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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">sibadi</journal-id><journal-title-group><journal-title xml:lang="ru">Научный рецензируемый журнал "Вестник СибАДИ"</journal-title><trans-title-group xml:lang="en"><trans-title>The Russian Automobile and Highway Industry Journal</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2071-7296</issn><issn pub-type="epub">2658-5626</issn><publisher><publisher-name>The Siberian State Automobile and Highway University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26518/2071-7296-2020-17-3-364-373</article-id><article-id custom-type="elpub" pub-id-type="custom">sibadi-1100</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>ТРАНСПОРТ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>TRANSPORT</subject></subj-group></article-categories><title-group><article-title>МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ПРОЦЕССА ДВИЖЕНИЯ ПАЛЛЕТЫ ПО ТОРМОЗНОМУ РОЛИКУ МАГНИТНОГО ТИПА</article-title><trans-title-group xml:lang="en"><trans-title>MATHEMATICAL MODEL OF THE MOTION PALLET PROCESS ON BRAKE MAGNETIC TYPE ROLLER</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>Шарифуллин</surname><given-names>И. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Sharifullin</surname><given-names>I. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Шарифуллин Ильдар Азатович – аспирант кафедры «Подъемно-транспортные системы»</p><p>105005, г. Москва, 2-я Бауманская ул., д. 5</p><p>(499) 263–65–92</p></bio><bio xml:lang="en"><p>Ildar A. Sharifullin - a postgraduate of the Lifting and Transport Systems Department</p><p>105005, Moscow, 2 Baumanskaia Street., 5, building 1</p><p>(499) 263–65–92</p></bio><email xlink:type="simple">formyjob94@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>Носко</surname><given-names>А. Л.</given-names></name><name name-style="western" xml:lang="en"><surname>Nosko</surname><given-names>A. L.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Носко Андрей Леонидович - д-р техн. наук, доц., проф. кафедры «Подъемно-транспортные системы»</p><p>Scopus Author ID 6507019256</p><p>105005, г. Москва, 2-я Бауманская ул., д. 5, стр. 1</p><p>(499) 263–65–92</p><p> </p></bio><bio xml:lang="en"><p>Andrei L. Nosko - Dr. of Sci., Associate Professor, Professor of the the Lifting and Transport Systems Department</p><p>Scopus Author ID 6507019256</p><p>105005, Moscow, 2 Baumanskaia Street., 5, building 1</p><p>(499) 263–65–92</p></bio><email xlink:type="simple">nosko@bmstu.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>Сафронов</surname><given-names>Е. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Safronov</surname><given-names>E. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Сафронов Евгений Викторович - канд. техн. наук, доц. кафедры «Подъемно-транспортные системы»</p><p>Scopus Author ID 36943598600</p><p>105005, г. Москва, 2-я Бауманская ул., д. 5, стр. 1</p><p>(499) 263–65–92</p></bio><bio xml:lang="en"><p>Evgenii V. Safronov - Cand. of Sci., Associate Professor of the Lifting and Transport Systems Department</p><p>105005, Moscow, 2 Baumanskaia Street., 5, building 1</p><p>(499) 263–65–92</p></bio><email xlink:type="simple">gen-s@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>МГТУ им. Н.Э. Баумана</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Bauman Moscow State Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2020</year></pub-date><pub-date pub-type="epub"><day>21</day><month>07</month><year>2020</year></pub-date><volume>17</volume><issue>3</issue><fpage>364</fpage><lpage>373</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Шарифуллин И.А., Носко А.Л., Сафронов Е.В., 2020</copyright-statement><copyright-year>2020</copyright-year><copyright-holder xml:lang="ru">Шарифуллин И.А., Носко А.Л., Сафронов Е.В.</copyright-holder><copyright-holder xml:lang="en">Sharifullin I.A., Nosko A.L., Safronov E.V.</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://vestnik.sibadi.org/jour/article/view/1100">https://vestnik.sibadi.org/jour/article/view/1100</self-uri><abstract><sec><title>Введение</title><p>Введение. Одним из основных элементов безопасной эксплуатации гравитационных роликовых конвейеров, применяемых в стеллажах для паллет, является тормозной ролик. Наиболее перспективной конструкцией является тормозной ролик магнитного (вихретокового) типа. Принцип работы таких роликов основан на законах электромагнитной индукции и предполагает торможение движущегося в магнитном поле проводника, обусловленное взаимодействием возникающих в объеме проводника вихревых токов (или токов Фуко) с внешним магнитным полем. Однако на рынке складского стеллажного оборудования тормозные магнитные ролики не нашли широкого применения ввиду своей высокой стоимости, которая в первую очередь обусловлена отсутствием отечественных конструкций и методик их расчета. Цель данной работы – разработка математической модели процесса движения паллеты по тормозному ролику магнитного типа.</p></sec><sec><title>Материалы и методы</title><p>Материалы и методы. В статье представлены результаты теоретического исследования по разработке математической модели процесса движения паллеты по тормозному ролику магнитного типа, изложенные в работах по центробежным фрикционным роликам и по вихретоковым тормозным устройствам.</p></sec><sec><title>Результаты</title><p>Результаты. Установлено, что основным параметром, определяющим функции тормозного магнитного ролика, а значит и скорость движения паллеты по гравитационному роликовому конвейеру, является коэффициент магнитной вязкости. Построена зависимость скорости движения паллеты по тормозному магнитному ролику при различных значениях коэффициента магнитной вязкости, проведен ее анализ.</p></sec><sec><title>Заключение</title><p>Заключение. Разработана математическая модель процесса движения паллеты по тормозному магнитному ролику. Получено уравнение скорости движения паллеты по тормозному магнитному ролику. Для обоснованного выбора конструктивных параметров тормозного магнитного ролика требуются экспериментальные исследования по определению коэффициента магнитной вязкости.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Introduction</title><p>Introduction. One of the main elements of the safe operation of gravity roller conveyors used in pallet racks is a brake roller. The most promising design is the brake roller magnetic (eddy current) type. The operation principle of such rollers is based on the laws of electromagnetic induction and involves the braking of a conductor moving in a magnetic field, due to the interaction of eddy currents (or Foucault currents) arising in the volume of the conductor with an external magnetic field. However, in the market of warehouse shelving equipment, brake magnetic rollers are not widely used due to their high cost, which is primarily due to the lack of domestic designs and methods for their calculation. The aim of the work is to develop a mathematical model of the moving pallets process on a magnetic type brake roller.</p></sec><sec><title>Materials and methods</title><p>Materials and methods. The paper presented the theoretical study results on the development of a mathematical model of the moving pallets process on a magnetic type brake roller, described in works on centrifugal friction rollers and eddy current brake devices.</p></sec><sec><title>Results</title><p>Results. The main parameter determining the functions of the brake magnetic roller and hence the speed of the pallet along the gravity roller conveyor is a magnetic viscosity coefficient. The speed dependence of the pallets on the brake magnetic roller for various values of a magnetic viscosity coefficient is determined, its analysis is carried out.</p></sec><sec><title>Conclusions</title><p>Conclusions. A mathematical model of the moving pallets process on a brake magnetic roller is developed. The movement speed equation of the pallets on the brake magnetic roller is obtained. For a reasonable choice of the design parameters of the magnetic brake roller, experimental studies are required to determine a magnetic viscosity coefficient.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>паллета</kwd><kwd>стеллаж</kwd><kwd>гравитационный роликовый конвейер</kwd><kwd>магнитный (вихретоковый) тормозной ролик</kwd><kwd>коэффициент магнитной вязкости</kwd></kwd-group><kwd-group xml:lang="en"><kwd>pallet</kwd><kwd>rack</kwd><kwd>gravity roller conveyor</kwd><kwd>magnetic (eddy current) brake roller</kwd><kwd>magnetic viscosity coefficient</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Авторы выражают благодарность рецензентам статьи.</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">N. Boysen, D. Boywitz, F. Weidinger. Deeplane storage of time-critical items: one-sided versus two-sided access // OR Spectrum. 2018. Vol. 40, No. 4. Pp. 1141–1170.</mixed-citation><mixed-citation xml:lang="en">N. Boysen, D. Boywitz, F. Weidinger. Deeplane storage of time-critical items: one-sided versus two-sided access // OR Spectrum. 2018; 40, 4: 1141– 1170.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">D. Boywitz, N. Boysen N. Robust storage assignment in stack- and queue-based storage systems // Comput. Oper. Res. 2018. Vol. 100. Pp. 189–200.</mixed-citation><mixed-citation xml:lang="en">D. Boywitz, N. Boysen N. Robust storage assignment in stack- and queue-based storage systems // Comput. Oper. Res. 2018; 100: 189–200.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">R. Accorsi, G. Baruffaldi, R. Manzini, Design and manage deep lane storage system layout. An iterative decision-support model // Int. J. Adv. Manuf. Technol. 2017. Vol. 92, No. 1-4. Pp. 57–67.</mixed-citation><mixed-citation xml:lang="en">R. Accorsi, G. Baruffaldi, R. Manzini, Design and manage deep lane storage system layout. An iterative decision-support model // Int. J. Adv. Manuf. Technol. 2017; 92 (1-4): 57–67.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">R. Vujanac, N. Miloradovic, S. Vulovic. Dynamic storage systems // ANNALS of Faculty Engineering Hunedoara – International Journal of Engineering. 2016. Vol. XIV. Pp. 79–82.</mixed-citation><mixed-citation xml:lang="en">R. Vujanac, N. Miloradovic, S. Vulovic. Dynamic storage systems // ANNALS of Faculty Engineering Hunedoara – International Journal of Engineering. 2016; 14: 79–82.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">S. Wu, Ya. Wu, Ya. Wang. A structured comparison study on storage racks system // J. Residuals Sci. Tech. 2016. Vol. 13, No. 8.</mixed-citation><mixed-citation xml:lang="en">S. Wu, Ya. Wu, Ya. Wang. A structured comparison study on storage racks system // J. Residuals Sci. Tech. 2016; 13 (8).</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">L. Ghomri, Z. Sari. Mathematical modeling of the average retrieval time for flow-rack automated storage and retrieval systems // J. Manuf. Syst. 2017. Vol. 44. Pp. 165–178.</mixed-citation><mixed-citation xml:lang="en">L. Ghomri, Z. Sari. Mathematical modeling of the average retrieval time for flow-rack automated storage and retrieval systems // J. Manuf. Syst. 2017; 44: 165–178.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">M. A. Hamzaoui, Z. Sari. Optimal dimensions minimizing expected travel time of a single machine flow rack AS/RS // Mechatronics. 2015. Vol. 31. Pp. 158–168.</mixed-citation><mixed-citation xml:lang="en">M. A. Hamzaoui, Z. Sari. Optimal dimensions minimizing expected travel time of a single machine flow rack AS/RS // Mechatronics. 2015; 31: 158–168.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Сафронов Е.В., Шарифуллин И.А., Носко А.Л. Устройства безопасной эксплуатации гравитационных роликовых конвейеров паллетного типа: монография. Москва, Университетская книга, 2018. 72 с.</mixed-citation><mixed-citation xml:lang="en">Safronov E.V., Sharifullin I.A., Nosko A.L. Ustroystva bezopasnoy ekspluatatsii gravitatsionnykh rolikovykh konveyyerov palletnogo tipa: Monografiya [Devices for safe operation of pallet type gravity roller conveyors: Monograph]. Moscow. Universitetskaya kniga. 2018: 72. (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Носко А.Л., Сафронов Е.В. Методика определения максимально допустимой скорости движения поддона на гравитационном роликовом конвейере // Известия высших учебных заведений. Машиностроение. 2017. № 8 (689). С. 33–41.</mixed-citation><mixed-citation xml:lang="en">Nosko A.L., Safronov E.V. Metodika opredeleniya maksimal’no dopustimoy skorosti dvizheniya poddona na gravitatsionnom rolikovom konveyyere [Methodology for determining the maximum allowable speed of a pallet on a gravity roller conveyor]. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroyeniye. 2017; 8 (689): 33–41. (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Мартыненко Ю. Г. Движение твердого тела в электрических и магнитных полях: монография. Москва, Наука. 1988. 368 с.</mixed-citation><mixed-citation xml:lang="en">Martynenko U. G. Dvizheniye tverdogo tela v elektricheskikh i magnitnykh polyakh: monografiya [Motion of a solid in electric and magnetic fields: monograph]. Moscow. Nauka. 1988: 368. (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Озолин А.Ю., Скубов Д.Ю., Штукин Л.В. Способы торможения падающего лифта с помощью постоянных магнитов / Научно-технические ведомости Санкт-Петербургского государственного политехнического университета. 2008. № 6 (70). С. 82–86.</mixed-citation><mixed-citation xml:lang="en">Ozolin A.U., Skubov D.U., Shtukin L.V. Sposoby tormozheniya padayushchego lifta s pomoshch’yu postoyannykh magnitov [Methods of braking a falling lift with the help of permanent magnets]. Nauchno-tekhnicheskiye vedomosti Sankt-Peterburgskogo gosudarstvennogo politekhnicheskogo universiteta. 2008; 6 (70): 82–86. (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Носко А. Л., Сафронов Е. В. Методика расчета тормозного ролика центробежного типа применительно к гравитационным роликовым кон- вейерам для паллет // Механизация строительства. 2017. Том 78, № 6. С. 26–31.</mixed-citation><mixed-citation xml:lang="en">Nosko A. L., Safronov E. V. Metodika rascheta tormoznogo rolika tsentrobezhnogo tipa primenitel’no k gravitatsionnym rolikovym konveyyeram dlya pallet [Calculation method of the centrifugal type brake roller as applied to gravity roller conveyors for pallets]. Mekhanizatsiya stroitel’stva. 2017; 78; 6: 26–31. (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">E. Simeu, D. Georges. Modeling and control of an eddy current brake // Control Engineering Practise. 1996. Vol.4. No.1. Pp. 19–26.</mixed-citation><mixed-citation xml:lang="en">E. Simeu, D. Georges. Modeling and control of an eddy current brake // Control Engineering Practise. 1996; 4 (1): 19–26.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Озолин А.Ю., Скубов Д.Ю., Штукин Л.В. Исследование вихретокового дискового тормоза // Научно-технические ведомости Санкт-Петербургского государственного политехнического университета. 2009. № 1 (74). С. 57–60.</mixed-citation><mixed-citation xml:lang="en">Ozolin A.U., Skubov D.U., Shtukin L.V. Issledovaniye vikhretokovogo diskovogo tormoza [Research eddy current disc brake]. Nauchnotekhnicheskiye vedomosti Sankt-Peterburgskogo gosudarstvennogo politekhnicheskogo universiteta. 2009; 1 (74): 57–60. (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Лускань О.А. Определение скорости транспортирования штучных грузов на инерционном роликовом конвейер / Изв. ТулГУ. Подъемно-транспортные машины и оборудование. – Тула: ТулГУ. 2003. Вып. 4. С. 84–89.</mixed-citation><mixed-citation xml:lang="en">Luskan’ O.A. Opredeleniye skorosti transportirovaniya shtuchnykh gruzov na inertsionnom rolikovom konveyyer [Determining the speed of piece goods transportation on an inertial roller conveyor]. Izv. TulGU. Pod”yemno-transportnyye mashiny i oborudovaniye. Tula: TulGU. 2003; 4: 84–89. (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Зенков Р.Л., Ивашков И.И., Колобов Л.Н. Машины непрерывного транспорта. М.: Машиностроение, 1987. 431 с.</mixed-citation><mixed-citation xml:lang="en">Zenkov R.L., Ivashkov I.I., Kolobov L.N. Mashiny nepreryvnogo transporta [Continuous transport machines]. Moscow. Mashinostroyeniye. 1987: 431. (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Лускань О.А. Теоретические основы перемещения грузов импульсными конвейерами: монография. Саратов, Сарат. гос. техн. ун-т, 2010. 99 с.</mixed-citation><mixed-citation xml:lang="en">Luskan’ O.A. Teoreticheskiye osnovy peremeshcheniya gruzov impul’snymi konveyyerami: Monografiya [Theoretical foundations of the goods movement by pulse conveyors: Monograph]. Saratov: Sarat. gos. tekhn. un-t. 2010: 99. (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Лускань О.А. Инженерный расчет импульсных конвейеров: монография. Саратов, Сарат. гос. техн. ун-т, 2011. 80 с.</mixed-citation><mixed-citation xml:lang="en">Luskan’ O.A. Inzhenernyy raschet impul’snykh konveyyerov: Monografiya [Engineering calculation of pulse conveyors: Monograph]. Saratov: Sarat. gos. tekhn. un-t. 2011: 80. (in Russian)</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Hollowell, Thomas Culver; Kahl, Justin Tyme; Stanczak, Matthew Don; Wang, Yizhou. Eddy Current Brake Design for Operation with Extreme Backdrivable Eddy Current Motor // Mechanical Engineering Undergraduates. 2010.</mixed-citation><mixed-citation xml:lang="en">Hollowell, Thomas Culver; Kahl, Justin Tyme; Stanczak, Matthew Don; Wang, Yizhou. Eddy Current Brake Design for Operation with Extreme Backdrivable Eddy Current Motor. Mechanical Engineering Undergraduates. 2010.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Andrew H. C. Gosline, Vincent Hayward. Eddy Current Brakes for Haptic Interfaces: Design, Identification, and Control // IEEE/ASME Transactions on Mechatronics. 2008. Vol.13, No.6. Pp. 669–677.</mixed-citation><mixed-citation xml:lang="en">Andrew H. C. Gosline, Vincent Hayward. Eddy Current Brakes for Haptic Interfaces: Design, Identification, and Control. IEEE/ASME Transactions on Mechatronics. 2008; 13 (6): 669–677.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Karakoc Kerem, Suleman Afzal, Park Edward J. Analytical modeling of eddy current brakes with the application of the time varying magnetic fields // Applied Mathematical Modeling, Netherlands. 2015. Pp. 1168–1179.</mixed-citation><mixed-citation xml:lang="en">Karakoc Kerem, Suleman Afzal, Park Edward J. Analytical modeling of eddy current brakes with the application of the time varying magnetic fields. Applied Mathematical Modeling, Netherlands. 2015. 1168–1179.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Karakoc Kerem, Park Edward J., Suleman Afzal. Improved braking torque generation capacity of an eddy current brake with time varying magnetic fields: A numerical study // Finite Elements in Analysis and Design. Elsevier. 2012. Vol. 59. Pp. 66–75.</mixed-citation><mixed-citation xml:lang="en">Karakoc Kerem, Park Edward J., Suleman Afzal. Improved braking torque generation capacity of an eddy current brake with time varying magnetic fields: A numerical study. Finite Elements in Analysis and Design. Elsevier. 2012; 59: 66–75.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">K. Lee, K. Park. Modeling eddy currents with boundary conditions by sing Coulomb’s law and the method of images // IEEE Transactions on Magnetics. 2002. Vol. 38, No. 2. Pp. 1333–1340.</mixed-citation><mixed-citation xml:lang="en">K. Lee, K. Park. Modeling eddy currents with boundary conditions by sing Coulomb’s law and the method of images. IEEE Transactions on Magnetics. 2002; 38 (2): 1333–1340.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">M.A. Heald. Magnetic braking: Improved theory // American Journal of Physics. 1988. Vol. 56, No. 6. Pp. 521–522.</mixed-citation><mixed-citation xml:lang="en">M.A. Heald. Magnetic braking: Improved theory. American Journal of Physics. 1988; 56 (6): 521–522.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">S. Anwar. A parametric model of an eddy current electric machine for automotive braking applications // IEEE Transactions on Control Systems Technology. 2002. Vol. 12, No. 3. Pp. 422–427.</mixed-citation><mixed-citation xml:lang="en">S. Anwar. A parametric model of an eddy current electric machine for automotive braking applications. IEEE Transactions on Control Systems Technology. 2002; 12 (3): 422–427.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Hyeon-Jae Shin, Jang-Young Choi, Han-Wook Cho, Seok-Myeong Jang. Analytical torque calculations and Experimental testing of permanent magnet Axial eddy current brake // IEEE Transactions of Magnetics. 2013. Vol. 49, No. 7. Pp. 4152–4155.</mixed-citation><mixed-citation xml:lang="en">Hyeon-Jae Shin, Jang-Young Choi, Han-Wook Cho, Seok-Myeong Jang. Analytical torque calculations and Experimental testing of permanent magnet Axial eddy current brake. IEEE Transactions of Magnetics. 2013; 49 (7): 4152–4155.</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>
