Hemispherical Resonator Gyro Research Articles

4.11-million Q-factor whole-angle MEMS hemispherical resonator gyroscope with 0.013°/h bias instability

Abstract The MEMS μHRG offers high potential in achieving a high quality factor (Q-factor) and the corresponding detection accuracy, thus holding significant prospects for applications in the field of high-precision inertial measurement. This paper introduces a whole-angle (WA) mode MEMS hemispherical resonator gyroscope (WA-μHRG) with a high Q-factor (4.11 million) and presents a WA mode control scheme. Specifically, the paper establishes a frequency tuning technique that leverages precession angle control and quadrature control loop switching. Adjusting the quadrature control loop at special precession angles can effectively achieve alignment of the stiffness axis and reduction of frequency split. The impacts of frequency mismatch on the WA gyroscope were investigated through simulations, which validated the efficacy of mode matching in improving the accuracy and performance of gyro, as evidenced by the reduction in angle-dependent bias (ADB) drift. Experimental results demonstrate that this method can reduce the frequency difference from initial 110 mHz to 3.91 mHz. In the presence of mode matching, the ADBs drift dropped by 81.39%, from 2.586°s−1 to 0.481°s−1. Ultimately, the WA-μHRG exhibits an angular gain of 0.695, a bandwidth of 12 Hz, and a measurement range of ±500°s−1. More importantly, the gyro achieves a bias instability of 0.013°h−1.

Identification and compensation method for unbalance error in signal detection chain of Rate-Integrating hemispherical resonator gyro

In this work, a notable effective method is proposed to actualize the identification and compensation for unbalance error in signal detection chain of Rate-Integrating Hemispherical Resonator Gyro (RI-HRG). RI-HRG has excellent dynamic performance and measuring range, which has been verified in multiple field applications. Firstly, the unbalance error model is established with equivalent electrode-misalignment-angle and equivalent relative-chain-gain-deviation, considering about the effect of the inevitable signal coupling, assembly error and electronic components parameter inconsistency error. Then, a high-efficient and high-accuracy identification method is proposed based on the parameter estimation of the free vibration signal envelope, by which the adverse effect of gyro circumferential asymmetry is effectively suppressed. Finally, the compensation method based on feedforward gain controller is designed and implemented with digital control circuit. The experimental results show that the zero bias stability of RI-HRG is improved from 1.0461°/h to 0.0494°/h, which strongly prove the effectiveness of the proposed methods.

Experimental studies on dynamic response of piezoelectric based hemispherical resonator gyroscope

Experimental studies on dynamic response of piezoelectric based hemispherical resonator gyroscope

Achieving Sub-5-mHz Frequency Split Trimming of Micro Hemispherical Resonator Gyroscope With Method of Mass–Stiffness Decoupling

Achieving Sub-5-mHz Frequency Split Trimming of Micro Hemispherical Resonator Gyroscope With Method of Mass–Stiffness Decoupling

Identification and Compensation Method of Unbalanced Error in Driving Chain for Rate-Integrating Hemispherical Resonator Gyro.

The accuracy of the signal within a driving chain for the rate-integrating hemispherical resonator gyro (RI-HRG) plays a crucial role in the overall performance of the gyro. In this paper, a notable and effective method is proposed to realize the identification and compensation of the unbalanced error in the driving chain for the RI-HRG that improved the performance of the multi-loop control applied in the RI-HRG. Firstly, the assembly inclination and eccentricity error of the hemispherical resonator, the inconsistent metal conductive film layer resistance error of the resonator, the coupling error of the driving chain, and the parameter inconsistency error of the circuit components were considered, and the impact of these errors on the multi-loop control applied in the RI-HRG were analyzed. On this basis, the impact was further summarized as the unbalanced error in the driving chain, which included the unbalanced gain error, equivalent misalignment angle, and unbalanced equivalent misalignment angle error. Then, a model between the unbalanced error in the driving chain and a non-ideal precession angular rate was established, which was applicable to both single channel asynchronous control and dual channel synchronous control of the RI-HRG. Further, an unbalanced error identification and compensation method is proposed by utilizing the RI-HRG output with the virtual precession control. Finally, the effectiveness of the proposed method was verified through simulation and experiments in kind. After error compensation, the zero-bias instability of the RI-HRG was improved from 3.0950°/h to 0.0511°/h. The results of experiments in kind demonstrated that the proposed method can effectively suppress the non-ideal angular rate output caused by the unbalanced error in the driving chain for the RI-HRG, thereby further improving the overall performance of the RI-HRG.

High-precision identification and compensation of nonlinear error in hemispherical resonator gyro

This paper presents a novel nonlinear error identification and compensation method for the Hemispherical Resonator Gyro (HRG) from the signal processing perspective. Firstly, the paper establishes an HRG nonlinear error model that reveals the quantitative correlation between angle measurement error and the amplitude-gap ratio. Subsequently, a dynamic analysis model for gyro drift is developed using nonlinear motion equations. Based on this, a scalar factor nonlinear identification model encompassing assembly and nonlinear errors is proposed. Nonlinear optimization is then used to identify error parameters accurately. Finally, a joint compensation method is devised to mitigate assembly and nonlinear error issues. Empirical findings provide concrete validation for the precision of the identification and compensation method. The experimental results demonstrate that reductions of 97%, 89%, and 40% after the joint compensation are achieved in the fourth harmonic component, scale factor nonlinearity, and bias instability of the gyro, respectively.

A rate hemispherical resonator gyroscope with bias stability of 0.0056°/h with compensation of phase delay

This paper demonstrated a high accuracy rate hemispherical resonator gyroscope (HRG) with compensation of the phase delay induced by the front-end amplifier and the digital control circuit. Due to the existence of the phase delay, the output of the gyroscope is affected not only by the damping mismatch, but also by the frequency split of the resonator gyroscope, which is the main cause of the bias drift and the scale factor nonlinearity of rate resonator gyroscopes. Based on the results of theoretical analysis, a novel calibration method for the phase delay was proposed by monitoring the scale factor of the quadrature control loop. Detailed experimental results show that with phase delay compensation, the bias instability (BI) was improved from 0.0089°/h to 0.0027°/h, the angle random walk (ARW) was improved from 0.0047°/√h to 0.003°/√h, and the scale factor nonlinearity was decreased by 93.8 % from 734.8 ppm to 45.1 ppm. Measurement of one rate HRG after phase compensation at room temperature with duration of 7 hours shows a bias stability of better than 0.00658°/h and a bias repeatability of 0.0053°/h. The results show that the rate HRG with accurate phase delay compensation can achieve excellent accuracy and repeatability in long-time operation.

Frequency mismatch analysis of hemispherical shell resonators with both radius and thickness imperfections

The hemispherical shell resonator (HSR) is the core element of the hemispherical resonator gyroscope (HRG), and its frequency mismatch is a key property influencing gyroscope accuracy. Investigating the mechanism of frequency mismatch is vital for improving the quality of HSRs and performance of HRGs. Midsurface radius imperfections and thickness imperfections are two principal causes of frequency mismatch, but their combined effects have rarely been discussed. This paper develops a model to comprehensively analyze the frequency mismatch of HSRs with both radius and thickness imperfections. The model derives a quantitative relation between the frequency mismatch and the two imperfections, and provides principles for evaluating dominant imperfections. To validate the model, we conduct experiments on a batch of 12 HSRs with random geometric imperfections. We apply the model in calculating the theoretical frequency mismatches of these HSRs, and the results agree well with the experimental data. The experiment also confirms that for macro-HSRs, thickness imperfections have a larger impact than radius imperfections, and the frequency mismatch is approximately linear to the fourth thickness harmonic. Our research can be a useful reference for the design and fabrication of HSRs and may open new possibilities for high-precision manufacture of HRGs.

The Influence of Nonlinear High-Intensity Dynamic Processes on the Standing Wave Precession of a Non-Ideal Hemispherical Resonator.

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.

Identification Method for Assembly Pose Errors of Flat Electrode Hemispherical Resonator Gyro

Identification Method for Assembly Pose Errors of Flat Electrode Hemispherical Resonator Gyro

Separation of mass and gap errors of hemispherical resonator gyroscopes by varying bias voltage

For hemispherical resonator gyroscopes (HRGs), mass imperfections and capacitive gap nonuniformity jointly influence the frequency mismatch and degrade the gyroscope performance. However, the coupling mechanism and separation of these two errors are rarely discussed. This paper proposes, for the first time, a novel method of separating mass imperfections and gap nonuniformity of HRGs, based on a dynamics model considering both the two errors. By measuring the frequency mismatches and principal axes of stiffness at different bias voltages, the mass imperfections and gap nonuniformity can be separately obtained. The method is investigated in detail by simulation, and validated by experiment on three different HRGs. The experimental results agree well with the theoretical analysis, demonstrating the effectiveness of the model and the separation method. Our method may contribute to high-precision HRG manufacture, and can be conveniently applied to other Coriolis vibrating gyroscopes (CVGs) with electrostatic actuation.

A fusion algorithm for HRG output errors based on improved support function and MDTW

To improve the accuracy of hemispherical resonator gyro (HRG) output errors, a novel fusion algorithm is proposed based on improved support function and multi-dimensional dynamic time warping. By analyzing the temperature characteristics and big data characteristics of HRG, the eigenvectors are initially selected, and the correlation and redundancy are later removed by Kernel principal component analysis. To obtain potential relationships between different time series, an improved support function based on grey incidence analysis theory is brought in to reduce the computational complexity, and the genetic algorithm is introduced to identify the optimal parameters rather than manually setting them. To accurately quantify how similar or different a time series is compared with another, multi-dimensional dynamic time warping which utilizes Mahalanobis distance is introduced instead of dynamic time warping. Experiment results show that the proposed algorithm performs better in both accuracy and universality compared with the other three comparative methods.

Self-calibration of hemispherical resonator gyroscopes under drastic changes of ambient temperature based on mode reversal

The drift caused by temperature variation is a crucial factor limiting the bias stability of hemispherical resonator gyroscopes. In this paper, mode reversal is applied to calibrate for the temperature drift of the hemispherical resonator gyroscope in the case of drastic change of ambient temperature. The control algorithm is proposed and the self-calibration by mode reversal is theoretically analyzed. The influence of mode reversal period on calibration is investigated experimentally. The experiment is conducted in a temperature chamber with a temperature range from −10 ℃ to 40 ℃. The effect of self-calibration by mode reversal is compared under different reversal periods and different change rates of temperature. Results suggested that the bias stability after calibration can be improved by shortening the mode reversal period. When the temperature changes sharply with a change rate of 10 ℃/min, the bias stability is improved by about 30 times. The research offers a new way for hemispherical resonator gyroscope to maintain excellent performance in the environment of drastic temperature changes.

Identification and Calibration of the Detection Signal Distortion in Whole Angle Mode Hemispherical Resonator Gyro

Identification and Calibration of the Detection Signal Distortion in Whole Angle Mode Hemispherical Resonator Gyro

Optimizing HRG assembly through mathematical modeling of pose adjustment

The alignment accuracy between the hemispherical resonator and the electrode carrier directly impacts the assembly performance of the hemispherical resonator gyro. Currently, the assembly process suffers from low efficiency as well as accuracy due to its reliance on manual pose adjustment based on capacitance uniformity. To address this issue, a mathematical model is developed in the spherical coordinate system to calculate capacitance considering non-ideal poses, allowing us to analyze the effect of pose errors on capacitance. Additionally, a finite element model is established using COMSOL Multiphysics software to account for assembly pose errors and capacitance. The accuracy of the mathematical model for assembly pose errors and capacitance is validated through this approach. This research provides a theoretical basis for adjusting the assembly pose between the hemispherical resonator and electrode carrier, resulting in significant improvements in both the assembly quality and efficiency of the hemispherical resonator gyro.

Self-Excitation Enabled Decoupling, Calibration, and Compensation of Errors for Whole-Angle Hemispherical Resonator Gyroscope

Self-Excitation Enabled Decoupling, Calibration, and Compensation of Errors for Whole-Angle Hemispherical Resonator Gyroscope

Simulation and Optimization of Hemispherical Resonator's Equivalent Bottom Angle for Frequency-Splitting Suppression.

As an inertial sensor with excellent performance, the hemispherical resonator gyro is widely used in aerospace, weapon navigation and other fields due to its advantages of high precision, high reliability, and long life. Due to the uneven distributions of material properties and mass of the resonator in the circumferential direction, the frequencies of the two 4-antinodes vibration modes (operational mode) of resonator in different directions are different, which is called frequency splitting. Frequency splitting is the main error source affecting the accuracy of the hemispherical resonator gyro and must be suppressed. The frequency splitting is related to the structure of the resonator. For the planar-electrode-type hemispherical resonator gyro, in order to suppress the frequency splitting from the structure, improve the accuracy of the hemispherical resonator gyro, and determine and optimize the equivalent bottom angle parameters of the hemispherical resonator, this paper starts from the thin shell theory, and the 4-antinodes vibration mode and waveform precession model of the hemispherical resonator are researched. The effect of the equivalent bottom angle on the 4-antinodes vibration mode frequency value under different boundary conditions is theoretically analyzed and simulated. The simulation results show that the equivalent bottom angle affects the 4-antinodes vibration mode of the hemispherical resonator through radial constraints. The hemispherical resonator with mid-surface radius R=15 mm and shell thickness h=1 mm is the optimization object, and the stem diameter D and fillet radius R1 are experimental factors, with the 4-antinodes vibration mode frequency value and mass sensitivity factor as the response indexes. The central composite design is carried out to optimize the equivalent bottom angle parameters. The optimized structural parameters are: stem diameter D=7 mm, fillet radii R1=1 mm, R2=0.8 mm. The simulation results show that the 4-antinodes vibration mode frequency value is 5441.761 Hz, and the mass sensitivity factor is 3.91 Hz/mg, which meets the working and excitation requirements wonderfully. This research will provide guidance and reference for improving the accuracy of the hemispherical resonator gyro.

High-precise trimming method for micro hemispherical resonator gyroscopes based on mass-stiffness decoupling

High-precise trimming method for micro hemispherical resonator gyroscopes based on mass-stiffness decoupling

Design and Optimization of Hemispherical Resonators Based on PSO-BP and NSGA-II.

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.

A novel method of water bath heating assisted small ball-end magnetorheological polishing for hemispherical shell resonators

Hemispherical shell resonator (HSR) is the core component of hemispherical resonator gyro. It is a ψ-shaped small-bore complex component with minimum curvature radius less than 3 mm. Thus, traditional polishing methods are difficult to polish it. Small ball-end magnetorheological polishing method can polish the small components with complicated three-dimensional surface and obtain non-destructive surface. Therefore, this method is suitable for polishing HSR. However, the material removal rate of the ordinary small ball-end magnetorheological polishing is low, leading to long polishing time and low output of HSR. To solve this problem, a water bath heating assisted small ball-end magnetorheological polishing method is proposed in this research. The influence rule of processing parameters on the material removal rate is studied experimentally. A set of optimal processing parameters is obtained to maximize the material removal rate. Compared with the ordinary method, the material removal rate of the new method can be improved by 143%. Subsequently, an HSR is polished by the new method. The results show that the polishing time can be reduced by 55%, and the polished surface roughness can reach 7.7 nm. The new method has the great potential to be used in actual production to improve the polishing efficiency of HSR.