Topology of calculating pressure and friction coefficients for time-dependent human hip joint lubrication

• Autorzy: Wierzcholski K.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with the calculations of the unsteady, impulsive pressure distributions, carrying capacities and friction forces under unsteady conditions in a super-thin layer of biological synovial fluid inside the slide biobearing gap limited by a spherical bone head. Unsteady and random flow conditions for the biobearing lubrication are given. Moreover, the numerical topology of pressure calculation for a difference method is applied. From a mathematical viewpoint the present method for the solution of the modified Reynolds equation allows this problem to be resolved by the partial recurrence nonhomogeneous equation of the second order with variable coefficients. To the best of the author knowledge, an adaptation of the known numerical difference method to the spherical boundary conditions applied during the pressure calculations for a human hip bonehead seems to be decisive.

Słowa kluczowe

EN

pressure; carrying capacity; unsteady conditions; new numerical difference method

PL

ciśnienie; nośność; niestabilne warunki; nowe metody numerycznej różnicy

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Acta of Bioengineering and Biomechanics
• Rocznik: 2011
• Tom: Vol. 13, no. 1
• Strony: 41--56
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

Wierzcholski K.

• Pomeranian Academy of Słupsk, Institute of Applied Mathematics,

Bibliografia

• [1] DOWSON D., Bio-Tribology of Natural and Replacement Synovial Joints, [in:] Van Mow C., Ratcliffe A., Woo S.L-Y., Biomechanics of Diarthrodial Joint, Springer-Verlag, New York–Berlin–London–Paris–Tokyo–Hong Kong, 1990, Vol. 2, Chap. 29, 305–345.
• [2] KNOPP K., Szeregi nieskończone, PWN, Warszawa, 1956.
• [3] MERKHER Y., SIVAN S., ETSION I., MAROUDAS A., HALPERINA G., YOSEF A., Rational human joint friction test, Tribological Letter, 2006, 22(1), 29–36.
• [4] MOW V.C, RATCLIFFE A., WOO S., Biomechanics of Diarthrodial Joints, Springer-Verlag, Berlin–Heidelberg–New York, 1990.
• [5] NAKA M. H., HASUO M., FUWA Y., IKEUCHI K., Correlation between friction of articular cartilage and reflectance intensity from superficial image, Tribology International, 2007, 40(2), 200–207.
• [6] NORTHWOOD E., FISHER J., A multi-directional in vitro investigation into friction coefficient of articular cartilage depends on the contact area, Journal of Biomechanics, 2007, 40, 3257–3260.
• [7] RALSTON A., A First Course in Numerical Analysis, McGraw-Hill Co., New York–Toronto–London–Sydney, 1965.
• [8] TEIPEL I., The impulsive motion of a flat plate in a viscoelastic fluid, Springer-Verlag, Acta Mechanica, 1981, 39, 277–279.
• [9] TRUESDELL C.A., First Course in Rational Continuum Mechanics, Maryland, John Hopkins University, Baltimore, 1972.
• [10] UNGETHÜM M., WINKLER-GNIEWEK W., Tribologie in Medizin, Tribologie Schmierungstechnik, 1990, 5, 268–277.
• [11] WIERZCHOLSKI K., PYTKO S., Metoda wyznaczania parametrów biołożyska smarowanego cieczą nienewtonowską, Tribologia, 1993, 1, 9–12.
• [12] 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, 1975–1980.
• [13] WIERZCHOLSKI K., Oil velocity and pressure distribution in short journal bearing under Rivlin Ericksen lubrication, System Analysis Modeling and Simulations, OPA Overseas Publishers. Assoc. N.V., 1998, Vol. 32, 205–228.
• [14] 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.
• [15] WIERZCHOLSKI K., Capacity of deformed human hip joint gap in time dependent magnetic field, Acta of Bioengineering and Biomechanics, 2003, Vol. 5, No. 1, 43–65.
• [16] 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, 24–46.
• [17] WIERZCHOLSKI K., Tribologie für menschliche Gelenke, Tribologie und Schmierungstechnik, 2002, 5, 5–13.
• [18] WIERZCHOLSKI K., Comparison between impulsive and periodic non-Newtonian lubrication of human hip joint, Engineering Transactions, 2005, 53, 1, 69–114.
• [19] WIERZCHOLSKI K., Lubrication of deformed hip joint, International Conference System Modelling and Control, Zakopane, 2007, 1–8.
• [20] WIERZCHOLSKI K., MISZCZAK A., Flow on the bio-cell surfaces as an element of the microbearing tribology, Journal of Kones Powertrain and Transport, 2007, Vol. 14, No. 2, 553–560.
• [21] WIERZCHOLSKI K., MISZCZAK A., Load carrying capacity of microbearings with parabolic journal, Solid State Phenomena, Trans. Technical Publications, Switzerland, 2009, Vol. 147–149, 542–547.
• [22] WIERZCHOLSKI K., Hydrodynamic pressure, carrying capacity, friction forces in biobearing gap, Acta of Bioengineering and Biomechanics, 2009, Vol. 11, No. 2, 31–44.
• [23] WIERZCHOLSKI K., Friction force and pressure calculations for time dependet impulsive intelligent lubrication of human hip joint, Acta of Bioengineering and Biomechanics, 2010, Vol. 12, No. 3, 95–101.