Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems
| Autor: | Amin Saghafi, Anoshirvan Farshidianfar |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Period-doubling bifurcation
Mathematics::Dynamical Systems Applied Mathematics Mechanical Engineering Mathematical analysis Aerospace Engineering Ocean Engineering Saddle-node bifurcation Phase plane Bifurcation diagram Nonlinear Sciences::Chaotic Dynamics Nonlinear system Transcritical bifurcation Control and Systems Engineering Control theory Homoclinic bifurcation Electrical and Electronic Engineering Nonlinear Sciences::Pattern Formation and Solitons Bifurcation Mathematics |
| Zdroj: | Nonlinear Dynamics. 75:783-806 |
| ISSN: | 1573-269X 0924-090X |
| DOI: | 10.1007/s11071-013-1104-4 |
| Popis: | The global homoclinic bifurcation and transition to chaotic behavior of a nonlinear gear system are studied by means of Melnikov analytical analysis. It is also an effective approach to analyze homoclinic bifurcation and detect chaotic behavior. A generalized nonlinear time varying (NLTV) dynamic model of a spur gear pair is formulated, where the backlash, time varying stiffness, external excitation, and static transmission error are included. From Melnikov method, the threshold values of the control parameter for the occurrence of homoclinic bifurcation and onset of chaos are predicted. Additionally, the numerical bifurcation analysis and numerical simulation of the system including bifurcation diagrams, phase plane portraits, time histories, power spectras, and Poincare sections are used to confirm the analytical predictions and show the transition to chaos. |
| Databáze: | OpenAIRE |
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