Chaotic Behavior in Gear System. Adaptation of Bifurcation Diagrams and Method of Statistical Mechanics.

Abstract

Our numerical studies have shown the existence of chaotic motion in gear systems. However, we have not yet investigated the relationship between chaotic behavior and variations in system parameters. In this paper, we calculate bifurcation diagrams in order to investigate this relationship. These bifurcation diagrams enable us to determine which set of parameter values leads to chaotic motion. By comparing these diagrams of different parameter values, it is possible to determine how the region of chaotic motion changes in accordance with the parameter values. In our previous paper, we used a method of statistical mechanics in order to characterize the chaotic motion. This paper shows that the method is also effective for analyzing the gear system, taking account of the effect of shaft stiffness.