Design of Inertial Class Gyroscope Resonator with Ultrahigh Quality Factor for Interplanetary Space Missions
01 Jan 2020-pp 1071-1084
TL;DR: In this article, the role of TEDD when the resonator is operating in its functional vibration mode is discussed and a sensitivity analysis of different parameters like resonator material properties, operating temperature, size, geometry, conductive metallic coating materials, multilayer coating, and coating thickness is carried out.
Abstract: High Quality factor (Q factor) resonator is a mandatory requirement for very fine resolution Hemispherical Resonator Gyroscope (HRG). It is a measure of damping. This paper discusses the role of Thermo Elastic Dynamic Damping (TEDD) when the resonator is operating in its functional vibration mode. Finite Element (FE) method is used to solve the coupled thermal and mechanical equations. A sensitive analysis of the effect of different parameters like resonator material properties, operating temperature, size, geometry, conductive metallic coating materials, multilayer coating, and coating thickness is carried out. The uniqueness of the present work is the sensitivity study of ultrathin coating (volume fraction of 0.01%), multilayer coating, and different partial coating configurations. The coating can reduce Q factor by orders compared to uncoated shell. It is found that the coating material selection and the coating configuration are very important factors and a Q factor of 5.5 × 106 in the final optimum coating configuration is achieved.
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01 Mar 2000
Abstract: The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer- and nanometer-scale electromechanical systems. The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener’s well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.
106 citations
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).
10 citations
TL;DR: In this paper, the authors presented a high reliable hemispherical resonator gyroscope (HRG) with a solution of an oven control system, and the experimental verification results illustrate a comprehensive improvement for the HRG.
Abstract: This work presents a high reliable hemispherical resonator gyroscope (HRG) with a solution of an oven control system. The dynamics and thermal characteristics are firstly analyzed with a indication that the conventional look-up table (LUT) method can not fully compensate the HRG errors. The temperature cycling experiments show the hysteresis effect of the key parameters of HRG and fit the theoretical analysis. Then an advanced oven control approach is proposed to solve the challenges with optimized mechanical isolation, sensing and actuation electronics. The experimental verification results illustrate a comprehensive improvement for the HRG. Particularly, the bias instability (BI) is one order of magnitude better than uncompensated HRG that reaches a sub 0.001°/hr level. The daily bias and scale factor repeatability is $6\times $ and $3\times $ improved with a 1 week measurement, respectively. It also shows an excellent robustness to the environmental variation by doing a temperature cycling test. The bias level error of the uncompensated system is improved by $40\times $ , and the scale factor stability can be also increased up to $19\times $ . The BI and rate random walk (RRW) are all significantly enhanced to show a good environmental adaptability of the proposed ovenized HRG.
5 citations
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.
5 citations
TL;DR: In this paper, the authors carried out a detailed study of the effect of thin film coating and different coating configurations on the performance of Hemispherical Resonator Gyroscopes (HRG).
1 citations
References
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TL;DR: In this paper, the importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer-and nanometer-scale electromechanical systems.
Abstract: The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer- and nanometer-scale electromechanical systems. The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener’s well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.
1,028 citations
TL;DR: In this article, several techniques for calculating the mechanical-thermal noise in acoustic and vibration sensors in general, and in micromachined sensors in particular, are reviewed and compared.
Abstract: The small moving parts in acoustic and vibration microsensors are especially susceptible to mechanical noise resulting from molecular agitation. For sensors designed for small-signal applications, this mechanical-thermal noise is often one of the limiting noise components. Several techniques for calculating the mechanical-thermal noise in acoustic and vibration sensors in general, and in micromachined sensors in particular, are reviewed. >
783 citations
TL;DR: In this article, the internal friction associated with this hybrid type of vibration is calculated from thermodynamical considerations, and it is predicted that the internal interferences are of a larger order of magnitude than that due to all other causes.
Abstract: In a vibrating reed opposite sides have dilations of opposite signs. Thus when one side is heated the other is cooled. At low frequencies the vibrations are isothermal. At high frequencies they are adiabatic. At intermediate frequencies they are of a hybrid type accompanied by internal friction. In this paper this internal friction is calculated solely from thermodynamical considerations. It is predicted that the internal friction associated with this hybrid type of vibration is of a larger order of magnitude than that due to all other causes.
762 citations
TL;DR: In this article, measurements of the mechanical quality factor Q for arrays of silicon-nitride, polysilicon, and single-crystal silicon cantilevers have been obtained by studying the dependence of Q on cantilever material, geometry, and surface treatments.
Abstract: Micromechanical cantilevers are commonly used for detection of small forces in microelectromechanical sensors (e.g., accelerometers) and in scientific instruments (e.g., atomic force microscopes). A fundamental limit to the detection of small forces is imposed by thermomechanical noise, the mechanical analog of Johnson noise, which is governed by dissipation of mechanical energy. This paper reports on measurements of the mechanical quality factor Q for arrays of silicon-nitride, polysilicon, and single-crystal silicon cantilevers. By studying the dependence of Q on cantilever material, geometry, and surface treatments, significant insight into dissipation mechanisms has been obtained. For submicron-thick cantilevers, Q is found to decrease with decreasing cantilever thickness, indicating surface loss mechanisms. For single-crystal silicon cantilevers, significant increase in room temperature Q is obtained after 700/spl deg/C heat treatment in either N/sub 2/ Or forming gas. At low temperatures, silicon cantilevers exhibit a minimum in Q at approximately 135 K, possibly due to a surface-related relaxation process. Thermoelastic dissipation is not a factor for submicron-thick cantilevers, but is shown to be significant for silicon-nitride cantilevers as thin as 2.3 /spl mu/m.
684 citations
TL;DR: In this paper, the generalized thermoelastic theory with one relaxation time was used to analyze the micro-beam damping of a single-beam resonator, and the results showed that the amplitude of deflection and thermal moment are attenuated and the vibration frequency is increased with thermo-elastic coupling effect.
207 citations