Structural identification of the mathematical model of the functioning of tribosystems under conditions of boundary lubrication
DOI:
https://doi.org/10.31891/2079-1372-2021-100-2-26-33Keywords:
tribosystem; mathematical model; differential equations; structural identification; gain; time constant; boundary lubrication; quality factor of tribosystem; dissipation speedAbstract
In the work, a methodological approach to obtaining mathematical models was further developed, which describe the functioning of tribosystems in stationary and transient modes under boundary lubrication conditions.The structural identification of the tribosystem as an object of modeling the functioning of tribosystems in the conditions of boundary lubrication is performed. It is established that the operation of tribosystems is described by a third-order differential equation and, in contrast to the known ones, takes into account the function of changing the quality factor of the tribosystem during running-in. It is shown that the nature of the functioning of tribosystems under conditions of ultimate lubrication depends on the gain and time constants included in the differential equation. It is shown that the coefficient К1 takes into account the degree of influence of the input signal (load, sliding speed, tribological characteristics of the lubricating medium), on the value of the output signal (quality factor of the tribosystem). Coefficient К2 takes into account the magnitude of the change of the output parameters (volumetric wear rate and friction coefficient) when changing the values of the input parameters (load, sliding speed, quality factor of the tribosystem. Coefficient К3 takes into account the degree of influence of the input signal on the restructuring of the material structure in the surface layers of the triboelements.The time constants of the tribosystem characterize the inertia of the processes occurring in the tribosystem, during running-in, or during changes in operating modes. Increasing the time constants makes the process less susceptible to changes in the input signal, the running-in process increases over time, and the tribosystem becomes insensitive to small changes in load and slip speed. Conversely, the reduction of time constants makes the tribosystem sensitive to any external changes
References
2. Zaspa, Y., Dykha, A., Marchenko, D., et al. Exchange interaction and models of contact generation of disturbances in tribosystems. Eastern-European Journal of Enterprise Technologies, 2020, 4(5–106), р. 25–34. https://doi.org/10.15587/1729-4061.2020.209927 [English]
3. Sorokatyi, R., Chernets, M., Dykha, A., et al. (2019). Phenomenological Model of Accumulation of Fatigue Tribological Damage in the Surface Layer of Materials. In Mechanisms and Machine Science, 2019, V. 73, p. 3761–3769. Springer Netherlands. https://doi.org/10.1007/978-3-030-20131-9_371 [English]
4. Dykha, A., Aulin, V., Makovkin, O., et al. Determining the characteristics of viscous friction in the sliding supports using the method of pendulum. Eastern-European Journal of Enterprise Technologies, 2017, 3(7–87), 4–10. https://doi.org/10.15587/1729-4061.2017.99823 [English]
5. Vojtov V.A., Zakharchenko M.B. Modelirovaniye protsessov treniya iznashivaniya v tribosistemakh v usloviyakh granichnoy smazki. Chast' 1. Raschet skorosti raboty dissipatsii v tribosistemakh / Problemi tribologii. – 2015. – № 1. – S. 49-57. [Russian]
6. Vojtov V.A., Zakharchenko M.B. Modelirovaniye protsessov treniya iznashivaniya v tribosistemakh v usloviyakh granichnoy smazki. Chast' 2. Rezul'taty modelirovaniya / Problemi tribologii. – 2015. – № 2. – S. 36-45. [Russian]
7. Viktor Vojtov, Abliatif Biekirov, Anton Voitov. The quality of the tribosystem as a factor of wear resistance // International Journal of Engineering & Technology, 2018, Vol 7, № 4.3 Р. 25-29. DOI: 10.14419/ijet.v7i4.3.19547 [English]
8. Vojtov V.A., Voitov A.V. Assessment of the quality factor of tribosystems and it’s relationship with tribological characteristics // Problems of Tribology, V. 25, No 4/97 – 2020, 45-49. DOI: 10.31891/2079-1372-2020-97-3-45-49 [English]
9. Gusev A. N., Ishkov S. A. Osnovy teorii avtomaticheskogo upravleniya: Uchebn. posobiye Samar. gos. aerokosm. un-t. Samara, 2005. -164 s. [Russian]
10. Vojtov V. A., Biekirov A. Sh., Voitov A. V. and Tsymbal В. M. 2019 Running-in procedures and performance tests for tribosystems, Journal of Friction and Wear, 40(5), pp. 376–383. DOI: 10.3103/S1068366619050192 [English]
