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  • Author: Krzysztof Wierzcholski x
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K. Wierzcholski

Abstract

This paper presents some applications of summation equations with regard to the calculation prognosis of micro-bearing wear parameters. Summation equations are presented in a new form of difference and recurrence equations where the unknown micro-bearing wear function occurs as the argument of the reciprocal unified operator of summation (UOS). In this paper the properties of the UOS and reciprocal UOS as well as the unitary translation operator (UTO) are defined and applied to a micro-bearing wear determination. The approach of both dual and interaction between summation and recurrence equations and micro-bearing wear determination, makes this paper unique.

Open access

K. Wierzcholski and A. Miszczak

Abstract

This paper presents the methods of control problem solutions using recurrence equations implementation and UOS transformation for the bearing wear estimation during the finite and infinite time units of an operation process. If we have two wear value increase processes then very important is information which process is divergent more slowly. On the other hand, in comparison with two convergent processes we must decide which process is convergent more quickly. The wear process is determined mostly by the summation factor method. Such a method is applied for the solutions of recurrence equations with variable coefficients

Open access

Andrzej Miszczak and Krzysztof Wierzcholski

Abstract

The considerations presented in this paper include a computer analysis of slide bearing wear prognosis using the solutions of recurrence equations complemented with the experimental data values. On the ground of the results obtained from analytical and computational numerical calculations, and taking into account the experimental parameters of bearing material and operation boundary conditions, the control problems of slide bearing wear surfaces have been presented. The obtained results allow us to see a connection between roughness, material properties, the amplitude of vibrations, the kind of the friction forces, the hardness of materials, the sliding speed in one side and the wear increments in succeeding time units of the exploitation process in other side.