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Journal articles on the topic 'Hemispherical resonator gyroscope'

Author: Grafiati

Published: 4 June 2025

Last updated: 15 July 2025

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Chen, Yimo, Xiang Xi, Yan Shi, Kun Lu, Dingbang Xiao, and Xuezhong Wu. "Unbalanced Mass Identification Method for Micro-Hemispherical Resonators Based on Spurious Mode Decoupling." Journal of Physics: Conference Series 2982, no. 1 (2025): 012036. https://doi.org/10.1088/1742-6596/2982/1/012036.

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Abstract This paper introduces a method for detecting the first three harmonics of unbalanced mass in micro-hemispherical resonators, a critical issue impacting the performance of micro-hemispherical resonator gyroscopes. Unbalanced mass, resulting from uneven mass distribution due to non-ideal fabrication processes. Due to the large-curved surface and thin-wall characteristics of the resonator, the detection of unbalanced mass, especially the first three harmonics, is one of the most difficult challenges to improve the performance of the micro-hemispherical resonator gyroscope. This paper analyzes the impact of unbalanced mass on the dynamics of micro-hemispherical resonators and proposes a first three harmonics identification scheme based on the decoupling of spurious modes. A finite element simulation model and an experimental platform were constructed to preliminarily verify the scheme for the micro-hemispherical resonator samples, which contributes to the refinement of mass balancing technology for micro-hemispherical resonator.

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Yuan, Lishan, Ning Wang, Ronghao Xie, Zhennan Wei, Qingshuang Zeng, and Changhong Wang. "Study on the Mechanism of Energy Dissipation in Hemispherical Resonator Gyroscope." Sensors 25, no. 1 (2024): 74. https://doi.org/10.3390/s25010074.

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The hemispherical resonator gyroscope is a gyroscope based on the principle of Coriolis vibration, widely used in inertial measurement systems of spacecraft. This article decomposes the gyroscope into two parts: the resonator shell and the gyroscope head, establishes the energy dissipation mechanism of the gyroscope, and conducts experimental verification. Firstly, based on the working principle of the gyroscope, a mechanical analysis model of the hemispherical resonator gyroscope head with a resonator spherical shell containing quality defects under second-order vibration state was established. The unbalanced force applied by the resonator spherical shell to the hemispherical resonator gyroscope head was analyzed, and the energy transfer path and dissipation mechanism from the spherical shell to the hemispherical resonator gyroscope head were explained. Finally, through the constructed testing platform, the circumferential quality factor test of the hemispherical resonator gyroscope before and after assembly was completed according to the designed experimental plan, and the consistency between theory and experimental phenomena was verified experimentally.

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Liu, Xiaohao, Xin Jin, Chaojiang Li, Yumeng Ma, Deshan Xu, and Simin Guo. "Comprehensive Performance-Oriented Multi-Objective Optimization of Hemispherical Resonator Structural Parameters." Micromachines 16, no. 3 (2025): 287. https://doi.org/10.3390/mi16030287.

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The hemispherical resonant gyroscope is the highest-precision solid-state vibration gyroscope, widely applied in aviation, aerospace, marine, and other navigation fields. As the core component of the hemispherical resonant gyroscope, the design of its structural parameters directly influences the key performance parameters of the resonator—specifically, the thermoelastic damping quality factor and the minimum frequency difference from interference modes—affecting the operational accuracy and lifespan of the gyroscope. However, existing research, both domestic and international, has not clarified the effect of structural parameters on performance laws. Thus, studying the mapping relationship between the resonator’s performance and structural parameters is essential for optimization. In this study, a hemispherical resonator with a midplane radius of 10 mm serves as the research object. Based on a high-precision finite element simulation model of an ideal hemispherical resonator, the mechanism of thermoelastic damping and the influence of structural parameters on performance are analyzed. A PSO-BP neural network mapping model is then developed to relate the resonator’s structural and performance parameters. Subsequently, the NSGA-II algorithm is applied to perform multi-objective mapping of these parameters, achieving an optimized resonator with a 4.61% increase in the minimum frequency difference from interference modes and a substantial improvement in thermoelastic damping of approximately 70.41%. The comprehensive, performance-oriented multi-objective optimization method for the structural parameters of hemispherical resonators proposed in this paper offers a cost-effective approach to high-performance design and optimization, and it can also be applied to other manufacturing processes under specific conditions.

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Li, Jiacheng, Kun Lu, Xiang Xi, et al. "Research on frequency trimming of uncoated micro hemispherical resonator using ion beam etching." Journal of Physics: Conference Series 2982, no. 1 (2025): 012018. https://doi.org/10.1088/1742-6596/2982/1/012018.

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Abstract The fused micro hemispherical resonator gyroscope (MHRG) possesses notable advantages such as a high quality factor and excellent structural symmetry, making it one of the most precise micro electromechanical system (MEMS) gyroscopes available today. Frequency split is a critical factor affecting the performance of the MHRG. Due to material defects and manufacturing errors, the initial frequency split of the MHRG is relatively large, necessitating trimming techniques to reduce frequency splitting and enhance gyroscope performance. Therefore, low-damage and high-precision frequency trimming is an effective mean to improve gyroscope performance. This paper proposes a frequency split trimming technology for uncoated micro hemispherical resonator structures based on ion beam etching. Through theoretical and simulation analysis, the influence of the shell surface trimming model on the frequency splitting of the resonator structure is examined. For detecting frequency splitting in uncoated micro hemispherical resonator, a planar interdigital electrode testing system is established to accurately identify the magnitude of frequency split and the direction of the rigid axis. Finally, an ion beam trimming experiment is designed, The experiments achieved frequency splits below 100 mHz for uncoated resonator and below 50 mHz for coated resonator. These results experimentally validate the accuracy of the trimming model., thereby effectively enhancing the performance of the micro hemispherical resonator gyroscope.

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Demenkov, N. P., I. A. Mochalov, and D. M. Tran. "Fuzzy Phase Trajectories in Hemispherical Resonator Gyroscopes." Herald of the Bauman Moscow State Technical University. Series Instrument Engineering, no. 1 (134) (March 2021): 78–101. http://dx.doi.org/10.18698/0236-3933-2021-1-78-101.

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The paper considers elementary fuzzy oscillator models represented by hard and fuzzy second-order differential equations with hard and fuzzy initial conditions. Linear models describe wave processes in ring resonators of hemispherical resonator gyroscopes.We show that in the case 1 (a hard model with fuzzy initial conditions), when there is no internal friction (model 1), phase trajectories appear as a fuzzy centre shaped as an elliptical ring. When internal friction is present (model 2), phase trajectories appear as a fuzzy focus shaped as a circular logarithmic spiral. In the case 2, for a fuzzy hemispherical resonator gyroscope model with hard initial conditions, when there is no internal friction (model 1), a representative point of a fuzzy phase trajectory does not stop or increase its oscillations with time, meaning that the system is asymptotically unstable, while for the model 2 the origin singularity is a fuzzy stable focus. In the case 3, for a fuzzy hemispherical resonator gyroscope model with fuzzy initial conditions, when there is no internal friction (model 1), there is a fuzzy asymptotic instability in the model 1 of a hemispherical resonator gyroscope, while in the presence of internal friction (model 2), the phase trajectory is also a function of time and controls the asymptotic stability of the fuzzy model 2 of a hemispherical resonator gyroscope. Asymptotic stability is determined for all cases and models

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Spiridonov, Fedor, Ramis Mingazov, and Konstantin Shishakov. "Technological process automation of balancing quartz resonators of solid state wave gyroscopes." Automation and modeling in design and management 2023, no. 1 (2023): 21–31. http://dx.doi.org/10.30987/2658-6436-2023-1-21-31.

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The paper discusses the main issues that arise while developing and implementing automatic process control systems (APCS) in relation to the technological operations of balancing quartz hemispherical resonators of solid-state wave gyroscopes. For this, the article gives a general algorithm for performing the technological process of resonator balancing; block diagrams of the automatic process control system of balancing and the general algorithm for balancing the resonators. The latter discloses internal algorithms for determining the physical parameters of the gyroscope resonator, for making a decision on resonator balancing and controlling the etching process of the gyroscope quartz resonator. The necessary application software (SW) for the automatic process control system for balancing gyroscope resonators is considered separately. The paper states that to build the first version of the automatic process control system for balancing resonators, it is recommended, as an intermediate step, to modernise and work out the “advising” automatic process control system, which, in the development of the existing locally automatic process control system, should be supplemented by solving the following important tasks: increasing the accuracy of determining physical parameters, calculating the efficiency of the ongoing balancing operation and estimating the effective control of the ion-plasma source. In the considered automatic process control system for balancing the resonators of the solid state wave gyroscopes (SSWG), it is not supposed to completely exclude the system operator’s role and importance. He performs the primary check of the stand, the installation of the resonator in the stand, as well as the initial setup. Automation at the first stage will consist of closing the operations of determining the physical parameters, calculating the balancing efficiency and ion-plasma etching of the quartz resonator. The closure of these operations is carried out with the help of application software installed on the central control computer of the automated workplace of the balancing system operator.

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Cheng, Wei, Shunqing Ren, Boqi Xi, Zhen Tian, Youhuan Ning, and Yan Huo. "The Influence of Nonlinear High-Intensity Dynamic Processes on the Standing Wave Precession of a Non-Ideal Hemispherical Resonator." Sensors 24, no. 9 (2024): 2709. http://dx.doi.org/10.3390/s24092709.

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The properties of small size, low noise, high performance and no wear-out have made the hemispherical resonator gyroscope a good choice for high-value space missions. To enhance the precision of the hemispherical resonator gyroscope for use in tasks with large angular velocities and angular accelerations, this paper investigates the standing wave precession of a non-ideal hemispherical resonator under nonlinear high-intensity dynamic conditions. Based on the thin shell theory of elasticity, a dynamic model of a hemispherical resonator is established by using Lagrange’s second kind equation. Then, the dynamic model is equivalently transformed into a simple harmonic vibration model of a point mass in two-dimensional space, which is analyzed using a method of averaging that separates the slow variables from the fast variables. The results reveal that taking the nonlinear terms about the square of the angular velocity and the angular acceleration in the dynamic equation into account can weaken the influence of the 4th harmonic component of a mass defect on standing wave drift, and the extent of this weakening effect varies with the dimensions of the mass defects, which is very important for steering the development of the high-precision hemispherical resonator gyroscope.

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Zhao, Yuqian, Fei Li, Kexian Liu, Junfeng Liu, and Tao Lai. "Research on the Measurement Method of Key Shape and Position Errors of Hemispherical Harmonic Oscillator." Journal of Physics: Conference Series 2463, no. 1 (2023): 012018. http://dx.doi.org/10.1088/1742-6596/2463/1/012018.

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Abstract Hemispherical resonance gyroscope originated in the 1960s. With its outstanding advantages of high precision, simple structure and long service life, it is increasingly widely used in aerospace, tactical weapons and other fields. The hemispherical resonator, the core part of the gyroscope, is a thin-walled part with high steepness curved surface and hard and brittle material. Limited by the current processing level, it is difficult to obtain good shape and position accuracy, resulting in uneven mass distribution and frequency cracking, which affects the accuracy of the gyroscope. Based on the precision machining of hemispherical resonator, this paper carries out the research on the measurement method of shape and position error, focuses on the measurement method of the roundness and end face of the resonator, uses the cylindricity meter to complete the measurement of the roundness error of the inner and outer hemispherical shell of the resonator, and uses the white light interferometer and the subaperture stitching technology to realize the measurement of the full aperture surface of the end face of the hemispherical shell. This work provides theoretical guidance for subsequent processing and is of great significance to improve the quality of harmonic oscillator.

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Wang, Yuting, Yao Pan, Tianliang Qu, Yonglei Jia, Kaiyong Yang, and Hui Luo. "Decreasing Frequency Splits of Hemispherical Resonators by Chemical Etching." Sensors 18, no. 11 (2018): 3772. http://dx.doi.org/10.3390/s18113772.

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The hemispherical resonator gyroscope (HRG) has attracted the interest of the world inertial navigation community because of its exceptional performance, ultra-high reliability and its potential to be miniaturized. These devices achieve their best performance when the differences in the frequencies of the two degenerate working modes are eliminated. Mechanical treatment, laser ablation, ion-beams etching, etc., have all been applied for the frequency tuning of resonators, however, they either require costly equipment and procedures, or alter the quality factors of the resonators significantly. In this paper, we experimentally investigated for the first time the use of a chemical etching procedure to decrease the frequency splits of hemispherical resonators. We provide a theoretical analysis of the chemical etching procedure, as well as the relation between frequency splits and mass errors. Then we demonstrate that the frequency split could be decreased to below 0.05 Hz by the proposed chemical etching procedure. Results also showed that the chemical etching method caused no damage to the quality factors. Compared with other tuning methods, the chemical etching method is convenient to implement, requiring less time and labor input. It can be regarded as an effective trimming method for obtaining medium accuracy hemispherical resonator gyroscopes.

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Ranji, Ahmad Rahbar, Vijayakanthan Damodaran, Kevin Li, Zilang Chen, Shahpour Alirezaee, and Mohammed Jalal Ahamed. "Recent Advances in MEMS-Based 3D Hemispherical Resonator Gyroscope (HRG)—A Sensor of Choice." Micromachines 13, no. 10 (2022): 1676. http://dx.doi.org/10.3390/mi13101676.

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Macro-scale, hemispherical-shaped resonating gyroscopes are used in high-precision motion and navigation applications. In these gyroscopes, a 3D wine-glass, hemispherical-shaped resonating structure is used as the main sensing element. Motivated by the success of macroscale hemispherical shape gyroscopes, many microscale hemispherical-shaped resonators have been produced due to the rapid advancement in semiconductor-based microfabrication technologies. The dynamic performance of hemispherical resonators depends on the degree of symmetry, uniformity of thickness, and surface smoothness, which, in turn, depend on the type of materials and fabrication methods. The main aim of this review paper is to summarize the materials, characterization and fabrication methods reported in the literature for the fabrication of microscale hemispherical resonator gyroscopes (µHRGs). The theory behind the development of HRGs is described and advancements in the fabrication of microscale HRGs through various semiconductor-based fabrication techniques are outlined. The integration of electrodes with the hemispherical structure for electrical transduction using other materials and fabrication methods is also presented. A comparison of different materials and methods of fabrication from the point of view of device characteristics and dynamic performance is discussed. This review can help researchers in their future research and engineers to select the materials and methods for µHRG development.

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Shishakov, K. V. "Vibrational and Dissipative Characteristic Measurement of Solid-state Wave Gyroscope Resonators: Algorithms Based on the Identification of Free Oscillation Equations." Intellekt. Sist. Proizv. 22, no. 2 (2024): 4–18. http://dx.doi.org/10.22213/2410-9304-2024-2-4-18.

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The article describes the methodological basis for constructing computational circuits of different complexity degrees and different purposes for solving a wide range of industrial and laboratory problems to measure angular irregularity of vibrational-dissipative resonatorcharacteristics of integrating solid-state wave gyroscopes. The main method to solve such problems is the identification of the coefficients of the differential equations of quartz hemispherical resonator state in the mode of its free oscillations. The resonator oscillation equations both in the fixed measuring axes and in the moving axes of standing waves were chosen as the equations of state. After reduction to slow variables, only slowly changing amplitudeequations are left for identification problems. In all the described circuits, it is assumed that the information signals for the solved identification tasks are formed in a measuring device similar to the standard gyroscope device. These algorithms make it possible to measure the vibrational and dissipative characteristics of resonators with different degrees of completeness and directionality for different standard initial requirements to themeasurement accuracy and experimental modes, which makes it possible to reduce the measurement time and labor intensity of the established set of production control operations. Among the tasks to be solved for the free run-down mode of the resonator wave pattern are the following: angular irregularity measurement of the gyroscope resonator dissipative properties under conditions of low and significant residual frequency difference; angular non-uniformity measurement of gyroscope resonator vibrational properties (its different frequency); simultaneous measurement of resonator oscillatory and dissipative characteristics for fixed and special rotating gyroscope modes. The detailed processing of the computational schemes for the implementation of these algorithms is focused on their practical application for various tasks of production operational control. At the same time, the choice of the most suitable computational algorithm from the considered options depends on the conditions, requirements and specifics of measurements.

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Mingazov, R. I., F. I. Spiridonov, and K. V. Shishakov. "Identification of Solid-State Wave Gyroscopes Resonator Mechanical Errors in the Mode of Free Run-out of Standing Waves." Intellekt. Sist. Proizv. 20, no. 2 (2022): 4–19. http://dx.doi.org/10.22213/2410-9304-2022-2-4-19.

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To improve the accuracy of the output signals of solid-state wave integrating gyroscopes, various options for algorithms to identify mechanical errors of their resonators in the mode of occasionally switched mode of standing waves free run-out are considered. The measured physical parameters selected are: multi-frequency, Q factor and multi-potency, viscosity axes and stiffness axes of gyroscope resonators. Most algorithms are designed for methods of resonator mechanical errors production control and include the following stages: swinging a standing wave in the selected angular direction; circuit cut off of its active excitation; signal recording and analysis within two axes of measuring device; identification of mathematical model parameters for standing waves, recorded in their slowly changing amplitudes. Additionally, to search for stiffness axes, a technique with adjustable gyroscope resonator rotation axis is given. As a mathematical basis for the derivation and justification of the proposed identification algorithms, the necessary theoretical dependencies are given, explaining the processes of formation and processing the internal measuring signals in solid-state wave gyroscopes. As a practical testing of the most common identification technique, a laboratory study of one technological specimen of a quartz hemispherical gyroscope resonator was performed. To measure its free oscillations, a measuring system of the balancing stand was used, with measurement error up to 1% and a means of analog signals measurment, with an error of 0.05% when measuring a DC voltage of 10V. The experiment carried out showed the effective use of electrode excitation lines of standing wave for four angles {0°, 22.5°, 45°, 67.5°}. At the same time, the measurement time at each angular position was 60 seconds, and the sampling frequency of a separate measuring channel was 33,333 Hz. Herewith, each value of the wave variables was identified at 340 periods of resonant oscillations.

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Shtek, S. G., M. A. Zheglov, and M. M. Isaev. "Development of a converter unit for reading signals from a wave solid-state gyroscope with a quartz resonator." Journal of «Almaz – Antey» Air and Defence Corporation, no. 2 (July 19, 2020): 65–73. http://dx.doi.org/10.38013/2542-0542-2020-2-65-73.

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This paper describes the main principles of constructing systems for deriving information from wave solidstate gyroscopes with a hemispherical quartz resonator. A method for obtaining the necessary information by demodulating amplitude-modulated gyroscope signals is discussed. An electrical schematic diagram for the amplifier of the signal acquisition unit was developed using a domestic electronic component base. Computer simulation was carried out in the Micro-Cap environment. The prototyping was carried out, and the waveforms of the output signals of the proposed amplifier are presented.

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Shi, Yan, Xiang Xi, Bin Li, et al. "Micro Hemispherical Resonator Gyroscope With Teeth-Like Tines." IEEE Sensors Journal 21, no. 12 (2021): 13098–106. http://dx.doi.org/10.1109/jsen.2021.3065818.

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Trutnev, G. A. "Model of the hemispherical resonator gyroscope construction damping." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 29, no. 1 (2019): 84–91. http://dx.doi.org/10.20537/vm190108.

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Guo, Kechen, Yulie Wu, Yongmeng Zhang, Jiangkun Sun, Dingbang Xiao, and Xuezhong Wu. "Damping Asymmetry Trimming Based on the Resistance Heat Dissipation for Coriolis Vibratory Gyroscope in Whole-Angle Mode." Micromachines 11, no. 10 (2020): 945. http://dx.doi.org/10.3390/mi11100945.

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Damping asymmetry is one of the most important factors that determines the performance of Coriolis Vibratory Gyroscope. In this paper, a novel damping tuning method for the resonator with parallel plate capacitors is presented. This damping tuning method is based on resistance heat dissipation and the tuning effect is characterized by the control force in Whole-Angle mode. As the damping tuning and stiffness tuning in the resonator with parallel plate capacitors are coupled with each other, a corresponding tuning system is designed. To verify the tuning effects, experiments are conducted on a hemispherical resonator gyroscope with Whole-Angle mode. The damping tuning theories is demonstrated by the testing results and 87% of the damping asymmetry is reduced by this tuning method with a cost of 3% decaying time. Furthermore, the angle-dependent drift in rate measurement after tuning is only 15.6% of the one without tuning and the scale factor nonlinearity decreases from 5.49 ppm to 2.66 ppm. The method can be further applied on the damping tuning in other resonators with symmetrical structure.

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Wei, Zhennan, Guoxing Yi, Yan Huo, Ziyang Qi, and Zeyuan Xu. "The Synthesis Model of Flat-Electrode Hemispherical Resonator Gyro." Sensors 19, no. 7 (2019): 1690. http://dx.doi.org/10.3390/s19071690.

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The Hemispherical Resonator Gyro (HRG) is a solid-state and widely used vibrating gyroscope, especially in the field of deep space exploration. The flat-electrode HRG is a new promising type of gyroscope with simpler structure that is easier to be fabricated. In this paper, to cover the shortage of a classical generalized Coriolis Vibration Gyroscope model whose parameters are hard to obtain, the model of flat-electrode HRG is established by the equivalent mechanical model, the motion equations of unideal hemispherical shell resonator are deduced, and the calculation results of parameters in the equations are verified to be reliable and believable by comparing with finite element simulation and the reported experimental data. In order to more truthfully reveal the input and output characteristics of HRG, the excitation and detection models with assemble errors and parameters are established based on the model of flat-electrode capacitor, and they convert both the input and output forms of the HRG model to voltage changes across the electrodes rather than changes in force and capacitance. An identification method of assemble errors and parameters is proposed to evaluate and improve the HRG manufacturing technology and adjust the performance of HRG. The average gap could be identified with the average capacitance of all excitation and detection capacitors; fitting the approximate static capacitor model could identify the inclination angle and direction angle. With the obtained model, a firm and tight connection between the real HRG system and theoretical model is established, which makes it possible to build a fully functional simulation model to study the control and detection methods of standing wave on hemispherical shell resonator.

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Trutnev, G. A., and A. V. Shchenyatskiy. "Computational Component in a Hemispherical Resonator Gyroscope with its Measuring Component Utilising Alternating Voltage." Herald of the Bauman Moscow State Technical University. Series Instrument Engineering, no. 3 (140) (September 2022): 78–91. http://dx.doi.org/10.18698/0236-3933-2022-3-78-91.

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The paper considers a hemispherical resonator gyroscope. It describes the structure of a hemispherical resonator gyroscope as a measuring and computing system, as well as the problems and main factors involved in increasing its accuracy. We studied a measuring component utilising alternating voltage, its circuit layout and mathematical model. We stated the problem of synthesising a computational component taking into account possible computational resource limitations in the device in the form of a system of nonlinear algebraic equations. We considered the specifics and implementation requirements concerning the computational algorithm, as well as the specifics of utilising redundant information about the wave pattern state in the gyroscope. The equation system proposed is overdetermined. We analysed the issues peculiar to the iterative method of solving this nonlinear system, which we propose to use as the basis for the mathematical model of the computational component. The method described may be generalised as the Gauss --- Newton method. The paper provides alternative iterative methods for designing the computational component. We investigated convergence issues for the computational component model obtained via the Gauss --- Newton method. The paper presents computational component simulation results and concludes that using the computational component model obtained is possible and feasible

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Gu, Xibing, Zhong Su, Xiangxian Yao, and Sirui Chu. "Research on the Configuration Optimization of All-Metal Micro Resonant Hemisphere." Sensors 24, no. 22 (2024): 7132. http://dx.doi.org/10.3390/s24227132.

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As the core component of the all-metal micro resonant gyroscope, the structural parameters and form and position errors of the resonator significantly influence its vibration characteristics, and consequently, the accuracy of the gyroscope. By establishing the finite element model of an ideal hemispherical resonator and optimizing the meshing method, we refined the frequency difference to 0.1 Hz, enhancing the accuracy of the simulation model. Through finite element simulation, we examined the impact of various structural parameters and processing errors on the natural frequencies of each mode. We analyzed how form and position errors, including shell thickness error, central axis error, equatorial plane error, and edge rectangular tooth position error, affect the frequency splitting of the resonator. We provided optimization suggestions for the structural parameters, ensuring frequency splitting variations of less than 1 Hz. Theoretical modeling and simulation analysis indicated that the primary factors influencing the vibration modes and frequency splitting are the rectangular tooth structure and shell thickness. Following the optimized parameters, the frequency splitting of the All-Metal Micro Resonant Hemisphere was reduced by an order of magnitude to 14 Hz, demonstrating that these optimized conditions can significantly enhance the resonator’s performance.

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Parkhomey, Igor, Juliy Boiko, Irina Zeniv, and Taras Bondarenko. "Method for measuring voltages in channels of a hemispherical resonator gyroscope with an arbitrary orientation axes." Indonesian Journal of Electrical Engineering and Computer Science 29, no. 2 (2023): 715. http://dx.doi.org/10.11591/ijeecs.v29.i2.pp715-724.

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<span>The article deals with issues related to solid wave gyroscopes, which are used as a sensor in inertial navigation systems. The article considers a variant of solving problem, when oscillations of the resonator are excited in directions that coincide with their own axes, oriented a priori is unknown. The main contribution this article is the method is proposed for measuring signal amplitudes in virtual main and quadrature channels, the orientation of which does not coincide with the orientation of the signal pickup electrodes. This is achieved by modeling algorithms for measuring the slope of the resonator's own axes and signal amplitudes in virtual channels are evaluation. In order to verify the adequacy of the proposed models simplified calculation formulas for programming microcontrollers are presented. An estimate of the error due to the use of simplified formulas is made. It is assumed that the use of this method will reduce the requirements for the quality of balancing the resonators of gyroscopes. The findings will be useful for mass production of navigation systems with gyroscopes, which have a small drift and are capable of experiencing large shock linear accelerations, for example, in underground inclined drilling, and in meteorological rockets.</span>

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Liu, Jinghao, Pinghua Li, Xuye Zhuang, et al. "Design and Optimization of Hemispherical Resonators Based on PSO-BP and NSGA-II." Micromachines 14, no. 5 (2023): 1054. http://dx.doi.org/10.3390/mi14051054.

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Although one of the poster children of high-performance MEMS (Micro Electro Mechanical Systems) gyroscopes, the MEMS hemispherical resonator gyroscope (HRG) is faced with the barrier of technical and process limits, which makes it unable to form a resonator with the best structure. How to obtain the best resonator under specific technical and process limits is a significant topic for us. In this paper, the optimization of a MEMS polysilicon hemispherical resonator, designed by patterns based on PSO-BP and NSGA-II, was introduced. Firstly, the geometric parameters that significantly contribute to the performance of the resonator were determined via a thermoelastic model and process characteristics. Variety regulation between its performance parameters and geometric characteristics was discovered preliminarily using finite element simulation under a specified range. Then, the mapping between performance parameters and structure parameters was determined and stored in the BP neural network, which was optimized via PSO. Finally, the structure parameters in a specific numerical range corresponding to the best performance were obtained via the selection, heredity, and variation of NSGAII. Additionally, it was demonstrated using commercial finite element soft analysis that the output of the NSGAII, which corresponded to the Q factor of 42,454 and frequency difference of 8539, was a better structure for the resonator (generated by polysilicon under this process within a selected range) than the original. Instead of experimental processing, this study provides an effective and economical alternative for the design and optimization of high-performance HRGs under specific technical and process limits.

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Huo, Yan, Shunqing Ren, Zhennan Wei, and Guoxing Yi. "Standing Wave Binding of Hemispherical Resonator Containing First–Third Harmonics of Mass Imperfection under Linear Vibration Excitation." Sensors 20, no. 19 (2020): 5454. http://dx.doi.org/10.3390/s20195454.

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Due to complicated processing technology, the mass distribution of a hemispherical resonator made of fused silica is not uniform, which can affect the azimuth of the standing wave of a resonator under the linear vibration excitation. Therefore, the analysis of standing wave evolution of a resonator with mass imperfection under linear vibration excitation is of significance for the improvement of the output accuracy of a gyroscope. In this paper, it is assumed that the resonator containing the first–third harmonics of mass imperfection is excited by horizontal and vertical linear vibration, respectively; then, the equations of motion of an imperfect resonator under the second-order vibration mode are established by the elastic thin shell theory and Lagrange mechanics principle. Through error mechanism analysis, it is found that, when the frequency of linear vibration is equal to the natural frequency of resonator, the standing wave is bound in the azimuth of different harmonics of mass imperfection with the change in vibration excitation direction. In other words, there are parasitic components in the azimuth of the standing wave of a resonator under linear vibration excitation, which can cause distortion of the output signal of a gyroscope. On the other hand, according to the standing wave binding phenomenon, the azimuths of the first–third harmonics of mass imperfection of a resonator can also be identified under linear vibration excitation, which can provide a theoretical method for the mass balance of an imperfect resonator.

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Igor, Parkhomey, Boiko Juliy, Zeniv Irina, and Bondarenko Taras. "Method for measuring voltages in channels of a hemispherical resonator gyroscope with an arbitrary orientation axes." Method for measuring voltages in channels of a hemispherical resonator gyroscope with an arbitrary orientation axes 29, no. 2 (2023): 715–24. https://doi.org/10.11591/ijeecs.v29.i2.pp715-724.

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The article deals with issues related to solid wave gyroscopes, which are used as a sensor in inertial navigation systems. The article considers a variant of solving problem, when oscillations of the resonator are excited in directions that coincide with their own axes, oriented a priori is unknown. The main contribution this article is the method is proposed for measuring signal amplitudes in virtual main and quadrature channels, the orientation of which does not coincide with the orientation of the signal pickup electrodes. This is achieved by modeling algorithms for measuring the slope of the resonator's own axes and signal amplitudes in virtual channels are evaluation. In order to verify the adequacy of the proposed models simplified calculation formulas for programming microcontrollers are presented. An estimate of the error due to the use of simplified formulas is made. It is assumed that the use of this method will reduce the requirements for the quality of balancing the resonators of gyroscopes. The findings will be useful for mass production of navigation systems with gyroscopes, which have a small drift and are capable of experiencing large shock linear accelerations, for example, in underground inclined drilling, and in meteorological rockets.

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Yu, Zhihao, Libin Zeng, Changda Xing, Lituo Shang, Xiuyue Yan, and Jingyu Li. "Comparative Noise Analysis of Readout Circuit in Hemispherical Resonator Gyroscope." Micromachines 16, no. 7 (2025): 802. https://doi.org/10.3390/mi16070802.

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In high-precision Hemispherical Resonator Gyroscope (HRG) control systems, readout circuit noise critically determines resonator displacement detection precision. Addressing noise issues, this paper compares the noise characteristics and contribution mechanisms of the Transimpedance Amplifier (TIA) and Charge-Sensitive Amplifier (CSA). By establishing a noise model and analyzing circuit bandwidth, the dominant role of feedback resistor thermal noise in the TIA is revealed. These analyses further demonstrate the significant suppression of high-frequency noise by the CSA capacitive feedback network. Simulation and experimental results demonstrate that the measured noise of the TIA and CSA is consistent with the theoretical model. The TIA output noise is 25.8 μVrms, with feedback resistor thermal noise accounting for 99.8%, while CSA output noise is reduced to 13.2 μVrms, a reduction of 48.8%. Near resonant frequency, the equivalent displacement noise of the CSA is 1.69×10−14m/Hz, a reduction of 86.7% compared to the TIA’s 1.27×10−13m/Hz, indicating the CSA is more suitable for high-precision applications. This research provides theoretical guidance and technical references for the topological selection and parameter design of HRG readout circuits.

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Bataronov, I. L., G. E. Shunin, S. A. Kostryukov, V. V. Peshkov, and S. A. Pisarev. "Effect of Piezoelectric Transducers on the Resonator Frequencies of a Hemispherical Resonator Gyroscope." Bulletin of the Russian Academy of Sciences: Physics 83, no. 9 (2019): 1110–13. http://dx.doi.org/10.3103/s1062873819090028.

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Sharma, N. G., Sundararajan T., and G. S. Singh. "Thermoelastic Damping Based Design, Sensitivity Study and Demonstration of a Functional Hybrid Gyroscope Resonator for High Quality Factor." Giroskopiya i Navigatsiya 29, no. 1 (2021): 70–96. http://dx.doi.org/10.17285/0869-7035.0057.

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The most critical element of Hemispherical Resonator Gyroscope (HRG) is the high quality factor (Q-factor) mechanical resonator. This paper discusses the role of thermoelastic damping (TED) on effective Q-factor. Finite element method (FEM) is used to solve this highly coupled field problem involving vibration, solid mechanics, heat transfer and thermodynamics. The major contribution of this paper is the sensitivity analysis of the effect of material property, operating temperature and dimensions to arrive at macro scale resonator configuration. Hybrid hemispherical-cylindrical configuration is proposed by studying the performance parameters such as effective mass and angular gain.The uniqueness of the present work is the sensitivity study of ultra thin film coating (volume fraction of 0.01%), coating variations and different coating configurations. The coating can reduce the Q-factor by a few orders compared to uncoated shell. It has been found that coating material selection and coating configuration are very important factors. Another significance of the present work is the realization and detailed characterization of the hybrid fused silica resonator. Thin film gold coating is done on the 3D surfaces of the realized precision resonator. Detailed coating characterization is carried out using sophisticated instruments. Very fine balancing to the order of a few mHz is achieved after coating. Q-factor measurement of the coated resonator is carried out using LDV and achieved a few millions in the final functional hybrid resonator.

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Wei, Lei, Xuebao Kuai, Yidi Bao, et al. "The Recent Progress of MEMS/NEMS Resonators." Micromachines 12, no. 6 (2021): 724. http://dx.doi.org/10.3390/mi12060724.

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MEMS/NEMS resonators are widely studied in biological detection, physical sensing, and quantum coupling. This paper reviews the latest research progress of MEMS/NEMS resonators with different structures. The resonance performance, new test method, and manufacturing process of single or double-clamped resonators, and their applications in mass sensing, micromechanical thermal analysis, quantum detection, and oscillators are introduced in detail. The material properties, resonance mode, and application in different fields such as gyroscope of the hemispherical structure, microdisk structure, drum resonator are reviewed. Furthermore, the working principles and sensing methods of the surface acoustic wave and bulk acoustic wave resonators and their new applications such as humidity sensing and fast spin control are discussed. The structure and resonance performance of tuning forks are summarized. This article aims to classify resonators according to different structures and summarize the working principles, resonance performance, and applications.

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Kim, Myeongseop, Bobae Cho, Hansol Lee, Taeil Yoon, and Byeongha Lee. "Implementation of Hemispherical Resonator Gyroscope with 3 × 3 Optical Interferometers for Analysis of Resonator Asymmetry." Sensors 22, no. 5 (2022): 1971. http://dx.doi.org/10.3390/s22051971.

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A hemispherical resonator gyroscope (HRG) has been implemented by using a consumer wineglass as the resonator and 3 × 3 optical interferometers as the detectors. The poorness of the off-the-shelf wineglass as the resonator can be overcome by the high performance of the optical interferometer. The effects of asymmetries in stiffness and absorption of the resonator are analyzed theoretically and confirmed experimentally. We prove that the trace of the amplitude ratio of two n = 2 fundamental resonant modes of the resonator follows a straight line in a complex plane. By utilizing the straightness of the ratio and the high performance of the optical interferometer, we extract four real constant parameters characterizing the HRG system. Experimentally, by using a resonator having an average resonance frequency of 444 Hz and Q value of 1477.2, it was possible to measure the Coriolis force at the level of industrial grade. The bias stability was measured as small as 2.093°/h.

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Sharma, G. N., Sundararajan T., and G. S. Singh. "Design to Operational Parameters Dependency on Quality Factor of Sensor Mechanical Resonators." Giroskopiya i Navigatsiya 29, no. 2 (2021): 3–34. http://dx.doi.org/10.17285/0869-7035.0060.

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The critical functional part of any high performance resonance based sensor is a mechanical resonator. The performance is measured by resonator quality factor (Q-factor). Damping mechanisms such as thermoelastic damping (TED), anchor loss, surface loss, material internal friction, fluid damping and electronics damping are covered in this review with more focus on gyroscope resonators. Dissipations can be reduced by different means. Hence, the effects of various design to operational parameters on the Q-factor for different configurations, sizes and materials are reviewed in detail. Micro scale ring resonators can achieve a Q-factor of the order of hundreds of thousands. Macro scale hemispherical resonators are suitable for ultrahigh Q-factors. High temperature sensor operation is not preferred because of TED, while sub-zero operation is limited by material internal friction. Few orders of dissipation increase are seen with thin film metallic coating due to TED and coating material internal friction. High precision fabrication is mandatory to achieve the designed minimum anchor loss as it is highly sensitive to fabrication imperfections. Q-factor sensitivity to operating pressure is different for different resonator configurations. This review study helps to build a comprehensive mechanical resonator design, realization and operation strategy to achieve high sensor performance. A roadmap on future research requirements for developing compact mass producible CVG type sensors with ultrahigh Q-factor is also highlighted.

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Trutnev, G. A. "The model of hemispherical resonator gyroscope in terms of slow variables." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 25, no. 3 (2015): 421–29. http://dx.doi.org/10.20537/vm150312.

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Guo, Kechen, Yulie Wu, Yongmeng Zhang, Dingbang Xiao, and Xuezhong Wu. "Adaptive compensation of damping asymmetry in whole-angle hemispherical resonator gyroscope." AIP Advances 10, no. 10 (2020): 105109. http://dx.doi.org/10.1063/5.0026821.

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Trutnev, G. A., K. K. Perevozchikov, and S. B. Nazarov. "Sensing System and Methods for Measuring Oscillations in the Resonator of a Hemispherical Resonator Gyroscope." Herald of the Bauman Moscow State Technical University. Series Instrument Engineering, no. 1 (130) (February 2020): 50–63. http://dx.doi.org/10.18698/0236-3933-2020-1-50-63.

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The paper considers a hemispherical resonator gyroscope and methods for combining eight capacitive displacement sensors into a measuring instrument. We propose a circuit diagram for a measuring instrument based on operational amplifiers. The diagram makes it possible to implement oscillation measurement for direct and alternating resonator voltages as well as a combined scenario. We derived a mathematical model simulating the output signal of the measuring instrument. We analysed the sensitivity of our system for different implementations of the measuring instrument. For the case when the modulating signal frequency and resonator oscillation frequency are multiples of each other, we derived expressions to find the angular wave position and offset signals for the control system. We used the linear term of the signal model to derive these equations, provided estimations of the errors occurring and guidelines on reducing them. We also investigated the case when the frequencies of the modulating and modulated signals are not multiples. We consider a general approach to evaluating wave pattern parameters, taking the emerging errors into account

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Xu, Zeyuan, Guoxing Yi, Meng Er, and Chao Huang. "Effect of Uneven Electrostatic Forces on the Dynamic Characteristics of Capacitive Hemispherical Resonator Gyroscopes." Sensors 19, no. 6 (2019): 1291. http://dx.doi.org/10.3390/s19061291.

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The hemispherical resonator gyroscope (HRG) is a typical capacitive Coriolis vibratory gyroscope whose performance is inevitably influenced by the uneven electrostatic forces caused by the uneven excitation capacitance gap between the resonator and outer base. First, the mechanism of uneven electrostatic forces due to the significantly uneven capacitance gap in that the non-uniformity of the electrostatic forces can cause irregular deformation of the resonator and further affect the performance and precision of the HRG, was analyzed. According to the analyzed influence mechanism, the dynamic output error model of the HRG was established. In this work, the effect of the first four harmonics of the uneven capacitance gap on the HRG was investigated. It turns out that the zero bias and output error, caused by the first harmonic that dominates mainly the amplitude of the uneven capacitance gap, increase approximately linearly with the increase of the amplitude, and periodically vary with the increase of the phase. The effect of the other three harmonics follows the same law, but their amplitudes are one order of magnitude smaller than that of the first one, thus their effects on the HRG can be neglected. The effect of uneven electrostatic forces caused by the first harmonic on the scale factor is that its nonlinearity increases approximately linearly with the increase of the harmonic amplitude, which was analyzed in depth. Considering comprehensively the zero bias, the modification rate of output error, and scale factor nonlinearity, the tolerance towards the uneven excitation capacitance gap was obtained.

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Huang, Wenyi, Senyu Zhang, Jamal N. A. Hassan, et al. "High-precision angular rate detection based on an optomechanical micro hemispherical shell resonator gyroscope." Optics Express 31, no. 8 (2023): 12433. http://dx.doi.org/10.1364/oe.482859.

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Cavity optomechanics with picometer displacement measurement resolution has shown vital applications in high-precision sensing areas. In this paper, an optomechanical micro hemispherical shell resonator gyroscope (MHSRG) is proposed, for the first time. The MHSRG is driven by the strong opto-mechanical coupling effect based on the established whispering gallery mode (WGM). And the angular rate is characterized by measuring the transmission amplitude changing of laser coupled in and out from the optomechanical MHSRG based on the dispersive resonance wavelength shift and/or dissipative losses varying. The detailed operating principle of high-precision angular rate detection is theoretically explored and the fully characteristic parameters are numerically investigated. Simulation results show that the optomechanical MHSRG can achieve scale factor of 414.8 mV/ (°/ s) and angular random walk of 0.0555 °/ h1/2 when the input laser power is 3 mW and resonator mass is just 98 ng. Such proposed optomechanical MHSRG can be widely used for chip-scale inertial navigation, attitude measurement, and stabilization.

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Wang, Qi, Weinan Xie, Boqi Xi, Hanshi Li, and Guoxing Yi. "A Novel Closed-Loop Single-Channel Time Division Multiplexing Detection Circuit for Hemispherical Resonator Gyroscope." Micromachines 16, no. 3 (2025): 273. https://doi.org/10.3390/mi16030273.

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The vector control method is applied to a whole angle hemispherical resonator gyroscope (HRG). The detection and control of the resonator vibration state are implemented using orthogonal X/Y channels. However, the performance of the HRG is limited by the asymmetry in the gain and phase delay of X/Y channels. To address these issues, a novel detection circuit is proposed. The circuit leverages the closed-loop characteristics to achieve symmetry and stability in the X/Y channel gain while simultaneously eliminating phase delays within the loop. Firstly, a closed-loop single-channel time division multiplexing circuit is designed to overcome the deficiencies of the traditional dual-channel circuit. Secondly, a model is developed to analyze the time division detection errors, and an improved demodulation method is proposed to mitigate detection errors. Lastly, experimental results demonstrate that the designed circuit successfully suppresses drift in both gain and phase delay within the loop, confirming the effectiveness of the proposed solution in enhancing the performance of the HRG.

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Wang, Yu, Chaoliang Guan, Yifan Dai, and Shuai Xue. "Geometric Error Analysis and Compensation in Spherical Generating Grinding of Hemispherical Shell Resonators." Micromachines 13, no. 9 (2022): 1535. http://dx.doi.org/10.3390/mi13091535.

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The geometric accuracy of a hemispherical shell resonator (HSR) affects the assembly accuracy and final performance of a hemispherical resonant gyroscope in many ways. During the precision grinding of a resonator, the tool-setting error and wear error affect the form and positional accuracy of the inner and outer spherical surfaces. In this study, a compensation method for generating grinding of the HSR is proposed to address this problem. The geometric errors of the inner and outer spherical surfaces are systemically analyzed and a geometric model of the tool setting and wheel wear is established for generating grinding of the HSR. According to this model, a mapping relationship between the wheel pose and size, form, and positional error of the HSR was proposed. Experiments regarding machining, on-machine measurements, and error compensation were performed using the mapping relationship. The results demonstrate that the proposed method can reduce the radius error of the inner and outer spherical surfaces from 10 μm to 1 μm, sphericity from 5 μm to 1.5 μm, and concentricity from 15 μm to 3 μm following grinding. The form and positional errors are simultaneously improved, verifying the effectiveness of the proposed method.

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Trifonova, E. S., and P. A. Ushakov. "Method for Measuring the Rotation Angles of Hemispherical Resonator Gyroscope Using the Frequency Division." Intellekt. Sist. Proizv. 19, no. 1 (2021): 54. http://dx.doi.org/10.22213/2410-9304-2021-1-54-58.

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В работе отмечается, что для точного позиционирования объектов в пространстве широко используются устройства, содержащие три и более твердотельных волновых гироскопов (ТВГ). В известных на сегодняшний день подобных устройствах каждый ТВГ использует индивидуальный набор электроники для каждого гироскопического датчика, выполненный в виде индивидуальных сборок печатных плат с монтажом. Безусловно, это сказывается на массогабаритных и надежностных показателях приборов. Для улучшения этих показателей предлагается информацию от всех датчиков обрабатывать с помощью одного процессора, используя частотное разделение каналов передачи сигналов на плату обработки. В статье представлена методика измерения углов поворота ТВГ, использующая данный принцип построения системы измерения. На основе физических принципов формирования сигналов на обкладках емкостных датчиков ТВГ получены выражения для формы сигналов, снимаемых с i-го датчика. Представлена структурная схема формирования синусного и косинусного каналов передачи сигналов с датчиков, спектры которых не содержат высокочастотной несущей. Получены математические выражения и последовательность их обработки в процессоре, которые позволяют вычислить углы поворота каждого ТВГ в определенный момент времени.

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Lee, Jungshin, Sung Yun, and Jaewook Rhim. "Design and Verification of a Digital Controller for a 2-Piece Hemispherical Resonator Gyroscope." Sensors 16, no. 4 (2016): 555. http://dx.doi.org/10.3390/s16040555.

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Wang, Qi, Weinan Xie, Boqi Xi, Hanshi Li, and Guoxing Yi. "A drive error identification and compensation method for whole angle mode hemispherical resonator gyroscope." Sensors and Actuators A: Physical 387 (June 2025): 116402. https://doi.org/10.1016/j.sna.2025.116402.

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Sharma, G. N., Sundararajan T., and G. S. Singh. "Effect of Geometric Imperfections on Anchor Loss and Characterisation of a Gyroscope Resonator with High Quality Factor." Giroskopiya i Navigatsiya 28, no. 3 (2020): 18–31. http://dx.doi.org/10.17285/0869-7035.0037.

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A critical functional part of a hemispherical resonator gyroscope (HRG) is the mechanical resonator, and a few million quality factor (Q-factor) is needed for the lowest resolution. This paper focuses on anchor loss of a HRG of a few millimeters in size. A detailed parametric study of dimensions and shell imperfections due to fabrication is carried out. A sensitivity study of the effect of shell mean radius, shell thickness, stem radius, stem height on the Qanchor is carried out. The effect of geometric imperfections such as shell offset, shell tilt, shell thickness variation, and unbalance is studied in detail. From the study, it is inferred that the anchor loss becomes very significant and approaches other loss mechanisms even with minor geometric imperfections in the hardware realisation. Based on the sensitivity study, the dimensional and geometric tolerances are arrived for precision fabrication. Precision resonator is fabricated as per the requirement of minimum anchor loss. The significance of other damping mechanisms such as air damping, excitationinduced damping, thermoelastic dynamic damping and surface dissipation is also discussed. Surface characterisation before and after surface treatment has been carried out using nanoindentation technique with regard to surface loss. Functional parameters of operating frequency and Q-factor are evaluated using laser Doppler vibrometry (LDV).

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Raspopov, V. Ya, R. V. Alaluev, A. V. Ladonkin, V. V. Likhosherst, and S. I. Shepilov. "Tuning and Calibration of a Hemispherical Resonator Gyroscope with a Metal Resonator to Operate in Angular Rate Sensor Mode." Giroskopiya i Navigatsiya 28, no. 1 (2020): 31–41. http://dx.doi.org/10.17285/0869-7035.0019.

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Zhou, Xiaocong, Jiaqiang Wen, Shasha Han, and Chong Li. "Compensation of Temperature-Induced Bias Drift in Hemispherical Resonator Gyroscopes: An Inherent Data-Driven Architecture." Micromachines 16, no. 4 (2025): 357. https://doi.org/10.3390/mi16040357.

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To address the bias drift problem and hysteresis phenomenon of hemispherical resonator gyroscope (HRG) under temperature change, a temperature drift compensation method based on internal parameters is proposed. The influence model of zero-rate output bias is established with the parameters such as resonance frequency, driving signal amplitude and quadrature suppression voltage amplitude during HRG operation. The temperature cycle experiment is carried out in the range of −20 to 60 °C, and the relationship between internal parameters and working temperature is revealed. Using KAN neural network combined with time series data as input features, a real-time compensation model is designed to effectively improve the prediction accuracy of hysteresis phenomenon. The experimental results show that the model significantly reduces the output stability performance of HRG, from 0.022°/h to 0.013°/h, and the stability decreases from 1.1392°/h to 0.0651°/h, which improves the stability and reliability of HRG.

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Xiang, XI, XIAO Dingbang, LI Wei, et al. "Analysis of Assembly Errors and Design of Precise Micro-regulator for Micro-hemispherical Resonator Gyroscope (mHRG)." Journal of Mechanical Engineering 56, no. 13 (2020): 77. http://dx.doi.org/10.3901/jme.2020.13.077.

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Xu, Zeyuan, Guoxing Yi, and Weidong Zhu. "An accurate thermoelastic model and thermal output error analysis of a hemispherical resonator gyroscope under varying temperatures." Mechanical Systems and Signal Processing 170 (May 2022): 108760. http://dx.doi.org/10.1016/j.ymssp.2021.108760.

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Xu, Zeyuan, Boqi Xi, Guoxing Yi, and Danwei Wang. "A Novel Model for Fully Closed-Loop System of Hemispherical Resonator Gyroscope Under Force-to-Rebalance Mode." IEEE Transactions on Instrumentation and Measurement 69, no. 12 (2020): 9918–30. http://dx.doi.org/10.1109/tim.2020.3005282.

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Zhao, Jun, Rui Wang, Jinfeng Huang, Bingwen Hu, and Shiming Ji. "Micro ultrasonic machining hemispherical mold for MEMS resonator gyroscope using a novel ultraprecise ceramic entire-ball tool." Journal of Micromechanics and Microengineering 30, no. 7 (2020): 075007. http://dx.doi.org/10.1088/1361-6439/ab8be2.

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Chikovani, Valerii. "The sensitive element of the vibrating gyroscope is based on a quartz hemispherical resonator without a leg." MECHANICS OF GYROSCOPIC SYSTEMS, no. 43 (May 15, 2022): 79–89. http://dx.doi.org/10.20535/0203-3771432022275286.

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У роботі розглянути проблеми виготовлення складового без зубцевого кварцового півсферичного резонатора, що складається з ніжки та півсфери, які виготовляються окремо з використанням стандартних технологій виготовлення сферичних та циліндричних лінз. Після чого ці два виробу з’єднаються шляхом глибокого оптичного контакту. При цьому зростає технологічність та зменшується вартість виробу. Крім того, при виготовлені півсфери зростає якість обробки півсфери, що призводить до зменшення різночастотності резонатора. У роботі порівнюються динамічні параметри виготовлених складових резонаторів на другій та третій модах коливань. Для подальшого зменшення вартості виготовлення чутливого елементу розглядається не стандартний варіант побудови вібраційного гіроскопа на основі кварцового півсферичного резонатора без ніжки, що використовує третю моду коливань та детально аналізуються його переваги та недоліки у порівнянні зі традиційним вібраційним гіроскопом з кварцовим резонатором, виготовленим з цільного шматка кварцу.

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Zhao, Dongfang, Junning Cui, Xingyuan Bian, Zhenghao Li, and Yanxu Sun. "An Adaptive Multi-Population Approach for Sphericity Error Evaluation in the Manufacture of Hemispherical Shell Resonators." Sensors 24, no. 5 (2024): 1545. http://dx.doi.org/10.3390/s24051545.

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The performance of a hemispherical resonant gyroscope (HRG) is directly affected by the sphericity error of the thin-walled spherical shell of the hemispherical shell resonator (HSR). In the production process of the HSRs, high-speed, high-accuracy, and high-robustness requirements are necessary for evaluating sphericity errors. We designed a sphericity error evaluation method based on the minimum zone criterion with an adaptive number of subpopulations. The method utilizes the global optimal solution and the subpopulations’ optimal solution to guide the search, initializes the subpopulations through clustering, and dynamically eliminates inferior subpopulations. Simulation experiments demonstrate that the algorithm exhibits excellent evaluation accuracy when processing simulation datasets with different sphericity errors, radii, and numbers of sampling points. The uncertainty of the results reached the order of 10−9 mm. When processing up to 6000 simulation datasets, the algorithm’s solution deviation from the ideal sphericity error remained around −3 × 10−9 mm. And the sphericity error evaluation was completed within 1 s on average. Additionally, comparison experiments further confirmed the evaluation accuracy of the algorithm. In the HSR sample measurement experiments, our algorithm improved the sphericity error assessment accuracy of the HSR’s inner and outer contour sampling datasets by 17% and 4%, compared with the results given by the coordinate measuring machine. The experiment results demonstrated that the algorithm meets the requirements of sphericity error assessment in the manufacturing process of the HSRs and has the potential to be widely used in the future.

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Indeitsev, D. A., P. P. Udalov, I. A. Popov, and A. V. Lukin. "Nonlinear Dynamics of the Hemispherical Resonator of a Rate-Integrating Gyroscope under Parametric Excitation of the Free Precession Mode." Journal of Machinery Manufacture and Reliability 51, no. 5 (2022): 386–96. http://dx.doi.org/10.3103/s1052618822040082.

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Cheng, Ruizhao, Gongliu Yang, Qingzhong Cai, Xiaodi Yi, and Yongqiang Tu. "Identification and Compensation of Detection Gain Asymmetry Errors for Hemispherical Resonant Gyroscopes in Whole-Angle Mode." Actuators 14, no. 6 (2025): 275. https://doi.org/10.3390/act14060275.

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Detection gain asymmetry error is one of the primary errors of the hemispherical resonator gyroscope (HRG) in whole-angle (WA) mode. This paper analyzes the influence of detection gain asymmetry error and its coupling error with damping and stiffness asymmetry on the performance of HRG and proposes a novel compensation method for detection gain asymmetry error. Firstly, the nonlinear error model of HRG considering the detection gain asymmetry error and its coupling error is established by using the average method. The influence of the angle-dependent scale factor error (ADS) and angle-dependent bias error (ADB) caused by the detection gain asymmetry error is analyzed by numerical simulation. Secondly, a parameter estimation algorithm based on force-to-rebalance (FTR) mode is proposed to decouple and identify the detection gain asymmetry error and damping asymmetry error. The identified parameters are used for the calibration of the HRG. Finally, the method is applied to the HRG operating in WA mode. The effectiveness of the proposed method is verified by experiments. After compensation, the bias instability is reduced from 3.6°/h to 0.6°/h, the scale factor nonlinearity is reduced from 646.57 ppm to 207.43 ppm, and the maximum pattern angle deviation is reduced from 0.6° to 0.05°.

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