Nonlinear dynamics of a gear transmission system

Albert C. J. Luo, and Dennis O’Connor
Department of Mechanical and Industrial Engineering
Southern Illinois University Edwardsville
Edwardsville, IL 62026-1805, USA
aluo@siue.edu, doconn@siue.edu

In this paper, an investigation on nonlinear dynamical behaviors of a transmission system with a gear pair is conducted. The transmission system is described through an impact model with 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 of stick motions are developed, and the condition for maintaining the stick motion is achieved as well. The corresponding physics interpretation is given for a better understanding of nonlinear behaviors of gear transmission systems. Furthermore, such an understanding may be very helpful to improve the efficiency of power transmission systems. Periodic motions relative to the impacting chatter and stick in order to reduce the noise of such a gear transmission system are predicted analytically through the mapping structures, and the corresponding local stability and bifurcation analysis are carried out. The grazing and stick conditions are adopted to determine the existence of periodic motions, which cannot be achieved from the local stability analysis. Numerical simulations are performed to illustrate the periodic motions and stick motion criteria. Such an investigation may provide some clues to reduce the noise in gear transmission systems.