Effect of geometric imperfections on anchor loss and characterisation of a gyroscope resonator with high quality factor
TL;DR: A detailed parametric study of dimensions and shell imperfections due to fabrication is carried out in this paper, where a sensitivity study of the effect of shell mean radius, shell thickness, stem radius, stem height on the Qanchor was carried out.
Abstract: 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, excitation-induced 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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30 May 2022
TL;DR: In this article , the authors studied the dynamics of the wave solid-state gyroscope operating in the compensation mode of the angular velocity sensor and derived a mathematical model of the thin elastic ring resonator dynamics.
Abstract: The dynamics of the wave solid-state gyroscope operating in the compensation mode of the angular velocity sensor is studied. Frequency difference and quality factor difference are taken into account in the new mathematical model of the thin elastic ring resonator dynamics. The formulas that make it possible to analyze the impact of various gyroscope parameters on the gyroscope scale factor are obtained. A numerical example is given.
1 citations
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TL;DR: In this article, the effects of various design to operational parameters on the resonator quality factor (Q-factor) for different configurations, sizes and materials are reviewed in detail, and a roadmap on future research requirements for developing compact mass producible CVG type sensors with ultrahigh Q-factor is also highlighted.
Abstract: 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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TL;DR: In this paper , an error parameters identification method based on nonlinear optimization is proposed to realize the synchronous identification of the two channels' gain ratio and misalignment angle, and a signal demodulation compensation scheme is designed to compensate the error parameters.
Abstract: The hemispherical resonator and the electrode base are prone to tilt and eccentricity during the assembly process, which greatly restricts the working accuracy of gyro. In order to reduce this impact, the influence of the resonator assembly error on gyro drift under different electrode configuration schemes is analyzed. Secondly, an error parameters identification method based on nonlinear optimization is proposed, which can realize the synchronous identification of the two channels' gain ratio and misalignment angle. Finally, a signal demodulation compensation scheme is designed to compensate the error parameters. The experimental results show that after the feedforward compensation, the angular rate oscillation amplitude under dynamic conditions is reduced by two orders of magnitude, and the bias stability of gyro output is improved by 5 times.
1 citations
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TL;DR: In this article, the effect of material properties, operating temperature and dimensions on the performance parameters of a high quality factor (Q-factor) mechanical resonator was discussed. And the role of thermoelastic damping (TED) on effective Q-factor was discussed and the sensitivity analysis of ultra thin film coating (volume fraction of 0.01%), coating variations and different coating configurations was carried out.
Abstract: 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 hs 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.
1 citations
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TL;DR: Parkhomey, Parkhomey et al. as mentioned in this paper , Juliy Boiko, Irina Zeniv, and Taras Bondarenko Department of Software Engineering, National Aviation University, Kyiv, Ukraine Department of Telecommunications, Media and Intelligent Technologies, Khmelnytskyi National University, Karpathy et al., 2014.
Abstract: Igor Parkhomey, Juliy Boiko, Irina Zeniv, Taras Bondarenko Department of Software Engineering, National Aviation University, Kyiv, Ukraine Department of Telecommunications, Media and Intelligent Technologies, Khmelnytskyi National University, Khmelnytskyi, Ukraine Department of Information Systems and Technologies, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine Department of Telecommunications Systems and Networks, State University of Telecommunications, Kyiv, Ukraine
References
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TL;DR: The keynote paper reviews the state-of-the-art regarding applied grinding tools, ultra-precision machine tools and grinding processes for electronic and optical industries as well as for astronomical applications.
Abstract: Ultra-precision grinding is primarily used to generate high quality and functional parts usually made from hard and difficult to machine materials. The objective of ultra-precision grinding is to generate parts with high surface finish, high form accuracy and surface integrity for the electronic and optical industries as well as for astronomical applications. This keynote paper introduces general aspects of ultra-precision grinding techniques and point out the essential features of ultra-precision grinding. In particular, the keynote paper reviews the state-of-the-art regarding applied grinding tools, ultra-precision machine tools and grinding processes. Finally, selected examples of advanced ultra-precision grinding processes are presented.
359 citations
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TL;DR: In this article, the authors presented an analytical model for support loss in clamped-free (C-F) and clampedclamped (C -C) micromachined beam resonators with in-plane flexural vibrations.
Abstract: This paper presents an analytical model for support loss in clamped–free (C–F) and clamped–clamped (C–C) micromachined beam resonators with in-plane flexural vibrations. In this model, the flexural vibration of a beam resonator is described using the beam theory. An elastic wave excited by the shear stress of the beam resonator and propagating in the support structure is described through the 2D elastic wave theory, with the assumption that the beam thickness (h) is much smaller than the transverse elastic wavelength (λT). Through the combination of these two theories and the Fourier transform, closed-form expressions for support loss in C–F and C–C beam resonators are obtained. Specifically, closed-form expression for the support loss in a C–C beam resonator is derived for the first time. The model suggests lower support quality factor (Qsupport) for higher order resonant modes compared to the fundamental mode of a beam resonator. Through comparison with experimental data, the validity of the presented analytical model is demonstrated. © 2003 Elsevier B.V. All rights reserved.
346 citations
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TL;DR: In this paper, the anchor loss is computed using an absorbing boundary based on a perfectly matched layer (PML) which absorbs incoming waves over a wide frequency range for any nonzero angle of incidence.
Abstract: Electromechanical resonators and filters, such as quartz, ceramic, and surface-acoustic wave devices, are important signal-processing elements in communication systems. Over the past decade, there has been substantial progress in developing new types of miniaturized electromechanical resonators using microfabrication processes. For these micro-resonators to be viable they must have high and predictable quality factors (Q). Depending on scale and geometry, the energy losses that lower Q may come from material damping, thermoelastic damping, air damping, or radiation of elastic waves from an anchor. Of these factors, anchor losses are the least understood because such losses are due to a complex radiation phenomena in a semi-infinite elastic half-space. Here, we describe how anchor losses can be accurately computed using an absorbing boundary based on a perfectly matched layer (PML) which absorbs incoming waves over a wide frequency range for any non-zero angle of incidence. We exploit the interpretation of the PML as a complex-valued change of co-ordinates to illustrate how one can come to a simpler finite element implementation than was given in its original presentations. We also examine the convergence and accuracy of the method, and give guidelines for how to choose the parameters effectively. As an example application, we compute the anchor loss in a micro disk resonator and compare it to experimental data. Our analysis illustrates a surprising mode-mixing phenomenon which can substantially affect the quality of resonance.
148 citations
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TL;DR: In this article, the authors investigated the ultrasonic abrasion of different workpiece materials - alumina, zirconia, quartz, glass, ferrite and LiF - by using a stationary ultrasonic machine.
Abstract: Precision abrasive processes are commonly employed to machine glasses, single crystals and ceramic materials for various industrial applications. Until now, precision machining of hard and brittle solids are poorly investigated in Brazil from the fundamental and applied point of views. Taking into account the major technological importance of this subject to the production of functional and structural components used in high performance systems, the present study investigated the ultrasonic abrasion of different workpiece materials - alumina, zirconia, quartz, glass, ferrite and LiF - by using a stationary ultrasonic machine. Experiments were conducted using a rectangular shaped cutting toll and SiC particles with mean grain size of 15mm. The machined surfaces were characterized by surface profilometry and scanning electron microscopy. In the case of alumina, zirconia and quartz, the rates of material removal decrease with the depth of machining. The rate of material removal remained constant for the others materials. The micrographs showed that brittle microcracking was the primary mechanism involved with material removal. The rates of material removal and the machined surface topographies were discussed as a function of intrinsic stiffness, hardness and fracture toughness of workpiece materials.
66 citations
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TL;DR: In this article, the authors present an overview of recent advances in damping from the viewpoint of device design and discuss strategies for minimizing each source using a combination of models for dissipation and measurements of material properties, and formulate design principles for low-loss micromechanical and nanomechanical resonators.
Abstract: Damping is a critical design parameter for miniaturized mechanical resonators used in microelectromechanical systems (MEMS), nanoelectromechanical systems (NEMS), optomechanical systems, and atomic force microscopy for a large and diverse set of applications ranging from sensing, timing, and signal processing to precision measurements for fundamental studies of materials science and quantum mechanics. This paper presents an overview of recent advances in damping from the viewpoint of device design. The primary goal is to collect and organize methods, tools, and techniques for the rational and effective control of linear damping in miniaturized mechanical resonators. After reviewing some fundamental links between dynamics and dissipation for systems with small linear damping, we explore the space of design and operating parameters for micromechanical and nanomechanical resonators; classify the mechanisms of dissipation into fluid–structure interactions (viscous damping, squeezed-film damping, and acoustic radiation), boundary damping (stress-wave radiation, microsliding, and viscoelasticity), and material damping (thermoelastic damping, dissipation mediated by phonons and electrons, and internal friction due to crystallographic defects); discuss strategies for minimizing each source using a combination of models for dissipation and measurements of material properties; and formulate design principles for low-loss micromechanical and nanomechanical resonators.
48 citations
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