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1

A method of the wear prognosis of sliding bearings

Miszczak A., Wierzcholski K.

Archive of Mechanical Engineering

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2014

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Vol. LXI, nr 4

553--570

EN

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.

PL

Rozważania przedstawione w niniejszej pracy obejmują komputerową analizę prognozy zużycia łożyska ślizgowego z wykorzystaniem rozwiązań równań rekurencyjnych oraz danych eksperymentalnych. Problem optymalizacji zużycia powierzchni ślizgowych łożyska został rozwiązany przy wykorzystaniu obliczeń analitycznych i numerycznych a także przy uwzględnieniu materiału łożyskowego, parametrów doświadczalnych oraz warunków brzegowych. Uzyskane wyniki pozwalają nam dostrzec związek między chropowatością, właściwościami materiału, amplitudą drgań, rodzajem sił tarcia, twardością materiałów, prędkością ślizgania z jednej strony, a przyrostem zużycia w kolejnych jednostkach czasowych procesu eksploatacji z drugiej strony.

2

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

Wierzcholski K.

Journal of KONES

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2012

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Vol. 19, No. 2

543-550

EN

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.

3

Summation equation tools for slide microbearing systems wear prognosis

Wierzcholski K.

Journal of KONES

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2011

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Vol. 18, No. 2

463-470

EN

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.