Three Degrees Of Freedom Nonlinear Vibration Of Gear Transmission And Chaos Control

This dissertation mainly studies the non-linear dynamics and chaotic motions of 3-d.o.f geared rotor-bearing system with piecewise linear clearance. The periodic motions of such model are investigated by the incremental harmonic balance(IHB) method. On this basis, using continuous feedback chaos control method, the chaotic motions are effectively suppressed in this system.The IHB method is used to obtain periodic motions of a 3-d.o.f non-linear model of a geared rotor system subjected to parametric and external harmonic excitations. The stability of the periodic motions is investigated by the Floquet theory, the bifurcation behavior is traced. Parametric studies are performed to understand the effect of system parameters such as excitation frequency and bearing damping ratio on the nonlinear dynamic behaviors. In addition to the familiar period doubling bifurcation scenario leading to chaos, a quasiperiodic route to chaos is also observed which occurs through an initial Hopf bifurcation.The current chaos control methods are compared, the stabilization of unstable periodic orbits of this chaotic system is achieved by continuous feedback control method, the specially designed external oscillator which used as target motion orbit in continuous feedback control method is obtained directly from IHB method. Also, the effect of noise and improvements on the control method are studied.