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Unified summation equations and their applications in tribology wear process

Wierzcholski K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2013

Vol. 61, nr 2

405--417

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.

Summation equation tools for slide microbearing systems wear prognosis

Wierzcholski K.

Journal of KONES

2011

Vol. 18, No. 2

463-470

Efficient functioning of slide micro-bearings systems especially HDD micro-bearing require to recognition and modulation of the proper values of the friction forces and wear during the exploitation time. Possibility of modulation and control of mentioned problem belong to the artificial intelligence of HDD micro-bearing. This paper presents the some applications of summation equations regard to the calculation prognosis of micro-bearing parameters such as friction forces, ,friction coefficients and wear .Summation equations are presented a new form of difference and recurrence equations where the unknown function occurs as the argument of the reciprocal unified operator of summation (UOS) 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 summation equations have the same meaning as integral equations. This paper will present the transformation method of summation equations to recurrent equations. Recurrent equations for discrete function correspond to differential equations for the continuous function. 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.