1. bookVolume 26 (2019): Issue 4 (December 2019)
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20 Dec 2019
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access type Open Access

Operating Parameters of a Slide Bearing with Parabolic-Shaped Slide Surfaces with Consideration of the Stochastic Changes in the Lubrication Gap Height

Published Online: 24 Apr 2020
Page range: 171 - 178
Accepted: 18 Dec 2019
Journal Details
License
Format
Journal
First Published
20 Dec 2019
Publication timeframe
4 times per year
Languages
English

In this article, the authors present the equations of the hydrodynamic theory for a slide bearing with parabolic-shaped slide surfaces. The lubricating oil is characterized by non-Newtonian properties, i.e. an oil for which, apart from the classic oil viscosity dependence on pressure and temperature, also an effect of the shear rate is taken into account. The first order constitutive equation was adopted for considerations, where the apparent viscosity was described by the Cross equation. The analytical solution uses stochastic equations of the momentum conservation law, the stream continuity and the energy conservation law. The solution takes into account the expected values of the hydrodynamic pressure EX[p(ϕ,ζ)], of the temperature EX[T(ϕ,y,ζ)], of the velocity value of lubricating oil EX[vi(ϕ,y,ζ)], of the viscosity of lubricating oil EX[ηT(ϕ,y,ζ)] and of the lubrication gap height EX[εT(ϕ,ζ)]. It was assumed, that the oil is incompressible and the changes in its density and thermal conductivity were omitted. A flow of lubricating oil was laminar and non-isothermal. The research concerned the parabolic slide bearing of finite length, with a smooth sleeve surface, with a full wrap angle. The aim of this work is to derive the stochastic equations, that allow to determine the temperature distribution, hydrodynamic pressure distribution, velocity vector components, load carrying capacity, friction force and friction coefficient, in the parabolic sliding bearing, lubricated with non-Newton (Cross) oil, including the stochastic changes in the lubrication gap height. The paper presents the results of analytical and numerical calculation of flow and operating parameters in parabolic sliding bearings, taking into account the stochastic height of the lubrication gap. Numerical calculations were performed using the method of successive approximations and finite differences, with own calculation procedures and the Mathcad 15 software.

Keywords

[1] Bartz, W. J., u.a., Gleitlagertechnik, Expert Verlag, Grafenau 1981.Search in Google Scholar

[2] Dai, R. X., Dong, Q., Szeri, A. Z., Approximations in hydrodynamic lubrication, Transactions of the ASME, Journal of Tribology, Vol. 114, pp. 14-25, 1992.Search in Google Scholar

[3] Dunn, J. E., Rajagopal, K. R., Fluids of differential type: critical review and thermodynamic analysis, International Journal of Engineering Science, Vol. 33 (5), pp. 689-729, 1995.Search in Google Scholar

[4] Fisz, M., Rachunek prawdopodobieństwa i statystyka matematyczna, PWN, Warszawa 1967.Search in Google Scholar

[5] Galindo-Rosales, F. J, Rubio-Hernández, F. J., Sevilla, A., An apparent viscosity function for shear thickening fluids, Journal of Non-Newtonian Fluid Mechanics, Vol. 166, pp. 321-325, 2011.Search in Google Scholar

[6] Guha, S. K., Analysis of steady-state characteristics of misaligned hydrodynamic journal bearings with isotropic roughness effect, Elsevier, Tribology International, Vol. 33, pp. 1-12, 2000.Search in Google Scholar

[7] Hashimoto, H., Surface Roughness effects in high-speed hydrodynamic journal bearings, Transactions of the ASME, Journal of Tribology, Vol. 119, pp. 776-740, 1997.Search in Google Scholar

[8] Helwig, Z., Elementy rachunku prawdopodobieństwa i statystyki matematycznej, PWN, Warszawa 1977.Search in Google Scholar

[9] Miszczak, A., Analiza hydrodynamicznego smarowania łożysk ślizgowych cieczami o właściwościach nienewtonowskich, Monografia, Wydawnictwo Naukowe Instytutu Technologii Eksploatacji–PIB w Radomiu, pp. 1-336, Radom 2019.Search in Google Scholar

[10] Wierzcholski, K., Miszczak, A., Electro-magneto-hydrodynamic lubrication, Open Physics, Vol. 16 (1), pp. 285-291, 2018.Search in Google Scholar

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