A Model of Gear Transmission: Fractional Order System Dynamics | Zendy

Katica R. Hedrih | Zendy; Vera Nikolić-Stanojević | Zendy

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A Model of Gear Transmission: Fractional Order System Dynamics

Author(s) -

Katica R. Hedrih,

Vera Nikolić-Stanojević

Publication year - 2010

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2010/972873

Subject(s) - fractional calculus , connection (principal bundle) , viscoelasticity , transmission (telecommunications) , mathematics , ideal (ethics) , motion (physics) , mathematical analysis , geometry , computer science , physics , classical mechanics , telecommunications , philosophy , thermodynamics , epistemology

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

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