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Mathematical Problems in Engineering
Volume 2013, Article ID 932150, 14 pages
Research Article

A New Model of the Fractional Order Dynamics of the Planetary Gears

1State University of Novi Pazar, Novi Pazar, Serbia
2Faculty of Engineering Science, University of Kragujevac, Serbia

Received 9 November 2012; Revised 25 March 2013; Accepted 31 March 2013

Academic Editor: Jocelyn Sabatier

Copyright © 2013 Vera Nikolic-Stanojevic et al. 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.


A theoretical model of planetary gears dynamics is presented. Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. In the paper, it has been indicated that even the small disturbance in design realizations of this gear cause nonlinear properties of dynamics which are the source of vibrations and noise in the gear transmission. Dynamic model of the planetary gears with four degrees of freedom is used. Applying the basic principles of analytical mechanics and taking the initial and boundary conditions into consideration, it is possible to obtain the system of equations representing physical meshing process between the two or more gears. This investigation was focused to a new model of the fractional order dynamics of the planetary gear. For this model analytical expressions for the corresponding fractional order modes like one frequency eigen vibrational modes are obtained. For one planetary gear, eigen fractional modes are obtained, and a visualization is presented. By using MathCAD the solution is obtained.