Numerical contribution to the viscoelastic magnetic lubrication of human joint in periodic motion

• Autorzy: Wierzcholski K. Ch.
• Języki publikacji: EN

Abstrakty

EN

This paper presents the author's numerical contribution to unsymmetrical viscoelastic hydrodynamic lubrication of human joints with synovial fluid in periodically changed time and unsteady magnetic field. We assume that bone head in human joint moves in two directions, namely in circumference and meridian directions. Basic equations describing the flow of synovial fluid in human hip joint are solved analytically od numerically. Numerical calculations are performed in Mathcad 2000 Professional Program, taking into account the method of finite differences. This method satisfies stability of numerical solutions of partial differential equations and values of capacity forces occurring in human joints.

Słowa kluczowe

EN

biomechanics; periodic motion; magnetic field

PL

biomechanika; ruch okresowy; pole magnetyczne

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Acta of Bioengineering and Biomechanics
• Rocznik: 2004
• Tom: Vol. 6, nr 1
• Strony: 61--82
• Opis fizyczny: Bibliogr. 20 poz., rys., wykr.

Twórcy

autor

Wierzcholski K. Ch.

• Technical University of Gdansk, Faculty of Ocean Engineering and Ship Technology, 80-952 Gdansk, Gdynia Maritime University, Faculty of Marine Engineering

Bibliografia

• [1] DOWSON D., Bio-Tribology of Natural and Replacement Synovial Joints, [in:] Van Mow C., Ratcliffe A., Woo S.L-Y. (eds.), Biomechanics of Diarthrodial Joint, Springer-Verlag, New York, Berlin, Londyn, Paris, Tokyo, Hong Kong , 1990, Vol. 2, Chap. 29, pp. 305–345
• [2] KĄCKI E., Równania różniczkowe cząstkowe w zagadnieniach fizyki i techniki, WNT, Warszawa, 1989.
• [3] KNOPP K.,Szeregi nieskończone, PWN, 1956.
• [4] MOW V.C., HOLMES M.H., LAI W.M., Fluid transport and mechanical properties of articular cartilage, Journal of Biomechanics, 1984, 17, 337–394.
• [5] MOW V.C., RATCLIFFE A.,WOO S., Biomechanics of Diarthrodial Joints, Springer-Verlag, Berlin, Heidelberg, New York, 1990.
• [6] MOW V.C., SOSLOWSKY L.J., Friction, lubrication and wear of diarthrodial joints, [in:] Mow V.C., Hayes W. C. (eds.), Basic orthopedic biomechanics, New York, Raven Press, 1991, 254–291.
• [7] MOW V.C., GUILAK F., Cell Mechanics and Cellular Engineering, Springer-Verlag, Berlin, Heidelberg, New York, 1994.
• [8] OERTEL H., LAURIEN E., Numerische Strömungsmechanik, Vieweg, Braunschweig, Wiesbaden, 2003.
• [9] TEIPEL I., The Impulsive Motion of a Flat Plate in a Viscoelastic Fluid, Acta Mechanica, SpringerVerlag, 1981, 39, 277–279.
• [10] TRUESDELL C., A First Course in Rational Continuum Mechanics, Maryland, John Hopkins University, Baltimore, 1972.
• [11] UNGETHÜM M., WINKLER-GNIEWEK W., Tribologie in Medizin, Tribologie – Schmierungstechnik, 1990, 5, 268–277.
• [12] WIERZCHOLSKI K., PYTKO S., Metoda wyznaczania parametrów biołożyska smarowanego cieczą nienewtonowską, Tribologia, 1993, 1, 9–12.
• [13] WIERZCHOLSKI K., NOWOWIEJSKI R., MISZCZAK A., Numerical Analysis of Synovial Fluid Flow in Biobearing Gap, Proceedings of International Conference at System Modelling Control, Conference, 1995, 8, 2, 382–387.
• [14] WIERZCHOLSKI K., PYTKO S., Analytical calculations for experimental dependences between shear rate and synovial fluid viscosity, Proc. of Internat. Tribology Conference, Japan, Yokohama, 1995, Vol. 3. pp. 1975–1980.
• [15] WIERZCHOLSKI K., Oil velocity and pressure distribution in short journal bearing under Rivlin– Ericksen lubrication, 1998, SAMS, System Analysis Modeling and Simulations, OPA Overseas Publishers. Assoc. N.V., Vol. 32, 205–228.
• [16] WIERZCHOLSKI K., The method of solutions for hydrodynamic lubrication by synovial fluid flow in human joint gap, Control and Cybernetics, 2002, Vol. 31, No. 1, 91–116.
• [17] WIERZCHOLSKI K., Capacity of deformed human hip joint gap in time dependent magnetic field, Acta of Bioengineering and Biomechanics, 2003, Vol. 5, No. 1, pp. 43–65.
• [18] WIERZCHOLSKI K., Pressure distribution in human joint gap for elastic cartilage and time dependent magnetic field, Russian Journal of Biomechanics, Perm, 2003, Vol. 7, No. 1, pp. 24–46.
• [19] WIERZCHOLSKI K., Tribologie für menschliche Gelenke, Tribologie und Schmierungstechnik, 2002, 5, pp. 5–13.
• [20] Wierzcholski K., Tribologie für instabil belastete menschliche Gelenke im magnetischen Feld, International Colloquium of Tribology, Technische Akademie Esslingen, 2004, Vol. III, pp. 1717– 1724; paper presented additionally at Technical University of Karlsruhe, Faculty of Strömungs- lehre, 2 July, 2004.