Markov Approach to Constructing Rough Surfaces Interaction Models
Abstract
Interaction of rough surfaces determines many processes in electrical engineering, thermal engineering, machinery construction, motor vehicle industry, engine technology, and other industries. Rough surface relief is a space random function. It is shown that the change in rough surfaces that occurs during their contact interaction can be analyzed using the theory of Markov processes. Noteworthy is that this problem is not solved within the framework of existing models.
An approach in which each of two surfaces is represented by a set of protrusions is proposed. Each protrusion is described by its random state (a set of selected parameters), and each surface is described by a probability distribution in the set of states. When the surfaces move with respect to each other, the protrusions interact with one another, and the result of this interaction for two protrusions looks as a known two-dimensional function of interaction. The state of a fixed protrusion in the next moment is determined by its previous state and a random effect of the protrusion on the other surface. If these effects are independent, the state alteration process can be considered to be a Markovian.
Recurrent recalculation in time is valid for probability distributions. Recalculating the distributions, we obtain time-varying distributions, from which the desired characteristics of interaction are obtained, such as the average contact area, average height of protrusions, friction force, wear, etc. Choosing different options of what is understood to mean the protrusion state and the interaction function, the models of different complexity and precision are obtained.
The idea of bringing the interaction to a Markov model is illustrated on a simple discrete scheme with subsequently generalizing it. The approach is applied to analyzing a friction process and a fatigue failure (taking lubrication into account) that results from the protrusions repeatedly coming in contact with one another. An example of numerically analyzing the evolution of surfaces separated by a lubricant layer is given. The technical characteristics as functions of friction path and load are estimated.
References
2. Javorova J., Mazdrakova A., Andonov I., Radulescu A. Analysis of HD Journal Bearings Considering Elastic Deformation and Non Newtonian Rabinowitsch Fluid Model // Tribology in Industry. 2016. V. 38. No. 2. Pp. 186—196.
3. Holmberg K., Andersson P, Erdemir A. Global Energy Consumption Due to Friction in Passenger cars // Tribology International. 2012. V. 47. Pp. 221—234.
4. Задорожная Е.А., Мухортов И.В., Леванов И.Г. Применение неньютоновских моделей смазочных жидкостей при расчете сложнонагруженных узлов трения поршневых и роторных машин // Трение и смазка в машинах и механизмах. 2011. № 7. С. 22—30.
5. Чичинадзе А.В. и др. Основы трибологии (трение, износ, смазка). М.: Машиностроение, 2001.
6. Vorlaufer G., Ilincic S., Franek F., Pauschitz A. Wear Quantification by Comparison of Surface Topography Data // Encyclopedia of Tribology. 2012. Pp. 4087—4093.
7. Johansson S., Nilsson P.H., Ohlsson R. Bengt-göran Rosén Experimental Friction Evaluation of Cylinder Liner/ Piston Ring Contact // Wear. 2011. V. 271. Pp. 625—633.
8. Попов В.Л. Механика контактного взаимодействия и физика трения. М.: Физматлит, 2013.
9. Lazarev V., Gavrilov K., Doikin A., Vorlaufer G., Sequard-Base J. Estimation of the Tribotechnical Parameters of the «Piston Skirt — Cylinder Liner» Contact Interface from an Icengine for Decreasing the Mechanical Losses // WIT Trans. Ecology and the Environment. 2014. V. 190 (1). Pp. 625—635.
10. Amor M.B., Belghith S., Mezlini S. Finite Element Modeling of RMS Roughness Effect on the Contact Stiffness of Rough Surfaces // Tribology in Industry. 2016. V. 38. No. 3. Pp. 392—401.
11. Greenwood J.A., Williamson J.B.P. Contact of Nominally Flat Surfaces // Proc. Royal Soc. Series A. 1966. V. 295. Pp. 300—319.
12. Nayak P.R. Random Process Model of Rough Surfaces // J. Lubrication Techn. 1971. V. 93 (3). Pр. 398—407.
13. Демкин Н.Б. Контактирование шероховатых поверхностей. М.: Наука, 1970.
14. Крагельский И.В., Добычин М.Н., Комбалов В.С. Основы расчетов на трение и износ. М.: Машиностроение, 1977.
15. Тигетов Д.Г., Горицкий Ю.А. Марковская модель механического взаимодействия шероховатых поверхностей в процессе трения // Трение и смазка в машинах и механизмах. 2010. № 3. С. 4—13.
16. Горицкий Ю.А., Главатских С.Б., Бражникова Ю.С. Марковская модель взаимодействия шероховатых поверхностей // Трение и смазка в машинах и механизмах. 2014. № 2. С. 11—20.
17. Gavrilov K., Goritskiy Yu., Ismailova Yu., Rozhdestvensky Yu., Doikin A. A Numerical Model for Mechanical Interaction of Rough Surfaces of the «Piston- Cylinder Liner» Tribosystem // FME Trans. 2015. V. 43. No. 3. Pp. 249–253.
18. Gavrilov K., Goritskiy Yu., Migal I., Izzatulloev M. A Numerical Model for Estimation of Service Life of Tribological Systems of the Piston Engine // Tribology in Industry. 2017. V. 39. No. 3. Pp. 329—333.
19. Горицкий Ю.А., Гаврилов К.В., Исмаилова Ю.С., Шевченко О.В. Марковская модель изменения шероховатых поверхностей при механическом взаимодействии // Вестник МЭИ. 2017. № 5. С. 112—125.
20. Rozhdestvensky Yu., Zadorozhnaya E. A Simulation of the Thermal State of Heavily Loaded Tribounits and its Evaluation // Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software. 2014. V. 7 (4). Pp. 51—64.
---
Для цитирования: Горицкий Ю.А., Гаврилов К.В., Мигаль И.А. Марковский подход к построению моделей взаимодействия шероховатых поверхностей // Вестник МЭИ. 2019. № 1. С. 114—123. DOI: 10.24160/1993-6982-2019-1-114-123.
#
1. Vencl A. Rac А. Diesel Engine Crankshaft Journal Bearings Failures: Case Study. Engineering Failure Analysis. 2014;44:217—228.
2. Javorova J., Mazdrakova A., Andonov I., Radulescu A. Analysis of HD Journal Bearings Considering Elastic Deformation and Non Newtonian Rabinowitsch Fluid Model. Tribology in Industry. 2016;38;2:186—196.
3. Holmberg K., Andersson P, Erdemir A. Global Energy Consumption Due to Friction in Passenger cars. Tribology International. 2012;47:221—234.
4. Zadorozhnaya E.A., Muhortov I.V., Levanov I.G. Primenenie Nen'yutonovskih Modeley Smazochnyh Zhid-kostey pri Raschete Slozhnonagruzhennyh Uzlov Treniya Porshnevyh i Rotornyh Mashin. Trenie i Smazka v Mashinah i Mekhanizmah. 2011;7:22—30. (in Russian).
5. Chichinadze A.V. i dr. Osnovy Tribologii (Trenie, Iznos, Smazka). M.: Mashinostroenie, 2001. (in Russian).
6. Vorlaufer G., Ilincic S., Franek F., Pauschitz A. Wear Quantification by Comparison of Surface Topography Data. Encyclopedia of Tribology. 2012:4087—4093.
7. Johansson S., Nilsson P.H., Ohlsson R. Bengt-göran Rosén Experimental Friction Evaluation of Cylinder Liner/ Piston Ring Contact. Wear. 2011;271:625—633.
8. Popov V.L. Mekhanika Kontaktnogo Vzaimodeystviya i Fizika Treniya. M.: Fizmatlit, 2013. (in Russian).
9. Lazarev V., Gavrilov K., Doikin A., Vorlaufer G., Sequard-Base J. Estimation of the Tribotechnical Parameters of the «Piston Skirt — Cylinder Liner» Contact Interface from an Icengine for Decreasing the Mechanical Losses. WIT Trans. Ecology and the Environment. 2014;190 (1):625—635.
10. Amor M.B., Belghith S., Mezlini S. Finite Element Modeling of RMS Roughness Effect on the Contact Stiffness of Rough Surfaces. Tribology in Industry. 2016;38;3:392—401.
11. Greenwood J.A., Williamson J.B.P. Contact of Nominally Flat Surfaces. Proc. Royal Soc. Series A. 1966;295:300—319.
12. Nayak P.R. Random Process Model of Rough Surfaces. J. Lubrication Techn. 1971;93 (3):398—407.
13. Demkin N.B. Kontaktirovanie Sherohovatyh Poverhnostey. M.: Nauka, 1970. (in Russian).
14. Kragel'skiy I.V., Dobychin M.N., Kombalov V.S. Osnovy Raschetov na Trenie i Iznos. M.: Mashinostroenie, 1977. (in Russian).
15. Tigetov D.G., Goritskiy Yu.A. Markovskaya Model' Mekhanicheskogo Vzaimodeystviya Sherohovatyh Poverhnostey v Protsesse Treniya. Trenie i Smazka v Mashinah i Mekhanizmah. 2010;3:4—13. (in Russian).
16. Goritskiy Yu.A., Glavatskih S.B., Brazhnikova Yu.S. Markovskaya Model' Vzaimodeystviya Sherohovatyh Poverhnostey. Trenie i Smazka v Mashinah i Mekhanizmah. 2014;2:11—20.(in Russian).
17. Gavrilov K., Goritskiy Yu., Ismailova Yu., Rozhdestvensky Yu., Doikin A. A Numerical Model for Mechanical Interaction of Rough Surfaces of the «Piston- Cylinder Liner» Tribosystem. FME Trans. 2015;43;3: 249–253.
18. Gavrilov K., Goritskiy Yu., Migal I., Izzatulloev M. A Numerical Model for Estimation of Service Life of Tribological Systems of the Piston Engine. Tribology in Industry. 2017;39;3:329—333.
19. Goritskiy Yu.A., Gavrilov K.V., Ismailova Yu.S., Shevchenko O.V. Markovskaya Model' Izmeneniya Sherohovatyh Poverhnostey pri Mekhanicheskom Vzaimodeystvii. Vestnik MEI. 2017;5:112—125. (in Russian).
20. Rozhdestvensky Yu., Zadorozhnaya E. A Simulation of the Thermal State of Heavily Loaded Tribounits and its Evaluation. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software. 2014;7 (4):51—64.
---
For citation: Goritsky Yu.A., Gavrilov K.V., Migal′ I.A. Markov Approach to Constructing Rough Surfaces Interaction Model. MPEI Vestnik. 2019;1:114—123. (in Russian). DOI: 10.24160/1993-6982-2019-1-114-123
