Impulsive and periodic class of solutions for hydrodynamic theory of lubrication

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

Abstrakty

EN

In this paper, two different classes of lubricant flow conditions are basically indicated, i.e. for periodic solutions when pressure values and other flow parameters change periodically and for non-periodic solutions in the case of lubricating in the conditions of impulses and strokes. The Authors formulate the primary problem in the form of a system of 9 nonlinear non-homogeneous partial differential equations with variable and random coefficients in a curvilinear orthogonal system of coordinates which is supplemented with suitable constitutive dependences and conjugated with magnetic field equations with the Ohm equation. These equations include the following: three conservation equations of the lubricating liquid momentum, the stream continuity equation, the energy conservation equation, three equilibrium equations of the thin elastic superficial layer that are reduced to the differential equation in displacements, the heat transfer equation of the superficial layer that is flown around by the lubricating liquid. The following include those equations that describe constitutive dependences the Rivlin-Ericksen equation of physical dependences for viscoelastic ferrofluid, the equation of the physical dependences of the superficial layer of the surfaces lubricated, the equation of the physical dependences of the magnetic field. The unknown values of the material coefficients shall be determined experimentally. The following 9 unknowns are determined from the system of partial differential equations: three velocity components of the lubricating liquid, the hydrodynamic pressure, the temperature in the lubricating liquid, the three components of the superficial layer displacement and the temperature in the superficial layer. The mathematical solution of the problem presented requires a number of boundary conditions to be imposed. The Authors foresee quasi-analytical solutions of the system described of partial differential equations.

Słowa kluczowe

EN

injury solutions; periodic solutions; theory of lubrication; 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. 4
• Strony: 651--658
• Opis fizyczny: Bibliogr. 12 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

• [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] Parcus, H., Magneto und Elektroelastizität, ZAMM 53, T. 18, T. 24, 1973.
• [4] Teipel, I., The Impulsive Motion of a Flat Plate in a Viscoelastic Fluid, Acta Mech, Springer Verlag, 39, pp. 277-279, 1981.
• [5] Truesdell, C. A., First Course in Rational Continuum Mechanics, John Hopkins Univ., Baltimore Maryland, 1972.
• [6] Wierzcholski, K., Bio and slide bearings: their lubrication by non-Newtonian fluids and application in non conventional systems, Vol. I, Monograph, (pp.1-172), Published by Krzysztof Wierzcholski, Gdansk University of Technology, Gdańsk 2006.
• [7] Wierzcholski, K., Comparisson Between the Impulsive and Periodic Non-Newtonian Lubrication of the Human Hip Joint, Engineering Trans., 53, 1, pp. 69-114, 2005.
• [8] Wierzcholski, K., Mathematical implementation into computer calculations for microbearing capacities, XIII Journal of Applied Computer Science, Vol. 18, No. 1, pp.117-135, 2010.
• [9] Wierzcholski, K., Hydrodynamic pressure, carrying capacity, friction forces in biobearing gap, Acta of Bioengineering and Biomechanics, Vol. 11, No. 2, pp. 31-44, 2009.
• [10] Wierzcholski, K., Nowakowska, K., Pseudo-Gaussian density function for the gap height between two surfaces, XIII Journal of Applied Computer Science, Vol. 18, No. 2, pp. 79-90, 2010.
• [11] Wierzcholski, K., Miszczak, A., Load carrying capacity of microbearing with parabolic journal, Solid State Phenomena, Mechatronic Systems and Materials III, Vol. 147-149, pp. 542-547, 2009.
• [12] Wierzcholski, K., Bio and slide bearings, Monograph, Published by Krzysztof Wierzcholski, Gdansk University of Technology, Vol. III, pp. 1-129,Gdansk 2006-2007.