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

• Autorzy: Wierzcholski K.
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

wear prognosis; HDD micro-bearings; recurrence non-homogeneous equation

• Wydawca: Łukasiewicz Research Network - Institute of Aviation ; European Science Society of Powertrain and Transport KONES Poland ; Wydawnictwo Instytutu Technicznego Wojsk Lotniczych
• Czasopismo: Journal of KONES
• Rocznik: 2012
• Tom: Vol. 19, No. 2
• Strony: 543--550
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Wierzcholski K.

• Technical University of Koszalin Institute of Mechatronics, Nanotechnology and Vacuum Technique Śniadeckich Street 2, 75-453 Koszalin, Poland tel.:[phone], fax: [phone],

Bibliografia

• [1] Kącki, E., Partial Differential Equations in Physical and Technical Problems, WNT, Warsaw 1989.
• [2] Kosma, Z., Numerical Methods In Engineering Applications, Politechnika Radomska, 1999.
• [3] Koźniewska, I., Recurrence Equations, PWN, Warszawa 1973.
• [4] Nowicki, A., Recurrence Sequences, Wydawnictwo Wyższej Olsztyńskiej Szkoły Informatyki i Zarządzania, Olsztyn-Toruń 2010.
• [5] Wierzcholski, K., Summation equation tools for slide microbearing systems wear prognosis, Journal of KONES Powertrain and Transport, Vol. 18, No. 3, pp. 463-470, Warsaw 2011.
• [6] Wierzcholski, K., Mega algorithm for partial recurrence Reynolds equation, XIV International Conference System Modelling and Control, pp. 1-8.
• [7] Wierzcholski, K., Summation equations and their applications in mechanics, XIV International Conference System Modelling and Control, pp. 11-22.