omnaОмский научный вестникOmsk Scientific Bulletin1813-82252541-7541Омский государственный технический университет10.25206/1813-8225-2026-198-102-111NWVIQComna-414Research ArticleЭЛЕКТРОНИКА, ФОТОНИКА, ПРИБОРОСТРОЕНИЕ И СВЯЗЬELECTRONICS, PHOTONICS, APPLIANCE AND COMMUNICATIONSФормирование и исследование модели ступенчатого газового слоя для применения в опорах измерительного и диагностического оборудованияFormation and investigation of a stepped gas-layer model in measuring and diagnostic equipment supportshttps://orcid.org/0000-0002-3819-9743КурзаковА. С.KurzakovA. S.

Курзаков Андрей Сергеевич, кандидат технических наук, доцент, доцент кафедры «Конструкторско-технологическое обеспечение машиностро-ительных производств»    

660041, г. Красноярск, пр. Свободный, 79

AuthorID (РИНЦ): 361924

AuthorID (SCOPUS): 55850380100

ResearcherID: OYD-6605-2025

Kurzakov Andrey Sergeyevich, Candidate of Technical Sciences, Associate Professor, Associate Professor of the Design and Technological Support for Mechanical Engineering Production Department    

Svobodnyy Ave., 79, Krasnoyarsk, 660041

AuthorID (RSCI): 361924

AuthorID (SCOPUS): 55850380100

ResearcherID: OYD-6605-2025

kurzakov@list.ruСибирский федеральный университетРоссияSiberian Federal UniversityRussian Federation20260707202602102111Copyright © Курзаков А.С., 20262026Курзаков А.С.Kurzakov A.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://onv.omgtu.ru/jour/article/view/414

В статье представлены результаты разработки и исследования подхода, позволяющего построить расчётную сетку тонкого ступенчатого газового слоя, обеспечивающего несущую способность в опорах измерительного и диагностического оборудования высокой точности. Отмечается, что традиционные методы для автоматической генерации расчётной сетки обычно приводят к искажению исходной геометрии и, как следствие, к невозможности корректного моделирования течения газа.

Автором предложена методика, основанная на разложении модели на простые тела, которая позволяет формировать расчётную сетку правильной структуры с требуемой формой и ориентацией элементов. Важным компонентом предложенной методики является комплекс настроек, применяемых к модели с целью обеспечения межзонных интерфейсов, настройки граничных условий, а также для последующей инициализации решения и обеспечения сходимости при расчётах в системе ANSYS Fluent.

В исследовании также приведены результаты, иллюстрирующие ход тестовых расчётов и подтверждающие эффективность разработанного подхода при моделировании состояния смазочного газового слоя.

The article demonstrates the results of the development and research of an approach that allows constructing a computational grid of a thin stepped gas layer that provides load-bearing capacity in the supports of high-precision measuring and diagnostic equipment. Moreover, it is noted that traditional methods for automatic generation of the computational grid usually lead to distortion of the initial geometry and, as a result, to the impossibility of correct modeling of the gas flow.

The author suggests a method based on decomposing the model into simple bodies, which allows forming a computational grid of the correct structure with the required shape and orientation of the elements. An important component of the proposed methodology is a set of settings applied to the model in order to provide interband interfaces, adjust boundary conditions, as well as for subsequent initialization of the solution and ensure convergence in calculations in the ANSYS Fluent system.

In addition, the author presents the results that demonstrate the course of test calculations and validate the effectiveness of the proposed approach during the simulation of the lubricating gas layer.

газостатический подшипниктонкий смазочный слойструктурированная сеткаANSYS Fluentмежзонные интерфейсыраспределение давлениямоделирование теченияgasostatic bearingthin lubricating layerstructured meshANSYS Fluentzone interfacespressure distributionflow modelingReferencesGross W. A. Gas Film Lubrication. New York: John Wiley & Sons, 1962. 413 p.Gross W. A. Gas Film Lubrication. New York: John Wiley & Sons, 1962. 413 p.Hamrock B. J. Fundamentals of Fluid Film Lubrication. New York: McGraw-Hill, 2004. 728 p. ISBN 9780203021187.Hamrock B. J. Fundamentals of Fluid Film Lubrication. New York: McGraw-Hill, 2004. 728 p. ISBN 9780203021187.Шейнберг С. А. Газовая смазка подшипников скольжения // Трение и износ в машинах. 1953. № 8. С. 107–204.Sheynberg S. A. Gazovaya smazka podshipnikov skol’zheniya. Treniye i Iznos v Mashinakh. 1953;8:107–204. (In Russ.).Castelli V., Pirvics J. Review of Numerical Methods in Gas Bearing Film Analysis. Journal of Lubrication Technology. 1968;90(4):777–790. https://doi.org/10.1115/1.3601719.Castelli V., Pirvics J. Review of Numerical Methods in Gas Bearing Film Analysis. Journal of Lubrication Technology. 1968;90(4):777–790. https://doi.org/10.1115/1.3601719.Табачников Ю. Б. Методика расчета плоских кольцевых газостатических опор с круговой микроканавкой и ее экспериментальная проверка // Машиноведение. 1974. № 1. С. 96–103.Tabachnikov Yu. B. Metodika rascheta ploskikh kol’tsevykh gazostaticheskikh opor s krugovoy mikrokanavkoy i eye eksperimental’naya proverka. Mashinovedeniye. 1974;1:96–103. (In Russ.).Castelli V., Elrod H. G. Solution of the Stability Problem for 360 Deg Self-Acting, Gas-Lubricated Bearings. Journal of Basic Engineering. 1965;87(1):199–210. https://doi.org/10.1115/1.3650508.Castelli V., Elrod H. G. Solution of the Stability Problem for 360 Deg Self-Acting, Gas-Lubricated Bearings. Journal of Basic Engineering. 1965;87(1):199–210. https://doi.org/10.1115/1.3650508.Elrod H. G., McCabe J. T., Chu T. Y. Determination of Gas-Bearing Stability by Response to a Step-Jump. Journal of Lubrication Technology. 1967;89(4):493–498. https://doi.org/10.1115/1.3617042.Elrod H. G., McCabe J. T., Chu T. Y. Determination of Gas-Bearing Stability by Response to a Step-Jump. Journal of Lubrication Technology. 1967;89(4):493–498. https://doi.org/10.1115/1.3617042.Stout K. J., Pink E. G. Orifice compensated EP gas bearings: the significance of errors of manufacture. Tribology International. 1980;13(3):105–111. https://doi.org/10.1016/0301-679X(80)90052-3.Stout K. J., Pink E. G. Orifice compensated EP gas bearings: the significance of errors of manufacture. Tribology International. 1980;13(3):105–111. https://doi.org/10.1016/0301-679X(80)90052-3.Kwan Y.-B. P., Post J. B. A tolerancing procedure for inherently compensated, rectangular aerostatic thrust bearings. Tribology International. 2000;33(8):581–585. https://doi.org/10.1016/S0301-679X(00)00109-2.Kwan Y.-B. P., Post J. B. A tolerancing procedure for inherently compensated, rectangular aerostatic thrust bearings. Tribology International. 2000;33(8):581–585. https://doi.org/10.1016/S0301-679X(00)00109-2.Tsai M. H., Hsu T. Y., Pai K. R., Shih M. Ch. Precision position control of pneumatic servo table embedded with aerostatic bearing. Journal of System Design and Dynamics. 2008;2(4):940–949. https://doi.org/10.1299/jsdd.2.940.Tsai M. H., Hsu T. Y., Pai K. R., Shih M. Ch. Precision position control of pneumatic servo table embedded with aerostatic bearing. Journal of System Design and Dynamics. 2008;2(4):940–949. https://doi.org/10.1299/jsdd.2.940.Chen D., Bian Ya., Fan J. Experiments and Identification of the Unbalance of Aerostatic Guideways on the Micro-Scale. Sensors. 2014;14(3):4416–4427. https://doi.org/10.3390/s140304416.Chen D., Bian Ya., Fan J. Experiments and Identification of the Unbalance of Aerostatic Guideways on the Micro-Scale. Sensors. 2014;14(3):4416–4427. https://doi.org/10.3390/s140304416.Ding J., Chang Y., Chen P. [et al.]. Dynamic modeling of ultra-precision fly cutting machine tool and the effect of ambient vibration on its tool tip response. International Journal of Extreme Manufacturing. 2020;2(2):025301. https://doi.org/10.1088/2631-7990/ab7b59.Ding J., Chang Y., Chen P. [et al.]. Dynamic modeling of ultra-precision fly cutting machine tool and the effect of ambient vibration on its tool tip response. International Journal of Extreme Manufacturing. 2020;2(2):025301. https://doi.org/10.1088/2631-7990/ab7b59.Leach R. K., Giusca C. L., Naoi K. Development and characterization of a new instrument for the traceable measurement of areal surface texture. Measurement Science and Technology. 2009;20(12):125102. https://doi.org/10.1088/0957-0233/20/12/125102.Leach R. K., Giusca C. L., Naoi K. Development and characterization of a new instrument for the traceable measurement of areal surface texture. Measurement Science and Technology. 2009;20(12):125102. https://doi.org/10.1088/0957-0233/20/12/125102.Thomsen-Schmidt P. Characterization of a traceable profiler instrument for areal roughness measurement. Measurement Science and Technology. 2011;22(9):094019. https://doi.org/10.1088/0957-0233/22/9/094019.Thomsen-Schmidt P. Characterization of a traceable profiler instrument for areal roughness measurement. Measurement Science and Technology. 2011;22(9):094019. https://doi.org/10.1088/0957-0233/22/9/094019.Lee K.-W., Noh Y.-J., Gao W. [et al.]. Experimental investigation of an air-bearing displacement sensor for on-machine surface form measurement of micro-structures. International Journal of Precision Engineering and Manufacturing. 2011;12(4):671–678. https://doi.org/10.1007/s12541-011-0087-7.Lee K.-W., Noh Y.-J., Gao W. [et al.]. Experimental investigation of an air-bearing displacement sensor for on-machine surface form measurement of micro-structures. International Journal of Precision Engineering and Manufacturing. 2011;12(4):671–678. https://doi.org/10.1007/s12541-011-0087-7.Lian H. Ch. Rong, Li Yu. Influence of operating temperature on the static characteristics of an externally pressurized thrust bearing lubricated with refrigerant gas. Tribology Letters. 2021;69:123. https://doi.org/10.1007/s11249-021-01501-2.Lian H. Ch. Rong, Li Yu. Influence of operating temperature on the static characteristics of an externally pressurized thrust bearing lubricated with refrigerant gas. Tribology Letters. 2021;69:123. https://doi.org/10.1007/s11249-021-01501-2.Lu Z.-W., Zhang J.-A., Liu B. Study on the gas film flow field and its influencing factors at the outlet of the orifice of the aerostatic bearing. Shock and Vibration. 2020;2020:8891382. https://doi.org/10.1155/2020/8891382.Lu Z.-W., Zhang J.-A., Liu B. Study on the gas film flow field and its influencing factors at the outlet of the orifice of the aerostatic bearing. Shock and Vibration. 2020;2020:8891382. https://doi.org/10.1155/2020/8891382.Majumdar B. C. Zero-load stability of a rigid rotor supported on pressurized porous gas bearing. Mechanism and Machine Theory. 1977;12(4):303–310. https://doi.org/10.1016/0094-114X(77)90006-4.Majumdar B. C. Zero-load stability of a rigid rotor supported on pressurized porous gas bearing. Mechanism and Machine Theory. 1977;12(4):303–310. https://doi.org/10.1016/0094-114X(77)90006-4.Chen M. F., Lin Y. T. Static behavior and dynamic stability analysis of grooved rectangular aerostatic thrust bearings by modified resistance network method. Tribology International. 2002;35(5):329–338. https://doi.org/10.1016/S0301-679X(02)00012-9.Chen M. F., Lin Y. T. Static behavior and dynamic stability analysis of grooved rectangular aerostatic thrust bearings by modified resistance network method. Tribology International. 2002;35(5):329–338. https://doi.org/10.1016/S0301-679X(02)00012-9.Chen X.-D., He X.-M. The effect of the recess shape on performance analysis of the gas-lubricated bearing in optical lithography. Tribology International. 2006;39(11):1336–1341. https://doi.org/10.1016/j.triboint.2005.10.005.Chen X.-D., He X.-M. The effect of the recess shape on performance analysis of the gas-lubricated bearing in optical lithography. Tribology International. 2006;39(11):1336–1341. https://doi.org/10.1016/j.triboint.2005.10.005.Aoyama T., Kakinuma Y., Kobayashi Y. Numerical and experimental analysis for the small vibration of aerostatic guideways. CIRP Annals. 2006;55(1):419–422. https://doi.org/10.1016/S0007-8506(07)60449-1.Aoyama T., Kakinuma Y., Kobayashi Y. Numerical and experimental analysis for the small vibration of aerostatic guideways. CIRP Annals. 2006;55(1):419–422. https://doi.org/10.1016/S0007-8506(07)60449-1.Zhu J., Chen H., Chen X. Large eddy simulation of vortex shedding and pressure fluctuation in aerostatic bearings. Journal of Fluids and Structures. 2013;40:42–51. https://doi.org/10.1016/j.jfluidstructs.2013.03.012.Zhu J., Chen H., Chen X. Large eddy simulation of vortex shedding and pressure fluctuation in aerostatic bearings. Journal of Fluids and Structures. 2013;40:42–51. https://doi.org/10.1016/j.jfluidstructs.2013.03.012.Li Y., Lin Y., Zhu H., Sun Z. Research on the gas pressure fluctuation characteristics inside an aerostatic thrust bearing with a pocketed orifice-type restrictor. Tribology Transactions. 2014;57(1):28–35. https://doi.org/10.1080/10402004.2013.840406.Li Y., Lin Y., Zhu H., Sun Z. Research on the gas pressure fluctuation characteristics inside an aerostatic thrust bearing with a pocketed orifice-type restrictor. Tribology Transactions. 2014;57(1):28–35. https://doi.org/10.1080/10402004.2013.840406.Ramachandra S. A Solution of Reynolds equation for a full finite journal bearing. Journal of Basic Engineering. 1961;83(4):589–593. https://doi.org/10.1115/1.3662273.Ramachandra S. A Solution of Reynolds equation for a full finite journal bearing. Journal of Basic Engineering. 1961;83(4):589–593. https://doi.org/10.1115/1.3662273.Pandian M. C. A new method for the numerical solution of the Reynolds equation for gas-lubricated slider bearings. Journal of Engineering Mathematics. 1985;19:3–19. https://doi.org/10.1007/BF00055036.Pandian M. C. A new method for the numerical solution of the Reynolds equation for gas-lubricated slider bearings. Journal of Engineering Mathematics. 1985;19:3–19. https://doi.org/10.1007/BF00055036.Anaya-Dufresne M., Sinclair G. B. Some Exact Solutions of Reynolds Equation. Journal of Tribology. 1995;117(3):560–562. https://doi.org/10.1115/1.2831292.Anaya-Dufresne M., Sinclair G. B. Some Exact Solutions of Reynolds Equation. Journal of Tribology. 1995;117(3):560–562. https://doi.org/10.1115/1.2831292.Miyatake M., Yoshimoto Sh. Numerical investigation of static and dynamic characteristics of aerostatic thrust bearings with small feed holes. Tribology International. 2010;43(8):1353–1359. https://doi.org/10.1016/j.triboint.2010.01.002.Miyatake M., Yoshimoto Sh. Numerical investigation of static and dynamic characteristics of aerostatic thrust bearings with small feed holes. Tribology International. 2010;43(8):1353–1359. https://doi.org/10.1016/j.triboint.2010.01.002.Зернин М. В. Проблемы и перспективы построения эффективного конечно-элементного описания течения масла в зазоре опор жидкостного трения с учетом неоднородного распределения температур и деформаций поверхностей // Проблемы трибологии. 1997. № 1. С. 73–78. EDN: UQYQFH.Zernin M. V. Problemy i perspektivy postroyeniya effektivnogo konechnoelementnogo opisaniya techeniya masla v zazore opor zhidkostnogo treniya s uchetom neodnorodnogo raspredeleniya temperatur i deformatsiy poverkhnostey. Tribology Problems. 1997;1:73–78. EDN: UQYQFH. (In Russ.).Chang S. H., Chan C. W., Jeng Y. R. Numerical analysis of discharge coefficients in aerostatic bearings with orifice-type restrictors. Tribology International. 2015;90:157–163. https://doi.org/10.1016/j.triboint.2015.04.030.Chang S. H., Chan C. W., Jeng Y. R. Numerical analysis of discharge coefficients in aerostatic bearings with orifice-type restrictors. Tribology International. 2015;90:157–163. https://doi.org/10.1016/j.triboint.2015.04.030.Chen Y. S., Chiu C. C., Cheng Y. D. Influences of operational conditions and geometric parameters on the stiffness of aerostatic journal bearings. Precision Engineering. 2010;34(4):722–734. https://doi.org/10.1016/j.precisioneng.2010.04.001.Chen Y. S., Chiu C. C., Cheng Y. D. Influences of operational conditions and geometric parameters on the stiffness of aerostatic journal bearings. Precision Engineering. 2010;34(4):722–734. https://doi.org/10.1016/j.precisioneng.2010.04.001.Рыбкин Н. Н., Зернин М. В., Шилько С. В., Дробыш Т. В. Конечно-элементный анализ упругогидродинамического трения: учет деформаций деталей опор скольжения // Трение и износ. 2021. Т. 42, № 3. С. 254–267. https://doi.org/10.32864/0202-4977-2021-42-3-254-267. EDN: BGXNBN.Rybkin N. N., Zernin M. V., Shil’ko S. V., Drobysh T. V. Finite Element Analysis of Elasto-Hydrodynamic Friction: Taking into Account the Deformations of Sliding Bearing Parts. Friction and Wear. 2021;42(3):254–267. https://doi.org/10.32864/0202-4977-2021-42-3-254-267. EDN: BGXNBN. (In Russ.).Брунгардт М. В., Вавилов Д. В., Лукин Р. С. [и др.]. Численное исследование переходных процессов в самоустанавливающейся адаптивной гидростатической опоре // Технология машиностроения. 2016. № 2. С. 49–53. EDN: WAONYB.Brungardt M. V., Vavilov D. V., Lukin R. S. [et al.]. Chislennoye issledovaniye perekhodnykh protsessov v samoustanavlivayushcheysya adaptivnoy gidrostaticheskoy opore. Tekhnologiya Mashinostroyeniya. 2016;2:49–53. EDN: WAONYB. (In Russ.).Wang W., Cheng X., Zhang M. Effect of the deformation of porous materials on the performance of aerostatic bearings by fluid-solid interaction method. Tribology International. 2020;150:106391. https://doi.org/10.1016/j.triboint.2020.106391.Wang W., Cheng X., Zhang M. Effect of the deformation of porous materials on the performance of aerostatic bearings by fluid-solid interaction method. Tribology International. 2020;150:106391. https://doi.org/10.1016/j.triboint.2020.106391.Gao Q., Chen W., Lu L. [et al.]. Aerostatic bearings design and analysis with the application to precision engineering: State-of-the-art and future perspectives. Tribology International. 2019;135:1–17. https://doi.org/10.1016/j.triboint.2019.02.020.Gao Q., Chen W., Lu L. [et al.]. Aerostatic bearings design and analysis with the application to precision engineering: State-of-the-art and future perspectives. Tribology International. 2019;135:1–17. https://doi.org/10.1016/j.triboint.2019.02.020.Gao Q., Lu L., Chen W. [et al.]. A novel modeling method to investigate the performance of aerostatic spindle considering the fluid-structure interactio. Tribology International. 2017;115:461–469. https://doi.org/10.1016/j.triboint.2017.06.016.Gao Q., Lu L., Chen W. [et al.]. A novel modeling method to investigate the performance of aerostatic spindle considering the fluid-structure interactio. Tribology International. 2017;115:461–469. https://doi.org/10.1016/j.triboint.2017.06.016.

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