Analyzing the chaos phenomenon and bifurcation in gear systems nonlinear vibration using smoothing function approximation

Many researchers have conducted investigations in the field of gear system vibrations using numerical or approximate methods such as piecewise linearization. It should be noted that the presented methods could not predict some important nonlinear phenomena such as subharmonic responses and chaos. In certain intervals, the system has chaotic behavior, and as a result, intense and unpredictable vibrations are observed. This research deals with the analysis of gear system nonlinear vibrations and the chaos phenomena. The modeling of the gear system backlash approximation is presented using smoothening functions, and then the bifurcation phenomenon and chaos are investigated. For this purpose, the effective parameters as well as the change intervals of these parameters, which cause chaotic behavior in the system, are determined using the bifurcation diagram. The system design is based on these results to avoid chaotic zones.