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Differential and recurrence unified reynolds equations and mega algorithm for their numerical solutions

Wierzcholski K., Miszczak A.

Journal of KONES

2012

Vol. 19, No. 4

643-650

The objective of the research under the paper topic is an analytical, unified formulation of a new standardized view of general solution of hydrodynamic problem using algorithm to determine changes of the components of the velocity vector, the distributions of hydrodynamic pressure, load carrying capacity, of slide bearings with cooperating curvilinear, orthogonal surfaces that are lubricated with a various non-Newtonian lubricants. In this paper for non- Newtonian lubricants are questioning the hitherto prevailing assumptions using in hydrodynamic theory of lubrication such as constant value of lubricant viscosity and pressure in the thickness of lubricating gap i.e. in gap height direction. Finally, the non-homogeneous partial differential equation generated with variable coefficients that is the result of the various boundary conditions being imposed that are different for each problem solved is an equation that determines the distributions of hydrodynamic pressure values. This equation is to be written in the form of a unified non-homogenous partial recurrence equation with variable coefficients. The Authors foresee that a mega-algorithm will be developed for the solution of this equation in a numerical form. This equation in particular cases is an equivalent of modified Reynolds equations in the research that has been conducted so far concerning the hydrodynamic theory of lubrication.

Algorithm for friction force computation in intelligent micro-pairs system

Wierzcholski K. C.

Journal of Applied Computer Science

2011

Vol. 19, nr 1

139-160

The presented paper investigates the latest achievements of calculation algorithm and derivation for friction forces of intelligent micropairs, friction micro-joints and especially for friction forces of the conical, spherical, cylindrical, parabolic, hyperbolical micro-bearings particularly in HDD micro-bearings. Various bearing surfaces and oil dynamic viscosity changes in gap height directions are assumed. Author formulates one Theorem and some Corollaries where the calculation algorithm for friction forces determination was defined.