Differential and recurrence unified reynolds equations and mega algorithm for their numerical solutions

• Autorzy: Wierzcholski K. , Miszczak A.
• Języki publikacji: EN

Abstrakty

EN

The objective of the research under the paper topic is an analytical, unified formulation of a new standardized view of general solution of hydrodynamic problem using algorithm to determine changes of the components of the velocity vector, the distributions of hydrodynamic pressure, load carrying capacity, of slide bearings with cooperating curvilinear, orthogonal surfaces that are lubricated with a various non-Newtonian lubricants. In this paper for non- Newtonian lubricants are questioning the hitherto prevailing assumptions using in hydrodynamic theory of lubrication such as constant value of lubricant viscosity and pressure in the thickness of lubricating gap i.e. in gap height direction. Finally, the non-homogeneous partial differential equation generated with variable coefficients that is the result of the various boundary conditions being imposed that are different for each problem solved is an equation that determines the distributions of hydrodynamic pressure values. This equation is to be written in the form of a unified non-homogenous partial recurrence equation with variable coefficients. The Authors foresee that a mega-algorithm will be developed for the solution of this equation in a numerical form. This equation in particular cases is an equivalent of modified Reynolds equations in the research that has been conducted so far concerning the hydrodynamic theory of lubrication.

Słowa kluczowe

EN

partial differential form; partial recurrence form; unified Reynolds equation; mega algorithm

• Wydawca: Łukasiewicz Research Network - Institute of Aviation ; European Science Society of Powertrain and Transport KONES Poland ; Wydawnictwo Instytutu Technicznego Wojsk Lotniczych
• Czasopismo: Journal of KONES
• Rocznik: 2012
• Tom: Vol. 19, No. 4
• Strony: 643--650
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Wierzcholski K.

autor

Miszczak A.

• Technical University of Koszalin Institute of Mechatronics, Nanotechnology and Vacuum Technique Śniadeckich Street 2, 75-453 Koszalin, Poland tel.:[phone], fax: [phone],

Bibliografia

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• [2] Kącki, E., Partial Differential Equations in Physical and Technical Problems (Równania różniczkowe cząstkowe w zagadnieniach fizyki i techniki), WNT, Warsaw 1989.
• [3] Koźniewska, I., Recurrence Equations (Równania rekurencyjn), PWN, Warszawa 1973.
• [4] Miszczak, A., Analiza hydrodynamicznego smarowania ferrocieczą poprzecznych łożysk ślizgowych, Fundacja Rozwoju Akademii Morskiej w Gdyni, dysertacja habilitacyjna, 2006.
• [5] Walicki, E., Ruch płynów lepkich w szczelinach wzdłużnych łożysk ślizgowych, Wydawnictwo Uczelniane ATR Bydgoszcz, Mechanika, Z. 18 (50), Bydgoszcz 1977.
• [6] Wierzcholski, K., Estimation of solutions of basic equations for non Newtonian fluid flow in a film between two non- rotational surfaces. Rev. Roum. des Sci. Tech., Ser. de Mec. Appl. Editura Acad. Roum., No. 1-2, T. 36, pp. 103-122, 1991.
• [7] Wierzcholski, K., The method of solutions for hydrodynamic lubrication by synovial fluid flow in human joint gap, Control and Cybernetics, Vol. 31, No. 1, pp.91-116, 2002.
• [8] Wierzcholski, K., Comparisson Between Impulsive and Periodic Non-Newtonian Lubrication of Human Hip Joint, Engineering Trans., 53, 1, pp. 69-114, 2005.
• [9] Wierzcholski, K., Mathematical implementation into computer calculations for micro-bearing capacities, XIII Journal of Applied Computer Science, Vol. 18, No. 1, pp. 117-135, 2010.
• [10] Wierzcholski, K., Algorithm for Friction Force Computation in Intelligent Micro-Pairs System, XIII Journal of Applied Computer Science, Vol. 19, No. 1, pp.139-160, 2011.