donstuAdvanced Engineering Research (Rostov-on-Don)Advanced Engineering Research (Rostov-on-Don)2687-1653Don State Technical University10.23947/2687-1653-2024-24-4-360-368BSOKNMdonstu-2302Research ArticleMACHINE BUILDING AND MACHINE SCIENCEМАШИНОСТРОЕНИЕ И МАШИНОВЕДЕНИЕExperimental Study of the Kinematics of a Double-Row Planetary Mechanism Using Two Elliptical External GearsЭкспериментальное исследование кинематики двухрядной планетарной передачи эллиптическими зубчатыми колесами с двумя внешними зацеплениямиhttps://orcid.org/0000-0002-3885-8235ПриходькоА. А.PrikhodkoA. A.

Александр Александрович Приходько, кандидат технических наук, доцент кафедры технической механики и специальных машин имени профессора А.А. Петрика

350072, г. Краснодар, ул. Московская, 2

Alexander A. Prikhodko, Cand.Sci. (Eng.), Associate Professor of the Department of Technical Mechanics and Special Machines named after Professor A.A. Petrik

2, Moskovskaya Str., Krasnodar, 350072

sannic92@gmail.comhttps://orcid.org/0000-0002-0010-3910БелинаН. Н.BelinaN. N.

Наталия Николаевна Белина, кандидат технических наук, доцент кафедры технической механики и специальных машин имени профессора А.А. Петрика

350072, г. Краснодар, ул. Московская, 2

Nataliya N. Belina, Cand.Sci. (Eng.), Associate Professor of the Department of Technical Mechanics and Special Machines named after Professor A.A. Petrik

2, Moskovskaya Str., Krasnodar, 350072

belinann@mail.ruhttps://orcid.org/0009-0005-4834-072XНовицкийА. В.NovitskiyA. V.

Андрей Владимирович Новицкий, аспирант кафедры технической механики и специальных машин имени профессора А.А. Петрика

350072, г. Краснодар, ул. Московская, 2

Andrey V. Novitskiy, postgraduate student of the Department of Technical Mechanics and Special Machines named after Professor A.A. Petrik

2, Moskovskaya Str., Krasnodar, 350072

novitskiy_19@mail.ruhttps://orcid.org/0009-0005-1233-2525ЩетининМ. М.ShchetininM. M.

Максим Максимович Щетинин, студент кафедры технической механики и специальных машин имени профессора А.А. Петрика

350072, г. Краснодар, ул. Московская, 2

Maksim M. Shchetinin, student of the Department of Technical Mechanics and Special Machines named after Professor A.A. Petrik

2, Moskovskaya Str., Krasnodar, 350072

maks.shchetinin202@mail.ruКубанский государственный технологический университетРоссияKuban State Technological UniversityRussian Federation202425122024244360368Copyright © Prikhodko A.A., Belina N.N., Novitskiy A.V., Shchetinin M.M., 20242024Приходько А.А., Белина Н.Н., Новицкий А.В., Щетинин М.М.Prikhodko A.A., Belina N.N., Novitskiy A.V., Shchetinin M.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.vestnik-donstu.ru/jour/article/view/2302

Introduction. Mechanisms with non-circular gears are of wide interest to researchers and inventors due to their compactness and the implementation of a wide range of transfer functions. The development of this area is stimulated by the advancements and reduction in cost of mechanical processing and additive manufacturing technologies, as well as the use of applied mathematical modeling packages for the analysis and synthesis of non-circular gears. Traditionally, noncircular gears are used to transmit rotational motion between parallel axes with a variable ratio of angular velocities. However, their use in planetary gear schemes provides implementing various types of output link motion. The analysis of the papers on the research area shows that gears with movable rotation axes have not been sufficiently studied from the point of view of kinematics and dynamics. Most research papers reveal the theory of such mechanisms without verifying the results obtained in practice. This work is aimed at the experimental verification of the kinematics of a planetary mechanism with two external engagements, which contains elliptical gears.Materials and Methods. The kinematic model of the mechanism under study is built on the basis of the velocity diagram of its links, which made it possible to obtain expressions for finding an analogue of the angular velocity and the position function of the output shaft. The experimental study of kinematics was performed on a laboratory stand containing a model of a planetary mechanism with a set of replaceable gear wheels, absolute encoders on the input and output shafts of the mechanism, a controller, and a PC for recording and processing the signal. The analysis of the obtained results was performed on a computer using statistical analysis methods.Results. As a result of kinematic analysis, position functions were constructed for three alternative planetary mechanisms, which had different geometric parameters of the gears and made it possible to implement various types of motion of the output shaft: swinging motion, discontinuous motion, and unilateral uneven rotation.Discussion and Conclusion. The analysis of the experimental results showed the adequacy of the constructed mathematical model of kinematics to real mechanisms. The confidence interval of measuring errors at a reliability level of 95% was 0.16±0.08° for the first version of the mechanism, 0.57±0.22° — for the second version, and 0.08±0.26° — for the third. The proposed planetary mechanism with elliptical gears for implementing various types of motion can be used in drives of process equipment in numerous industries: chemical and food (mixers), oil refining (pumping units for crude production), mechanical engineering (compressors, pumps, automated machines), and others. The conducted kinematic studies of the planetary mechanism and their experimental analysis are needed for further dynamic and force investigations, as well as for the design of drives based on the proposed transmission.

Введение. Механизмы с некруглыми зубчатыми колесами вызывают широкий интерес исследователей и изобретателей вследствие их компактности и реализации широкого спектра передаточных функций. Развитие данной области стимулируется развитием и удешевлением технологий механической обработки и аддитивного производства, а также применением прикладных пакетов математического моделирования для анализа и синтеза некруглых зубчатых колес. Некруглые зубчатые колеса традиционно служат для передачи вращательного движения между параллельными осями с переменным отношением угловых скоростей. Однако их применение в схемах планетарных передач позволяет реализовать различные виды движения выходного звена. Анализ работ по тематике исследования показывает, что передачи с подвижными осями вращения недостаточно исследованы с точки зрения кинематики и динамики. Большинство научных работ раскрывают теорию таких механизмов, не проводя верификации полученных результатов на практике. Целью настоящей работы является экспериментальная верификация кинематики планетарного механизма с двумя внешними зацеплениями, имеющего в своем составе эллиптические зубчатые колеса.Материалы и методы. Кинематическая модель исследуемого механизма построена на базе плана скоростей его звеньев, который позволил получить выражения для нахождения аналога угловой скорости и функции положения выходного вала. Экспериментальное исследование кинематики выполнено на лабораторном стенде, содержащем макет планетарного механизма с набором сменных зубчатых колес, абсолютные энкодеры на входном и выходном валах механизма, контроллер и ПК для регистрации и обработки сигнала. Анализ полученных результатов проведен на ЭВМ с использованием методов статистического анализа.Результаты исследования. В результате кинематического анализа построены функции положения для трех вариантов планетарного механизма, имеющих различные геометрические параметры зубчатых колес и позволяющих реализовать различные виды движения выходного вала: возвратно-вращательное движение, движение с остановками и одностороннее неравномерное вращение.Обсуждение и заключение. Анализ результатов эксперимента показал адекватность построенной математической модели кинематики реальным механизмам. Доверительный интервал ошибок измерения при уровне достоверности 95 % составил для первого варианта механизма 0,16 ± 0,08, для второго варианта — 0,57 ± 0,22 и для третьего — 0,08 ± 0,26. Предложенный планетарный механизм с эллиптическими зубчатыми колесами для реализации различных видов движения может быть применен в приводах технологического оборудования многих отраслей промышленности: химической и пищевой (перемешивающие устройства), нефтеперерабатывающей (станки-качалки для добычи нефти), машиностроительной (компрессоры, насосы, станки-автоматы) и других. Проведенные кинематические исследования планетарного механизма и их экспериментальный анализ необходимы при дальнейшем динамическом и силовом исследованиях, а также при проектировании приводов на базе предложенной передачи.

планетарный механизмэллиптические зубчатые колесакинематический анализфункция положениястатистический анализнеопределенность измерениядоверительный интервалplanetary mechanismelliptical gearskinematic analysisposition functionstatistical analysisuncertainty of measurementconfidence intervalИсследование выполнено при финансовой поддержке Кубанского научного фонда в рамках научно-инновационного проекта № НИП–20.1/135 «Конструирование и исследование планетарной передачи эллиптическими зубчатыми колесами в составе привода поршневого компрессора».The work was done with the financial support from the Kuban Science Foundation within the framework of the research and innovative project no. NIP–20.1/135 “Design and Study of a Planetary Transmission with Elliptical Gears as Part of a Piston Compressor Drive”.ReferencesLozzi A. Non-Circular Gears — Graphic Generation of Involutes and Base Outlines. 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The authors declare that there are no conflicts of interest present.