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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">gyroscopy</journal-id><journal-title-group><journal-title xml:lang="ru">Гироскопия и навигация</journal-title><trans-title-group xml:lang="en"><trans-title>Giroskopiya i Navigatsiya / Gyroscopy and Navigation</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0869-7035</issn><issn pub-type="epub">2075-0927</issn><publisher><publisher-name>AO «Концерн «ЦНИИ «Электроприбор»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17285/0869-7035.0057</article-id><article-id custom-type="elpub" pub-id-type="custom">gyroscopy-164</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Гибридный резонатор твердотельного волнового гироскопа с высокой добротностью: конструкция с использованием термоупругого демпфирования, исследование чувствительности и определение характеристик</article-title><trans-title-group xml:lang="en"><trans-title>Thermoelastic Damping Based Design, Sensitivity Study and Demonstration of a Functional Hybrid Gyroscope Resonator for High Quality Factor</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Шарма</surname><given-names>Н. Г.</given-names></name><name name-style="western" xml:lang="en"><surname>Sharma</surname><given-names>G.N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Шарма Н. Гириш. Научный сотрудник</p></bio><bio xml:lang="en"><p>Sharma, G.N. </p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Сундарараджан</surname><given-names>Т.</given-names></name><name name-style="western" xml:lang="en"><surname>Sundararajan</surname><given-names>T.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Сундарараджан Т. Научный сотрудник</p></bio><bio xml:lang="en"><p>Sundararajan T. </p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Сингх</surname><given-names>Гаутам Сачин</given-names></name><name name-style="western" xml:lang="en"><surname>Singh</surname><given-names>G.S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Сингх Гаутам Сачин. Старший преподаватель</p></bio><bio xml:lang="en"><p>Singh, G.S. </p></bio><xref ref-type="aff" rid="aff-3"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Индийская организация космических исследований, подразделение инерциальных систем (г. Тируванантапурам, Керала).</institution><country>Индия</country></aff><aff xml:lang="en"><institution>ISRO Inertial Systems Unit, Thiruvananthapuram, Kerala, India</institution><country>India</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Космический центр им. Викрама Сарабхаи (г. Тируванантапурам, Керала).</institution><country>Индия</country></aff><aff xml:lang="en"><institution>Vikram Sarabhai Space Centre, Thiruvananthapuram, Kerala, India</institution><country>India</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Индийский технологический институт (г. Гувахати)</institution><country>Индия</country></aff><aff xml:lang="en"><institution>Indian Institute of Technology, Guwahati, India</institution><country>India</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2021</year></pub-date><pub-date pub-type="epub"><day>26</day><month>09</month><year>2025</year></pub-date><volume>29</volume><issue>1</issue><fpage>70</fpage><lpage>96</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Шарма Н., Сундарараджан Т., Сингх Г., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Шарма Н., Сундарараджан Т., Сингх Г.</copyright-holder><copyright-holder xml:lang="en">Sharma G., Sundararajan T., Singh G.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.gyroscopy.ru/jour/article/view/164">https://www.gyroscopy.ru/jour/article/view/164</self-uri><abstract><p>Важнейшим элементом твердотельного волнового гироскопа является механический резонатор, обладающий высокой добротностью. В работе рассматривается влияние термоупругого демпфирования на добротность. Для решения данной многогранной эксплуатационной задачи, относящейся к области колебаний, механики твердого тела, теплопередачи и термодинамики, используется метод конечных элементов. Основное внимание в статье уделяется зависимости добротности от свойств материала, рабочей температуры и размеров, позволяющих получить требуемую конфигурацию резонатора. По результатам изучения рабочих параметров, таких как эффективная масса и коэффициент преобразования угловой скорости в кориолисово ускорение, предложена гибридная полусферически-цилиндрическая конфигурация резонатора. Уникальность данной работы состоит в исследовании влияния на добротность ультратонкопленочного покрытия (объемная концентрация 0,01%), вариантов и различных комбинаций покрытий. Покрытие способно снижать добротность на несколько порядков в сравнении с непокрытым резонатором. Выяснилось, что выбор материала покрытия и его конфигурация являются очень важными факторами. Другой значимый аспект данной работы – изготовление и подробное описание характеристик гибридного резонатора из кварцевого стекла, на трехмерные поверхности которого наносится тонкопленочное золотое покрытие для получения прецизионных характеристик. После нанесения покрытия производится сверхтонкая балансировка до уровня единиц мГц. Измерение добротности резонатора с нанесенным покрытием выполнено методом лазерной доплеровской виброметрии. Достигнутый уровень добротности окончательной версии функционального гибридного резонатора составляет несколько миллионов единиц.</p></abstract><trans-abstract xml:lang="en"><p>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 has 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.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Твердотельный волновой гироскоп</kwd><kwd>эллиптические моды колебаний</kwd><kwd>добротность</kwd><kwd>термоупругое демпфирование</kwd><kwd>тонкопленочное покрытие.</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Нemispherical resonator gyroscope</kwd><kwd>elliptical modes</kwd><kwd>Q-factor</kwd><kwd>thermoelastic damping</kwd><kwd>thin film coating.</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Xu, W., Wenqi, W., Bing, L., and Yun, L., The modelling of hemispherical gyro and its space applications, Proceedings of 7th International Symposium on Precision Engineering Measurements and Instrumentation, 2011, 8321(1), 4–9.</mixed-citation><mixed-citation xml:lang="en">Xu, W., Wenqi, W., Bing, L., and Yun, L., The modelling of hemispherical gyro and its space applications, Proceedings of 7th International Symposium on Precision Engineering Measurements and Instrumentation, 2011, 8321(1), 4–9.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Choudhary, V. and Iniewski, K., MEMS: Fundamental technology and applications, CRC Press, 2013.</mixed-citation><mixed-citation xml:lang="en">Choudhary, V. and Iniewski, K., MEMS: Fundamental technology and applications, CRC Press, 2013.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Joshi, S., Hung, S., and Vengallatore, S., Design strategies for controlling damping in micromechanical and nanomechanical resonators, EPJ Techniques and Instrumentation, 2014, 1(5), 1–14.</mixed-citation><mixed-citation xml:lang="en">Joshi, S., Hung, S., and Vengallatore, S., Design strategies for controlling damping in micromechanical and nanomechanical resonators, EPJ Techniques and Instrumentation, 2014, 1(5), 1–14.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Imboden, M. and Mohanty, P., Dissipation in nanoelectromechanical systems, Physics Reports, 2014, 534(3), 89–146.</mixed-citation><mixed-citation xml:lang="en">Imboden, M. and Mohanty, P., Dissipation in nanoelectromechanical systems, Physics Reports, 2014, 534(3), 89–146.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Zener, C., Internal friction in solids. 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