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Wear process in successive time units described by first order recurrences

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Abstrakty
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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.
Twórcy
  • Technical University of Koszalin, Institute of Technology and Education Śniadeckich Street 2, 75-453 Koszalin, Poland tel.:+48 94 3478344,fax: +48 94 3426753
Bibliografia
  • [1] Bharat, Bhushan, Handbook of Micro/Nano Tribology’ second ed. CRC Press, Boca Raton, London, New York, Washington D.C. 1999.
  • [2] Bharat, Bhushan, Nanotribology and nanomechanics of MEMS/NEMS and BioMEMS/BioNEMS materials and devices, Microelectr. Engineering, 84, pp. 387-412, 2007.
  • [3] Chizhik, S.,Wierzcholski, K., Trushko, A., Zbytkova, M., Miszczak, A., Properties of Cartilage on Micro- and Nanolevel, Advances in Tribology, Vol. 2010,
  • [4] Jang, G. H., Seo, C. H., Ho Scong Lee, Finite element model analysis of an HDD considering the flexibility of spinning disc-spindle, head-suspension-actuator and supporting structure, Microsystem Technologies, 13, pp. 837-847, 2007.
  • [5] Kącki, E., Partial Differential Equations in Physical and Technical Problems, WNT, Warsaw 1989.
  • [6] Kim, K. T., Ludema, K. C., Low cycle fatigue as an initiating mechanism of scuffing, ASME, Joumal Tribology, 117, 231. 1995
  • [7] Kosma, Z., Numerical Methods In Engineering Applications, Politechnika Radomska,1999.
  • [8] Koźniewska, I., Recurrence Equations, PWN, Warszawa 1973.
  • [9] Ludema, K.C., Friction, Wear, Lubrication, CRC Press, N.Y., London, Tokyo 1996.
  • [10] Nowicki, A., Recurrence Sequences, Wydawnictwo Wyższej Olsztyńskiej Szkoły Informatyki i Zarządzania, Olsztyn-Toruń 2010.
  • [11]Rezaei, Ali, WimVan Paepegem,De Baest Patrick, Wouter Ost, Degrieck Joris, Adaptive finite element simulation of wear evolution in radial sliding bearings, Wear, 296, pp. 660­671,2012.
  • [12] W ierzcholski, K., Summation equation tools for slide microbearing systems wear prognosis, Journal of KONES Powertrain and Transport, Vol. 18, No. 3, pp. 463-470, 2011.
  • [13] Wierzcholski, K., Unified summation equations and their applications in tribology wear process, Bulletin of the Polish Academy of Sci. Technical Sci., Vol. 61, No. 1, pp. 1-21, 2013.
  • [14] Wierzcholski, K., Summation equations and their applications in mechanics, XIV International Conference System Modelling and Control, pp. 11-22, 2011.
  • [15] Wierzcholski, K., Solution of recurrences with variable coefficients for slide bearing wear determination, Journal of KONES Powertrain and Transport, Vol. 20, No. 3, pp.427-433, 2013.
  • [16] Yang, L. J., A test methodology for the determination of wear coefficient, Wear, 259, pp. 1453-1461,2005.
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Bibliografia
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