sibsutisВестник СибГУТИThe Herald of the Siberian State University of Telecommunications and Information Science1998-6920СибГУТИ10.55648/1998-6920-2025-19-1-54-64sibsutis-923Research ArticleСтатьиРазработка нового математического метода моделирования движения микрополярного смазочного материала в рабочем зазоре модифицированной конструкции подшипникаDevelopment of a new mathematical method for modeling the movement of a micropolar lubricant in the working gap of a modified bearing structurehttps://orcid.org/0000-0003-2810-3047МукутадзеМурман АлександровичMukutadzeMurman Alexandrovichmurman1963@yandex.ruhttps://orcid.org/0000-0002-3012-4181ЧубЕлена ГригорьевнаChubElena Grigorievnahttps://orcid.org/0000-0002-0737-1846БолговаЕкатерина АлександровнаBolgovaEkaterina AlexandrovnaЗадорожнаяНаталья СергеевнаZadorozhnayaNatalya SergeevnaРостовский государственный университет путей сообщенияРоссияRostov State Transport UniversityRussian Federation202521032025191Вестник СибГУТИ5464Copyright © Мукутадзе М.А., Чуб Е.Г., Болгова Е.А., Задорожная Н.С., 20252025Мукутадзе М.А., Чуб Е.Г., Болгова Е.А., Задорожная Н.С.Mukutadze M.A., Chub E.G., Bolgova E.A., Zadorozhnaya N.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.sibsutis.ru/jour/article/view/923

Движущийся в зазоре жидкий смазочный материал неизбежно содержит атмосферные газы, которые значительно влияют на такое эксплуатационное свойство смазочного материала, как сжимаемость. Данное исследование включает разработку и анализ математической модели микрополярного смазочного материала в подшипнике скомпозиционными фторопластсодержащими покрытиями и опорным профилем, адаптированным к конкретным условиям трения. На основе уравнения движения исследуемого жидкого смазочного материала, уравнения неразрывности и уравнения состояния получены новые математические модели, учитывающие дополнительносжимаемость смазочного материала. Существенно расширены возможности применения на практике полученных авторами математических моделей модифицированной конструкции радиального подшипника с учетом новых факторов, которые позволяют проводить оценку эксплуатационных характеристик радиальных подшипников. Модифицированная конструкция радиального подшипника скольжения позволила уточнить, при учете дополнительного фактора – сжимаемости смазочного материала,несущую способность на 8–10 %, а коэффициент трения – на 7–9 % в диапазоне исследованных режимов

The liquid lubricant moving in the gap inevitably contains atmospheric gases, which significantly affect such an operational property of the lubricant as compressibility. This study includes the development and analysis of a mathematical model of a micro-polar lubricant in a bearing with composite fluoroplastic coatings and a support profile adapted to specific friction conditions. Based on the equation of motion of the liquid lubricant under study, the continuity equation and the equation of state, new mathematical models are obtained that additionally take into account the compressibility of the lubricant. The possibilities of applyingin practice the mathematical models of the modified radial bearing structure obtained by the authors have been significantly expanded, taking into account new factors that make it possible to evaluate the performance characteristics of radial bearings. The modified design of the radialsliding bearing made it possible to clarify, taking into account an additional factor – the compressibility of the lubricant, the bearing capacity by 8–10 %, and the coefficient of friction by 7–9 % in the range of the studied modes

сжимаемостьмодифицированная конструкцияпокрытиегидродинамический режиммикрополярный смазочный материаладаптированный профиль.compressibilitymodified designcoatinghydrodynamic modemicropolar lubricantadapted profileReferencesIsaacs N.S. Liquid phase high pressure chemistry. New York – Chichester Brisbane – Toronto: Wiley-Interscience; 1981. 414 p.Isaacs N. S. Liquid phase high pressure chemistry. New York – Chichester Brisbane – Toronto,le Noble W.H. Organic high pressure chemistry. – Amsterdam – Oxford – New York – Tokyo: Elsevier; 1988. 489 p.Wiley-Interscience, 1981. 414 p.Marcus Y., Hefter G.T. The compressibility of liquids at ambient temperature and pressure. H. Mol. Liquids. 1997;73–74:61–74.le Noble W. H. Organic high pressure chemistry. Amsterdam – Oxford – New York – Tokyo,Kiselev V.D., Kashaeva E.A., Konovalov A.I. Pressure effect on the rate and equilibrium constant of the Diels-Alder reaction 9-chloroanthracene with tetracyanoethylene. Tetrahedron. 1999;55:1153–1162.Elsevier, 1988. 489 p.Киселев В.Д., Болотов А.Вю., Кашаева Е.А., Коновалов А.И. Определение изотермической сжимаемости растворителя по изменению оптической плотности раствора красителя под давлением. Изв. РАН. Сер. хим. 2006;12:2049–2052.Marcus Y., Hefter G. T. The compressibility of liquids at ambient temperature and pressure. JournalRiddick J.A. Organic solvents. New York: John Wiley & Sons; 1986. 1325 p.of Molecular Liquids. 1997, vol. 73–74, pp. 61–74.Cibulka I., Zikova M. Liquid densities at elevated pressures of l-alkanols from C1 to C10: a critical evaluation of experimental data. J. Chem. Eng. Data. 1994;39: 876–886.Kiselev V. D., Kashaeva E. A., Konovalov A. I. Pressure effect on the rate and equilibrium constantCibulka I., Hnedkovsky L. Liquid densities at elevated pressures of n-alkanes from C5 to C16: a critical evaluation of experimental data. J. Chem. Eng. Data. 1996;41:657–668.of the Diels-Alder reaction 9-chloroanthracene with tetracyanoethylene. Tetrahedron, 1999, vol. 55.Cibulka I., Hnedkovsky L., Takagi T. P-d-T data of liquids: summarization and evaluation. 3. Ethers, ketones, aldehydes, carboxylic acids, and esters. J. Chem. Eng. Data. 1997;42:2–26.pp. 1153–1162.Cibulka I., Hnedkovsky L., Takagi T. P-d-T data of liquids: summarization and evaluation. 4. Higher l-alkanols (C11, C12, C14, C16), secondary, tertiary, and branched alkanols, cycloalkanoles, alkanediols, alkanetriols. ether alkanols, and aromatic hydroxyl derivatives. J. Chem. Eng. Data. 1997;42:415–433.Kiselev V. D., Bolotov A. V., Kashaeva E. A., Konovalov A. I. Opredelenie izotermicheskojCibulka I., Takagi T. P-d-T data of liquids: summarization and evaluation. 5. Aromatic hydrocarbons. J. Chem. Eng. Data. 1999;44:411–429.szhimaemosti rastvoritelya po izmeneniyu opticheskoj plot-nosti rastvora krasitelya pod davleniemCibulka I., Takagi T. P-d-T data of liquids: summarization and evaluation. 6. Nonaromatic hydrocarbons (Cn, n ≥ 5) except n-alkanes C5 to C16. J. Chem. Eng. Data. 1999;44:1105–1128.[Determination of the isothermal compressibility of a solvent by changing the optical density of aCibulka I., Takagi T., Ruzicka K. P-d-T data of liquids: summarization and evaluation. 7. Selected halogenated hydrocarbons. J. Chem. Eng. Data. 2001;46:2–28.dye solution under pressure]. Izvestiya RAN. Seriya himicheskaya, 2006, no. 12, pp. 2049–2052.Cibulka I., Takagi T. P-d-T data of liquids: summarization and evaluation. 8. Miscellaneous compounds. J. Chem. Eng. Data. 2002;47:1037–1070.Riddick J. A. Organic solvents. New York: John Wiley & Sons, 1986. 1325 p.Циклис Д.С. физико-химических исследований при высоких и сверхвысоких давлениях. М.: Химия; 1976. 430 с.Cibulka I., Zikova M. Liquid densities at elevated pressures of l-alkanols from C1 to C10: a criticalБриджмен П.В. Физика высоких давлений. М.: Объединен. науч-техн. изд-во НКТП СССР; 1935. 402 с.evaluation of experimental data. Journal of Chemical & Engineering Data, 1994, vol. 39, pp. 876–Разумихин В.Н. Гидростатический метод определения плотности жидкстей при давлении до 5000 кгс/см2. Труды институтов Комитета стандартов мер и измерительных приборов. 1960; 46(106); 96–106.Разумихин В.Н. Гидростатический метод определения плотности жидкстей при давлении до 5000 кгс/см2. Труды институтов Комитета стандартов мер и измерительных приборов. 1960; 46(106); 96–106.Hayward A.T.J. How to measure the isothermal compressibility of liquids accurately. J. Phys. D.: Appl. Phys. 1971; 4; 938–950.Разработка нового математического метода моделирования микрополярного движения... 63Hayward A.T.J. Compressibility equations for liquids: A comparative Study. British J. Appl. Phys. 1967; 18:965–977.Cibulka I., Hnedkovsky L. Liquid densities at elevated pressures of n-alkanes from C5 to C16: aКиселев В.Д., Болотов А.В., Сатонин А.П., Кашаева Е.А., Коновалов А.И. Сжимаемость жидкости и её внутреннее давление. Ученые записки Казанского государственного университета. 2008;150;3:76–90.critical evaluation of experimental data. Journal of Chemical & Engineering Data, 1996. vol. 41,Василенко В.В., Кирищиева В.И., Мукутадзе М.А., Шведова В.Е. Исследование износостойкости подшипника скольжения с полимерным покрытием опорного кольца, имеющего канавку. Advanced Engineering Research. 2022;22;4:365–372.pp. 657–668.Ахвердиев К.С., Лагунова Е.О., Василенко В.В. Расчетная модель радиального подшипника, смазываемого расплавом, с учетом зависимости вязкости от давления. Вестник Донского государственного технического университета. 2017;17(3):27–37.Cibulka I., Hnedkovsky L., Takagi T. P-d-T data of liquids: summarization and evaluation. 3. Ethers,ketones, aldehydes, carboxylic acids, and esters. Journal of Chemical & Engineering Data, 1997, vol.ketones, aldehydes, carboxylic acids, and esters. Journal of Chemical & Engineering Data, 1997, vol.42, pp. 2–26.42, pp. 2–26.Cibulka I., Hnedkovsky L., Takagi T. P-d-T data of liquids: summarization and evaluation. 4. HigherCibulka I., Hnedkovsky L., Takagi T. P-d-T data of liquids: summarization and evaluation. 4. Higherl-alkanols (C11, C12, C14, C16), secondary, tertiary, and branched alkanols, cycloalkanoles,l-alkanols (C11, C12, C14, C16), secondary, tertiary, and branched alkanols, cycloalkanoles,alkanediols, alkanetriols. ether alkanols, and aromatic hydroxyl derivatives. Journal of Chemical &alkanediols, alkanetriols. ether alkanols, and aromatic hydroxyl derivatives. Journal of Chemical &Engineering Data, 1997, vol. 42, pp. 415–433.Engineering Data, 1997, vol. 42, pp. 415–433.Cibulka I., Takagi T. P-d-T data of liquids: summarization and evaluation. 5. AromaticCibulka I., Takagi T. P-d-T data of liquids: summarization and evaluation. 5. Aromatichydrocarbons. Journal of Chemical & Engineering Data, 1999, vol. 44, pp. 411–429.hydrocarbons. Journal of Chemical & Engineering Data, 1999, vol. 44, pp. 411–429.Cibulka I., Takagi T. P-d-T data of liquids: summarization and evaluation. 6. NonaromaticCibulka I., Takagi T. P-d-T data of liquids: summarization and evaluation. 6. Nonaromatichydrocarbons (Cn, n ≥ 5) except n-alkanes C5 to C16. Journal of Chemical & Engineering Data,hydrocarbons (Cn, n ≥ 5) except n-alkanes C5 to C16. Journal of Chemical & Engineering Data,1999, vol. 44, pp. 1105–1128.1999, vol. 44, pp. 1105–1128.Cibulka I., Takagi T., Ruzicka K. P-d-T data of liquids: summarization and evaluation. 7. SelectedCibulka I., Takagi T., Ruzicka K. P-d-T data of liquids: summarization and evaluation. 7. Selectedhalogenated hydrocarbons. Journal of Chemical & Engineering Data, 2001, vol. 46, pp. 2–28.halogenated hydrocarbons. Journal of Chemical & Engineering Data, 2001, vol. 46, pp. 2–28.Cibulka I., Takagi T. P-d-T data of liquids: summarization and evaluation. 8. MiscellaneousCibulka I., Takagi T. P-d-T data of liquids: summarization and evaluation. 8. Miscellaneouscompounds. Journal of Chemical & Engineering Data, 2002, vol. 47, pp. 1037–1070.compounds. Journal of Chemical & Engineering Data, 2002, vol. 47, pp. 1037–1070.Tsiklis D. S. Tekhnika fiziko-himicheskih issledovanij pri vysokih i sverhvysokih davleniyahTsiklis D. S. Tekhnika fiziko-himicheskih issledovanij pri vysokih i sverhvysokih davleniyah[Technique of physico-chemical research at high and ultrahigh pressures]. Moscow, Chemistry,[Technique of physico-chemical research at high and ultrahigh pressures]. Moscow, Chemistry,430 p.430 p.Bridgman P. V. Fizika vysokih davlenij [Physics of high pressures]. Moscow, Ob"edinyonnoeBridgman P. V. Fizika vysokih davlenij [Physics of high pressures]. Moscow, Ob"edinyonnoenauchno-tekhnicheskoe izdatel'stvo NKTP SSSR, 1935. 402 p.nauchno-tekhnicheskoe izdatel'stvo NKTP SSSR, 1935. 402 p.Razumikhin V. N. Gidrostaticheskij metod opredeleniya plotnosti zhidkostej pri davlenii do 5000Razumikhin V. N. Gidrostaticheskij metod opredeleniya plotnosti zhidkostej pri davlenii do 5000kgs/sm2 [Hydrostatic method for determining the density of liquids at pressures up to 5000kgs/sm2 [Hydrostatic method for determining the density of liquids at pressures up to 5000kgf/cm2]. Trudy institutov Komiteta standartov mer i izmeritel'nyh priborov, 1960, vol. 46(106), pp.kgf/cm2]. Trudy institutov Komiteta standartov mer i izmeritel'nyh priborov, 1960, vol. 46(106), pp.96–106.96–106.Hayward A. T. J. How to measure the isothermal compressibility of liquids accurately. Journal ofHayward A. T. J. How to measure the isothermal compressibility of liquids accurately. Journal ofPhysics D: Applied Physics, 1971, vol. 4, pp. 938–950.Physics D: Applied Physics, 1971, vol. 4, pp. 938–950.Hayward A. T. J. Compressibility equations for liquids: A comparative study. British Journal ofHayward A. T. J. Compressibility equations for liquids: A comparative study. British Journal ofApplied Physics, 1967, vol. 18, pp. 965–977.Applied Physics, 1967, vol. 18, pp. 965–977.Kiselev V. D., Bolotov A.V., Satonin A. P., Kashaeva E. A., Konovalov A. I. Szhimaemost' zhidkosti iKiselev V. D., Bolotov A.V., Satonin A. P., Kashaeva E. A., Konovalov A. I. Szhimaemost' zhidkosti ieyo vnutrennee davlenie [Compressibility of a liquid and its internal pressure]. Uchenye Zapiskieyo vnutrennee davlenie [Compressibility of a liquid and its internal pressure]. Uchenye ZapiskiKazanskogo Universiteta, 2008, vol. 150, no. 3. pp. 76–90.Kazanskogo Universiteta, 2008, vol. 150, no. 3. pp. 76–90.Vasilenko V. V., Kirishchieva V. I., Mukutadze M. A., Shvedova V. E. Issledovanie iznosostojkostiVasilenko V. V., Kirishchieva V. I., Mukutadze M. A., Shvedova V. E. Issledovanie iznosostojkostipodshipnika skol'zheniya s polimernym pokrytiem opornogo kol'ca, imeyushchego kanavkupodshipnika skol'zheniya s polimernym pokrytiem opornogo kol'ca, imeyushchego kanavku[Investigation of the wear resistance of a sliding bearing with a polymer coating of a support ring[Investigation of the wear resistance of a sliding bearing with a polymer coating of a support ringhaving a groove]. Advanced Engineering Research (Rostov-on-Don), 2022, vol. 22, no. 4. pp. 365–having a groove]. Advanced Engineering Research (Rostov-on-Don), 2022, vol. 22, no. 4. pp. 365–Akhverdiev K. S., Lagunova E. O., Vasilenko V. V. Raschetnaya model' radial'nogo podshipnika,Akhverdiev K. S., Lagunova E. O., Vasilenko V. V. Raschetnaya model' radial'nogo podshipnika,smazyvaemogo rasplavom, s uchetom zavisimosti vyazkosti ot davleniya [Calculation model of asmazyvaemogo rasplavom, s uchetom zavisimosti vyazkosti ot davleniya [Calculation model of aradial bearing lubricated by melt, taking into account the dependence of viscosity on pressure].radial bearing lubricated by melt, taking into account the dependence of viscosity on pressure].Vestnik Donskogo Gosudarstvennogo Tekhnicheskogo Universiteta, 2017, no. 17(3), pp. 27–37Vestnik Donskogo Gosudarstvennogo Tekhnicheskogo Universiteta, 2017, no. 17(3), pp. 27–37

The authors declare that there are no conflicts of interest present.