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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">ipolytech</journal-id><journal-title-group><journal-title xml:lang="ru">iPolytech Journal</journal-title><trans-title-group xml:lang="en"><trans-title>iPolytech Journal</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2782-4004</issn><issn pub-type="epub">2782-6341</issn><publisher><publisher-name>Irkutsk National Research Technical University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21285/1814-3520-2024-4-488-503</article-id><article-id custom-type="edn" pub-id-type="custom">KNPZMP</article-id><article-id custom-type="elpub" pub-id-type="custom">ipolytech-880</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>МАШИНОСТРОЕНИЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MECHANICAL ENGINEERING</subject></subj-group></article-categories><title-group><article-title>Оценка эффективности подавления автоколебаний при резании по изменению объёма их энергии</article-title><trans-title-group xml:lang="en"><trans-title>Suppression efficiency of self-excited vibrations in machining evaluated by changes in their energy</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>Свинин</surname><given-names>В. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Svinin</surname><given-names>V. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Свинин Валерий Михайлович, д.т.н., профессор, профессор кафедры технологии и оборудования машиностроительных производств</p><p>664074, г. Иркутск, ул. Лермонтова, 83</p></bio><bio xml:lang="en"><p>Valery M. Svinin, Dr. Sci. (Eng.), Professor, Professor of the Department of Mechanical Engineering Production Technologies and Equipment</p><p>83, Lermontov St., Irkutsk 664074</p></bio><email xlink:type="simple">svinin_vm@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ушаков</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Ushakov</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ушаков Владислав Александрович, аспирант</p><p>664074, г. Иркутск, ул. Лермонтова, 83</p></bio><bio xml:lang="en"><p>Vladislav A. Ushakov, Postgraduate Student</p><p>83, Lermontov St., Irkutsk 664074</p></bio><email xlink:type="simple">kaivokaiva@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Савилов</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Savilov</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Савилов Андрей Владиславович, к.т.н., доцент, доцент кафедры технологии и оборудования машиностроительных производств</p><p>664074, г. Иркутск, ул. Лермонтова, 83</p></bio><bio xml:lang="en"><p>Andrey V. Savilov, Cand. Sci. (Eng.), Associate Professor, Associate Professor of the Department of Mechanical Engineering Production Technologies and Equipment</p><p>83, Lermontov St., Irkutsk 664074</p></bio><email xlink:type="simple">saw@istu.edu</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-4116-9190</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Пятых</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Pyatykh</surname><given-names>А. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Пятых Алексей Сергеевич, к.т.н., доцент кафедры технологии и оборудования машиностроительных производств</p><p>664074, г. Иркутск, ул. Лермонтова, 83</p></bio><bio xml:lang="en"><p>Aleksey S. Pyatykh, Cand. Sci. (Eng.), Associate Professor of the Department of Mechanical Engineering Production Technologies and Equipment</p><p>83, Lermontov St., Irkutsk 664074</p></bio><email xlink:type="simple">pyatykhas@ex.istu.edu</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Иринчеев</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Irincheev</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Иринчеев Андрей Андреевич, аспирант</p><p>664074, г. Иркутск, ул. Лермонтова, 83</p></bio><bio xml:lang="en"><p>Andrey A. Irincheev, Postgraduate Student</p><p>83, Lermontov St., Irkutsk 664074</p></bio><email xlink:type="simple">andrey.iaa2000@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Иркутский национальный исследовательский технический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Irkutsk National Research Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>04</day><month>01</month><year>2025</year></pub-date><volume>28</volume><issue>4</issue><fpage>488</fpage><lpage>503</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Свинин В.М., Ушаков В.А., Савилов А.В., Пятых А.С., Иринчеев А.А., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Свинин В.М., Ушаков В.А., Савилов А.В., Пятых А.С., Иринчеев А.А.</copyright-holder><copyright-holder xml:lang="en">Svinin V.M., Ushakov V.A., Savilov A.V., Pyatykh А.S., Irincheev A.A.</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://ipolytech.elpub.ru/jour/article/view/880">https://ipolytech.elpub.ru/jour/article/view/880</self-uri><abstract><p>Цель – создание инструмента исследователя для оценки и выбора мероприятий по подавлению нежелательных автоколебаний при резании. В качестве количественного критерия эффективности подавления автоколебаний использован объем их внутренней энергии, создаваемой работой радиальной составляющей силы резания. Было принято допущение, что данная работа пропорциональна разности площадей участков срезаемого слоя металла при выходе инструмента из заготовки и врезании в каждом колебании. В качестве объекта исследований был использован маложесткий вал диаметром 48 мм, закрепленный консольно с вылетом 150 мм. Для оценки изменения объема энергии автоколебаний был использован программный продукт на языке SciLab. Обработку вала проводили проходным резцом при частоте вращения шпинделя 208 об/мин с подачей 0,122 мм/ об и глубине резания 0,8 мм. Частоту модуляции скорости резания за оборот заготовки приняли равной 0,5. Изменение разности площадей участков срезаемого слоя металла при выходе инструмента из заготовки и врезании рассчитывали последовательно при варьировании глубины модуляции скорости резания в диапазоне от 0 до 30% с интервалом 1%. По результатам расчета получен график изменения относительной разности площадей участков срезаемого слоя (пропорциональной внутренней энергии автоколебаний), аналогичный графику косинусоиды с убывающим размахом. Установлено, что с повышением глубины модуляции скорости резания объем внутренней энергии автоколебаний резко снижается, периодически пульсируя около нулевых значений. Показано, что условию подавления автоколебаний соответствуют локальные минимумы графика. Для практического использования выбран четвертый локальный минимум, соответствующий глубине модуляции скорости резания, равной 13,5%. Показано, что модуляция скорости резания на данной глубине обеспечила по сравнению с постоянной скоростью резания снижение размаха колебаний более 10 раз, а амплитуды автоколебаний – более 12 раз. Полученные результаты доказывают эффективность предложенного способа оценки изменения объема энергии автоколебаний.</p></abstract><trans-abstract xml:lang="en"><p>The aim was to develop an approach for evaluation and suppression of undesirable self-excited vibrations during the machining process. The suppression efficiency of self-excited vibrations was evaluated by the amount of their internal energy created by the radial cutting force. This force was assumed to be proportional to the difference in the area of the cut metal layer at the tool exit from the workpiece and penetration in each vibration. The research object was a low-rigidity shaft with a diameter of 48 mm, cantilevered with an outreach of 150 mm. Changes in the energy of self-excited vibrations were evaluated using a software package in the SciLab language. The shaft was machined with a cutting tool at a spindle speed of 208 rpm with a feed of 0.122 mm/rev and a cutting depth of 0.8 mm. The modulation frequency of the cutting speed per workpiece revolution was assumed to be 0.5. The difference in the area of the cut metal layer at the tool exit from the workpiece and penetration was calculated sequentially when varying the depth of cutting speed modulation in the range from 0 to 30% with an interval of 1%. The results obtained were used to draw a plot of changes in the relative difference of the cut layer areas (proportional to the internal energy of self-excited vibrations), similar to a cosine curve with a decreasing magnitude. An increase in the depth of cutting speed modulation was established to sharply reduce the internal energy of self-excited vibrations, periodically pulsing around zero values. The local minima of the plot corresponded to the condition of suppression of self-excited vibrations. The fourth local minimum corresponding to the depth of cutting speed modulation equal to 13.5% was selected as a parameter for practical use. At this depth, cutting speed modulation ensured a more than 10-fold decrease in the vibration range and a 12-fold decrease in the vibration amplitude, in comparison with similar parameters at the constant cutting speed. The results obtained confirm the efficiency of the proposed method for evaluating changes in the energy of self-excited vibrations during the machining process. </p></trans-abstract><kwd-group xml:lang="ru"><kwd>автоколебания при резании</kwd><kwd>объем внутренней энергии</kwd><kwd>разность площадей участков срезаемого слоя</kwd><kwd>модуляция скорости резания</kwd><kwd>амплитуда автоколебаний</kwd></kwd-group><kwd-group xml:lang="en"><kwd>self-oscillation under cutting</kwd><kwd>volume of internal energy</kwd><kwd>difference in areas of the cut layer sections</kwd><kwd>cutting speed modulation</kwd><kwd>self-oscillation amplitude</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Представленная в данной статье работа реализуется в рамках стратегического проекта ФГБОУ ВО «ИРНИТУ» i.DIT – Байкальский центр цифровых производственных технологий (Программа «Приоритет 2030»)</funding-statement><funding-statement xml:lang="en">The work presented in this article is implemented within the framework of the strategic project i.DIT – Baikal Center for Digital Production Technologies (Priority 2030 Program) of the Federal State Budget Educational Institution of Higher Education «Irkutsk National Research Technical University»</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Quintana G., Ciurana J. Chatter in machining processes // International Journal of Machine Tools and Manufacture. 2011. Vol. 51. P. 363–376. https://doi.org/10.1016/j.ijmachtools.2011.01.001.</mixed-citation><mixed-citation xml:lang="en">Quintana G., Ciurana J. Chatter in machining processes. International Journal of Machine Tools and Manufacture. 2011;51:363-376. https://doi.org/10.1016/j.ijmachtools.2011.01.001.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Munoa J., Beudaert X., Dombovari Z., Altintas Y., Budak E., Brecher C., et al. Chatter suppression techniques in metal cutting // CIRP Annals. 2016. Vol. 65. Iss. 2. Р. 785–808. https://doi.org/10.1016/j.cirp.2016.06.004.</mixed-citation><mixed-citation xml:lang="en">Munoa J., Beudaert X., Dombovari Z., Altintas Y., Budak E., Brecher C., et al. Chatter suppression techniques in metal cutting. CIRP Annals. 2016;65(2):785-808. https://doi.org/10.1016/j.cirp.2016.06.004.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Кудинов В.А. Динамика станков. М.: Изд-во Машиностроение, 1967. 359 с.</mixed-citation><mixed-citation xml:lang="en">Kudinov V.A. Machine tool dynamics. Moscow: Mashinostroenie; 1967, 359 р. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Ташлицкий Н.И. Первичный источник энергии возбуждения автоколебаний при резании металлов // Вестник машиностроения. 1960. № 2. С. 45–50.</mixed-citation><mixed-citation xml:lang="en">Tashlitskiy N.I. Primary source of self-oscillation excitation energy during metal cutting. Russian Engineering Research. 1960;2:45-50. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Зарс В.В. Оценка некоторых механизмов возбуждения вибрации при точении // Автоколебания станков. Вопросы механики и машиностроения: сб. науч. тр. Рига: Рижский технический университет,1967. Вып. 6. С. 15–46.</mixed-citation><mixed-citation xml:lang="en">Zars V.V. Evaluating some vibration excitation mechanisms under turning. In: Avtokolebaniya stankov. Voprosy mekhaniki i mashinostroeniya: sbornik nauchnyh trudov = Self-Oscillations of machine tools. Questions of mechanics and mechanical engineering: collected scientific papers. Riga: Rīgas Tehniskā universitāte; 1967, iss. 6, р. 15-46. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Свинин В.М., Самсонов А.В., Большухин А.О. Подавление автоколебаний при точении нежестких валов пружинящим резцом // Механики – XXI веку. 2014. № 13. С. 112–119. EDN: TIYQNJ.</mixed-citation><mixed-citation xml:lang="en">Svinin V.M., Samsonov A.V., Bol’shuhin A.O. Suppression of self-excited oscillations during turning of non-rigid shafts with a springy cutter. Mechanical engineers to XXI century. 2014;13:112-119. (In Russ.). EDN: TIYQNJ.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Свинин В.М. Фрезерование с модулированной скоростью резания. Иркутск: ИрГТУ, 2007. 302 с.</mixed-citation><mixed-citation xml:lang="en">Svinin V.M. Milling with modulated cutting speed. Irkutsk: Irkutsk National Research Technical University; 2007, 302 р. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Merritt H.E. Theory of self-excited machine tool chatter // Journal of Engineering for Industry-Trans- actions of the ASME. 1965. Vol. 87. P. 447–454.</mixed-citation><mixed-citation xml:lang="en">Merritt H.E. Theory of self-excited machine tool chatter. Journal of Engineering for Industry-trans- actions of the ASME. 1965;87:447-454. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Свинин В.М. Самоорганизация вторичных автоколебаний при лезвийной обработке // СТИН. 2006. № 1. С. 7–13.</mixed-citation><mixed-citation xml:lang="en">Svinin V.M. Self-organization of secondary self-oscillations in edge cutting machining. Machines and Tooling. 2006;1:7-13. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Al-Regib E., Ni Jun, Lee Soo-Hun. Programming spindle speed variation for machine tool chatter suppression // International Journal of Machine Tools and Manufacture. 2003. Vol. 43. Iss. 12. P. 1229–1240. https://doi.org/10.1016/S0890-6955(03)00126-3.</mixed-citation><mixed-citation xml:lang="en">Al-Regib E., Ni Jun, Lee Soo-Hun. Programming spindle speed variation for machine tool chatter suppression. International Journal of Machine Tools and Manufacture. 2003;43(12):1229-1240. https://doi.org/10.1016/S0890-6955(03)00126-3.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang H., Ni Jun. Internal energy based analysis on mechanism of spindle speed variation for regenerative chatter control // Journal of Vibration and Control. 2010. Vol. 16. Iss. 2. P. 281–301. https://doi.org/10.1177/1077546309103562.</mixed-citation><mixed-citation xml:lang="en">Zhang H., Ni Jun. Internal energy based analysis on mechanism of spindle speed variation for regenerative chatter control. Journal of Vibration and Control. 2010;16(2):281-301. https://doi.org/10.1177/1077546309103562.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Yamato S., Ito T., Matsuzaki H., Kakinuma Y. Programmable optimal design of sinusoidal SSV for regenerative chatter suppression // Procedia Manufacturing. 2018. Vol. 18. P. 152–160. https://doi.org/10.1016/J.PROMFG.2018.11.020.</mixed-citation><mixed-citation xml:lang="en">Yamato S., Ito T., Matsuzaki H., Kakinuma Y. Programmable optimal design of sinusoidal SSV for regenerative chatter suppression. Procedia Manufacturing. 2018;18:152-160. https://doi.org/10.1016/J.PROMFG.2018.11.020.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Yamato S., Ito T., Matsuzaki H., Fujita J., Kakinuma Yа. Self-acting optimal design of spindle speed variation for regenerative chatter suppression based on novel analysis of internal process energy behavior // International Journal of Machine Tools and Manufacture. 2020. Vol. 159. Part A. Р. 103639. https://doi.org/10.1016/j.ijmachtools.2020.103639.</mixed-citation><mixed-citation xml:lang="en">Yamato S., Ito T., Matsuzaki H., Fujita J., Kakinuma Yа. Self-acting optimal design of spindle speed variation for regenerative chatter suppression based on novel analysis of internal process energy behavior. International Journal of Machine Tools and Manufacture. 2020;159(A):103639. https://doi.org/10.1016/j.ijmachtools.2020.103639.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Шнепс В.А. Экспериментальное исследование влияния синусоидального изменения скорости на устойчивость резания // Вопросы динамики и прочности. 1970. Вып. 20. С. 123–130.</mixed-citation><mixed-citation xml:lang="en">Shneps V.A. Experimental study of the effect of sinusoidal speed variation on cutting stability. Voprosy dinamiki i prochnosti. 1970;20:123-130. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Takemura T., Kitamura T., Hoshi T., Okushimo K. Active suppression of chatter by programmed variation of spindle speed // CIRP Annals. 1974. Vol. 23. Iss. 1. P. 62–76.</mixed-citation><mixed-citation xml:lang="en">Takemura T., Kitamura T., Hoshi T., Okushimo K. Active suppression of chatter by programmed variation of spindle speed. CIRP Annals. 1974;23(1):62-76.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Inamura T., Sata T. Stability analysis of cutting under varying spindle speed // CIRP Annals. 1974. Vol. 23. Iss. 1. P. 119–120. https://doi.org/10.2493/JJSPE1933.43.80.</mixed-citation><mixed-citation xml:lang="en">Inamura T., Sata T. Stability analysis of cutting under varying spindle speed. CIRP Annals. 1974;23(1):119-120. https://doi.org/10.2493/JJSPE1933.43.80.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Hoshi T., Sakisaka N., Moriyama I., Sato M., Higashimoto A., Tokunaga T. Study on practical application of fluctuating speed cutting for regenerative chatter control // The Japan Society of Mechanical Engineers. 1978. Vol. 44. Iss. 379. P. 1085–1093. https://doi.org/10.1299/kikai1938.44.1085.</mixed-citation><mixed-citation xml:lang="en">Hoshi T., Sakisaka N., Moriyama I., Sato M., Higashimoto A., Tokunaga T. Study on practical application of fluctuating speed cutting for regenerative chatter control. The Japan Society of Mechanical Engineers. 1978;44(379):1085- 1093. https://doi.org/10.1299/kikai1938.44.1085.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Sexton J., Stone B. The stability of machining with continuously varying spindle speed // CIRP Annals. 1978. Vol. 27. Iss. 1. P. 317–326.</mixed-citation><mixed-citation xml:lang="en">Sexton J., Stone B. The stability of machining with continuously varying spindle speed. CIRP Annals. 1978;27(1):317-326.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Jemielniak K., Widota A. Suppression of self-excited vibration by the spindle speed variation method // International Journal of Machine Tool Design and Research. 1984. Vol. 24. Iss. 3. P. 207–214. https://doi.org/10.1016/0020-7357(84)90005-2.</mixed-citation><mixed-citation xml:lang="en">Jemielniak K., Widota A. Suppression of self-excited vibration by the spindle speed variation method. International Journal of Machine Tool Design and Research. 1984;24(3):207-214. https://doi.org/10.1016/0020-7357(84)90005-2.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Jayaram S., Kapoor S., DeVor R. Analytical stability analysis of variable spindle speed machining // Journal of Manufacturing Science &amp; Engineering. 2000. Vol. 122. Iss. 3. P. 391–397. https://doi.org/https://doi.org/10.1115/1.1285890.</mixed-citation><mixed-citation xml:lang="en">Jayaram S., Kapoor S., DeVor R. Analytical stability analysis of variable spindle speed machining. Journal of Manufacturing Science &amp; Engineering. 2000;122(3):391-397. https://doi.org/https://doi.org/10.1115/1.1285890.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Insperger T., Stepan G. Stability analysis of turning with periodic spindle speed modulation via semi-discretisation // Journal of Vibration &amp; Control. 2004. Vol. 10. Iss. 12. P. 1835–1855. https://doi.org/10.1177/1077546304044891.</mixed-citation><mixed-citation xml:lang="en">Insperger T., Stepan G. Stability analysis of turning with periodic spindle speed modulation via semi-discretisation. Journal of Vibration &amp; Control. 2004;10(12):1835–1855. https://doi.org/10.1177/1077546304044891.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Otto A., Radons G. Application of spindle speed variation for chatter suppression in turning // CIRP Journal of Manufacturing Science and Technology. 2013. Vol. 6. Iss. 2. P. 102–109. https://doi.org/10.1016/j.cirpj.2013.02.002.</mixed-citation><mixed-citation xml:lang="en">Otto A., Radons G., Application of spindle speed variation for chatter suppression in turning. CIRP Journal of Manufacturing Science and Technology. 2013;6(2):102-109. https://doi.org/10.1016/j.cirpj.2013.02.002.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Urbikain G., Olvera D., De Lacalle L.N.L., Elías-Zúñiga A. Spindle speed variation technique in turning operations: modeling and real implementation // Journal of Sound and Vibration. 2016. Vol. 383. P. 384–396. https://doi.org/10.1016/j.jsv.2016.07.033.</mixed-citation><mixed-citation xml:lang="en">Urbikain G., Olvera D., De Lacalle L.N.L., Elías-Zúñiga A. Spindle speed variation technique in turning operations: modeling and real implementation. Journal of Sound and Vibration. 2016;383:384-396. https://doi.org/10.1016/j.jsv.2016.07.033.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Longyang Ding, Sun Yuxin, Xiong Zhenhua. Active chatter suppression in turning by simultaneous adjustment of amplitude and frequency of spindle speed variation // Journal of Manufacturing Science and Engineering. 2020. Vol. 142. Iss. 2. Р. 021004-1–021004-10. https://doi.org/10.1115/1.4045618.</mixed-citation><mixed-citation xml:lang="en">Longyang Ding, Sun Yuxin, Xiong Zhenhua. Active chatter suppression in turning by simultaneous adjustment of amplitude and frequency of spindle speed variation. Journal of Manufacturing Science and Engineering. 2020;142(2):021004-1–021004-10. https://doi.org/10.1115/1.4045618.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">СвининВ.М. Выборпараметровмодуляциискоростирезаниядлягашениярегенеративныхавтоколебаний // Вестник Самарского государственного технического университета. Серия: Технические науки. 2006. № 41. С. 135–142. EDN: JWQPQV.</mixed-citation><mixed-citation xml:lang="en">Svinin V.M. Cutting speed modulation parameter selection for chatter suppression. Vestnik of Samara State Technical University. Technical Sciences Series. 2006;41:135-142. (In Russ.). EDN: JWQPQV.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
