Bifurcation and chaos analysis of spur gear pair with and without nonlinear suspension
type: Item
instance of: scholarly article
title: Bifurcation and chaos analysis of spur gear pair with and without nonlinear suspension
zbMATH Open document ID: 1269.70038
author: Cai-Wan Chang-Jian
author: Shiuh-Ming Chang
published in: Nonlinear Analysis. Real World Applications
publication date: 2011-01-18T00:00:00Z
review text: The authors carry out a numerical analysis of nonlinear dynamics of a spur gear system. For the linear suspension, the dynamics is chaotic for low values of the damping coefficient. Increasing this coefficient, yields a six-fold periodic motion. For a gear system with nonlinear suspension, the behaviour is generically chaotic. However, in different windows of damping coefficient, there appears a periodic motion. Beyond a certain value of the coefficient, the system shows an inverse period-doubling bifurcation. In the standard analysis, the only used control parameter is the rotation speed. From this study, it is evident that knowing the rotational speed and the damping coefficient for which the dynamics is chaotic, one can avoid these and ensure a smooth running of the spur gear system. The coupled equations for the angular displacement of two spur gears are solved using the usual fourth-order Runge-Kutta method. Various measures of chaos, like e.g. the Lyapunov exponent, the correlation dimension and Poincaré sections, are studied to validate the conclusions.
Mathematics Subject Classification ID: 70K55
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 70K50
zbMATH DE Number: 5838179
zbMATH Keywords: damping coefficient
zbMATH Keywords: inverse period-doubling bifurcation
zbMATH Keywords: rotational speed
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: Lyapunov exponent
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2010.08.021
OpenAlex ID: W2087810388
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DOI: 10.1016/J.NONRWA.2010.08.021
description: scientific article; zbMATH DE number 5838179