Operating parameters of a slide bearing with parabolic-shaped slide surfaces with consideration of the stochastic changes in the lubrication gap height
Operating parameters of a slide bearing with parabolic-shaped slide surfaces with consideration of the stochastic changes in the lubrication gap height
In this article, the authors present the equations of the hydrodynamic theory for a slide bearing with parabolicshaped slide surfaces. The lubricating oil is characterized by non-Newtonian properties, i.e. an oil for which, apart
from the classic oil viscosity dependence on pressure and temperature, also an effect of the shear rate is taken into
account. The first order constitutive equation was adopted for considerations, where the apparent viscosity was
described by the Cross equation. The analytical solution uses stochastic equations of the momentum conservation law,
the stream continuity and the energy conservation law. The solution takes into account the expected values of the
hydrodynamic pressure EX[p(ϕ,ζ)], of the temperature EX[T(ϕ,y,ζ)], of the velocity value of lubricating oil
EX[vi(ϕ,y,ζ)], of the viscosity of lubricating oil EX[ηT(ϕ,y,ζ)] and of the lubrication gap height EX[εT(ϕ,ζ)]. It was
assumed, that the oil is incompressible and the changes in its density and thermal conductivity were omitted. A flow
of lubricating oil was laminar and non-isothermal. The research concerned the parabolic slide bearing of finite
length, with a smooth sleeve surface, with a full wrap angle. The aim of this work is to derive the stochastic equations,
that allow to determine the temperature distribution, hydrodynamic pressure distribution, velocity vector components,
load carrying capacity, friction force and friction coefficient, in the parabolic sliding bearing, lubricated with nonNewton (Cross) oil, including the stochastic changes in the lubrication gap height. The paper presents the results of
analytical and numerical calculation of flow and operating parameters in parabolic sliding bearings, taking into
account the stochastic height of the lubrication gap. Numerical calculations were performed using the method of
successive approximations and finite differences, with own calculation procedures and the Mathcad 15 software.
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