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1 2012

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Impulsive and periodic class of solutions for hydrodynamic theory of lubrication

Wierzcholski K., Miszczak A.

Journal of KONES

2012

Vol. 19, No. 4

651-658

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.