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Numerical studies of nonlinear gearing models using bond graph method

Margielewicz J., Wojnarowski J., Zawiślak S.

International Journal of Applied Mechanics and Engineering

2018

Vol. 23, no. 4

885--896

The present paper is dedicated to computer simulations performed using a numerical model of a one-stage gear. The motion equations were derived utilizing the bond graph method. The formulated model takes into consideration the variable stiffness of toothings as well as an inter-tooth clearance which has been represented via discontinuous elements with so called dead zones. As a result of these assumptions, the nonlinear model was obtained which enables representation of the dynamic phenomena of the considered gear. In the paper, an influence of errors of gear wheels’ co-operation on the character of excited dynamic phenomena was studied. The methodology of the analyses consists in utilization of the following tools: color maps of distribution of the maximal Lapunov coefficient and bifurcation diagrams. Based upon them, the parameters were determined, for which the Poincare portrait represents a structure of the chaotic attractor. For the identified attractors, the initial attractors were calculated numerically - which along with the changes of the control parameters are subjected to multiplication, stretching or rotation.

O stabilności dyskretnych i ciągłych układów liniowych o zmiennych skokowo współczynnikach*

Bal A.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

2008

z. 151

11-18

W pracy przedstawiono problem stabilności dla dyskretnych i ciągłych układów liniowych o zmiennych współczynnikach w czasie, w których funkcja przełączająca jest przedziałami stała. Dla takich układów wyznaczone zostały warunki stabilności za pomocą wykładników Lapunowa.

In this paper stability of discrete and continuous time-varying linear systems with piecewise constant switching signal is presented. For such systems the stability conditions are proposed with the aid of Lapunov exponent.