Fast-slow Dynamical Analysis in Harmonic Gear Transmission System with Non-smooth Gear Clearance Condition

Harmonic gear reducer is a new type of mechanical transmission device, which has the advantages of simple structure, small size, high precision, large transmission ratio, and high transmission efficiency, which cannot be realized by ordinary gear transmission devices. Due to the presence of various nonlinear factors in the harmonic gear reducer system, it often exhibits relatively complex dynamical behaviors, which has an adverse effect on the transmission accuracy and transmission efficiency of the system. There are many non-smooth factors in the transmission system, and gear clearance, as one of the common non-smooth factors in the harmonic gear transmission system, has made it difficult to control the relationship between the output angular displacement and the input angular displacement of the system, which reduces the stability and transmission accuracy. Therefore, we establish the dynamics model of the non-smooth harmonic gear transmission system, based on the fast-slow dynamical knowledge and numerical simulation, and analyze the dynamical behaviors of the system under this non-smooth factor. The research shows that when the value of the gear clearance is in a definite zone, the change of the value of the gear clearance will only quantitatively change the dynamic characteristics of the system, but not fundamentally change the motion characteristics of the system. When a smaller torsional stiffness coefficient is adopted, the vibration frequency of the dynamic error response of the system increases obviously, but the corresponding vibration amplitude does not change to a significant extent, which shows that the appropriate torsional stiffness can improve the dynamic response of the system and enhance the ability of the system to absorb external disturbances and resist shocks. In order to make the harmonic reducer satisfy more application situations, the evolution of the dynamical behavior of the system under different external excitations is investigated. When the system is under a light load, it works as a bilateral shock condition. And when it is in the heavy load state, the system switches to the unilateral shock state, and the larger load moment leads to multiple vibration responses in the dynamic error trajectory of the system, which may lead to the phenomenon of speed fluctuation at the output of the system.