Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 972873, 23 pages
doi:10.1155/2010/972873
Research Article

A Model of Gear Transmission: Fractional Order System Dynamics

Katica (Stevanović) Hedrih1,2 and Vera Nikolić-Stanojević3,4

1Mathematical Institute SANU, Belgrade, Serbia
2Faculty of Mechanical Engineering, University of Niš, Yu-18 000, ul. Vojvode Tankosića 3/22, Niš, Serbia
3State University of Novi Pazar, Novi Pazar, Serbia
4Faculty of Mechanical Engineering, University of Kragujevac, Kragujevac, Serbia

Received 24 January 2010; Revised 2 March 2010; Accepted 6 May 2010

Academic Editor: Alexander P. Seyranian

Copyright © 2010 Katica (Stevanović) Hedrih and Vera Nikolić-Stanojević. 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.

Abstract

A theoretical model of multistep gear transmission dynamics is presented. This model is based on the assumption that the connection between the teeth of the gears is with properties within the range from ideal clasic to viscoelastic so that a new model of connection between the teeth was expressed by means of derivative of fractional order. For this model a two-step gear transmision with three degrees of freedom of motion has been used. The obtained solutions are in the analytic form of the expansion according to time. As boundary cases this model gives results for the case of ideally elastic connection of the gear teeth and for the case of viscoelastic connection of the gear teeth, as well. Eigen fractional modes are obtained and a vizualization is done.