Analysis of Nonlinear Dynamics and Chaos Control in Gear Transmission System with Stochastic Perturbation

Abstract

In order to study the chaotic characteristics and control chaotic vibration in the gear transmission system. The dynamical equation and the state equation of gear transmission system are established by Newton's rule under considering stochastic perturbation of gear backlash, gear damping ratio, meshing frequency meshing stiffness and input torque fluctuation. The complex dynamics characters of gear transmission system are investigated. Five methods of controlling chaos are used to guide chaotic motions towards regular motions. Numerical simulation shows that the period doubling bifurcation, Hopf bifurcation and chaotic vibration exists in the gear transmission system. The effectiveness and feasibility of two kinds of feedback control method and three kinds of non-feedback control method to get rid of chaos by stabilizing the related unstable periodic orbit are verified.

DOI: http://dx.doi.org/10.5755/j01.mech.23.2.13576