A STUDY OF DYNAMICAL MECHANISMS OF THE FAST-SLOW OSCILLATIONS OF HARMONIC GEAR SYSTEM

A harmonic gear reducer is an advanced driving device, and it has been widely used because of many advantages. A harmonic gear reducer involves the coupling of different oscillation scales. This usually induces complex fast-slow oscillations, which have great impact on the proper operation of the system. In this paper, a harmonic gear system with the nonlinear factor of torsional stiffness is considered. The purpose of this paper is to study fast-slow dynamics of the system and to reveal a novel dynamical mechanism of the fast-slow oscillations. To begin with, the fast-slow dynamical model of the harmonic gear reducer with the nonlinear factor of torsional stiffness is built. Then, the transition of the system from normal oscillations to the fast-slow oscillations is obtained by varying the torsional stiffness. Subsequently, we give a brief description of the basic theory related to fast-slow systems. Based on this, dynamical characteristics of the fast subsystem are investigated by the fast-slow analysis and the generation mechanisms of fast-slow oscillations are revealed. Our results show that, when the system parameter is varied, the equilibrium curve of the fast subsystem does not lose its stability or bifurcate. However, near some point, a sharp quantitative change can be observed in the equilibrium point curve, characterized by the fact that the equilibrium point is able to undertake a fast transition between positive and negative coordinate values in a local small area of the equilibrium point curve. Based on this, we reveal a novel dynamical mechanism underlying the appearance of fast-slow oscillations, and compare the mechanism with other related dynamical mechanisms of fast-slow oscillations. Our results enrich the routes of dynamical systems to the fast-slow oscillations, and besides our study provides important reference to the research on the dynamical mechanisms and control of fast-slow oscillations in the actual systems of harmonic gear drive.