splitting, caused by periodic deviations induced by the fourth harmonic of the azimuth angle *f*. Simultaneously, the off-diagonal elements represent orthogonal interference due to structural stiffness asymmetry. This interference introduces energy coupling, causing phase drift and energy leakage in the supposedly independent drive and detection modes, reducing system stability and measurement accuracy. During detection, orthogonal interference can transfer the vibration component of the drive mode into the detection mode, generating additional error signals and affecting signal purity.

[0079] To address these issues, electrostatic tuning is used to decouple the modes of the metal resonant gyroscope. By applying a mode decoupling voltage, the electrostatic stiffness between the electrodes can be altered, thereby controlling the energy distribution and mode shape stability of the driving and sensing modes. Mathematically, this process involves applying equations... Cross-coupling terms in the stiffness matrix Adjusting it to zero eliminates coupling interference and achieves modal decoupling.

[0080]

[0081] in, It is the mode decoupling matrix. Total equivalent stiffness introduced by voltage, Indicates equivalent mass. It is the inherent frequency after mode decoupling. Meanwhile, This indicates the azimuth angle of the mode decoupling electrode.

[0082] After mode decoupling, the stiffness matrix of the high-precision ring resonator is transformed into an optimized stiffness matrix (K), specifically represented as:

[0083]

[0084] in, It is the optimized stiffness matrix. After applying a tuning voltage, the circumferential stiffness of the metallic resonator can be considered uniform and expressed as: .

[0085] Step S208: Actively suppress frequency fragmentation.

[0086] To gain a more comprehensive understanding of the equivalent stiffness model introduced by electrostatic tuning, this application further analyzes the formation mechanism of electrostatic negative stiffness and its directional control method. In a typical parallel plate structure, assuming the electrode area is φ, the electrode spacing is d, the applied voltage is φ, and the capacitance under the electric field is φ = φ / d, then its electrostatic attraction can be derived from the electrostatic potential energy as follows:

[0087]

[0088] Further differentiating this force with respect to displacement yields the equivalent negative stiffness in the direction:

[0089]

[0090] This equivalent negative stiffness will directly affect the local stiffness matrix of the metal resonator structure, resulting in a decrease in modal frequency.

[0091] Considering that the actual resonant structure has 16 equally spaced electrodes, each electrode has a different modal stiffness modulation effect in different polarization directions. Let the direction of action of a certain tuning electrode pair be θa, and the direction of the principal axis of modal stiffness be θn. Then the component of the tuning stiffness in that direction can be written as:

[0092]

[0093] To effectively address the frequency splitting problem commonly found in metal resonant gyroscopes, this application proposes a tuning scheme that electrostatically alters the stiffness of the resonator. In this application, the resonator is made of a highly conductive metallic material. Compared to traditional fused silica, metallic materials offer significant advantages in charge response speed, electrostatic coupling efficiency, and mechanical strength. When an external electric field is applied between the electrodes and the metallic resonator, free electrons within the metal rapidly accumulate, generating a strong electrostatic force in a very short time. This characteristic greatly shortens the charge redistribution time and reduces the delay in electrostatic response. Simultaneously, the excellent conductivity of the metallic material ensures a more uniform charge distribution on the electrode surface.

[0094] To suppress frequency splitting and improve the modal purity and output stability of the resonator, this application introduces additional negative stiffness by applying a directional DC voltage through the tuning electrodes, thereby reconstructing the principal stiffness matrix of the structure. Unlike traditional frequency-matching-based tuning methods, this application's strategy focuses on weakening modal cross-coupling terms, i.e., eliminating secondary peaks in the frequency domain by suppressing the vibration paths of submodal modes. This can be considered a modal path intervention-type tuning method.

[0095] To address frequency splitting and modal coupling caused by structural manufacturing errors, this application proposes an electrostatic tuning method that significantly weakens modal coupling terms through electrostatic tuning, thereby exhibiting a single-mode response target. A corresponding stiffness tuning modeling theoretical framework is also constructed. The core idea of ​​this method is to introduce equivalent negative stiffness by applying a directional DC voltage in a specific direction along the circumference of the structure, thereby disrupting the conditions for the formation of the original sub-mode standing waves and achieving modal decoupling. This method differs from traditional frequency axis alignment strategies; its physical effect is not to make the two modal frequencies completely identical, but to actively interfere with the energy formation path of the sub-mode, preventing it from establishing standing waves, ultimately resulting in the disappearance of the secondary peak in the frequency response. The tuning electrode introduces electrostatic negative stiffness in a certain direction of the structure, causing asymmetric perturbation of the structural stiffness matrix, controllable changes in modal frequencies, and affecting the equivalent coupling stiffness in the sub-mode direction. This has a direct impact, leading to a decrease in cross-mode energy transfer efficiency and ultimately preventing the formation of a stable standing wave mode.

[0096] From the formula achievable

[0097]

[0098] The relationship between mode decoupling voltage and stiffness can be expressed as follows:

[0099]

[0100] It is the tuning azimuth angle of the frequency axis. It is the stiffness introduced by the mode decoupling voltage. ρ is the dielectric constant, d is the distance between the plate and the resonant capacitor, and S is the area of ​​the plate. This formula gives a quantitative relationship between the additional stiffness introduced by electrostatic tuning and the voltage. It shows that by increasing the tuning voltage, the stiffness disturbance can be enhanced, thereby achieving more effective compensation of the coupling terms.

[0101] The response changes of the secondary peaks in the frequency domain can also be further quantified using a response amplitude model. When the system is excited in the direction of the principal mode, the frequency response amplitude in the direction of the secondary mode can be expressed as:

[0102]

[0103] As can be seen from the above formula, the magnitude of the secondary peak in the frequency domain is directly proportional to the coupling term Δt. Therefore, as the tuning voltage changes, the compensation of the coupling term increases, causing Δt to decrease. Consequently, the submodal response of the system will also decay synchronously until it is no longer visible in the frequency response of the secondary peak in the frequency domain. In summary, the electrostatic tuning method proposed in this application is an engineering strategy oriented towards modal decoupling. By applying a DC voltage to symmetrically arranged electrodes that are offset from the principal axis, the modal coupling term is adjusted in the form of directional stiffness perturbation, thereby actively intervening in the formation path of the submode.

[0104] Step S210: Simulation verification.

[0105] To verify the effectiveness of electrostatic tuning in eliminating frequency splitting and reducing orthogonal components, this application systematically simulates and analyzes the dynamic characteristics of a metal resonator based on finite element simulation. The simulation study mainly includes simulation environment and model construction, frequency splitting simulation under mass disturbance, and electrostatic tuning effect simulation, exploring the influence of different tuning strategies on the stability of the resonator. In the construction of the simulation environment, this application selects ANSYS Workbench and COMSOL Multiphysics as finite element simulation tools to study the frequency response characteristics of the resonator under different external conditions through finite element simulation.

[0106] Figure 4 Figure (a) shows a physical fabrication diagram of the metal resonator. As can be seen from the figure, certain defects exist in the actual production of the metal gyroscope. Therefore, in the simulation analysis, to study the influence of local stiffness disturbances on the frequency fragmentation characteristics of the metal resonator, this application places an equivalent mass block at a specific position on the surface of the resonator shell to introduce a non-uniform stiffness distribution, such as... Figure 4 (b) In this study, the frequency difference caused by the perturbation effect of the local additional load on the structural stiffness field is characterized. Based on this, the mass of the mass block is further increased step by step to enhance the local stiffness asymmetry, thereby explicitly stimulating the frequency fragmentation phenomenon of the structure in the working mode.

[0107] The mass of the block was increased from 0.005 mg to 0.03 mg, with a simulation step size of 0.0025 mg. The bottom was fixed with support. Simulation results show a clear linear relationship between the mass shift and frequency fragmentation. Figure 4 (c) indicates that as the mass of the mass block increases, the frequency splitting value of the metal resonator continuously increases. By fitting the data points, it can be seen that there is a clear linear relationship between mass shift and frequency splitting.

[0108] After establishing the defect model of the resonator, the effectiveness of electrostatic tuning in suppressing frequency fragmentation and secondary peak response in the frequency domain of the metal resonator is verified, and the optimal tuning electrode combination is selected. This application conducts systematic simulation test design and establishes a three-dimensional electrostatic-structural coupling model of the metal hemispherical resonator-electrode system, such as... Figure 4 As shown in (d).

[0109] In the simulation experiment phase, a pair of symmetrical electrodes were selected as excitation electrodes to apply sinusoidal excitation signals to excite the working mode of the metal resonator. The electrodes were numbered for easy identification of different combinations. According to the preset electrode combination scheme, one or more sets of electrodes were selected as tuning electrodes. During tuning, the tuning voltage was gradually increased linearly from a low initial value, and the amplitude-frequency response curve of the resonator was recorded at fixed voltage step intervals until the secondary peak in the frequency domain completely decayed. This process covered the entire spectral evolution from the initial state of frequency splitting to the final state of tuning stability. The ability of different electrode combinations to suppress secondary peaks in the frequency domain during electrostatic tuning was systematically evaluated. This application selected multiple sets of electrode combinations for electrostatic tuning simulation, recording the percentage decrease in secondary peaks in the frequency domain for each combination under multiple voltage levels. Invalid data were removed, leaving seven effective tuning combinations. For example... Figure 5 Figures (a) and (b) show the trend curves of the frequency domain secondary peak reduction ratio as a function of voltage for single and multiple tuned electrode pairs under different tuning voltages. The results show that the frequency domain secondary peak reduction ratio of the G5, G6, and G7 combinations all exceed 98%, while G1 and G2 perform moderately, achieving better suppression effects from 30V to 40V, but G2 exhibits some rebound at high voltage levels. G3 and G4 have limited overall suppression capabilities, with relatively high residual frequency domain secondary peaks. Figure 5 (c) visually presents the relative strength of the frequency domain subpeak suppression for each combination at different voltage levels, further confirming that the tuning advantage range of G5, G6, and G7 is concentrated in the 35-45V range. G4, however, shows only average performance across the entire voltage range compared to other combinations. Figure 5 (d) visually demonstrates the minimum tuning voltage corresponding to the minimum frequency domain subpeak amplitude achieved by each combination.

[0110] To systematically identify the optimal electrode combination scheme in the electrostatic tuning of a metal hemispherical resonator, a phased, multi-index decision-making framework is proposed, such as... Figure 5 As shown in (g), by establishing a finite element simulation model of multiple electrode combinations, for each candidate combination, the minimum tuning voltage 𝑉opt when the secondary peak in the frequency domain completely disappears and the final secondary peak suppression ratio 𝑅supp in the frequency domain are extracted to form the original data matrix. Meanwhile, to eliminate the influence of the dimensions of different indicators, 𝑉opt and 𝑅supp are substituted into the formula. Standardization is performed, normalizing the data to the [0,1] interval, allowing for quantitative comparison of different combinations within the same evaluation system. A weighted comprehensive scoring function λ is introduced. Considering that energy efficiency and frequency domain secondary peak suppression capability are equally important in practical applications, this application sets the weighting factor to λ=0.5, meaning both contribute equally to achieve a balance. Based on the weighted comprehensive scoring function, the electrode combination with the highest comprehensive score is selected as the theoretically optimal tuning scheme.

[0111]

[0112]

[0113]

[0114] in and These represent the normalized minimum tuning voltage and the frequency domain subpeak rejection ratio, respectively, with λ being the weighting factor.

[0115] The voltage normalization index V* and the suppression ratio normalization index R* are calculated and plotted. Figure 5 (e) Scatter plot of normalized index, Figure 5 (f) presents a comprehensive scoring function constructed based on a weighted average method to rank the performance of each combination. The results show that combination G5 ranks first with the highest score of 0.748, reflecting its optimal balance between voltage efficiency and suppression strength. Combinations G2 and G7 scored 0.538 and 0.510 respectively, showing different degrees of optimization characteristics. The scores of G3 and G4 are significantly lower, indicating that their tuning configurations are not suitable for high-efficiency frequency domain subpeak suppression scenarios.

[0116] The experimental procedure is divided into three stages: system initialization, benchmark testing, and tuning optimization. In the initialization stage, the effects of environmental noise and equipment drift on measurement accuracy are eliminated through vacuum calibration, laser optical path alignment, and power supply stability testing. In the benchmark testing, a swept-frequency excitation signal source is used to excite the multi-mode resonator, and frequency splitting characteristics in the untuned state are obtained through frequency domain analysis. To verify the effectiveness of the simulation model and evaluate the electrostatic tuning performance of different electrode combinations under atmospheric and vacuum environments, this application selects combinations 2, 5, and 7, which have the highest simulation scores, for experimental testing. As shown in Fig. 3h, the gain values ​​of the primary and secondary modes are measured under different tuning voltages, and the energy ratio of the secondary peak relative to the primary peak and the decrease ratio of the secondary peak in the frequency domain are calculated.

[0117] like Figure 6As shown in (a) and (b), the secondary peak reduction ratios of the three electrode combinations G2, G5, and G7 all exhibit a significant suppression trend with increasing tuning voltage in both atmospheric and vacuum environments, demonstrating the effectiveness of electrostatic tuning in controlling secondary mode energy. In the atmospheric environment, the G5 combination shows the best tuning performance, with its secondary peaks beginning to decay rapidly at low voltages, reaching a reduction ratio of approximately 97% at around 40V, achieving near-complete secondary mode suppression. The tuning process of the G2 combination is relatively stable, requiring high voltages of 40 and 50V to achieve a secondary peak reduction ratio of approximately 85%. The G7 combination has a slower response at low voltages, but its secondary peak reduction ratio increases rapidly within a certain voltage range, achieving a high suppression level. Compared to the atmospheric environment, the overall secondary mode suppression capability is significantly enhanced in the vacuum environment, indicating that the electrostatic negative stiffness plays a more significant role under low-damping conditions, which is beneficial for the stable realization of mode decoupling. Figure 6 (c) and (d) further describe the change in the proportion of sub-mode energy relative to the main mode using the relative power ratio of the sub-peaks. As the tuning voltage gradually increases, the relative power ratio of the sub-peaks decreases significantly, reflecting the gradual concentration of mode energy towards the main mode. Under atmospheric conditions, the lowest relative power ratio of the G5 combination is about 0.02, achieving significant energy suppression; the relative power ratio of the G2 and G7 combinations remains at around 0.05 under high voltage, exhibiting some residual sub-mode energy. Under vacuum conditions, the sub-mode energy decays more thoroughly, with the G5 combination reaching a minimum of about 0.016, almost achieving complete mode decoupling; the G2 and G7 combinations also exhibit a significant energy concentration effect, further demonstrating that electrostatic tuning combined with a low-damping environment can significantly improve the problem of uneven mode energy distribution caused by frequency splitting.

[0118] Figure 6 Figure (e) shows the measured frequency response curves of a typical tuned combination under atmospheric and vacuum environments. Before tuning, the frequency response of the metal resonant gyroscope exhibits a bimodal structure, reflecting typical frequency fragmentation and modal coupling effects. As the electrostatic tuning voltage is gradually applied, the secondary peaks in the frequency domain gradually decrease, eventually evolving into a single, sharp, and centrally located main peak structure under the gradually increasing voltage. This indicates that the modal frequencies have been effectively aligned, the system's modal decoupling process is basically complete, and the vibration modes are approaching the ideal state. Under vacuum conditions, the main peak is sharper and the Q value is significantly improved, showing that the stability of modal decoupling is enhanced after the system damping is reduced; this verifies the feasibility and effectiveness of electrostatic tuning in practical devices.

[0119] Overall, the experimental results fully verify the effectiveness of the electrostatic tuning strategy proposed in this application in suppressing submodal responses, mitigating frequency fragmentation, and achieving approximate mode decoupling in metal resonant gyroscopes. The results also demonstrate that this method can significantly improve the frequency domain characteristics and signal purity of resonant gyroscopes, providing reliable experimental evidence for high-precision inertial measurement and engineering applications.

[0120] To ensure the reliability and comparability of the experimental results, this application systematically completed the packaging and manufacturing process of the metal resonant gyroscope before building the tuning experimental platform, ensuring that the device meets the tuning test requirements in terms of structural consistency, electrical connectivity, and operational stability. Figure 7 As shown, firstly, the machined resonator and base assembly undergo a quality sorting process, where automated equipment screens for geometric parameters and surface defects, rejecting unqualified parts. Subsequently, the devices enter a plasma treatment process. This step performs micro-nano-level cleaning and activation of the resonator and base surfaces, removing organic contaminants and surface-adsorbed impurities, improving the adhesion and uniformity of subsequent metal layer deposition. After surface treatment, qualified devices enter an immersion coating process, where a dense conductive coating is formed on their surface through chemical deposition, improving conductivity and enhancing oxidation resistance. The coated resonator assembly then enters an automated parallel seam welding machine for structural encapsulation. This equipment integrates a high-precision optical alignment system and an automated robotic arm, enabling seam welding connections between the resonator and base with micron-level precision, forming a closed and stable shell structure to prevent environmental interference and particulate contamination from affecting the internal structure. After structural encapsulation, a gold wire bonding machine completes the electrical connection between the internal electrodes and external leads. This process utilizes high-purity gold wire material and precisely controls the welding temperature to ensure reliable bonding of the gold wire joints.

[0121] Finally, the device undergoes visual inspection of the solder joints, with the system identifying defects such as cold solder joints, misaligned solder joints, or broken wires through image analysis. After the resonator is fabricated and assembled, a highly coupled finite element model is constructed to simulate the modal evolution and frequency response of the sample under different manufacturing errors, boundary conditions, and tuning voltages. This verifies whether the resonator can work effectively and allows for further research, while also exploring the control mechanism of DC bias voltage on frequency fragmentation and modal coupling behavior.

[0122] To verify the actual effectiveness of the electrostatic tuning method in suppressing frequency splitting, this application constructs an experimental verification platform based on a metal resonant gyroscope. Through modular design, it achieves coordinated control of electrostatic stiffness tuning and dynamic response. The experimental system is as follows: Figure 8(a) A fully closed-loop test architecture was formed by integrating a Doppler single-point laser vibrometer, a vacuum environment unit, a swept-frequency excitation signal source, and a high-stability DC power supply module, supplemented by a vibration isolation table and a data acquisition system, to conduct experiments on metal resonant gyroscopes. Further electrostatic stiffness tuning experiments on metal microresonators were carried out based on this system. By precisely controlling the electrode voltages in each direction, active adjustment of the resonant frequency and optimization of axisymmetricity were achieved to eliminate frequency splitting and enhance the stability and gyroscopic response capability of the resonator.

[0123] To further verify the effectiveness of the proposed electrostatic tuning method, this application constructed a motion signal processing and testing system based on STM32H750. This system consists of a metal resonant gyroscope, a signal detection module, a signal processing module, a host computer, and a high-voltage drive unit, as follows: Figure 8 As shown in (c). The system works as follows: a high-voltage drive circuit excites the resonator to generate steady-state vibration. The signal detection board collects the capacitance changes caused by the resonator's vibration in real time and outputs them to the signal processing board. The signal processing board completes the sampling, quadrature demodulation, and filtering of the motion signal, extracting the amplitude envelope information. Finally, the processing results are transmitted to the host computer for visualization and recording analysis via the RS422 interface. In the rotation test, the tuned metal resonator gyroscope prototype is fixed on a high-precision turntable, an angular rate input is applied, and the demodulated signal is collected in real time to evaluate the gyroscope's sensitivity. Figure 8 As shown in (d), the experimental results show that the amplitude does not change significantly in the static state; when the gyroscope rotates, the demodulated capacitor signal effectively characterizes its rotation speed, indicating that the tuned gyroscope can accurately characterize the rotation input and realize sensitive detection under actual working conditions.

[0124] This application addresses the frequency fragmentation problem in metal resonant gyroscopes caused by manufacturing errors and structural asymmetries. It proposes an active tuning method based on electrostatic stiffness control, achieving modal decoupling and frequency uniformity control without altering the device's physical structure. Through theoretical analysis, a dynamic model considering local stiffness perturbations and modal energy coupling is established, and the suppression mechanism of electrostatic negative stiffness on frequency fragmentation and submodal response of the resonator is derived. Based on this, a finite element simulation platform with multiple electrode combinations is constructed, enabling quantitative prediction of submodal energy attenuation and optimal tuning voltage under different tuning strategies. Furthermore, a multi-index comprehensive scoring method based on minimum tuning voltage and sub-peak suppression ratio is proposed to select the optimal tuning combination.

[0125] Experimental results demonstrate that after electrostatic tuning, the proportion of secondary peak energy in the frequency domain of the resonator decreases from approximately 73% in the baseline state to less than 2%, and the secondary peak suppression ratio exceeds 98%. This significantly weakens the amplitude-frequency asymmetry caused by orthogonal mode coupling and makes the frequency response characteristics closer to the ideal circularly symmetric mode. Comparative tests under atmospheric and vacuum environments further verify the effectiveness and stability of the proposed tuning method. Combination 2, which received the highest simulation score, also exhibited the best secondary mode suppression capability in the experiment. The measured trend is highly consistent with the simulation prediction, with only a slight residual in the extreme suppression stage, mainly due to the influence of micro-defects in actual processing, non-ideal electric field distribution, and gas damping. Furthermore, the tuned gyroscope accurately characterizes the angular rate input in the rotation test, proving that electrostatic tuning not only optimizes the modal response but also effectively improves the inertial sensitivity and signal purity of the device under actual dynamic conditions.

[0126] In summary, the electrostatic stiffness tuning strategy proposed in this application provides a low-power, repeatable, and packaged engineering solution for frequency fragmentation suppression and mode decoupling in metal resonant gyroscopes. This method provides theoretical support and experimental basis for the structural uniformity design, dynamic tuning control, and multiphysics coupling optimization of high-performance inertial devices, and has important reference value for the future engineering application and industrialization of high-precision metal resonant gyroscopes.

[0127] This application also provides an electrostatic tuning optimization device for a metal resonant gyroscope, such as... Figure 9 As shown, it includes: a model building module 92, configured to establish a multi-degree-of-freedom dynamic model based on the geometric structural parameters and working modes of the metal resonant gyroscope, using structural symmetry perturbation and coupled stiffness effects as a dynamic model describing the vibration modal characteristics of the metal resonant gyroscope; and a matrix building module 94, configured to calculate the modal frequency distribution of the metal resonant gyroscope at different azimuth angles based on the dynamic model, obtain modal frequency difference data, and construct an equivalent stiffness distribution model based on the modal frequency difference data to quantify the stiffness non-uniformity of the resonant structure and obtain a stiffness perturbation model. The matrix optimization module 96 is configured to determine the applied voltage distribution of the electrostatic tuning electrodes based on the stiffness perturbation model, obtain voltage control parameters corresponding to each azimuth angle, apply the voltage control parameters to multiple electrostatic tuning electrodes of the metal resonant gyroscope, adjust the equivalent electrostatic stiffness distribution of the local region of the metal resonator, and obtain an optimized stiffness matrix; the splitting suppression module 98 is configured to recalculate the modal frequencies of the metal resonator based on the optimized stiffness matrix, obtain the tuned modal frequency difference, and actively suppress frequency splitting based on the tuned modal frequency difference.

[0128] It should be noted that the electrostatic tuning optimization device for the metal resonant gyroscope provided in the above embodiments is only an example of the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the electrostatic tuning optimization device for the metal resonant gyroscope provided in the above embodiments and the electrostatic tuning optimization method embodiments for the metal resonant gyroscope belong to the same concept, and the specific implementation process is detailed in the method embodiments, which will not be repeated here.

[0129] Figure 10 A schematic diagram of a computer device suitable for implementing embodiments of the present disclosure is shown. It should be noted that... Figure 10 The computer device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments disclosed herein.

[0130] like Figure 10 As shown, the computer device includes a central processing unit (CPU) 1001, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage section 1008 into a random access memory (RAM) 1003. The RAM 1003 also stores various programs and data required for system operation. The CPU 1001, ROM 1002, and RAM 1003 are interconnected via a bus 1004. An input / output (I / O) interface 1005 is also connected to the bus 1004.

[0131] The following components are connected to I / O interface 1005: an input section 1006 including a keyboard, mouse, etc.; an output section 1007 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and speakers, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN card, modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to I / O interface 1005 as needed. A removable medium 1011, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on drive 1010 as needed so that computer programs read from it can be installed into storage section 1008 as needed.

[0132] The above description is only a preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A method for optimizing the electrostatic tuning of a metal resonant gyroscope, characterized in that, include: Based on the geometric parameters and operating modes of the metal resonant gyroscope, a dynamic model based on structural symmetry perturbation and coupling stiffness effect is established, wherein the dynamic model is used to describe the vibration mode characteristics of the metal resonator. Based on the dynamic model, the modal frequency distribution of the metal resonant gyroscope under different azimuth angles is calculated to obtain modal frequency difference data. Based on the modal frequency difference data, an equivalent stiffness distribution model is constructed to quantify the stiffness non-uniformity of the resonant structure and obtain the stiffness matrix. Based on the stiffness matrix, the applied voltage distribution of the electrostatic tuning electrodes is determined, and voltage control parameters corresponding to each azimuth angle are obtained. The voltage control parameters are applied to multiple electrostatic tuning electrodes of the metal resonant gyroscope to adjust the equivalent electrostatic stiffness distribution of the local region of the metal resonator, thereby obtaining the optimized stiffness matrix. Based on the optimized stiffness matrix, the modal frequencies of the metal resonator are recalculated to obtain the tuned modal frequency difference, and based on the tuned modal frequency difference, active suppression of frequency fragmentation is achieved.

2. The method according to claim 1, characterized in that, Based on the geometric parameters and operating modes of a metal resonant gyroscope, a dynamic model is established based on structural symmetry perturbation and coupled stiffness effects, including: Obtain the geometric parameters and operating modes of the metal resonant gyroscope, and establish a basic dynamic model under an ideal symmetrical structure; In the basic dynamic model, a structural symmetry perturbation term and a coupling stiffness term are introduced. The structural symmetry perturbation term characterizes the mass deviation and geometric distortion caused by manufacturing errors, and the coupling stiffness term is used to describe the energy coupling effect between different vibration modes. The structural symmetry perturbation term and coupling stiffness term are superimposed and corrected with the mass matrix and stiffness matrix in the basic dynamic model to form a corrected dynamic model based on perturbation and coupling effects. By performing modal analysis on the modified dynamic model, the natural frequencies and mode shape vectors of each mode are obtained, thus forming a dynamic model that can describe the vibration modal characteristics of the metal harmonic oscillator.

3. The method according to claim 1, characterized in that, Based on the aforementioned dynamic model, the modal frequency distribution of the metal resonant gyroscope at different azimuth angles is calculated, yielding modal frequency difference data, including: Multiple azimuth angle parameters are set, and the dynamic model under each azimuth angle is solved to obtain the corresponding modal frequency distribution; Based on the modal frequency distribution, the frequency values ​​of the two degenerate modes with the closest frequencies are extracted, and their difference is calculated to obtain the modal frequency difference at the corresponding azimuth angle. The modal frequency differences are statistically analyzed and normalized according to their azimuth angles to form modal frequency difference data that reflects the degree of frequency fragmentation of the metal resonator in different directions.

4. The method according to claim 1, characterized in that, Based on the modal frequency difference data, an equivalent stiffness distribution model is constructed to quantify the stiffness non-uniformity of the resonant structure, resulting in a stiffness matrix, including: Based on the modal frequency difference data, a mapping relationship model between the modal frequency difference and the equivalent stiffness of the structure is established; Based on the mapping relationship model, the equivalent stiffness distribution under each azimuth angle is calculated using the azimuth angle and modal frequency difference information in the modal frequency difference data, and the equivalent stiffness distribution is obtained. The equivalent stiffness distribution is discretized by matrixing, and the local stiffness deviation is converted into stiffness disturbance, which is then assembled into the stiffness matrix.

5. The method according to claim 1, characterized in that, Based on the stiffness matrix, the applied voltage distribution of the electrostatic tuning electrodes is determined, and voltage control parameters corresponding to each azimuth angle are obtained. These voltage control parameters are then applied to multiple electrostatic tuning electrodes of the metal resonant gyroscope to adjust the equivalent electrostatic stiffness distribution in a local region of the metal resonator, resulting in an optimized stiffness matrix, including: Based on the stiffness matrix, the least squares method or gradient descent algorithm is used to solve the target voltage distribution of each electrostatic tuning electrode under different azimuth angles, and the voltage control parameters corresponding to the azimuth angle are obtained. Based on the voltage control parameters, corresponding voltages are applied to the multiple electrostatic tuning electrodes of the metal resonant gyroscope to adjust the equivalent electrostatic stiffness of the local region of the metal resonator, thereby obtaining updated equivalent stiffness distribution data. Based on the updated equivalent stiffness distribution data, the stiffness matrix is ​​iteratively corrected to obtain an optimized stiffness matrix.

6. The method according to claim 1, characterized in that, Based on the optimized stiffness matrix, the modal frequencies of the metal resonator are recalculated to obtain the tuned modal frequency difference. Based on this tuned modal frequency difference, active suppression of frequency fragmentation is achieved, including: Based on the optimized stiffness matrix, the vibration characteristics of the metal harmonic oscillator at multiple azimuth angles are solved to obtain the modal frequencies; Extract the frequency values ​​of adjacent degenerate modes from the modal frequencies, calculate their differences, and obtain the tuned modal frequency differences for each corresponding azimuth angle; Based on the tuned modal frequency difference, the changing trend of the frequency difference before and after tuning is compared to determine the degree of suppression of frequency splitting, and the performance index results used to evaluate the tuning effect are obtained, so as to achieve active suppression of frequency splitting.

7. An electrostatic tuning optimization device for a metal resonant gyroscope, characterized in that, include: The model building module is configured to establish a multi-degree-of-freedom dynamic model based on the geometric structural parameters and working modes of the metal resonant gyroscope, using the structural symmetry perturbation and coupling stiffness effect as the dynamic model describing the vibration mode characteristics of the metal resonator. The matrix construction module is configured to calculate the modal frequency distribution of the metal resonant gyroscope at different azimuth angles based on the dynamic model, and obtain... The modal frequency difference data is used to construct an equivalent stiffness distribution model based on the modal frequency difference data, and the stiffness non-uniformity of the resonant structure is quantified to obtain the stiffness matrix. The matrix optimization module is configured to determine the applied voltage distribution of the electrostatic tuning electrodes based on the stiffness matrix, obtain voltage control parameters corresponding to each azimuth angle, apply the voltage control parameters to multiple electrostatic tuning electrodes of the metal resonant gyroscope, adjust the equivalent electrostatic stiffness distribution of the local region of the metal resonator, and obtain the optimized stiffness matrix. The frequency fragmentation suppression module is configured to recalculate the modal frequencies of the metal resonator based on the optimized stiffness matrix, obtain the tuned modal frequency difference, and actively suppress frequency fragmentation based on the tuned modal frequency difference.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device on which the computer-readable storage medium is located to perform the method according to any one of claims 1 to 6.

9. A computer device, characterized in that, include: Memory and processor The memory stores computer programs; The processor is configured to execute a computer program stored in the memory, wherein when the computer program is executed, the processor performs the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

Images