fwjТрение и и износTitle in english0000-00000000-0000AGU10.32864/0202-4977-2026-47-4-404-414fwj-136Research ArticleСтатьиПотенциал управления трением скольжения вращающихся систем на основе параметризации геометрии периодического микрорельефа поверхностиPotential for Controlling Sliding Friction of Rotating Systems Based on Periodic Surface Micro-Texturing Geometry ParameterizationБашмурК. А.BashmurK. A.

пр-т Свободный, 79, г. Красноярск 660041

Svobodny pr., 79, Krasnoyarsk 660041

bashmur@bk.ruСибирский федеральный университетРоссияSiberian Federal UniversityRussian Federation202601102026474404414Copyright © AGU, 20262026AGUAGUhttps://fwj.ejournal.by/jour/about/submissions#copyrightNoticehttps://fwj.ejournal.by/jour/article/view/136

Статья посвящена исследованию технологии использования периодического микрорельефа поверхности как пассивного метода управления трением скольжения.

На примере радиального подшипника скольжения многоступенчатого центробежного насоса с помощью компьютерного гидродинамического моделирования и средств автоматизированного проектирования рассматривается параметрическая оптимизация геометрии микрорельефа поверхности в форме эллиптических дискретных впадин-ячеек для снижения коэффициента трения в системе «ротор–подшипник».

Коэффициент трения гладкой поверхности соответствовал гидродинамическому режиму смазки. Изменение целевой функции при однофакторном варьировании параметров не превышало 2 %. Выявленные зависимости носят нелинейный характер: с ростом длин осей эллипса L и H (то есть площади, занимаемой рельефом) коэффициент трения убывает и экспоненциально стремится к пороговому значению, а с ростом глубины D проходит через минимум. Минимум по глубине обусловлен конкуренцией убывающей адгезионной и возрастающей деформационной составляющих трения, вихреобразованием на входе в ячейку и эффектом гидродинамического клина; наибольшее влияние оказал параметр H (длина малой оси эллипса). Оптимальная конфигурация (D = 63 мкм, L = 250 мкм, H = 150 мкм) обеспечила снижение коэффициента трения на 6,18 % относительно гладкой поверхности.

Таким образом, посредством технологии использования периодического микрорельефа поверхности можно добиться как снижения коэффициента трения, так и его увеличения, что может найти отражение во множестве технических приложений.

This article explores the use of periodic surface micro-texturing as a passive method for controlling sliding friction.

Using a plain journal bearing of a multistage centrifugal pump as an example, computational fluid dynamics modeling and computer-aided design are used to examine the parametric optimization of surface micro-texturing geometry in the form of discrete elliptical dimples to reduce the friction coefficient in a rotorbearing system.

The friction coefficient of the smooth surface corresponded to the hydrodynamic lubrication regime. Under single-factor variation of the parameters, the change in the objective function did not exceed 2 %. The identified relationships were nonlinear: with increasing ellipse axis lengths L and H (the area occupied by the texture), the friction coefficient decreased and tended exponentially toward a threshold value, whereas with increasing depth D it passed through a minimum. The minimum with respect to depth arose from the competition between the decreasing adhesion and increasing deformation components of friction, vortex formation at the dimple inlet, and the hydrodynamic-wedge effect; the parameter H (the minor axis of the ellipse) had the largest influence. The optimal configuration (D = 63 µm, L = 250 µm, H = 150 µm) reduced the friction coefficient by 6.18 % relative to the smooth surface.

Thus, using periodic surface micro-texturing technology, it is possible to both reduce and increase the friction coefficient, which can be applied in a variety of technical applications.

автоматизированное проектированиеизноскомпьютерное гидродинамическое моделированиекоэффициент трениярадиальный подшипник скольжениямикрорельеф поверхностицентробежный агрегатэллиптические впадиныCADwearCFDfriction coefficientplain journal bearingsurface micro-texturingcentrifugal unitelliptical dimplesReferencesTang X., Lan Y., Bosiakov S., Zhuravkov M., He T., Xia Y., and Lyu Y. Investigation on the Coupling Effect of Bionic Micro-Texture Shape and Distribution on the Tribological Performance of WaterLubricated Sliding Bearings // Lubricants. — 2025 (13), no. 7, 305. DOI: 10.3390/lubricants13070305Tang X., Lan Y., Bosiakov S., Zhuravkov M., He T., Xia Y., and Lyu Y. Investigation on the Coupling Effect of Bionic Micro-Texture Shape and Distribution on the Tribological Performance of WaterLubricated Sliding Bearings // Lubricants. — 2025 (13), no. 7, 305. DOI: 10.3390/lubricants13070305Petrovsky E.A., Bashmur K.A., Shadchina Yu.N., Bukhtoyarov V.V., and Tynchenko V.S. Study of Microrelief Forming Technology on Sliding Bearings for Oil and Gas Centrifugal Units // Journal of Physics: Conference Series. — 2019 (1399), no. 5, 055032. DOI: 10.1088/1742-6596/1399/5/055032Petrovsky E.A., Bashmur K.A., Shadchina Yu.N., Bukhtoyarov V.V., and Tynchenko V.S. Study of Microrelief Forming Technology on Sliding Bearings for Oil and Gas Centrifugal Units // Journal of Physics: Conference Series. — 2019 (1399), no. 5, 055032. DOI: 10.1088/1742-6596/1399/5/055032Мышкин Н.К., Григорьев А.Я., Джанг Г. Устойчивое развитие и трибология полимеров // Трение и износ. — 2022 (43), № 6, 539—547. DOI: 10.32864/0202-4977-2022-43-6-539-547Myshkin N.K., Grigoriev A.Y., and Zhang G. Sustainable Development and Polymer Tribology // Journal of Friction and Wear. — 2022 (43), no. 6, 353—358. DOI: 10.3103/S1068366622060113Patel R., Khan Z.A., Saeed A., and Bakolas V. A Review of Mixed Lubrication Modelling and Simulation // Tribology in Industry. — 2022 (44), no. 1, 150—168. DOI: 10.24874/ti.1186.09.21.11Patel R., Khan Z.A., Saeed A., and Bakolas V. A Review of Mixed Lubrication Modelling and Simulation // Tribology in Industry. — 2022 (44), no. 1, 150—168. DOI: 10.24874/ti.1186.09.21.11Андриевский Б.Р., Фрадков А.Л. Управление хаосом: методы и приложения. II. Приложения // Автоматика и телемеханика. — 2004, № 4, 3—34.Andrievskii B.R. and Fradkov A.L. Control of Chaos: Methods and Applications. II. Applications // Automation and Remote Control. — 2004 (65), no. 4, 505—533. DOI: 10.1023/B:AURC.0000023528.59389.09Bulatov V.P., Krasny V.A., and Schneider Y.G. Basics of Machining Methods to Yield Wear- and Fretting-Resistive Surfaces, Having Regular Roughness Patterns // Wear. — 1997 (208), no. 1–2, 132—137. DOI: 10.1016/S0043-1648(96)07403-0Bulatov V.P., Krasny V.A., and Schneider Y.G. Basics of Machining Methods to Yield Wear- and Fretting-Resistive Surfaces, Having Regular Rough-ness Patterns // Wear. — 1997 (208), no. 1–2, 132—137. DOI: 10.1016/S0043-1648(96)07403-0Schnell G., Müller T., and Seitz H. Tribological Effects of Different Scaled Chevron-Shaped Microstructures on the Stribeck Curve of Parallel Contacts Under Unidirectional Friction // Tribology International. — 2023 (178 (B)), 108099. DOI: 10.1016/j.triboint.2022.108099Schnell G., Müller T., and Seitz H. Tribological Effects of Different Scaled Chevron-Shaped Microstructures on the Stribeck Curve of Parallel Contacts Under Unidirectional Friction // Tribology International. — 2023 (178 (B)), 108099. DOI: 10.1016/j.triboint.2022.108099Nakano M., Korenaga A., Korenaga A., Miyake K., Murakami T., Ando Y., Usami H., and Sasaki S. Applying Micro-Texture to Cast Iron Surfaces to Reduce the Friction Coefficient Under Lubricated Conditions // Tribology Letters. — 2007 (28), no. 2, 131—137. DOI: 10.1007/s11249-007-9257-2Nakano M., Korenaga A., Korenaga A., Miyake K., Murakami T., Ando Y., Usami H., and Sasaki S. Applying Micro-Texture to Cast Iron Surfaces to Reduce the Friction Coefficient Under Lubricated Conditions // Tribology Letters. — 2007 (28), no. 2, 131—137. DOI: 10.1007/s11249-007-9257-2Song F., Yang X., Dong W., Zhu Y., Wang Z., and Wu M. Research and Prospect of Textured Sliding Bearing // The International Journal of Advanced Manufacturing Technology. — 2022 (121), 1—25. DOI: 10.1007/s00170-022-09281-2Song F., Yang X., Dong W., Zhu Y., Wang Z., and Wu M. Research and Prospect of Textured Sliding Bearing // The International Journal of Advanced Manufacturing Technology. — 2022 (121), 1—25. DOI: 10.1007/s00170-022-09281-2Башмур К.А., Загуляев А.В., Агафонов Е.Д., Небылицын М.В. Потенциал устойчивого развития горной техники с опорами скольжения на основе концепций «зеленая трибология» // Устойчивое развитие горных территорий. — 2025 (17), № 2, 787—797. DOI: 10.21177/1998-4502-2025-17-2-787-797Bashmur K.A., Zagulyaev A.V., Agafonov E.D., Nebylitsyn M.V. Green tribology concepts: a potential for sustainable development of themining machinery with sliding bearings // Sustainable Development of Mountain Territories. — 2025 (17), no. 2, 787—797. DOI: 10.21177/1998-4502-2025-17-2- 787-797 (in Russian)Ding S., Wei H., Yang O., Deng L., and Mu D. Tribological Behaviors of Laser Textured Surface Under Different Lubrication Conditions for Rotary Compressor // Scientific Reports. — 2023, no. 13, 5378. DOI: 10.1038/s41598-023-32490-yDing S., Wei H., Yang O., Deng L., and Mu D. Tribological Behaviors of Laser Textured Surface Under Different Lubrication Conditions for Rotary Compressor // Scientific Reports. — 2023, no. 13, 5378. DOI: 10.1038/s41598-023-32490-yChen Q., Yu A., Zhao S., Wu M., Yuan J., Sun L., and Chi J. Effect of Magnetic Field on Tribological Performance of Laser Dimple Textured Surface // Wear. — 2021 (468–469), 203584. DOI: 10.1016/j.wear.2020.203584Chen Q., Yu A., Zhao S., Wu M., Yuan J., Sun L., and Chi J. Effect of Magnetic Field on Tribological Performance of Laser Dimple Textured Surface // Wear. — 2021 (468–469), 203584. DOI: 10.1016/j.wear.2020.203584Myshkin N.K. and Grigoriev A.Y. Problems in Friction Analysis // In: Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science / Uhl T. (eds). — Singapore: Springer. — 2019, no. 73, 3779—3788. DOI: 10.1007/978-3-030-20131-9_374Myshkin N.K. and Grigoriev A.Y. Problems in Friction Analysis // In: Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science / Uhl T. (eds). — Singapore: Springer. — 2019, no. 73, 3779—3788. DOI: 10.1007/978-3-030-20131-9_374Fu G. and Untaroiu A. An Optimum Design Approach for Textured Thrust Bearing with EllipticalShape Dimples Using Computational Fluid Dynamics and Design of Experiments Including Cavitation // Journal of Engineering for Gas Turbines and Power. — 2017 (139), no. 9, 092502. DOI: 10.1115/1.4036188Fu G. and Untaroiu A. An Optimum Design Approach for Textured Thrust Bearing with EllipticalShape Dimples Using Computational Fluid Dynamics and Design of Experiments Including Cavitation // Journal of Engineering for Gas Turbines and Power. — 2017 (139), no. 9, 092502. DOI: 10.1115/1.4036188Сплавский И.С. Особенности изнашивания и механизмы разрушения рабочих ступеней высокооборотного насоса // Трение и износ. — 2024 (45), № 4, 310—318. DOI: 10.32864/0202-4977-2024-45-4-310-318Splavskiy I.S. The Wear Features and Destruction Mechanisms of the Working Stages of a High-Speed Pump // Journal of Friction and Wear. — 2024 (45), no. 4, 211—216. DOI: 10.3103/S1068366624700314Menter F. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications // AIAA Journal. — 1994 (32), no. 8, 1598—1605. DOI: 10.2514/3.12149Menter F. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications // AIAA Journal. — 1994 (32), no. 8, 1598—1605. DOI: 10.2514/3.12149Lu X. and Khonsari M.M. An Experimental Investigation of Dimple Effect on the Stribeck Curve of Journal Bearings // Tribology Letters. — 2007 (27), 169—176. DOI: 10.1007/s11249-007-9217-xLu X. and Khonsari M.M. An Experimental Investigation of Dimple Effect on the Stribeck Curve of Journal Bearings // Tribology Letters. — 2007 (27), 169—176. DOI: 10.1007/s11249-007-9217-xZhang H., Hua M., Dong G., Zhang D., and Chin K. A Mixed Lubrication Model for Studying Tribological Behaviors of Surface Texturing // Tribology International. — 2016 (93(B)), 583—592. DOI: 10.1016/j.triboint.2015.03.027Zhang H., Hua M., Dong G., Zhang D., and Chin K. A Mixed Lubrication Model for Studying Tribological Behaviors of Surface Texturing // Tribology International. — 2016 (93(B)), 583—592. DOI: 10.1016/j.triboint.2015.03.027Liu S., Sai Q., Wang S., and Williams J. Effects of Laser Surface Texturing and Lubrication on the Vibrational and Tribological Performance of Sliding Contact // Lubricants. — 2022 (10), no. 1, 10. DOI: 10.3390/lubricants10010010Liu S., Sai Q., Wang S., and Williams J. Effects of Laser Surface Texturing and Lubrication on the Vibrational and Tribological Performance of Sliding Contact // Lubricants. — 2022 (10), no. 1, 10. DOI: 10.3390/lubricants10010010Steege T., Bernard G., Darm P., Kunze T., and Lasagni A.F. Prediction of Surface Roughness in Functional Laser Surface Texturing Utilizing Machine Learning // Photonics. — 2023 (10), no. 4, 361. DOI: 10.3390/photonics10040361Steege T., Bernard G., Darm P., Kunze T., and Lasagni A.F. Prediction of Surface Roughness in Functional Laser Surface Texturing Utilizing Machine Learning // Photonics. — 2023 (10), no. 4,361. DOI: 10.3390/photonics10040361Dokshanin S.G., Tynchenko V.S., Bukhtoyarov V.V., Bashmur K.A., and Kukartsev V.V. Investigation of the Tribological Properties of Ultrafine Diamond-Graphite Powder as an Additive to Greases // IOP Conference Series: Materials Science and Engineering. — 2019 (560), 012192. DOI: 10.1088/1757-899X/560/1/012192Dokshanin S.G., Tynchenko V.S., Bukhtoyarov V.V., Bashmur K.A., and Kukartsev V.V. Investigation of the Tribological Properties of Ultrafine Diamond-Graphite Powder as an Additive to Greases // IOP Conference Series: Materials Science and Engineering. — 2019 (560), 012192. DOI: 10.1088/1757-899X/560/1/012192Керопян А.М., Албагачиев А.Ю. Исследование основных факторов, влияющих на повышение коэффициента трения взаимодействующих поверхностей рельсовых транспортных средств // Проблемы машиностроения и надежности машин. — 2024, № 3, 9—13. DOI: 10.31857/S0235711924030022Keropyan A.M. and Albagachiev A.Y. Study of the Main Factors Affecting the Increase in the Friction Coefficient of Interacting Surfaces of Rail Vehicles // Journal of Machinery Manufacture and Reliability. — 2024 (53), no. 3, 208—211. DOI: 10.1134/S1052618824700055Voyer J., Klien S., Velkavrh I., Ausserer F., and Diem A. Static and Dynamic Friction of Pure and Friction-Modified PA6 Polymers in Contact with Steel Surfaces: Influence of Surface Roughness and Environmental Conditions // Lubricants. — 2019 (7), no. 2, 17. DOI: 10.3390/lubricants7020017Voyer J., Klien S., Velkavrh I., Ausserer F., and Diem A. Static and Dynamic Friction of Pure and Friction-Modified PA6 Polymers in Contact with Steel Surfaces: Influence of Surface Roughness and Environmental Conditions // Lubricants. — 2019 (7), no. 2, 17. DOI: 10.3390/lubricants7020017Xu R., Sheng W., Zhou F., and Persson B.N.J. Rubber Wear: History, Mechanisms, and Perspectives // Tribology Letters. — 2025 (73), 90. DOI: 10.1007/s11249-025-02025-9Xu R., Sheng W., Zhou F., and Persson B.N.J. Rubber Wear: History, Mechanisms, and Perspectives // Tribology Letters. — 2025 (73), 90. DOI: 10.1007/s11249-025-02025-9Petrovskii É.A., Bashmur K.A., and Nashivanov I.S. Adaptive Control of Drill String Vibrations // Chemical and Petroleum Engineering. — 2019 (54), no. 9-10, 711—716. DOI: 10.1007/s10556-019-00538-4Petrovskii É.A., Bashmur K.A., and Nashivanov I.S. Adaptive Control of Drill String Vibrations // Chemical and Petroleum Engineering. — 2019 (54), no. 9-10, 711—716. DOI: 10.1007/s10556-019-00538-4

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