Solutions of recurrence and summation equations and their applications in slide bearing wear calculations

The investigations under the paper include a derivation of a non-homogenous recurrence equation of the second and higher orders with variable coefficients, whose particular solutions, with the boundary conditions set and obtained from experimental measurements, will be the sequences of the wear value of the bearing in the successive years of operation. Owing to these investigations, it will be possible to predict for example the wear values of slide bearings. Moreover, this paper presents the some particular applications of recurrence equations with regard to the calculation prognosis of micro-bearing parameters such as friction forces, friction coefficients and wear. Recurrence equations are presented in a form of difference equations where the unknown functions occur as the main terms of the sequence of inquired values. In this paper, the properties of the particular values of recurrence equations are defined. Possibility of modulation and control of mentioned problem belong to the artificial intelligence of HDD microbearing. Presented problem describes not continuous relations hence determines the mathematical and numerical solutions in discrete spaces. Properly in the case of continuous functions, the mentioned recurrence equations have the same meaning as differential equations. Recurrent equations for discrete function correspond to differential equations for the continuous function. In final conclusions, the application of presented theory in this paper contains the numerical solutions referring the wear values of HDD bearing system in the indicated period of operating time.