Avoidance of Internal Resonances in Hemispherical Resonator Assemblies from Fused Quartz Connected by Indium Solder

Sergii A. Sarapuloff(세르게이 사라플로프),Huinam Rhee(이희남),Sang-Jin Par(박상진) 한국소음진동공학회 2013 한국소음진동공학회 학술대회논문집 Vol.2013 No.4

Modern solid-state gyroscopes (HRG) with hemispherical resonators from high-purity quartz glass and special surface superfinishing and ultrathin gold coating become the best instruments for precise-grade inertial reference units (IRU) targeting long-term space missions. Designing of these sensors could be a notable contribution into development of Korea as a space nation. In participial, 40mm diameter thin-shell resonator from high-purity fused quartz, fabricated as a single-piece with its supporting stem has been designed, machined, etched, tuned, tested, and delivered by STM Co. (ATS of Ukraine) several years ago; an extremely-high Q-factor (upto 10~20 millions) has been shown. Understanding of the best way how to match such a unique sensor with inner glass assembly of the gyro means how to use the high potential in a maximal extent; and this has become the urgent task. Inner quartz glass assembly has a very thin indium (In) layer soldered the resonator and its silica base (case), but effects of internal resonances between operational modal pair of the shell-cup and its side (parasitic) modes can notable degrade the potential of the sensor as a whole, instead of so low level of resonator’s intrinsic losses. Unfortunately, there are special combinations of dimensions of the parts (so-called, “resonant sizes”), when intensive losses of energy occurs. The authors proposed to use the length of stem’s fixture as an additional design parameter to avoid such cases. So-called, a cyclic scheme of finite element method (FEM) and ANSYS software were employed to estimate different combinations of gyro assembly parameters. This variant has no mismatches of numerical origin due to FEM’s discrete mesh. The optimum length and dangerous “resonant lengths” have been found. The special attention has been paid to analyses of 3D effects in a cup-stem transient zone, including determination of a difference between the positions of geometrical Pole of the resonant hemisphere and of its “dynamical Pole”, i.e., its real zone of oscillation node. Boundary effects between the shell (cup) and 3D short “beams” (inner and outer stems) have been ranged. The results of the numerical experiments have been compared with the classic model of a quasi-hemispherical shell band with inextensional midsurface, and the solution using Rayleigh’s functions of the 1<SUP>st</SUP> and 2<SUP>nd</SUP> kinds. To guarantee the truth of the recommended sizes to a designer of the real device, the analytical and FEM results have been compared with experimental data for a party of real resonators. The consistency of the results obtained by different means has been shown with errors less than 5%. The results notably differ from the data published earlier by different researchers.

Polarization Precession Effects for Shear Elastic Waves in Rotated Solids

Sergii A.Sarapuloff(세르게이 사라플로프) 한국소음진동공학회 2013 한국소음진동공학회 학술대회논문집 Vol.2013 No.4

Developments of Solid-State Gyroscopy during last decades are impressive and were based on thin-walled shell resonators like HRG or CRG made from fused quartz or leuko-sapphire. However, a number of design choices for inertial-grade gyroscopes, which can be used for high-g applications and for mass- or middle- scale production, is still very limited. So, considerations of fundamental physical effects in solids that can be used for development of a miniature, completely solid-state, and lower-cost sensor look urgent. There is a variety of different types of bulk acoustic (elastic) waves (BAW) in anisotropic solids. Shear waves with different variants of their polarization have to be studied especially carefully, because shear sounds in glasses and crystals are sensitive to a turn of the solid as a whole, and, so, they can be used for development of gyroscopic sensors. For an isotropic medium (for a glass or a fine polycrystalline body), classic Lame’s theorem (so-called, a general solution of Elasticity Theory or Green-Lame’s representation) has been modified for enough general case: an elastic medium rotated about an arbitrary set of axes. Travelling, standing, and mixed shear waves propagating in an infinite isotopic medium (or between a pair of parallel reflecting surfaces) have been considered too. An analogy with classic Foucault’s pendulum has been underlined for the effect of a turn of a polarizational plane (i.e., an integration effect for an input angular rate) due to a medium’s turn about the axis of the wave propagation. These cases demonstrate a whole-angle regime of gyroscopic operation. Single-crystals are anisotropic media, and, therefore, to reflect influence of the crystal’s rotation, classic Christoffel-Green’s tensors have been modified. Cases of acoustic axes corresponding to equal velocities for a pair of the pure-transverse (shear) waves have of an evident applied interest. For such a special direction in a crystal, different polarizations of waves are possible, and the gyroscopic effect of “polarizational precession” can be observed like for a glass. Naturally, formation of a wave pattern in a massive elastic body is much more complex due to reflections from its boundaries. Some of these complexities can be eliminated. However, a non-homogeneity has a fundamental nature for any amorphous medium due to its thermodynamically-unstable micro-structure, having fluctuations of the rapidly-frozen liquid. For single-crystalline structures, blockness (walls of dislocations) plays a similar role. Physical nature and kinematic particularities of several typical “drifts” in polarizational BAW gyros (P-BAW) have been considered briefly too. They include irregular precessions (“polarizational beats”) due to: nonhomogeneity of mass density and elastic moduli, dissymmetry of intrinsic losses, and an angular mismatch between propagation and acoustic axes.

Bryan’s Factor of a Hemispherical Resonator due to Coriolis Effect

Huinam Rhee(이희남),Sangjin Park(박상진),Sergii A. Sarapuloff(세르게이 사라플로프),Sunu Han(한순우),Jinho Park(박진호) 한국소음진동공학회 2014 한국소음진동공학회 학술대회논문집 Vol.2014 No.10

세차계수는 플랫폼의 각속도 혹은 회전각에 대한 공진기에 형성되는 탄성 정상파의 각속도 혹은 회전각의 비율로 정의된다. 본 논문에서는 코리올리 효과에 의한 반구형 공진기의 세차계수에 대한 연구를 레일리-리츠법과 라그랑지안 역학을 이용하여 수행하였으며 쉘의 중립면이 레일리 모드 변형을 한다는 조건을 적용하였고 계산 결과를 이전 연구자들의 결과들과 비교하였다. Precession coefficient is defined by the ratio of the angular rate or rotational angle of the standing wave formed in an elastic resonator with respect to that of the platform. In this paper the precession of a hemispherical resonator due to Coriolis’ effect is studied through Rayleigh-Ritz’s method and Lagrangian Mechanics when the resonator undergoes Rayleigh’s mode deformation. The calculation result was compared with studies by other researchers.

Mid-Surface Inextensibility of a Cylindrical Resonator for Various Boundary Conditions

Sanjin Park,Huinam Rhee,Sergii A. Sarapuloff,Soon Woo Han,Jin Ho Park 대한기계학회 2014 대한기계학회 춘추학술대회 Vol.2014 No.11

The resonator of a Cylindrical Resonator Gyroscope (CRG) is a cantilevered thin shell structure which is designed based on inextensible eigenmodes. Often an assumed mode method is used to obtain the operational frequencies analytically and to predict Bryan’s Factor due to Coriolis’ effect. Because the real boundary condition for the cylindrical resonator is not exactly known, kinematically admissible modes are usually assumed. However their boundary conditions may contradict the inextensibility, especially near the boundary. This paper deals with the study on the inextensibility of the mid-surface of a cylindrical resonator for various boundary conditions. Under an inextensibility constraint, the mathematical expressions of eigenfrequency for different boundary conditions have been obtained through Rayleigh-Ritz’ method and Lagrangian Mechanics. In order to observe the contradiction of the boundary condition with the inextensibility, the strain distribution on the mid-surface has been checked using the finite element analysis. The results of this study signify the necessity of knowing the correct boundary conditions to predict the performance of the CRG.

Analysis of the Thermo-Elastic Damping of a Beam-Type Resonator

Huinam Rhee(이희남),Junsung Park(박준성),Sergii A. Sarapuloff(세르게이 사라플로프),Soon Woo Han(한순우),Jin Ho Park(박진호) 한국소음진동공학회 2014 한국소음진동공학회 학술대회논문집 Vol.2014 No.10

This paper deals with the thermo-elastic damping (TED) due to the temperature change in a beam when it is in a resonant condition. Based on previous references, the analytical formulation for TED of a resonant thin beam was derived, and then TED was expressed as a function of the geometry of the beam, especially, its thickness. It was clearly shown that TED of a resonant beam is significantly varied for different thickness. Finally, the worst thickness of the beam has been identified in regard to the high-Q factor, and the result was compared to the finite element analysis.

Analysis of Thermo-Elastic Damping of a Ring-Type Resonator

Huinam Rhee,Sergii A. Sarapuloff,J-S Park,Soon Woo Han,Jin Ho Park 대한기계학회 2014 대한기계학회 춘추학술대회 Vol.2014 No.11

The ring-type resonator can be used for the Coriolis’ Vibratory Gyroscopes (CVG). In order to have a high Q-factor the resonator should be designed to achieve as low damping as possible. Among various damping mechanisms, in this paper, the thermo-elastic phenomenon has been studied, which is related to the damping effect due to the temperature change when the resonator is oscillating. The thermo-elastic damping depends on the geometry of the resonator and on the material properties. This paper especially deals with the dependency of the thermo-elastic damping on the thickness of the ring. It is shown that through the mathematical formulation the worst thickness of the ring resonator can be analytically determined so that the worst design can be effectively avoided in regard to the high-Q factor. The multiphysics finite element analysis was also performed for the thermo-elastic damping and its results were compared to the analytical results.

An Acoustical Experiment on the Bryan’s Effect of a Vibrating Structure

Huinam Rhee(이희남),Sangjin Park(박상진),Sergii A. Sarapuloff(세르게이 사라플로프),Soon Woo Han(한순우),Jin Ho Park(박진호) 대한기계학회 2015 대한기계학회 춘추학술대회 Vol.바이오공학 No.-