Abstract
The homoclinic bifurcation and transition to chaos in gear systems are studied both analytically and numerically. Applying Melnikov analytical method, the threshold values for the occurrence of chaotic motion are obtained. The influence of system parameters on the character of vibration is studied. The numerical simulation of the system including bifurcation diagram, phase plane portraits, Fourier spectra, and time histories is considered to confirm the analytical predictions for the occurrence of homoclinic bifurcation and chaos in nonlinear gear systems.
Highlights
Gear systems are known as one of the important sources of noise and vibration in industrial rotating machinery and power transmission systems
Sato et al [1] established a nonlinear model of gear system with the time dependence of tooth stiffness and backlash
Chang-Jian and Chang [5] investigated the dynamic responses of a single-degree-of freedom spur gear system with and without nonlinear suspension and found the bifurcation and chaotic dynamics in this system
Summary
Gear systems are known as one of the important sources of noise and vibration in industrial rotating machinery and power transmission systems. Sato et al [1] established a nonlinear model of gear system with the time dependence of tooth stiffness and backlash They investigated the bifurcation and chaotic phenomena by using a shooting method. Melnikov analysis is one of the few analytical methods to provide an approximate criterion for the occurrence of hetero/homoclinic bifurcation and chaos in nonlinear systems. According to this theory, the existence of transversal intersection of stable and unstable manifolds of saddle fixed points implies the occurrence of the chaos [6,7,8]. Some numerical simulation of the system including bifurcation diagrams, plane phase portraits, Fourier spectra, and time histories is used to confirm the analytical predictions and show the transition to chaotic motion
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