The Lipschitz Picard successive step method in hydrodynamic lubrication problem

• Autorzy: Wierzcholski K.
• Języki publikacji: EN

Abstrakty

EN

The paper shows the successive steps of approximation of Picard unification for the solution of the non-isothermal fluid flow in thin layer including inertia forces and apparent viscosities described by the non-linear dependences. In this paper is presented a unified semi analytical method of solution of the asymmetrical, laminar, steady and unsteady, non-Newtonian lubrication problem flow between two non-rotational in general, convex, differentiable and movable surfaces when the time t depended gap between mentioned surfaces has quite an arbitrary geometry. The presented considerations relate not only to the rotational cooperating surfaces but also to the arbitrary non-rotational surfaces in general. The parallel and longitudinal intersections of mentioned surfaces are curvilinear and non-monotone in general. We consider the non-Newtonian lubricant for non-linear constitutive equations taking into account Reiner Rivlin power law relationship as well Rivlin-Ericksen formula for viscoelastic fluids. The non-Newtonian properties create non-linear dependencies between strain and stress. Moreover, the dynamic viscosity or apparent dynamic viscosity of numerous lubricant liquids with various additions often decreases along with shear rate increasing during motion. Dynamic viscosity of lubricant fluids inside very thin micro and nano boundary layers depends on Young’s modulus of the cell of surface body being in contact with the fluid.

Słowa kluczowe

EN

Unified Pickard method; approximation of solutions; system of partial differential equations

• 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. 1
• Strony: 483--490
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Wierzcholski K.

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

Bibliografia

• [1] Astarita, G., Marrucci, G., Principles of non-Newtonian fluid mechanics, McGraw Hill Co, 1974.
• [2] Miszczak, A., Analiza hydrodynamicznego smarowania ferrocieczą poprzecznych łożysk ślizgowych, Fundacja Rozwoju Akademii Morskiej w Gdyni, dysertacja habilitacyjna, 2006.
• [3] Truesdell, C. A., First Course in Rational Continuum Mechanics, John Hopkins Univ., Baltimore Maryland 1972.
• [4] Walicki, E., Ruch płynów lepkich w szczelinach wzdłużnych łożysk ślizgowych, Wydawnictwo Uczelniane ATR Bydgoszcz, Mechanika, Z. 18 (50), Bydgoszcz 1977.
• [5] Weinberger, H., Fo., A First Course In Partial Differentia Equations, John Willey & Sons, New York, Toronto, Singapore 1965.
• [6] Wierzcholski, K., Czajkowski, A., On the small parameter methods for the integration of non linear system of equations of the laminar non-Newtonian fluid flow in the thin layer on the rotating surface, Folia Scientis Scientiarum Lubliniensis, Mat-Fiz-Chem, Vol. 31, 1-2, pp. 9-16, 1989.
• [7] Wierzcholski, K., The Method of Solving of the System of non-Linear Differential Equations for non- Isothermic Laminar non-Newtonian Flow in the Thin Layer Between Two Certain Surfaces, Scientific Papers of the Institute of Machine Design and Operation Studies and Research: The boundary integral equation method in fluid mechanics, Technical University of Wroclaw, No. 59, Ser.: No. 26, pp. 134-144, 1993.
• [8] 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.
• [9] 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.
• [10] Wierzcholski, K., Comparisson Between Impulsive and Periodic Non-Newtonian Lubrication of Human Hip Joint, Engineering Trans., 53, 1, pp. 69-114, 2005.
• [11] Wierzcholski, K., Bio and slide bearings: their lubrication by non-Newtonian fluids and application in non conventional systems, Vol.III: Tribology process for chondrocytes,human joint and micro-bearing, Monograph, Published by Krzysztof Wierzcholski, Gdansk University of Technology, pp. 1-129, Gdańsk 2006-2007.
• [12] Wierzcholski, K., Mathematical implementation into computer calculations for microbearing capacities, XIII Journal of Applied Computer Science, Vol. 18, No. 1, pp. 117-135, 2010.
• [13] Wierzcholski, K., Computer Simulations of Short Radial Bearing Capacity for Rivlin Ericksen Oils. SAMS, System Analysis Modelling and Simulations OPA Overseas Publishers. Association N.V., Vol. 33, pp. 219-238, 1998.