Hemispherical Resonators Research Articles

Low-Damage Trimming of Micro Hemispherical Resonators by Chemical Etching.

To enhance the performance of micro-hemispherical gyroscopes, achieving low-damage and high-surface-quality trimming is essential. This enables greater stability and reliability for the gyroscopes. Current methods for reducing frequency split often come with drawbacks such as high cost, adverse effects on the Q-factor, or surface damage. In this paper, a chemical etching trimming method is proposed to reduce frequency split in micro-hemispherical resonators. This method allows for trimming with minimal damage, while also being cost-effective and easy to implement. The theoretical basis of this method was analyzed, followed by a simulation to determine the optimal trimming range and location on the resonator. The simulated Q-factor analysis before and after trimming preliminarily validated the method's low-damage characteristics. Ultimately, the frequency split of the resonator was reduced to below 1 Hz. Additionally, test results of the Q-factor and surface quality before and after trimming further confirmed that chemical etching offers effective low-damage trimming capabilities. The proposed method holds significant potential for improving the performance of micro-hemispherical resonator gyroscopes.

Manufacturing fused silica hemispherical resonators using polymer glass suspension and replication molding

This work introduces a new method for manufacturing fused silica (FS)-based hemispherical resonators (HSRs) using a printable polymer glass mixture and replication molding. This process involves 3D printing to create the mold, followed by the casting of a photo-reactive pre-polymer glass mixture. This technique allows us to produce complex 3D geometries and offers faster production of resonators compared to other traditional methods. In this study, we manufactured three devices and successfully identified resonance modes with two (N = 2), three (N = 3) and four (N = 4) nodes/antinodes in all three HSRs, demonstrating the repeatability of our new manufacturing method. The highest quality factor of 482 k was achieved for the N = 3 resonance mode using the ring-down method. Some of the key advantages of our method include producing multiple devices efficiently with relatively good surface quality, making it a viable option for producing high-precision devices in the future. Our new fabrication technique results in a device surface roughness of ∼100 nm (measured over an area of 250 μm × 250 μm) and manufacturing yield of over 90%. Moreover, all the steps involved in this method can be completed outside of a specialized cleanroom environment.

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.

Vibrations and thermoelastic quality factors of hemispherical shells with fillets

In engineering applications, hemispherical shell resonators are typically machined with fillets to reduce stress concentration and enhance structure strength. The fillets will inevitably affect the dynamic properties and the mechanical quality factor of hemispherical shell resonators, which has been seldom investigated before. In this paper, an effective analytical method is developed to explore the free vibration and thermoelastic damping (TED) characteristics of the hemispherical shell with fillets. The fillets are characterized by the variation in the thickness of the hemispherical shell during modelling. The first-order shear deformation theory (FSDT) is used to describe the theoretical formulas of the hemispherical shell with fillets. By employing the unified Jacobi polynomials and Fourier series as the assumed mode shape functions, the equation of motion of the structure is established by Hamilton's principle and the assumed mode method. The analytical model for thermoelastic quality factor (QTED) which is determined by TED is obtained by computing the dissipated energy and the maximum elastic potential energy of the hemispherical shell with fillets. The validity and accuracy of the present method are confirmed by comparing the present solutions with the published results and those obtained from the finite element method (FEM). The influences of fillets on the vibration behaviors and QTED characteristics of the hemispherical shells are analyzed in detail. The present model can be used to optimize the design of the fillets of the hemispherical shell resonators with high quality factors.

Analysis of excitation and detection capability of hemispherical resonator based on interdigital electrodes

In this paper, a theoretical model of excitation and detection is established based on the excitation and detection method of the uncoated hemispherical resonator with interdigital electrodes, which proves the feasibility of the excitation and detection of the interdigital electrodes in principle. The simulation and analysis of its influence parameters are also carried out to provide theoretical support for the design and optimization of the interdigital electrode to realize the excitation and detection of the hemispherical resonator. Finally, the excitation and detection of uncoated hemispherical resonators by interdigital electrodes were successfully verified through experiments.

An Adaptive Multi-Population Approach for Sphericity Error Evaluation in the Manufacture of Hemispherical Shell Resonators.

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.

Dynamic modelling and quality factor evaluation of hemispherical shell resonators

A novel strategy is proposed for the dynamic modelling and quality factor evaluation of the hemispherical shell resonators (HSR) considering the coupling of hemispherical shell and support rod. The artificial spring technique is introduced to realize the coupling connection of substructures and simulate the arbitrary boundary conditions. Hamilton's principle with the Rayleigh-Ritz method is employed to establish the equation of motion of the HSR, and the natural frequencies of the HSR are obtained by solving the eigenvalue problem of the equation of motion. The thermal energy method is applied to evaluate the thermoelastic damping (TED) of the HSR. The model of anchor loss is based on a separation and transfer method, in which the HSR and its substrate are first separated for analysis and then the stress from the clamped region of the support rod is transferred to the substrate for determining the vibration displacement across the clamped region. The energy losses to the substrate are formulated as the integral of the product of the stress and the vibration displacement across the clamped region per cycle of vibration. The results calculated from the present theoretical method are compared with those from the published literature and the finite element method (FEM), which validates the correctness and feasibility of the present theoretical model. The effects of the boundary conditions and geometrical parameters on the vibration behaviors of the HSR are analyzed, and the influences of the boundary conditions, geometrical parameters and material properties of the HSR on the quality factors related to the TED and anchor loss are investigated. The present model can be used to optimize the design of the HSR with a high quality factor.

Compact 3-D Printed Bandpass Filters Using Folded Mixed Hemispherical Resonators

Compact 3-D Printed Bandpass Filters Using Folded Mixed Hemispherical Resonators

Frequency splitting of hemispherical resonators trimmed with focused ion beams

This paper studies a high-precision etching process based on focused ion beam static trimming of the defective mass of fused silica hemispherical resonators to eliminate frequency splitting. This trimming method effectively overcomes the shortcomings of inefficiency and poor robustness, and the accuracy is seriously dependent on the stability of the trimming equipment in the traditional approach based on the harmonic form of trimming. The vibration model of an imperfect hemispherical resonator is firstly established by equating structural defects into point mass defective units, revealing that the frequency splitting is a function of the size of the equivalent defect mass and that the angular position of the stiffness axis is determined by the spatial distribution of the defect mass, which further elucidates that the frequency splitting of the resonator is the equivalent form of the defect mass on its low-frequency axis. To validate the accuracy of the present method, a simulation model of the imperfect resonator is established, and the results show that the theoretical model is in good agreement with the finite element method. Then, a high-precision nonlinear parameter identification model containing frequency splitting and low-frequency axis azimuth parameters is established based on the standing wave oscillation effect and spectral analysis, and the frequency splitting and low-frequency axis azimuth are identified by analyzing the vibration function of the hemispherical resonator. Finally, based on the parameter identification results and the ion beam removal function analysis, an ion beam trimming process is designed to eliminate frequency splitting by trimming the defective mass on the low-frequency axis. The results show that the frequency splitting after mass trimming is better than 0.001 Hz, significantly improving the hemispherical resonator's performance.

Surface evolution of fused silica hemispherical resonators and its influence on the quality factor

Investigating the surface loss mechanism of hemispherical resonators is essential to further improve the performance of hemispherical resonant gyroscopes. Although many studies have focused on the surface loss mechanism and surface treatment process of fused silica hemispherical resonators, the bulk fabrication of high-quality factor (Q factor) hemispherical resonators is still a significant factor limiting the widely applied hemispherical resonant gyroscopes. To address this practical need, this paper first analyzes the formation mechanism of surface defects and their effect on energy loss. Then, a cyclic chemical etching method using hydrofluoric acid as an etchant is proposed to significantly improve the Q factor of the hemispherical resonator by improving the surface morphology. Finally, a surface loss model was developed based on the experimental results to reveal the mechanism of the effect of surface morphology evolution on the change of the quality factor of the hemispherical resonator. The results show that the developed etching method can significantly improve surface quality with minimal damage to the substrate. The resonator’s Q factor increases to a final value of about 2 × 107 after chemical etching, which is improved by about 20 times. The developed loss model can screen hemispherical resonators with different performances according to the change of the Q factor during the etching process. The etching technique and screening method developed in this paper is essential for bulk fabricating high-quality factor hemispherical resonators.

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.

Автоматизация технологического процесса балансировки кварцевых резонаторов твердотельных волновых гироскопов

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.

Optimization of structural and technological modes of operation of the microwave wax melter

Introduction. The research is aimed at substantiating the optimal design and technological parameters and operating modes of the microwave installation being developed, designed to implement the process of processing wax raw materials with preliminary separation and preservation of honey fraction contained therein.Methodology. The effective modes of heat treatment of apiary raw materials in a microwave wax melter were determined through regression models obtained during the implementation of the matrix of threefactor active planning of a multifactorial experiment.Results. The main factors influencing the process of heat treatment of the sail are revealed: the specific power of microwave energy generators, the duration of exposure to the electromagnetic field of super high frequency, the humidity of the feedstock. The expediency of implementing microwave technology for processing wax raw materials in a two-module installation containing hemispherical resonators to ensure continuous operation in compliance with electromagnetic safety, as well as control of technological parameters is proved.

COMPARATIVE EVALUATION OF THE STRUCTURAL DESIGN OF MICROWAVE CONVECTIVE HOP DRYERS

In hop production, the main scientific problem is the low energy efficiency of hop dryers with convective heat supply and the absence of small-sized mobile continuous-flow hop dryers for farms that ensure the preservation of the consumer properties of hops at reduced operating costs. In order to reduce the operating costs of drying hops, work is being carried out aimed at clarifying the drying modes that contribute to the best preservation of consumer characteristics, and the improvement of technologies and technical means that would reduce operating costs. A new method of drying hops by ultra-high-frequency energy supply deserves attention. (Research purpose) The research purpose is revealing the effectiveness of an ultrahigh-frequency convective hop dryer of continuous-flow action by evaluating the developed structural designs of hop dryers with metal-dielectric resonators that ensure uniform drying and disinfection of freshly harvested hops and electromagnetic safety without a shielding housing at reduced operating costs in the conditions of hop farms. (Materials and methods) Carried out three-dimensional modeling of the structural designs of hop dryers in the Compass 20 program, determined the electrodynamic parameters of the ”generator-resonator“ system in CST Microwave Studio. (Results and discussion) Solved the problem of optimizing the structural design and dimensions of metal-electric resonators. It was shown that the main criteria are the correctly agreed parameters of the electrodynamic system ”generator-resonator“: the intrinsic Q-factor of the resonator, the voltage of the electric field, its uniformity of distribution, the power of the radiation flux, the volume of the resonator. The electro-dynamic parameters of 11 hop dryers with different designs of resonators were analyzed: hemispherical, semi-cylindrical, cylindrical, toroidal, prismatic, ellipsoid and others. (Conclusions) It was found that toroidal and hemispherical resonators have a maximum intrinsic Q-factor of up to 8000. It was determined during the evaluation of deviations from the average value of the intervals of variation of the criteria that hop dryers with resonators in the form of a paraboloid and hyperboloid, and semi-cylindrical, are effective.

On-Machine Measurement of Profile and Concentricity for Ultra-Precision Grinding of Hemispherical Shells.

The profile and concentricity of hemispherical shells affect the frequency split and quality factor of hemispherical resonators. To compensate for machining errors caused by tool wear and tool setting, an on-machine measurement (OMM) method for the profile and concentricity of hemispherical shells in ultra-precision grinding was developed without the removal of workpieces from the machine tool. The OMM utilizes an inductive lever probe to test the inner and outer surfaces of the shell. A standard sphere is utilized to calibrate the relative position of the inductive lever probe at the two different work positions. To enhance the test accuracy of the OMM, a zero-position trigger-sampling method for the inductive lever probe was developed. It was verified to achieve a stable repeatability accuracy of 0.04 μm when using the OMM to realize a single-point sampling. Hemispherical shells were tested using the proposed OMM method. The concentricity test’s accuracy was verified to achieve accuracy better than 1 μm using a coordinate measuring machine and a standard sphere. The accuracy was 0.26 μm for testing the profiles of the hemispherical shell. The proposed OMM system was integrated with an ultra-precision machine tool. It is hoped that this method can help realize the integration function of machining-measurement-compensation.

Recent Advances in MEMS-Based 3D Hemispherical Resonator Gyroscope (HRG)-A Sensor of Choice.

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.

Scanning measurement of surface error and thickness variation of the hemispherical resonator.

Hemispherical resonant gyroscopes (HRGs) are solid-state vibration gyroscopes with the highest precision and are widely used in the aerospace field. The core part of the gyroscope is the resonator, which is a thin-walled hemispherical shell. Surface error and thickness variation of a hemispherical shell causes frequency splitting, which degrades the performance of the HRG. In order to guide the mass leveling of hemispherical resonator, this paper presents a new method for scanning measurement of the surface error and thickness variation of hemispherical resonators. First, a multi-axis platform is designed for noncontact sensor scanning measurements along the meridian and latitudinal lines of the hemispherical resonator. Second, the error model of the measurement system is established. The surface error of the standard sphere is measured to calibrate and compensate for the assembly errors of the measuring device. In addition, the identification accuracy of assembly errors and the influence of assembly errors on thickness measurement are simulated by a computer. Finally, the surface error and thickness variation of the hemispherical resonators are measured. The method is experimentally demonstrated and validated with a wavefront interferometry test. The results show that the method can achieve high precision and high repeatability, which is instructive for assessment of the machining error and further evaluation of the hemispherical resonator.

Geometric Error Analysis and Compensation in Spherical Generating Grinding of Hemispherical Shell Resonators.

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.

Fused silica cylindrical shell resonators with 25 million Q factors

The Q factors of fused silica cylindrical shell resonators reaching 25 million is reported. The finite element method is employed to analyze the anchor loss and chemical etching is used to reduce the surface loss of cylindrical resonators. Two resonators with the same processing parameters are etched for 13 rounds with each round set as 5 min. After each round of chemical etching, the surface roughness, Q factors and resonant frequencies of the two resonators are measured. The Q factors of the two cylindrical resonators have both exceeded 25 million, reaching the level of that of fused silica hemispherical resonators. Results also indicate that the Q factors of fused silica cylindrical resonators are not related with their surface roughness. This study shows the potential of the cylindrical resonator gyroscope to achieve the same degree of precision as the hemispherical resonator gyroscope, which has presented outstanding performances.