Pseudo-Gaussian Density Functions for Gap Height Between Two Surfaces

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

Abstrakty

EN

The presented paper formulates the sequence of pseudo-Gaussian distributions where are presented the mathematical results of standard deviation and probability density function derivations for bio-and micro-bearing gap height on the basis of Mow, Dowson, Cwanek, Wierzcholski experimental results. The mathematical derivation of the optimum probability density functions and least standard deviation are illustrated in two cases. The first case relates to the height of the gap if vibration and unsteady load causes the random changes. The second case relates to the height of the gap if the asperities of the cartilage surface roughness cause the random changes. Author formulates one Theorem and some Corollaries where the sequence of pseudo-Gaussian-distributions are derived. The presented proof shows, that such sequence is convergent to the Gaussian distribution in infinity.

Słowa kluczowe

EN

probability density function; Gaussian distribution; probability density sequence; random roughness; optimum standard deviation

PL

funkcja gęstości prawdopodobieństwa; rozkład Gaussa

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Journal of Applied Computer Science
• Rocznik: 2010
• Tom: Vol. 18, nr 2
• Strony: 79--90
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Wierzcholski K. Ch.

autor

Nowakowska K.

• 1Institute of Applied Mathematics, Pomeranian University Arciszewskiego 22, 76-200 Słupsk, Poland,

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-Londyn-Paris-Tokyo-Hong Kong, 1990, Vol. 2, Chap. 29, pp. 305-345.
• [2] Mow, V. C. and Atesian, G. A., Basic Orthopedic Biomechanics., Edited by Van C. Mow andWilson C. Hayes Lippincott, Raven Publishers, Philadelphia, 1997.
• [3] Sobczyk, M., Statystyka., PWN, Warszawa, 1996, (in Polish).
• [4] Wierzcholski, K. and Cwanek, J., Measurements of surface roughness of heads of human hip joints in lubrication aspects. Proceedings of Applied Mechanics Faculty of Technical University of Gliwice, 2005, pp. 477-483.
• [5] Wierzcholski, K., Experimental measurements of artificial hip joint surfaces and applications for the pressure and capacity distributions. Journal of Kones Powertrain and Transport, Warsaw 2006, Vol. 13, No. 2, pp. 435-441.
• [6] Wierzcholski, K., Bio and slide bearings: their lubrication by non-Newtonian fluids and application in non conventional systems. Vol. II: The theory of human joint unsteady lubrication, Monograph (pp. 1-172), Published by Krzysztof Wierzcholski, Gdańsk University of Technology, ISBN 83-923367-0-4, Gdańsk 2006.