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Wear process in successive time units described by first order recurrences

Wierzcholski K.

Journal of KONES

2014

Vol. 21, No. 3

285--292

The numerous tribology problems occurring in power-train and transport industry lead to wear bearing determination solutions. Especially the project designer demand the more and more information referring the slide bearing wear anticipation in succeeding years of machine operations. In this paper a perspective will be provided on what is known about various types of influences which are caused wear effects. Some machinery eventually fails or becomes uneconomical to operate because of single causes for example types of wear, but most mechanical devices succumb to combinations of causes. A direct parallel is seems in the human machine. Therefore this paper presents the methods of solutions of some specific class of ordinary non-homogeneous recurrence equations of first order with variable coefficients occurring in hydrodynamic theory of bearing wear problems. The various coefficients occurring in considered recurrent equations are determined from experimental measurements where the influence of various operating parameters on the wear effects is taking into account. The influence of numerous operating parameters on the wear effects is experimentally determined in the case if mentioned parameters are independent as well if are mutually connected. Moreover in this paper the theorems will be presented of the existence, determination and an algorithm construction of discrete solutions of non-homogeneous, linear, first order recurrent equations with variable coefficients. The Lemmas and Theorem are formulated and proved by means of the Unified Operator of Summation (UOS operator) with a unitary translation operator, where the operator properties and features are taking into account. In the case of the space of solution functions, the above mentioned wear problems determination are attributed to practical applications related to the non-homogeneous, linear, first order differential equations. The examples presented in this paper for various variable coefficients i.e. for various operating conditions determine the wear values of micro- bearing system during the indicated time units of operating time.