In this paper, the authors present the equations of the hydrodynamic lubrication theory for conical slide
bearings lubricated with the oil with properties described by the Rivlin-Ericksen model. It is assumed, that the
considered lubricating oil shows non-Newtonian properties, i.e. it is an oil for which, apart from the classic
dependence of oil viscosity on pressure, temperature and operating time, there is also a change in dynamic
viscosity values caused by the changes of shear rate. The method of a small parameter was used to solve the
conservation of momentum, stream continuity, and energy conservation equations.
The small parameter method consists in presenting the sought functions (pressure, temperature, components
of the velocity vector) in the form of a uniformly convergent series expansion in powers of a constant small
parameter. These functions are substituted into the system of basic equations, and then the series are multiplied
by the Cauchy method. By a comparison of the coefficients with the same powers of a small parameter, we
obtain systems of partial differential equations, from which the subsequent approximations of unknowns of
the sought functions are determined. The small parameter method separates the non-linear system of partial
differential equations and creates several linear systems of equations.
The aim of this work is to derive the equations describing and allowing the determination of the temperature
distribution, hydrodynamic pressure distribution, velocity vector components, load carrying capacity, friction
force and friction coefficient in the gap of conical slide bearing, lubricated with the oil of the properties
described by the Rivlin-Ericksen model, taking into account its viscosity changes due to time of operation.