Analysis of nonlinear dynamics and chaos control in gear transmission system with stochastic perturbation

摘要

Gear transmission system is commonly used in automobile, robotics, machinery, aerospace and other areas. Scholars have done a lot of research on the nonlinear dynamic of gear transmission system [1-4]. Kahranman [5-7] et al. studied the dynamic response of gear transmission system under different forms of excitation. Theodossiades [8, 9] et al. investigated dynamics of a gear-pair system involving backlash and time-dependent mesh stiffness under the action of external excitation caused by torsional moments and gear geometry errors, and investigated dynamics of gear-pair systems driven by motors and presenting speed-dependent moment resistance. Huang and Liu [10] treated a spur gear tooth as a variable cross-section Timoshenko beam to construct a dynamic model, being able to obtain transient response for spur gears of involute profiles and investigated the dynamic responses of a single tooth and a gear pair. Howard [11] et al. studied the influence of gear tooth surface friction on system dynamjcs under various conditions. Shyyaba and Kahranman [12] used a non-linear time-varying dynamic model to investigate sub-harmonic and chaotic motions exhibited by a typical multi-mesh gear train. Litak and Friswell [13] examined the effect of tooth shape imperfections and defects. Parey [14] and Eritenel [15] et al. analyzed the changes impact of time-varying mesh stiffness, friction coefficient, tooth bending, coincidence degree and modal damping parameters on the stability of the boundary. Bonori and Pellicano [16] presented a method for analysing nonlinear vibrations of spur gears in presence of manufacturing errors. However, they rarely consider the influence of system parameters perturbation on the system dynamics. In recent years, some scholars have started to study the gear system as a stochastic system [ 17-19].