Authors: Hedrih, Katica (Stevanović) 
Nikolić-Stanojević, Vera
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A model of gear transmission: Fractional order system dynamics
Journal: Mathematical Problems in Engineering
Volume: 2010
Issue Date: 11-Aug-2010
Rank: M22
ISSN: 1024-123X
DOI: 10.1155/2010/972873
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.
Publisher: Hindawi
Project: Theoretical and Applied Mechanics of the Rigid and Solid Bodies. Mechanics of Materials 

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