Analysis of bifurcation and chaotic behavior for the flexspline of an electromagnetic harmonic drive system with movable teeth transmission

Abstract

To develop the miniaturization of the electromagnetic harmonic movable tooth drive system, a novel configuration with an inner stator is proposed to create a great compressed structure. To avoid undesirable design parameters that lead to bifurcation and chaotic behavior of the flexspline, the nonlinear dynamic equations of the flexspline are established, and the Duffing equation and analysis results for the chaotic vibration of the flexspline are obtained by using the Donnell-Karman theory of thin-walled cylindrical shells with employing large deflection, the Bubnov-Galerkin principle, and the Melnikov function, separately. According to initial system parameters, based on the bifurcation diagrams, phase diagrams, displacement time course diagrams, and Poincare maps of the flexspline vibration, the dynamic behaviors are investigated, and the stability and chaos intervals are obtained. This study aims to reveal the influence of parameters on the chaotic phenomenon of the flexspline and to provide a theoretical reference for the design of the electromagnetic movable teeth drive.