New Mathematical Models for Coefficients of Hydrodynamic Resistance to Rotation and Friction of Sliding Bearings of Ship Propulsion System for non Newtonian Lubricants

O. Kryvyi ¹

, M.V. Miyusov ¹

, M. Kryvyi ¹

¹ National University “Odessa Maritime Academy”, Odessa, Ukraine

DOI: 10.12716/1001.19.03.38

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ABSTRACT: The boundary value problem for the Reynolds differential equations for the lubricating layer in the sliding bearings of ship power plants and auxiliary ship equipment is solved by the boundary variation method. As a result, analytical representations for hydrodynamic pressure, shear stresses, and integral characteristics of the lubricating layer were obtained, as well as their refinement, which considers the presence of a lubricating layer outside the working zone of the sliding pair. This made it possible to build new, easy-to-use mathematical models for the coefficients of rotational resistance and hydrodynamic friction of sliding bearings of the ship's propulsion system, considering the non-Newtonian properties of lubricants, that is, in the case of the dependence of dynamic viscosity on pressure and temperature. The obtained mathematical models consider the geometric parameters of bearings, operational parameters: relative radial clearance and relative eccentricity, angular velocity, as well as viscous characteristics of lubricants, in particular, dynamic viscosity and piezo coefficient of viscosity of lubricants. A criterion for the applicability of non-Newtonian lubricants for given operating modes of the sliding bearing has been developed, which uses the viscosity characteristics of the lubricants. The research results are illustrated in the form of tables and graphs.

KEYWORDS: Sliding Bearings of Ship Propulsion System, Non-Newtonian Lubricants, Hydrodynamic Friction Modelling, Rotational Resistance Coefficients, Boundary Value Problem – Reynolds Equation, Viscosity Gradient, Regression-Based Analytical Models, Service Life Prediction Accuracy

REFERENCES

Kryvyi, O.; Miyusov, M.; Kryvyi, M. New mathematical models for the load factor of slip pairs in the ship propulsion system for non-Newtonian lubricants. Pomorstvo. 2024, 38(1), 114–125. - doi:10.31217/p.38.1.9

Deters, L. Plain Bearings. In: Mang, T. (eds) Encyclopaedia of Lubricants and Lubrication. Springer, Berlin, Heidelberg. 2014. - doi:10.1007/978-3-642-22647-2_14

Korovchinsky, М. V. Theoretical basis for plain bearings operation. Mashgiz, M. 1959.

Wael, A. Altabey. Chapter 14 - Sliding bearings, Editor(s): Wael A. Altabey, Fundamentals of Machine Component Design. Elsevier. 2024, 331-353. - doi:10.1016/B978-0-443-21449-3.00010-4

S. Balakrishnan, S.; Baker, C.E.; Rahnejat, H. 18 - Fundamentals of hydrodynamic journal bearings: an analytical approach, Editor(s): Homer Rahnejat, Tribology and Dynamics of Engine and Powertrain. Woodhead P. 2010. 591-614, - doi:10.1533/9781845699932.2.591

Deters, L. Plain Bearings. In: Mang, T. (eds) Encyclopedia of Lubricants and Lubrication. Springer, Berlin, Heidelberg. 2014. - doi:10.1007/978-3-642-22647-2_14

Hamrock, B.J.; Schmid, S.R.; & Jacobson, B.O. Fundamentals of Fluid Film Lubrication (2nd ed.). CRC Press. 2004. - doi:10.1201/9780203021187

Litwin, W. Marine Propeller Shaft Bearings under Low-Speed Conditions: Water vs. Oil Lubrication. Tribology Transactions, 2019, 62(5), 839–849. - doi:10.1080/10402004.2019.1625991

He, T.; Zou, D.; Lu, X.; Guo, Y.; Wang, Z.; Li, W. Mixed-lubrication analysis of marine stern tube bearing considering bending deformation of stern shaft and cavitation. Tribology International, 2014. 73, 108-116. - doi:10.1016/j.triboint.2014.01.013

Kryvyi, M.O.; Sagin, S.V. Determination of the influence of properties of engine oils on pressure distribution in friction pairs of marine diesel engines. Ship power plants. 2021. 43, 18-24. DOI:10.31653/smf343.2021.18-24. - doi:10.31653/smf343.2021.18-24

Sagin, S.V.; Kryvyi, M.O. Determination of pressure distribution in the nonnewtonian oil layer in ship energy plant. Herald of the Odessa national maritime university. 2020, 2(62), 160-170. DOI 10.47049/2226-1893-2020-1-160-170. - doi:10.47049/2226-1893-2020-2-160-170

Sagin, S.V.; Kryvyi, M.O. Calculation of contact pressure and contact zone in friction pairs of marine diesel engines. Automation of ship technical facilities. 2021, 27, 84-92. DOI: 10.31653/1819-3293-2021-1-27-84-92S - doi:10.31653/1819-3293-2021-1-27-84-92

Kryvyi M.O. Determination of the specific angles of friction pairs of ship power plants. Ship power plants. 2023. 47, 32-45. DOI: 10.31653/smf47.2023. 32-45. - doi:10.31653/smf47.2023

Kryvyi O., Miyusov M.V., Kryvyi M.: Construction and Analysis of New Mathematical Models of the Operation of Ship Propellers in Different Maneuvering Modes. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 17, No. 1, doi:10.12716/1001.17.01.09, pp. 95-102, 2023

Kryvyi O., Miyusov M.V., Kryvyi M.: Analysis of Known and Construction of New Mathematical Models of Forces on a Ship's Rudder in an Unbounded Flow. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 17, No. 4, doi:10.12716/1001.17.04.09, pp. 831-839, 2023

Jao, TC.; Verhelst, A. Marine Engine Oils. In: Wang, Q.J., Chung, YW. (eds) Encyclopedia of Tribology. Springer, Boston, MA. 2013. - doi:10.1007/978-0-387-92897-5_952

Habchi, W.; Bair, S. Quantifying the inlet pressure and shear stress of elastohydrodynamic lubrication. Tribology Int. 2023, 182(8):108351. - doi:10.1016/j.triboint.2023.108351

van Leeuwen, H. The determination of the pressure viscosity coefficient of a lubricant through an accurate film thickness formula and accurate film thickness measurements. Proc. of the I. Mech. E, Part J: of Engineering Tribology. 2009, 223(8), 1143-1163. doi:10.1243/13506501JET504 - doi:10.1243/13506501JET504

van Leeuwen, H. The determination of the pressure–viscosity coefficient of a lubricant through an accurate film thickness formula and accurate film thickness measurements. Part 2. Proc. of the I. Mech. E, Part J: J. of Engineering Tribology. 2011, 225(6), 449-464. doi:10.1177/ 1350650111398405 - doi:10.1177/1350650111398405

Lotfizadeh Dehkordi B.; Shiller, P. J.; Doll, G. L. Pressure- and Temperature-Dependent Viscosity Measurements of Lubricants with Polymeric Viscosity Modifiers. Front. Mech. Eng. 2019, 5, 18. doi: 10.3389/fmech.2019.00018. - doi:10.3389/fmech.2019.00018

Zhou, Y.; Li, W.; Stump, B. C.; Connatser, R.M.; Lazarevic, S; Qu, J. Impact of Fuel Contents on Tribological Performance of PAO Base Oil and ZDDP. Lubricants. 2018, 6(3), 79. - doi:10.3390/lubricants6030079

Matsushita, O.; Tanaka, M.; Kobayashi, M.; Keogh, P.; Kanki, H. Basics of Plain Bearings. In. Vibrations of Rotating Machinery. Mathematics for Industry. Springer, Tokyo. 2019. - doi:10.1007/978-4-431-55453-0_2

Kryvyi, O. F.; Miyusov, M. V. Mathematical model of hydrodynamic characteristics on the ship’s hull for any drift angles. Advances in Marine Navigation and Safety of Sea Transportation. CRC Press, 2019. 111-117. - doi:10.1201/9780429341939

Kryvyi O., Miyusov M.V.: Construction and Analysis of Mathematical Models of Hydrodynamic Forces and Moment on the Ship's Hull Using Multivariate Regression Analysis. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 15, No. 4, doi:10.12716/1001.15.04.18, pp. 853-864, 2021

Citation note:

Kryvyi O., Miyusov M.V., Kryvyi M.: New Mathematical Models for Coefficients of Hydrodynamic Resistance to Rotation and Friction of Sliding Bearings of Ship Propulsion System for non Newtonian Lubricants. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 19, No. 3, doi:10.12716/1001.19.03.38, pp. 1029-1039, 2025

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