Recurrence Contribution to Determining the Wear of Slide Bearings
Numerous problems of numerical calculations occurring in power-train tribology and transport concerning the process of determining the problems of worn out bearings demand more and more information referring to the anticipation of the wear of slide bearings in the succeeding years of machine operations. Therefore, the paper presents the methods for working towards solutions to some specific classes of second and higher order non-homogeneous recurrence equations with variable coefficients occurring in the hydrodynamic theory of the problems dealing with bearing wear. Contrary to linear recurrence equations with constant coefficients, linear recurrence equations with variable coefficients rarely have analytical solutions. Numerical answers to such equations are always practicable. With reference to a large number of analytical methods for solutions to linear recurrence equations with variable coefficients, three research directions are usually followed.The first one depends upon the successive determination of particular linear independent solutions to the considered recurrence equation. The second direction can be characterized by a reduction in the order of the recurrence equation for obtaining the first order always solved recurrence equation. The third direction of solutions to recurrence equations with variable coefficients contains the methods for analytical solutions by means of a summation factor.The majority of the general methods of analytical solutions to linear recurrence equations with variable coefficients constitute the adaptation of the methods applied in solutions to suitable differential equations. As regards the final conclusions, the application of the theory presented in this paper contains numerical solutions referring to the wear values of the slide journal-bearing system in the indicated period of operating time.
Algirdas V. Valiulis, Olegas Černašėjus and Vadim Mokšin
K. Wierzcholski and A. Miszczak, "Recurrence Contribution to Determining the Wear of Slide Bearings", Solid State Phenomena, Vols. 220-221, pp. 301-306, 2015