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Unified summation equations and their applications in tribology wear process

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Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
405--417
Opis fizyczny
Bibliogr. 20 poz., rys., wykr., tab.
Twórcy
  • Institute of Mechatronics Nanotechnology and Vacuum Technique, Koszalin University of Technology, 2 Śniadeckich St., 75-453 Koszalin, Poland
Bibliografia
  • [1] I. Koźniewska, Recurrence Equations, PWN Warsaw, 1973, (in Polish).
  • [2] H. Levy and F. Lessman, Finite Recurrence Equation, PWN, Warsaw, 1966, (in Polish).
  • [3] K.S. Miller, Linear Difference Equations, Macmillan, New York, 1968.
  • [4] A.A. Ralston, First Course in Numerical Analysis, PWN, Warsaw, 1971, (in Polish).
  • [5] A. Maciąg and J. Waue, “Wave polynomials for solving different types of two dimensional wave equations”, Computer AssistedMechanics and Engineering Sciences 12, 87-102 (2005).
  • [6] K. Wierzcholski, On Some n-Order Recurrence. About Somen-Order Recurrence, State Scientific Publishing House Pol. Acad. of Sci. (PWN), 1975, (in Polish).
  • [7] E. Kącki, Partial differential Equations in Physical and TechnicalProblems, WNT, Warsaw, 1989, (in Polish).
  • [8] A. Kiełbasiński and K. Schwetlick, Linear Numerical Algebra, Warsaw, WNT, 1994, (in Polish).
  • [9] T. Kaczorek, “Stability of continuous-discrete linear systems described by the general model”, Bull. Pol. Ac.: Tech. 59 (2), 189-192 (2011).
  • [10] Bharat Bhushan, “Nano-tribology and nano-mechanics of Mems/Nems and Bio-Mems, Bio-Nems materials and devices”, Microelectronic Engineering 84, 387-412 (2007).
  • [11] K. Wierzcholski, “Solutions of recurrence and sum- mation equations and their applications in slide bearing wear calculations”, J. Kones Powertrain and Transport 19 (2), 543-550 (2012).
  • [12] K. Wierzcholski, Bio and Slide Bearings, their Lubrication byNon-Newtonian Oils and Applications, Vol. 1, Gdansk Univ. of Technology, Gdańsk, 2004.
  • [13] K. Wierzcholski, S. Chizhik, A. Trushko, M. Zbytkova, and A. Miszczak, “Properties of cartilage on macro and nanolevel”, Adv. in Tribology 1, http://www.hindawi.com/apc.aspx?n=243150 (2010).
  • [14] G.H. Jang, C.H. Seo, and H. Scong Lee, “Finite element model analysis of an HDD considering the flexibility of spinning disc-spindle”, Microsystem Technologies 13, 837-847 (2007).
  • [15] I. Babuska and T. Strouboulis, The Finite Element Method andits Reliability, Clarendon Press, Oxford, 2001.
  • [16] I. Babuska and J. Chleboun, “Effect of uncentrainties in the domain on the solution of Dirichlet boundary value problem”, Numerisch Mathematik 93, 583-610 (2003).
  • [17] I. Babuska, J.T. Oden, T. Belytschko, and T.J.R. Hughes, “Research directions in computational mechanics”, ComputerMethods in Applied Mechanics and Engineering 192, 913-922 (2003).
  • [18] I. Babuska and S. Ohnimus, “A posteriori error estimation for the semi-discrete finite element method of parabolic differential equations”, Computer Methods in Applied Mechanics andEngineering 190 (35-36), 4691-4712 (2001).
  • [19] T. Kaczorek, “Computation of positive stable realiza-tion for linear continuous-time systems”, Bull. Pol. Ac.: Tech. 59 (3), 273-281 (2011).
  • [20] L. Demkowicz and J. Gopalakrishman, “A class of discontinuous Petrov-Galerkin methods. Optimal test functions”, Num. Math. for Part. Diff. Eq. 27, 70-105 (2011).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-69493b3c-aaba-47ed-a8aa-15b711f89c07
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