Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems

• Published in: Nonlinear dynamics Vol. 75; no. 4; pp. 783 - 806
• Main Authors: Farshidianfar, A., Saghafi, A.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2014; Springer Nature B.V
• Subjects: Automotive Engineering; Bifurcations; Chaos theory; Classical Mechanics; Computer simulation; Control; Dynamic models; Dynamical Systems; Engineering; Mathematical analysis; Mathematical models; Mechanical Engineering; Nonlinear analysis; Nonlinear dynamics; Nonlinearity; Numerical prediction; Original Paper; Spur gears; Stiffness; Transmission error; Vibration; Vibration analysis; Chaos; Melnikov method; Spur gear; Nonlinear vibration; Global homoclinic bifurcation
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-013-1104-4

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.