АНАЛІЗ КОНТАКТНОЇ ВЗАЄМОДІЇ СКЛАДНОПРОФІЛЬНИХ ЕЛЕМЕНТІВ РАДІАЛЬНО-ПОРШНЕВИХ ГІДРООБ’ЄМНИХ ПЕРЕДАЧ
Ключові слова:
кульковий поршень, бігова доріжка статорного кільця, контактна взаємодія, складопрофільне тіло, теорія варіаційних нерівностей, метод скінченних елементів.
Анотація
Анотація. Мета роботи – створення математичної моделі контактної взаємодії складнопрофільних елементів радіально-поршневих гідрооб’ємних передач та дослідження впливу форми їхніх контактуючих поверхонь на міцність цих елементів. Така модель будується на основі теорії розвитку та адаптації варіаційних нерівностей. Дискретизація задачі здійснюється із залученням методу скінченних елементів. За допомогою створеного засобу досліджень проаналізовано вплив форми поперечного перерізу бігової доріжки статорного кільця на розподіл контактного тиску у взаємодії із кульковим поршнем. На цій основі рекомендовані раціональні профілі поперечного перерізу бігової доріжки статорного кільця.
Посилання
1. Samorodov V., Avrunin G. Solution of the problem of calculating the leakage working fluid in eccentric gap of the ball piston pair hydraulic fluid power machine. Bulletin of the National Technical University «KhPI». Series: Hydraulic machines and hydraulic units, 2021. № 1, 81–87. https://doi.org/10.20998/2411-3441.2021.1.10
2. Dyyak I. I., Prokopyshyn I. I., Prokopyshyn I. A., Styahar A. O. Numerical analysis of contact between elastic bodies in the presence of thin coating and nonlinear winkler surface layers. In: Altenbach H., Bogdanov V., Grigorenko A. Y., Kushnir R. M., Nazarenko V. M., Eremeyev V. A. (eds) Selected problems of solid mechanics and solving methods. Advanced Structured Materials, 2024. 204. https://doi.org/10.1007/978-3-031-54063-9_9
3. Prokopyshyn I. I., Styahar A. O. Numerical analysis of contact of the elastic bodies one of which has a discontinuous thin coating. Materials Science, 2022. 57. 734–744. https://doi.org/10.1007/s11003-022-00602-0
4. Prokopyshyn І. І., Styahar А. О. Investigation of contact between elastic bodies one of which has a thin coating connected with the body through a nonlinear winkler layer by the domain decomposition methods. Journal of Mathematical Sciences, 2021. 258. 477–506. https://doi.org/10.1007/s10958-021-05562-5
5. Serednytska K. I., Martynyak R. M. Contact of the faces of an interface thermally insulated crack under thermomechanical loading. Materials Science, 2021. 57. 173–179. https://doi.org/10.1007/s11003-021-00528-z
6. Prokopyshyn І. І., Shakhno S. M. Differential-difference iterative domain decomposition methods for the problems of contact of elastic bodies with nonlinear winkler surface layers. Journal of Mathematical Sciences, 2022. 261, 41–58. https://doi.org/10.1007/s10958-022-05736-9
7. Burger Henning, Fabian Forsbach, Valentin L. Popov. Boundary element method for tangential contact of a coated elastic half-space. Machines, 2023. 11. 7. 694. https://doi.org/10.3390/ machines11070694
8. Noor M. A., Noor K. I., Rassias M. T. (). General variational inequalities and optimization. In: Pardalos P.M., Rassias T.M. (eds) Geometry and Non-Convex Optimization. Springer Optimization and Its Applications, 2025. 223. https://doi.org/10.1007/978-3-031-87057-6_14
9. Соляр Т. Я., Соляр О. І. Осесиметрична контактна задача для півпростору з незаданими ділянками взаємодії. Математичні методи та фізико-механічні поля, 2025. Т. 65, № 3–4, С. 178–187 (2022), https://doi.org/10.15407/mmpmf2022.65.3-4.178-187. Traslation: T. Y. Solyar, O. I. Soliar. Axisymmetric contact problem for a half space with nonspecified zones of interaction. Journal of Mathematical Sciences, 2025. 287 (2). 321–333, https://doi.org/10.1007/s10958-025-07593-8
10. Yao J., Ren G. Embedding Kalker’s variational theory into railway vehicle system dynamics and its efficiency improvement. Vehicle system dynamics, 2023. 62 (4). 932–954. https://doi.org/10.1080/00423114.2023.2235034
11. Vollebregt E., Six K., Polach O. Challenges and progress in the understanding and modelling of the wheel–rail creep forces. Vehicle system dynamics, 2021. 59 (7), 1026–1068. https://doi.org/10.1080/00423114.2021.1912367
12. Pérez-Ràfols F., Ciavarella M. Towards a universal scaling for the elastic contact between anisotropic and non-gaussian surfaces. Tribology Letters, 2025. 73, 62. https://doi.org/10.1007/s11249-025-01976-3
13. Ciavarella M., Pérez-Ràfols F. Strongly different adhesion reduction for 1D or 2D random fractal roughness, and an extension of the bam model to anisotropic surfaces. Tribology Letters, 2024. 72. 119. https://doi.org/10.1007/s11249-024-01916-7.
14. Li Q., Lyashenko I. A., Pohrt R., Popov V. L. Influence of a soft elastic layer on adhesion of rough surfaces. In: Borodich F.M., Jin X. (eds) Contact problems for soft, biological and bioinspired materials. Biologically-Inspired Systems, Springer, Cham, 2022.
15. https://doi.org/10.1007/978-3- 030-85175-0_5 15. He X., Li Q., Popov V. L. Strength of adhesive contact between a rough fibrillar structure and an elastic body: influence of fibrillar stiffness. The Journal of Adhesion, 2021. 98(12). 1820–1833. https://doi.org/10.1080/00218464.2021.1939017
16. Kniaziev S., Kniazieva H., Subbotina V., Volkov O., Riaboshtan V. Improving the technology of producing boron and siliconized layers and comparing their propertie. Physics and Chemistry of Solid State, 2025. 26(2. 436–441. https://doi.org/10.15330/pcss.26.2.436-441
17. Subbotina V., Bilozerov V., Subbotin O., Barmin O., Hryhorieva S., Pysarska N. Investigation of the influence of electrolyte composition on the structure and properties of coatings obtained by microarc oxidation. Physics and Chemistry of Solid State, 2022. 23(2). 380–386. https://doi.org/10.15330/pcss.23.2.380-386
18. Valentin L. Popov, Markus Heß, Emanuel Willert. Handbook of plane contact mechanics. Exact solutions of plane contact problems. Springer Berlin, Heidelberg, 2025, XII, 260 р. https://doi.org/doi.org/10.1007/978-3-662-70173-7
19. Marchenko D.D., Matvyeyeva K.S. Study of the Stress-Strain State of the Surface Layer During the Strengthening Treatment of Parts. Problems of Tribology, 2022. 27. 3/105. 82–88. https://doi.org/10.31891/2079-1372-2022-105-3-82-88
20. Tkachuk M. M., Skripchenko N., Tkachuk M. A., Grabovskiy A. Numerical methods for contact analysis of complex-shaped bodies with account for non-linear interface layers. Eastern- European Journal of Enterprise Technologies, 2018. 5(7 (95). 22–31. https://doi.org/10.15587/1729- 4061.2018.143193
21. Tkachuk M., Grabovskiy A., Tkachuk M., Hrechka I., Sierykov V. Contact interaction of a ball piston and a running track in a hydrovolumetric transmission. In: Ivanov V., Pavlenko I., Liaposhchenko O., Machado J., Edl M. (eds) Advances in Design, Simulation and Manufacturing IV. DSMIE 2021. Lecture Notes in Mechanical Engineering, 2021. 195–203. https://doi.org/10.1007/978- 3-030-77823-1_20
22. Tkachuk M., Grabovskiy A., Tkachuk M., Hrechka I., Tkachuk H. Contact interaction of a ball with a toroidal running track with a closely shaped power law profile. In: Tonkonogyi V., Ivanov V., Trojanowska J., Oborskyi G. (eds) Interpartner 2024: Advanced Manufacturing Processes VI. Lecture Notes in Mechanical Engineering, 2025. 628–638. https://doi.org/10.1007/978-3-031-82746- 4_56
23. Zienkiewicz O. C., Taylor R. L., Zhu J. Z. The Finite Element Method: Its Basis and Fundamentals. 7th ed. Oxford: Butterworth-Heinemann, 2013. 756 p.
2. Dyyak I. I., Prokopyshyn I. I., Prokopyshyn I. A., Styahar A. O. Numerical analysis of contact between elastic bodies in the presence of thin coating and nonlinear winkler surface layers. In: Altenbach H., Bogdanov V., Grigorenko A. Y., Kushnir R. M., Nazarenko V. M., Eremeyev V. A. (eds) Selected problems of solid mechanics and solving methods. Advanced Structured Materials, 2024. 204. https://doi.org/10.1007/978-3-031-54063-9_9
3. Prokopyshyn I. I., Styahar A. O. Numerical analysis of contact of the elastic bodies one of which has a discontinuous thin coating. Materials Science, 2022. 57. 734–744. https://doi.org/10.1007/s11003-022-00602-0
4. Prokopyshyn І. І., Styahar А. О. Investigation of contact between elastic bodies one of which has a thin coating connected with the body through a nonlinear winkler layer by the domain decomposition methods. Journal of Mathematical Sciences, 2021. 258. 477–506. https://doi.org/10.1007/s10958-021-05562-5
5. Serednytska K. I., Martynyak R. M. Contact of the faces of an interface thermally insulated crack under thermomechanical loading. Materials Science, 2021. 57. 173–179. https://doi.org/10.1007/s11003-021-00528-z
6. Prokopyshyn І. І., Shakhno S. M. Differential-difference iterative domain decomposition methods for the problems of contact of elastic bodies with nonlinear winkler surface layers. Journal of Mathematical Sciences, 2022. 261, 41–58. https://doi.org/10.1007/s10958-022-05736-9
7. Burger Henning, Fabian Forsbach, Valentin L. Popov. Boundary element method for tangential contact of a coated elastic half-space. Machines, 2023. 11. 7. 694. https://doi.org/10.3390/ machines11070694
8. Noor M. A., Noor K. I., Rassias M. T. (). General variational inequalities and optimization. In: Pardalos P.M., Rassias T.M. (eds) Geometry and Non-Convex Optimization. Springer Optimization and Its Applications, 2025. 223. https://doi.org/10.1007/978-3-031-87057-6_14
9. Соляр Т. Я., Соляр О. І. Осесиметрична контактна задача для півпростору з незаданими ділянками взаємодії. Математичні методи та фізико-механічні поля, 2025. Т. 65, № 3–4, С. 178–187 (2022), https://doi.org/10.15407/mmpmf2022.65.3-4.178-187. Traslation: T. Y. Solyar, O. I. Soliar. Axisymmetric contact problem for a half space with nonspecified zones of interaction. Journal of Mathematical Sciences, 2025. 287 (2). 321–333, https://doi.org/10.1007/s10958-025-07593-8
10. Yao J., Ren G. Embedding Kalker’s variational theory into railway vehicle system dynamics and its efficiency improvement. Vehicle system dynamics, 2023. 62 (4). 932–954. https://doi.org/10.1080/00423114.2023.2235034
11. Vollebregt E., Six K., Polach O. Challenges and progress in the understanding and modelling of the wheel–rail creep forces. Vehicle system dynamics, 2021. 59 (7), 1026–1068. https://doi.org/10.1080/00423114.2021.1912367
12. Pérez-Ràfols F., Ciavarella M. Towards a universal scaling for the elastic contact between anisotropic and non-gaussian surfaces. Tribology Letters, 2025. 73, 62. https://doi.org/10.1007/s11249-025-01976-3
13. Ciavarella M., Pérez-Ràfols F. Strongly different adhesion reduction for 1D or 2D random fractal roughness, and an extension of the bam model to anisotropic surfaces. Tribology Letters, 2024. 72. 119. https://doi.org/10.1007/s11249-024-01916-7.
14. Li Q., Lyashenko I. A., Pohrt R., Popov V. L. Influence of a soft elastic layer on adhesion of rough surfaces. In: Borodich F.M., Jin X. (eds) Contact problems for soft, biological and bioinspired materials. Biologically-Inspired Systems, Springer, Cham, 2022.
15. https://doi.org/10.1007/978-3- 030-85175-0_5 15. He X., Li Q., Popov V. L. Strength of adhesive contact between a rough fibrillar structure and an elastic body: influence of fibrillar stiffness. The Journal of Adhesion, 2021. 98(12). 1820–1833. https://doi.org/10.1080/00218464.2021.1939017
16. Kniaziev S., Kniazieva H., Subbotina V., Volkov O., Riaboshtan V. Improving the technology of producing boron and siliconized layers and comparing their propertie. Physics and Chemistry of Solid State, 2025. 26(2. 436–441. https://doi.org/10.15330/pcss.26.2.436-441
17. Subbotina V., Bilozerov V., Subbotin O., Barmin O., Hryhorieva S., Pysarska N. Investigation of the influence of electrolyte composition on the structure and properties of coatings obtained by microarc oxidation. Physics and Chemistry of Solid State, 2022. 23(2). 380–386. https://doi.org/10.15330/pcss.23.2.380-386
18. Valentin L. Popov, Markus Heß, Emanuel Willert. Handbook of plane contact mechanics. Exact solutions of plane contact problems. Springer Berlin, Heidelberg, 2025, XII, 260 р. https://doi.org/doi.org/10.1007/978-3-662-70173-7
19. Marchenko D.D., Matvyeyeva K.S. Study of the Stress-Strain State of the Surface Layer During the Strengthening Treatment of Parts. Problems of Tribology, 2022. 27. 3/105. 82–88. https://doi.org/10.31891/2079-1372-2022-105-3-82-88
20. Tkachuk M. M., Skripchenko N., Tkachuk M. A., Grabovskiy A. Numerical methods for contact analysis of complex-shaped bodies with account for non-linear interface layers. Eastern- European Journal of Enterprise Technologies, 2018. 5(7 (95). 22–31. https://doi.org/10.15587/1729- 4061.2018.143193
21. Tkachuk M., Grabovskiy A., Tkachuk M., Hrechka I., Sierykov V. Contact interaction of a ball piston and a running track in a hydrovolumetric transmission. In: Ivanov V., Pavlenko I., Liaposhchenko O., Machado J., Edl M. (eds) Advances in Design, Simulation and Manufacturing IV. DSMIE 2021. Lecture Notes in Mechanical Engineering, 2021. 195–203. https://doi.org/10.1007/978- 3-030-77823-1_20
22. Tkachuk M., Grabovskiy A., Tkachuk M., Hrechka I., Tkachuk H. Contact interaction of a ball with a toroidal running track with a closely shaped power law profile. In: Tonkonogyi V., Ivanov V., Trojanowska J., Oborskyi G. (eds) Interpartner 2024: Advanced Manufacturing Processes VI. Lecture Notes in Mechanical Engineering, 2025. 628–638. https://doi.org/10.1007/978-3-031-82746- 4_56
23. Zienkiewicz O. C., Taylor R. L., Zhu J. Z. The Finite Element Method: Its Basis and Fundamentals. 7th ed. Oxford: Butterworth-Heinemann, 2013. 756 p.
Опубліковано
2025-12-01
Розділ
ПРИКЛАДНА ГІДРОМЕХАНІКА. ГІДРОМАШИНИ І ГІДРОАГРЕГАТИ
