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Shock and Vibration
Volume 2014, Article ID 809739, 8 pages
Research Article

Bifurcation and Chaos Prediction in Nonlinear Gear Systems

Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran

Received 18 October 2012; Accepted 19 November 2012; Published 28 May 2014

Academic Editor: Abdolreza Ohadi

Copyright © 2014 Anooshirvan Farshidianfar and Amin Saghafi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The homoclinic bifurcation and transition to chaos in gear systems are studied both analytically and numerically. Applying Melnikov analytical method, the threshold values for the occurrence of chaotic motion are obtained. The influence of system parameters on the character of vibration is studied. The numerical simulation of the system including bifurcation diagram, phase plane portraits, Fourier spectra, and time histories is considered to confirm the analytical predictions for the occurrence of homoclinic bifurcation and chaos in nonlinear gear systems.