Impacting chatter and stick in a transmission system with two oscillators

Abstract

In this article, an investigation on non-linear dynamical behaviours of a transmission system with a gear pair is conducted. The transmission system is described through an impact model with a possible stick between the two gears. From the theory of discontinuous dynamical systems, the motion mechanism of impacting chatter with stick is investigated. The onset and vanishing conditions for stick motions are developed, and the condition for maintaining stick motion is obtained as well. The corresponding physical interpretation is given for a better understanding of non-linear behaviours of gear transmission systems. A parameter map is presented to provide a global picture of the relationship between system parameters and corresponding motion. Grazing and stick conditions are utilized to determine the existence of periodic motions. Such periodic motions are predicted analytically through mapping structures, and the corresponding local stability and bifurcation analyses are carried out. Numerical simulations are performed to illustrate periodic motions and stick motion criteria. A better understanding of the motion mechanism between two gears may be helpful for improving the efficiency of gear transmission systems.